This work has successfully arisen within the blessings, prosperity and love of our holly GOD, especially with COVID moments where "HOPE-" was "-LESS". During these days tightness with the family was from abroad,

unloaded quality factor 𝑄 𝑢 is extracted and compared for all different metal/oxide layer substrates from the BACK-END-OF-LINE (BEOL). Then, based on the extracted information, the suitable layers are chosen. Moreover, it is very important to have compact patch filter, a deep analysis of using grounded vias with patch resonators has encountered to understand its influence on size reduction and fundamental resonance modes. Grounded vias are used with antennas for modes suppression, but it is barely used with filters. This has led us to newly developing its synthesis methodology in order to design the asynchronous narrowband dual-mode bandpass filter. Moreover, filters with cascaded coupling scheme are conducted while using the traditional synthesis approach.

Implementation or layout scheme of the designed filters is pivotal in this work flow.

Based on the design rule manual (DRM) provided by the manufacturer, the characteristics of the oxide layers along with the conductivity of the metal layers and other elements, such as vias, are extracted. Due to the strict and picky design rules, especially for the Min/Max metal dimensions and surface metal densities, post-layout simulation is required to compensate their influence on the intended filter.

Last but not least, the presented developed filters showed a great performance in comparison to the state-of-the-art. Also, as a demonstration, we have shown that it is possible to realize integrated mm-wave diplexers at 90 GHz with narrow band filters (< 10%) presenting losses around 3 dB within the passband. and 60 GHz (57-66) for security and medical monitoring services that require very high data rates and bandwidths [START_REF] Shafi | 5G: A Tutorial Overview of Standards, Trials, Challenges, Deployment, and Practice[END_REF].

LIST OF FIGURES

LIST OF TABLES

Based on the presented motivation and in order to meet the expectations of the demanders to have 5G, and future 6G applications with high data rates and low power consumption, a revolution in the millimeter wave (mm-wave) circuit design is on the move.

For that purpose, advancements in Microwave Monolithic Integrated Circuits (MMIC) technologies like CMOS/BiCMOS have gained the attention of researchers in the last two decades for mm-wave circuit design. Nowadays, its high-performance transistor features (𝑓 𝑇 /𝑓 𝑚𝑎𝑥 around 500/600 GHz) makes it very suitable for 5G and 6G applications in the sub-THz band like automotive radars, imaging systems for medicine or security defense [START_REF] Zimmer | SiGe HBTs and BiCMOS Technology for Present and Future Millimeter-Wave Systems[END_REF]. To take advantage of these technologies, sophisticated transceivers must be developed.

However, today it comes up against several obstacles, mainly, (i) the connection of the antenna system to the (Bi)CMOS chips often with the need for a beam orientation capability, (ii) the energy efficiency of the chips, which is very limited with efficiencies Power Added Efficiency (PAE) of the order of 10% for power amplifiers in Silicon-Germanium (SiGe) technology in D-band, and last but not least (iii) the non-availability of diplexers.

For that purpose, diplexers are essential if the optimization of bandwidth is required, which is the case. But their realization relies on filters. Filters are a fundamental building block for any RF front-end of a transceiver. Nevertheless, it is problematic to combine the efficient active blocks developed on BiCMOS with filters and other passive blocks using different technologies due to the interconnection, for instance Ball Grid Array (BGA) and wafer bonding packaging parasitics become significant beyond 50-100 GHz. Apart from mobile terminals at RF bands, where the use of acoustic waves filters is the must, filters are mainly produced in Printed Circuit Board (PCB) or Low Temperature Co-fired Ceramics (LTCC) technologies in RF, up to a few tens of GHz, along with an undeniable appeal of Substrate Integrated Waveguide (SIW) technologies in particular as of today.

However, it is very tricky to use them, because the precision capabilities of these technologies does not make it possible to produce filters beyond 100 GHz, implying insufficient control of the resonance frequencies. Therefore, MMICs produced by BiCMOS technologies are a worthy choice for designing mm-wave integrated passive devices, not only because of its high-tech, but also with a moderate fabrication cost compared to Gallium Arsenide (GaAs) or Indium Phosphide (InP) counterparts.

Challenges Overview

Designing a good performed integrated passive filter while compensating the occurrence of high losses or parasitic effects, is really challenging. Filters based on lumped components topologies as inductors and capacitors are unsuitable at mm-waves, since the quality factor (𝑄𝐹) of capacitors drastically decreases with frequency. Hence, distributed circuits based on microstrip lines technology is preferable, as the 𝑄𝐹 of a Transmission Line (TLine) increases with frequency since the propagation constant, that is proportional to the frequency, increases faster than the attenuation constant. This is mainly driven by the skin depth and its frequency square root dependence. However, TLines based resonators are still considered lossy, since the width of the strips is limited by the reduced height of the Back-End-Of-Line (BEOL). Many promising studies based on slow-wave TLines, and in particular slow-wave coplanar waveguides (S-CPW) are considered a good resonator choice to have i) immunity against losses with better 𝑄𝐹 and ii) reduced dimensions [START_REF] Franc | High-Performance Shielded Coplanar Waveguides for the Design of CMOS 60-GHz Bandpass Filters[END_REF]. Nevertheless, the compactness induces a significant cost in terms of design, because mastering the concepts of S-CPW is not easy. Also, it seems complicated to simply transfer this approach to designers of mm-wave circuits, and last but not least, the S-CPW quality factor becomes lower than the one obtained by microstrip lines above about 150 GHz.

More generally, the literature has encountered few works for passive filters that operate at mm-wave band and implemented on CMOS/BiCMOS technologies . Only a single work exists for bandpass filter operating beyond 100 GHz [START_REF] Saadi | Design of Coupled Slow-Wave CPW Millimeter-Wave Bandpass Filter Beyond 100 GHz in 55-nm BiCMOS Technology[END_REF]. It uses the coupled S-CPW topology to have flexible responses with reduction of losses and existence of transmission zeros (TZs). However, its measured unloaded quality factor for single resonator is still limited. Moreover, the lowest achieved fractional bandwidth for acceptable losses was not less than 20 %, which is a common challenge for filters at mm-wave. Conversely, patch filters, which are sophistically designed at RF and microwave bands, are an earnest choice to support multi-modes functionality , and hence in fine lead to compact size, even if the patch approach is a priori not very compact. Its electrical properties allow to have infinite number of modes within a single resonator at different frequencies. Moreover, its design simplicity makes it possible to control its degenerated modes by inserting well known perturbations. A high-performance design for bandpass filter with multi-layering technique was developed in [61;62;65;68;70]. A wide range of frequency response flexibility was achieved with a multiple of controlled TZs, thanks to the use of cross slots.

Away from its good performance with higher power handling compared with microstrip topologies, designing compact patch filters is still an issue. Improving compactness would be possible by using shorting posts (vias). Theoretically, as reported in [START_REF] Porath | Theory of miniaturized shorting-post microstrip antennas[END_REF], a new generated 𝐿𝐶-mode appears at lower frequency as compared to the fundamental mode of the patch resonator. This has allowed to develop a wide band compact triple mode bandpass filter [73;75;76]. However, developing compact narrowband dual-mode bandpass filter based on patch resonators is still a challenge.

Patch filter concept has never been explored at mm-waves and CMOS/BiCMOS technology, to the author's best knowledge. This makes it complicated to understand its behavior with multi-layering structure of IC. Thus, it seemed interesting to explore the "patch approach" to realize mm-wave filters above 100 GHz in CMOS/BiCMOS technologies, and compare it to more conventional Tline-based approaches.

Objectives

This dissertation introduces the first patch filter design at mm-waves band above Since, the potentiality of the technology is not yet known for patch resonators, the unloaded quality factor 𝑄 𝑢 is extracted and compared for all different metal/oxide layer substrates from the BEOL. Then, based on the extracted information, the suitable layers are chosen.

It is very pivotal to have compact patch filters at mm-wave bands. Then, a deep analysis of using grounded vias with patch resonators has encountered to understand its influence on size reduction and fundamental resonance modes. Grounded vias are used with antennas for modes suppression, but it is barely used with filters. This has led us to newly developing its synthesis methodology in order to design the asynchronous narrowband dual-mode bandpass filter. Moreover, filters with cascaded coupling scheme are conducted while using the traditional synthesis approach.

Implementation or layout scheme of the designed filters is pivotal in this work flow.

Based on the design rule manual (DRM) provided by the manufacturer, the characteristics of the oxide layers along with the conductivity of the metal layers and other elements, such as vias models, are extracted. Due to the strict and picky design rules, especially for the Min/Max metal dimensions and surface metal densities, post-layout simulation is required to compensate their influence on the intended filter.

Organization

CHAPTER I is divided into two parts. Firstly, it shows the literature review of most designed dual-mode patch filters at RF and Microwave bands in order to classify and select the techniques used to provide the duality concept. Also, a literature review of the recent designed integrated filters at mm-wave highlighting the main challenges. In the second part, general patch resonator analysis is conducted while comparing the different extracted 𝑄 𝑢 in order to show the effect of BEOL height on the performance of the filter.

In CHAPTER II, the patch resonator theory, with and without vias, is recalled to examine the multi-resonance modes electrical performance. This helps in distinguishing the impact of using different perturbation elements techniques. Then, the full synthesis design methodology is thoroughly represented to design asynchronous tuned filters. The extraction of coupling matrix and its coupling scheme are also piloted.

CHAPTER III presents a full and detailed design study of several patch filters. It focuses on applying the design methodology presented in chapter III to synthesize the filter especially when using grounded vias as a new introduced mode. The extraction of external quality factor 𝑄 𝑒 is discussed to show the influence of the feeding position on the overall performance of the filter. Filters with dual-mode and dual-band performance are developed along with patch-like miniaturized cascaded 2 nd order filters that are designed and simulated.

In CHAPTER IV, the layout scheme and measurements of all developed filters are presented. It draws up the layout methodology that should be followed by passive integrated circuits designer in order to successfully implement and compensate the effect of unfavorable design rules. Then, 2-ports on-wafer measurements process and results are shown.

CHAPTER V opens the interval for discussion on what can be done in future. Also, it presents an interesting design for diplexer with RX/TX filter operating at 90 GHz. This will be considered the first integrated diplexer at mm-wave band.

Lastly, the whole work is concluded and summarized. makes it easy to be integrated with lumped components (𝐿,𝐶 and varactor diodes), and weight. These characteristics were exploited to develop RF and microwave filters using different topologies such as: coupled-line, rings, stubs, patches and others. Higher order filters with cascaded form can be easily implemented on planar technology in order to reach better performance. However, when multiple resonators are used the overall size of the filter is drastically increased. So, dual-and multi-mode filters with minimum number of cascaded resonators have become pivotal.

CHAPTER I: PATCH FILTER LITERATURE REVIEW

In this chapter, the literature review of designed patches at frequencies below 10 GHz is conducted to get inspired with patch geometry and used perturbation techniques. Then, the state-of-art for filters that are developed on integrated circuits beyond 30 GHz are presented to check the main filter design challenges and the margin of improvements with patch resonators. Lastly, the first general patch resonator analysis on BiCMOS 55nm technology is interpreted.

Patch Filters' Literature Review

In the 1950's, Lin [START_REF] Lin | Microwave Filters Employing a Single Cavity Excited in More than one Mode[END_REF] was the first to introduce the dual-mode concept. This new concept allows the increase of filter's order without adding more resonators. The idea is to create coupling between the so-called degenerated modes to split them and form the dualmode model. Initially, these modes operate at the same resonant frequency that is determined by the overall structure of the design, but with different Electro-Magnetic (EM) field distribution. Two decades later in 1971, Wolf [START_REF] Wolff | Microstrip bandpass filter using degenerate modes of a microstrip ring resonator[END_REF] used this concept on planar technology using circular dual mode ring resonator (Figure 1.1). In 1991, after the planar filters become more popular, Curtis and Fiedziuszko [START_REF] Curtis | Miniature dual mode microstrip filters[END_REF], took the initiative to present a miniaturized dual mode microstrip filter using full patch resonator as shown in Figure 1.2.

They split the degenerated modes using an edge cut (inductive loading).

Hong and Lancaster in [START_REF] Hong | Bandpass characteristics of new dual-mode microstrip square loop resonators[END_REF] and [START_REF] Hong | Microstrip bandpass filter using degenerate modes of a novel meander loop resonator[END_REF] developed the first sophisticated microwave dualmode ring filters in 1995. They are based on the study presented previously by Wolf. Two studies were conducted at that time: one using a rectangular loop resonator (Figure 1. In their study, the authors show that the patch unloaded quality factor 𝑄 𝑢 decreases with frequency, although its radiation losses are reduced due to the usage of slots.

After this work, a lot of filters were developed using slot perturbation technique to build dual-mode filters [START_REF] Zhu | New planar dual-mode filter using cross-slotted patch resonator for simultaneous size and loss reduction[END_REF][START_REF] Serrano | Dual-mode bandpass filter using triangular patch resonator with inverted T-shaped slot[END_REF][START_REF] Serrano | Synthesis Methodology Applied to a Tunable Patch Filter With Independent Frequency and Bandwidth Control[END_REF][START_REF] Liu | High-selective triple-mode bandpass filter using a new capacitive-loaded patch resonator[END_REF][START_REF] Liu | Dual-Mode Microstrip Patch Bandpass Filters With Generalized Frequency Responses[END_REF][START_REF] Liu | High-Selective Bandpass Filters Based on New Dual-Mode Rectangular Strip Patch Resonators[END_REF][START_REF] Hendry | Parallel Multimode Cavity Filters With Generalized Frequency Response[END_REF], dual-band filters [START_REF] Liu | Compact single-and dual-band bandpass filters with controllable transmission zeros using dual-layer dual-mode loop resonators[END_REF][START_REF] Li | Dual-Mode Dual-Band Bandpass Filter Based on a Stub-Loaded Patch Resonator[END_REF][START_REF] Zhang | Dual-Mode Dual-Band Bandpass Filter Using a Single Slotted Circular Patch Resonator[END_REF], Balun filters [START_REF] Zhang | Design of Multilayer Balun Filter With Independently Controllable Dual Passbands[END_REF][START_REF] Sun | Novel Dual-Mode Balun Bandpass Filters Using Single Cross-Slotted Patch Resonator[END_REF] and balanced filters [START_REF] Zhang | Novel balanced single/dual-band bandpass filters based on a circular patch resonator[END_REF][START_REF] Ji | Compact Balanced Bandpass Filter with High Selectivity Based on Two Coupled Dual-Mode Microstrip Loop Resonators[END_REF]. From design methodology perspective, dual-mode filters are synthesized using the asynchronous tuning method that was presented in [START_REF] Hong | Microstrip Filters for RF/MicrowaveApplications[END_REF]. This method was thoroughly discussed and firstly introduced in [START_REF] Serrano | Synthesis Methodology Applied to a Tunable Patch Filter With Independent Frequency and Bandwidth Control[END_REF] in order to build a tunable triangular patch filter. As shown in Figure 1.5, two etched slots were used to independently control each degenerated mode, where different biased varactors were inserted between the slots to provide tunability.

Despite their great performances, most of these filters still suffer from large size, which make filters using TLine topology more favorable. In order to overcome this issue, grounded vias were used. The corresponding theory was originally developed in [START_REF] Porath | Theory of miniaturized shorting-post microstrip antennas[END_REF]. It is modeled as an 𝐿𝐶 circuit, and its resonance frequency is named zero-mode since it appears below the fundamental frequency of the patch resonator. This new mode was used with square patch resonator in [START_REF] Janković | Compact UWB bandpass filter based on grounded square patch resonator[END_REF] to build a compact wide band filter. In this work, authors have combined both crossed slots with single via (Figure 1.6(a)). The two slots control the degenerated modes and the dimension of via controls its self-resonance frequency. Another approach for using vias was to build a 4 th order filter [START_REF] Radonic | Cross-coupled microstrip filter using grounded patch resonators[END_REF], where four grounded square resonators were implemented as shown in (Figure 1.6(b)). This time only via mode is used to build the filter using the cross-coupled synthesis methodology presented in [START_REF] Hong | Microstrip Filters for RF/MicrowaveApplications[END_REF].

Adjacent resonators were coupled by magnetic-coupling when vias are facing each other and by electric-coupling where vias are aside. This allowed flexibility in tuning the filter's performance.

Another approach for size reduction is to use technologies that support multilayer structures. Authors in [START_REF] Liu | High-selective triple-mode bandpass filter using a new capacitive-loaded patch resonator[END_REF] and [START_REF] Liu | Dual-Mode Microstrip Patch Bandpass Filters With Generalized Frequency Responses[END_REF] used the multi-layered PCB technology in order to increase the order of the filter without increasing its size. In [START_REF] Liu | High-selective triple-mode bandpass filter using a new capacitive-loaded patch resonator[END_REF], a triple-mode bandpass filter using single square patch resonator was realized. As shown in Figure 1.7(a), the approach was based on edged-cut perturbation to split the degenerated modes and an embedded mushroom load to perturb the first higher order mode. Another advanced approach is presented in [START_REF] Liu | Dual-Mode Microstrip Patch Bandpass Filters With Generalized Frequency Responses[END_REF] using multi-layered PCB with same height and relative dielectric constant 𝜀 𝑟 to build cascaded dual-mode patch filter in 3D sandwich, as shown in Figure 1.7(b). Both resonators provide dual-mode response using single diagonal etched slot. They are coupled to each other through aperture at ground level, which is in the middle. This work provides a 4 th order bandpass filter with generalized responses.

Based on the presented summary, Table 1.1 shows different perturbation techniques that were used with patch resonators, along with their functionality. Perturbations are classified into either inductive perturbation where surface current 𝐽 flow is affected, or capacitive perturbation where electric field 𝐸 is affected. More than one technique can be used at a time with single resonator to build more sophisticated filter with flexible response.

This will be discussed further in the coming chapters. could achieve a very good performance especially when 𝑄 𝑢 overcomes 100 at 30 GHz [START_REF] Zhu | Miniaturized Resonator and Bandpass Filter for Silicon-Based Monolithic Microwave and Millimeter-Wave Integrated Circuits[END_REF][START_REF] Yang | Design of a Miniaturized On-Chip Bandpass Filter Using Edge-Coupled Resonators for Millimeter-Wave Applications[END_REF][START_REF] Yang | Design of an Ultracompact On-Chip Bandpass Filter Using Mutual Coupling Technique[END_REF][START_REF] Feng | 28-GHz High-Selectivity Bandpass Filters With Dual-Behavior Resonators Using GaAs Technology[END_REF][START_REF] Shen | Millimeter-Wave Dual-Band Bandpass Filter With Large Bandwidth Ratio Using GaAs-Based Integrated Passive Device Technology[END_REF][START_REF] Xu | Compact Millimeter-Wave On-Chip Dual-Band Bandpass Filter in 0.15-μm GaAs Technology[END_REF][START_REF] Xu | 60-GHz Compact Dual-Mode On-Chip Bandpass Filter Using GaAs Technology[END_REF][START_REF] Guo | Millimeter-Wave On-Chip Bandpass Filter Based on Spoof Surface Plasmon Polaritons[END_REF]. This is due to their significant thickness height for BEOL. Nevertheless, it is unlikely to be combined with active circuits like PAs or LNAs that require transistors to have operation capabilities to be higher than 60 GHz, and high-density digital circuits, which is not offered by them. On the other side, technologies as PCB and LTCC that support multilayering structure are very usefull for frequencies below 60 GHz due to their availability.

However, with higher bands it is not favorable, since the interconnection parasitics become significant when connecting devices with different technologies. For these reasons and more, in this subsection a full review on the recorded designed filters using BiCMOS/CMOS technologies are only described . From Figure 1.8(a), the majority of the works exhibits 𝐹𝐵𝑊 that ranges between 15% and 30 % with insertion loss variation between 1. 25 with 𝐹𝐵𝑊 between 10 % and 30 %. Only two works, [12-c] and [START_REF] Vanukuru | Millimeter-wave bandpass filter using high-Q conical inductors and MOM capacitors[END_REF], have high 𝑄 𝑢 of 34 and 37, respectively, but with very bad selectivity and rejection levels. Filters in [START_REF] Saadi | Design of Coupled Slow-Wave CPW Millimeter-Wave Bandpass Filter Beyond 100 GHz in 55-nm BiCMOS Technology[END_REF] that operate at 120 GHz, have 𝑄 𝑢 around 17. It is very interesting to check that in order to expect the design challenges beyond 100 GHz. As mentioned before, this comparison is not really accurate because 𝑄 𝑢 depends normally on the technology used, which is not taken into consideration with this plot. In particular, CMOS technologies have different heights for BEOL, which directly effects the achieved 𝑄 𝑢 even for the same filter configuration. Last but not least, most of the filters have an average chip size below 0.15 mm 2 with some filters of ultra-compact size below 0.02 mm 2 .

n i i u dB g Q FBW IL     (1.1)
In comparison to the operating frequencies, more than 80 % of the presented works operate below 55 GHz, along with 15 % at around 70 GHz and few works above 100 GHz. This indicates that filters' behavior is not well discovered at very high frequencies.

Actually, it comes from the fact that defined applications are still few over this band.

Moreover, researchers whom are working on the filters synthesis, are still relatively far from microelectronics technologies, and its many constraints. However, since applications begin to emerge beyond 60 GHz, with medical monitoring or automotive radars and the back-haul for the future 6G telecommunication standard, as already mentioned in the introduction, it becomes necessary for our research community to be proactive in demonstrating the possibility to create filters with acceptable performances, which could be integrated into mm-wave front-ends. Moreover, the frequency band beyond 100 GHz is certainly little used today, and one might think that the filtering behavior of amplifiers is sufficient, but this will probably no longer be true when the operating frequency of many systems gradually increases. Secondly, it always proves dangerous to compare the performance of passive circuits (and even active ones) realized using different technologies from microelectronics. As we show later, the quality factor of a patch or TLines depends enormously on the thickness of the BEOL of the technology, so the performance sometimes turns out to be much more linked to the specificities of the technology rather than to the quality and to the originality of the design.

Nevertheless, and despite the two critical points just mentioned, this comparison is made to discuss the main challenges of filters design at mm-waves. It shows that designing a narrow band filter with 𝐹𝐵𝑊 below 20% and low insertion loss is considered the key challenge. In addition to that, especially for filters that operate at 𝑓 𝑐 > 65 GHz, they should have a very good selectivity at lower out-of-band rejection in order to suppress responses below 40 GHz because for the moment most of 5G frequency allocations are at this band, along with satellite communications. The third challenge is to design filters with specific applications in mind especially for those above 60 GHz. This can lead to completely different sets of design specifications, for example to reject specific frequency bands or provide notches at certain frequencies.

Skimming the topologies used with the presented filters, it appears that only filters with TLine resonators or coupled-line resonators were used. So, and to our best knowledge, filters at mm-wave bands with patch resonators topology are not recorded. Then it is interesting to check its potentiality with integrated circuits like BiCMOS, as explained in the coming subsection.

General Patch Resonator Analysis on BiCMOS 55 nm

STMicroelectronics offers two versions of BiCMOS 55 nm (B55) technology with different BEOL, i.e. 8ML and 9ML EVO. The choice of this high-performance technology was guided by the frequencies that were considered for the realized filters, i.e. beyond 150 GHz, for which transistors, having figures of merit (𝑓 𝑚𝑎𝑥 and 𝑓 𝑡 ) greater than 400 GHz, are necessary in order then be able to produce active circuits (LNA and PAs) with acceptable performance in terms of gain.

The overview structures of the 8ML and 9ML BEOL are shown in Figure 1.9 (a) and Figure 1.9 (b), respectively. The obligation of confidentiality does not allow us to disclose the thicknesses and conductivities of all metals, or even the dielectric constants of the materials between the metal layers. The BEOL consists of 8 and 9 copper layers: (M1 to M8U) for 8ML and (M1 to M9V) for 9ML, along with one top aluminum layer (AluCAP AP) for both. All metal layers are dipped in oxide, and each two consecutive metal layers are separated by dielectric layers stack with different relative dielectric constant 𝜀 𝑟 . Usually most of circuits that use B55 8ML technology, are implemented at M8U layer since it is the thicker (ℎ 𝑀8𝑈 = 3 μm), but AP (ℎ 𝐴𝑃 = 1.45 μm) seems to be useful too, since it makes the BEOL thicker as will be seen further. Moreover, the B55 9ML will be used in this dissertation for first time, because it was just released by the manufacturer. The advantage of using this version is simply due to the thicker BEOL, which improves 𝑄 𝑢 , as will be discussed in this subsection.

In order to check the potentiality of B55 technology with patch resonators, 𝑄 𝑢 is plotted for different patches' layouts (Rectangular R, Circular C, Hexagonal H and Octagonal O), as shown in Figure 1. 10 (a). The 8ML version is used with all patches, which are implemented on M8U with ground on M1. 𝑄 𝑢 is extracted at 100 GHz and 200 GHz from

(1.3) with weakly loaded patches (insertion loss > 30 dB):

𝑄 𝑢 = 𝑓 𝑐 𝐹𝐵𝑊 (1.3)
where fc is the center frequency and 𝐹𝐵𝑊 is the 3-dB fractional bandwidth. All of them have approximately the same 𝑄 𝑢 of 13.5 and 22 at 100 GHz and 200 GHz, respectively.

Nevertheless, 𝑅 has the smallest area size of 0.12 mm 2 at 200 GHz among them all (Figure 8ML and 9ML versions. This configuration leads to deep analysis for the effect of metal conductivity (between copper and aluminum) and layer's thickness on the extracted 𝑄 𝑢 . It is obviously shown that for all configurations, extracted 𝑄 𝑢 is increasing with 𝑠𝑢𝑏 ℎ . For example, with M9v:M1, it varies from 10 with 𝑠𝑢𝑏 ℎ = 2 μm up to 43 with 𝑠𝑢𝑏 ℎ = 14 μm.

Moreover, when GND layer becomes thicker (in case of M6z use), 𝑄 𝑢 improves to 14 and 54, respectively. It is of same behavior for the patch implemented at AP.

Next, for an exact extraction of 𝑄 𝑢 for the selected layers, single patch resonators were implemented on each stack to be operating, individually, at 𝑓 𝑐 = 60 GHz, 120 GHz and 200 GHz, respectively. The dimensions are summarized in Table 1.3 along with the width (𝑊 𝑇𝐿 ) of a 50-Ω TLine implemented on each stack. Note that for the 8ML BEOL, it couldn't be possible to select M6z layer for GND instead of M1 because 𝑠𝑢𝑏 ℎ would have This is due to the thicker constructed BEOL. This doesn't contradict with the results in equals 21 and 28 for 𝑠𝑢𝑏 ℎ around 6 μm and 10 μm, respectively. In comparison to 𝑄 𝑢 for patch resonator, it is observed that the usage of patch resonators leads to better performance than TLines. Note that it is clear that the width 𝑊 𝑇𝐿 is increasing with the BEOL. This could have a double impact for mm-wave filter design based on TLlines topologies. It is a kind of compromise between better 𝑄 𝑢 and higher design complexity, since, for large 𝑊 𝑇𝐿 , meandering and junctions become less flexible in design. This issue and others can be solved by using patch resonators instead.

Conclusion and Design Challenges

This chapter presented the state-of-art for main patch filter designs that were conducted at RF and microwave bands, in order to show the techniques used to gain flexibility in controlling the filters responses. It was underlined that patch resonators with grounded vias can have high miniaturization capabilities, which is necessary for integrated filter design.

On the other side, a full review for most of the recorded filters at mm-wave bands was conducted. The results show that the achieved dominant 𝐹𝐵𝑊 is between 25 and 30 %. So, it is clearly a key challenge, at mm-wave bands, to design narrow band filters with 𝐹𝐵𝑊 below 20% and acceptable losses.

Patch resonators, which were not used before for mm-wave filters, are implemented on BiCMOS 55 nm integrated technology to check their potentiality. The results show that 𝑄 𝑢 is increasing with BEOL height and frequency, and reaches, for specific stack, 53 at 200 GHz. At this frequency, the extracted 𝑄 𝑢 for patch resonators is better than TLinesbased resonators. Also, the filter design with TLine resonators becomes more complex.

Thanks to the availability of multi-layering BEOL with several thick metals, different designs for patch filters with dual-mode responses can be developed, as demonstrated in the next chapter.

CHAPTER II: PATCH RESONATOR DESIGN PRINCIPLES AND SYNTHESIS

The theory of bandpass filters based on patch resonators is well developed, but the key design challenge is relied on understanding its electro-magnetic (𝐸𝑀) fields distribution behavior and how each resonance mode can be perturbed independently. In this context, this chapter presents a full description of the patch resonator design principles along with its modes behavior. Also the detailed explanation of the synthesis design methodology that will be used further for designing dual-mode filters at mm-wave bands with grounded vias is conducted.

Square Patch Resonator Principle 2.1.1. Conventional Square Patch Resonator

The conventional square patch resonator in Figure 2.1 acts as a wheeler cavity with perfect electrical walls in the top and bottom metallic layers while surrounded by magnetic walls provided by middle dielectric layer. The 𝐸𝑀 modes existing inside the patch are the Transverse Magnetic (𝑇𝑀 𝑚𝑛 𝑧 ), where 𝑚 and 𝑛 are the order of the modes. It is defined that only electric field 𝐸 exists in the 𝑧 direction, which is perpendicular to the ground plane.

The 𝐸𝑀 modes and their corresponding resonance frequencies can be extracted from Maxwell equations as for patch antenna, which are summarized in (2.1) and (2.2), respectively [START_REF] Hong | Microstrip Filters for RF/MicrowaveApplications[END_REF]:

𝐸 𝑧 = 𝐴 𝑚𝑛 cos 𝑚𝜋 𝐿 𝑒𝑓 𝑥 cos 𝑛𝜋 𝐿 𝑒𝑓 𝑦 ∞ 𝑛=0 ∞ 𝑚 =0 , 𝐻 𝑥 = 𝑗𝜔𝜀 𝑟𝑒𝑓𝑓 𝑘 𝑐 2 𝜕𝐸 𝑧 𝜕𝑦 , 𝐻 𝑦 = - 𝑗𝜔𝜀 𝑟𝑒𝑓𝑓 𝑘 𝑐 2 𝜕𝐸 𝑧 𝜕𝑥 , 𝑘 𝑐 2 = 𝑚𝜋 𝐿 𝑒𝑓𝑓 2 + 𝑛𝜋 𝐿 𝑒𝑓𝑓 2 ,
(2.1)

𝑓 𝑚𝑛 0 = 𝑐 2𝐿 𝑒𝑓 𝜇 𝑟 𝜀 𝑒𝑓𝑓 𝑚 2 + 𝑛 2 (2.2)
where 𝐴 𝑚𝑛 is the 𝑚𝑛 mode 𝐸 field magnitude, 𝑚 and 𝑛 are infinite non-negative and non 𝑳 𝒑 rectangular patch length, 𝒔𝒖𝒃 𝒉 substrate height and 𝜺 𝒓 is the substrate relative permitivity

(2.3)
The first two modes, 𝑇𝑀 01 and 𝑇𝑀 10 , are considered the fundamental modes of the patch and their resonance frequency, which appears at 𝜆/2 is:

01 10 2 c eff r reff c f f f L m    (2.4)
These modes are naturally combined, and their splitting depends on perturbations, which generate coupling between them. Their 𝐸 fields equations and those for higher order modes are presented in Table 2.1. A general observation to the extracted equations allows to configure that each mode has its specific field distribution along the patch area, which in some cases appears to be uncoupled. For 𝑇𝑀 01 it is defined along y-axis while 𝑇𝑀 10 is along x-axis, where both modes are orthogonal to each other. Also, their electric fields change their phase for π along the patch. Therefore, theoretically, both modes have maximum electric field at the edges of the patch along their axis of definition and null in the middle. The first higher order mode, 𝑇𝑀 11 appears at 𝑓 11 = √2𝑓 𝑐 GHz, where 𝐸 field equation shows a maximum 𝐸 field at the 4 corners of the patch and null in the middle.

Afterwards, a generation of pair modes started to appear at resonance of 𝑖 • 𝑓 𝑐 , where 𝑖 is 2, 3, 4… etc. At the moment, higher order modes are out of interest.

For more illustration on the field distribution of the patch resonator in For demonstration, a patch resonator of 𝐿 𝑝 = 360 μm is implemented on B55 8ML technology using ANSYS HFSS software. The patch is weakly coupled through two-port structure and designed at M8U layer with ground at M1. which is 2 • 𝑓 𝑐 . It is worth to mention that at such high frequency band the only way to verify the simulated results for patch resonator, before the measurements, is by comparing it to the theoretical calculations because, for our best knowledge there is no records in the literature for patch resonators responses.

Grounded Square Patch Resonator

One of the weakness of patch resonators is their size compared to other topologies. As seen in the literature, different techniques were used to reduce its size, but the most efficient way is by inserting shorting posts (vias). The usage of vias has two main impacts: first it adds a new resonance mode to the patch recalled 𝐿𝐶-mode, and second it perturbs the conventional existing modes. 𝐿𝐶-mode is electrically modeled as 𝐿 𝑣𝑖𝑎 𝐶 𝑣𝑖𝑎 circuit, where the inductance 𝐿 𝑣𝑖𝑎 depends on the via's self-inductance, and the capacitance 𝐶 𝑣𝑖𝑎 depends on the patch capacitance 𝐶 𝑝 . Via has a direct impact on the overall size of the patch through adding a new lower resonance frequency 𝑓 𝐿𝐶-𝑚𝑜𝑑𝑒 , which allows patch compactness. Also, it perturbs the natural existing modes, especially when it splits the fundamental modes (this will be discussed further). It is worth to mention that 𝑓 𝐿𝐶-𝑚𝑜𝑑𝑒 is mainly controlled by the size of the via and its position along the patch. be changed from 𝜆/2 to 𝜆/4, 𝜆/5.7 and 𝜆/8, respectively. The miniaturization percentage %M can be calculated from (2.5).

%𝑀 = 1 - 𝐴𝑆 𝑚𝑖𝑛𝑖𝑎𝑡𝑢𝑟𝑒-𝐹𝑖𝑙𝑡𝑒𝑟 𝐴𝑆 𝑐𝑜𝑛𝑣𝑒𝑛𝑡𝑖𝑜𝑛𝑎𝑙-𝐹𝑖𝑙𝑡𝑒𝑟 × 100 (2.5)
where 𝐴𝑆 is the surface area of the patch resonator.

In this cases a massive area reduction of 94 % could be reached if the via is integrated at the corner.

Input/Output Feeding and External Quality Factor

Usually, to excite a specific mode inside the patch resonator, Input/Output (I/O) feeding ports should be placed at its maximum 𝐸 field or at a so-called radiating edge, otherwise this mode doesn't appear. By changing the I/O ports along its axis of definition, the input impedance 𝑍 𝑖𝑛-𝑇𝑀𝑚𝑛 of a given mode changes accordingly, and this leads to a variation in the external quality factor 𝑄 𝑒 . So, the feeding position should be chosen carefully because in some designs only "single point" could be efficient.

I/O Feeding

In order to illustrate more on the 𝑍 𝑖𝑛 variation with I/O, a conventional square patch resonator (Figure 2.9) of 𝐿 𝑝 = 360 μm is fed by a single port 𝑃 1 , which is deviated by distance 𝐷 𝑡 from the center of the patch. When 𝑃 1 is at the middle of the patch (𝐷 𝑡 = 0 μm), only 𝑇𝑀 10 is excited with 𝑓 𝑇𝑀10 = 200 GHz as shown in Figure 2.10(a), while other modes In collinear configuration, the behavior of the modes and their field distribution are those discussed earlier in this chapter, while for the orthogonal configuration, fields distribution of the fundamental modes are rotated by 45° as shown in Figure 2.12. This rotation is due to the change of the axis of symmetry from horizontal or vertical axes to the diagonal axes. The surface current 𝐽 of 𝑇𝑀 01 and 𝑇𝑀 10 flows diagonally along the AA' and BB', respectively. The 90° configuration is more flexible with perturbations where both fundamental modes can be excited at the same time. In this case, they are recalled as the even-and odd-modes. 𝑇𝑀 01 is the even-mode and 𝑇𝑀 10 is the odd-mode because 𝑃 1 and 𝑃 2 are at the same potential 𝐸 for 𝑇𝑀 01 while they are in differential with 𝑇𝑀 10 . This will be more elaborated in chapter III when discussing the dual mode filter design.

External Quality Factor

The flexibility in varying the position of the I/O ports, allows to determine the external quality factor 𝑄 𝑒 variation. It is an important parameter for building the synthesis of the filter. 𝑄 𝑒 represents the strength of coupling between a resonant 𝑇𝑀 mode and the input signal. Usually, 𝑄 𝑒 is extracted using a single port structure as in Figure 2.9 and its value is calculated from (2.6) [START_REF] Hong | Microstrip Filters for RF/MicrowaveApplications[END_REF]:

𝑄 𝑒 = 𝜔 0 ∆𝜔 ±90 ° (2.6)
where 𝜔 0 is the resonance frequency and 𝛥𝜔 ±90 ° is determined from resonance frequency at which the phase shift is equal to ± 90° with respect to the absolute phase at 𝜔 0 . Taking the example where only 𝑇𝑀 10 is excited (𝐷 𝑡 = 0 μm), Figure 2.13 (a) shows the 𝑆 11 (dB) and its phase 𝜑 𝑇𝑀10 (°) at 200 GHz. 𝑄 𝑒 will vary when 𝑍 𝑖𝑛 changes, it is not noticeable for 𝑇𝑀 10 with collinear feeding configuration, since it has uniform 𝐸 field along AA' axis.

However, it is not the case for 𝑇𝑀 11 , as shown in Figure 2.13 (b). When 𝑃 1 is moved toward the edges, its phase 𝜑 𝑇𝑀11 is widened with 𝐷 𝑡 , which increases 𝛥𝜔 ±90 ° , thus 𝑄 𝑒 varies and decreases accordingly.

Modified Patch Resonator

As mentioned above, patch resonators can support dual-mode concept through inserting perturbations across their axis of symmetry to create coupling between the degenerated modes and split them. Based on the presented techniques in CHAPTER I, this of coupling between modes is strongly linked to 𝑐𝑢𝑡 𝑑 . For example, when 𝑐𝑢𝑡 𝑑 is increased from 30 μm to 70 μm the splitting difference between degenerated resonance modes increases from 2 GHz to 28 GHz. This kind of perturbation doesn't have a lot of freedom since it is limited in the patch area and the performance cannot be flexible.

Cross Slots

It is the most used technique to split and control the degenerated modes. Adding more slot etches inside the patch resonator leads to more reduction in its overall size, which is an interesting feature for integrated circuits. Also, inserting slots in the design effectively helps in controlling the modes, once the perturbation is placed at the maximum 𝐽 in order to disturb the current flow of a specific mode.

For demonstration, square patch resonator of 𝐿 𝑝 = 360 μm with symmetrical and asymmetrical cross slots is implemented with collinear and orthogonal feeding as shown in Figure 2.17

Design Methodology for Dual-mode and Cascaded Patch Filters

It is pivotal to explain the design methodology that is followed in order to build up the intended filters, especially for mm-wave filter circuit design. Our interest is to present the synthesis methodology for narrowband dual-mode filters with grounded vias, which for our best knowledge was not recorded before. Moreover, a flow design chart is presented and thoroughly explained to bring an overview for any future filter design in integrated technology.

Dual-Mode Patch Filter Synthesis

Conventionally, filters based on patch cavity or microstrip topologies are synthesized through the general coupling scheme presented by Cameron in [START_REF] Cameron | General coupling matrix synthesis methods for Chebyshev filtering functions[END_REF]. Each resonator has a single resonance mode with single resonance frequency, which is either coupled to the successive resonator or to the source/load, where source/load is only coupled to one resonator. This type of synthesis can produce 𝑁 -2 frequency transmission zeros (FTZ)

where 𝑁 is the number of resonators. Thus, filters with low order 𝑁 < 3, can suffer from bad rejection bands due to the limitation in producing any FTZ. Moreover, filters with single resonator that support dual-mode resonances cannot be synthesized using such approach.

Another optimized approach is the adaptive synthesis methodology that was presented in [START_REF] Amari | Adaptive synthesis and design of resonator filters with source/load-multiresonator coupling[END_REF]. It is the evolution of Cameron's concept but obeys to source/load-multiresonator coupling. Its 𝑁 𝑡ℎ order coupling scheme is presented in Figure 2.20. The source S and load L are denoted by "white" nodes, while the resonators are denoted by "black" nodes. Our discussion here is about modes so each node can be referred to a single mode in the patch cavity instead of resonators. The main coupling or direct path between nodes is denoted by solid line and indirect coupling or an admittance inverter is denoted by dotted line. Such approach allows multiple couplings between source/loads and resonators (𝑀 𝑠𝑛 /𝑀 𝐿𝑛 ), resonators to resonators (𝑀 𝑛,𝑛+1 ) and between source and load (𝑀 𝑠𝐿 ) itself. So, the generation of FTZ depends on the multi-path between the source and load. This coupling scheme can be also expressed by a coupling matrix CM with 𝑁 + 2 rows and 𝑁 + 2 columns as in (2.7), where 𝑁 is the filter's order.

⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ 𝑀 𝑛𝑠 𝑀 𝑛1 𝑀 𝑛2 𝑀 𝑛3 ⋯ 𝑀 𝑛𝑛 𝑀 𝑛𝐿 𝑀 𝐿𝑠 𝑀 𝐿1 𝑀 𝐿2 𝑀 𝐿3 ⋯ 𝑀 𝐿𝑛 𝑀 𝐿𝐿 ] (2.7)
The first row designated to the source, the second up to the 𝑁 + 1 designated to the first up to the 𝑁 𝑡ℎ resonant mode, and the last row designated to the load. The matrix elements represent the normalized coupling coefficients between each part of the filter in the rows and columns, and are frequency-independent. The main diagonal has non-zero elements except for 𝑀 𝑆𝑆 and 𝑀 𝐿𝐿 , which are null terms with no meaning. The others represent the susceptance elements 𝑀 11 , 𝑀 22 , 𝑀 33 ,…𝑀 𝑛𝑛 of modes "1", "2", "3", … "𝑛", respectively. They are related to the offset of each self-resonance frequency (𝑓 01 , 𝑓 02 , 𝑓 03 , …𝑓 0𝑛 ) from the filter center frequency (𝑓 𝑐 ). 𝑀 𝑛𝑛 and 𝑓 𝑐 are calculated from (2.8) and (2.9), respectively [START_REF] Hong | Microstrip Filters for RF/MicrowaveApplications[END_REF]:

𝑀 𝑛𝑛 = 𝑓 𝑐 𝑓 0𝑛 - 𝑓 0𝑛 𝑓 𝑐 𝐹𝐵𝑊 3𝑑𝐵
(2.8)

𝑓 𝑐 = 𝑓 𝑖 𝑁 𝑖=1 1/𝑁
(2.9)

Source Load R1 R2 R3 Rn Ms1 Ms2 Ms3 MSL M13 M2n M2L M3L MnL
where 𝑓 0𝑛 is the self-resonance frequency of a given mode and 𝐹𝐵𝑊 3𝑑𝐵 is the 3-dB fractional bandwidth of the defined filter. The center frequency 𝑓 𝑐 is the geometric mean of all the resonant frequencies. By inspecting (2.8), it is deduced that if 𝑓 0𝑛 is less than 𝑓 𝑐 then 𝑀 𝑛𝑛 is positive, and vice versa. The farther 𝑓 0𝑛 from 𝑓 𝑐 the bigger is 𝑀 𝑛𝑛 coefficient.

In regards to the coupling between two resonators 𝑚 and 𝑛, the general coupling coefficient 𝑀 𝑚𝑛 is extracted from (2.10):

𝑀 𝑚𝑛 = ± 1 2 𝑓 0𝑚 𝑓 0𝑛 + 𝑓 0𝑛 𝑓 0𝑚 × 𝑓 𝑚 2 -𝑓 𝑛 2 𝑓 𝑚 2 + 𝑓 𝑛 2 2 - 𝑓 0𝑚 2 -𝑓 0𝑛 2 𝑓 0𝑚 2 + 𝑓 0𝑛 2 2 (2.10)
where 𝑓 0𝑚 and 𝑓 0𝑛 are the self-resonant frequencies of modes 𝑚 and 𝑛, and 𝑓 𝑚 and 𝑓 𝑛 are the resonant frequencies of modes 𝑚 and 𝑛 when coupled to each other. For a dual-mode patch resonator, both frequencies can be extracted from 𝐸𝑀 simulation. When the filter is simulated with weakly coupled feeding ports, 𝑓 𝑚 and 𝑓 𝑛 can be extracted, while 𝑓 0𝑚 and 𝑓 0𝑛 can be extracted using the method of placing magnetic wall or electric wall in the filter's axis of symmetry [START_REF] Serrano | Synthesis Methodology Applied to a Tunable Patch Filter With Independent Frequency and Bandwidth Control[END_REF]. This will excite only the even-modes or odd-modes, respectively. Another important element is related to the coupling coefficients 𝑀 𝑠𝑛 or 𝑀 𝐿𝑛 from (2.11) between the resonator 𝑛 and the S/L:

𝑀 𝑠𝑛 2 = 1 𝑄 𝑒𝑛 (2.11)
which is linked to external quality factor 𝑄 𝑒𝑛 of given mode. For even-mode, 𝑀 𝑠𝑛 = 𝑀 𝐿𝑛 but for odd mode 𝑀 𝑠𝑛 = -𝑀 𝐿𝑛 .

Synchronous and asynchronous tuning

According to the above general coupling matrix, two types of filters can be designed, i.e. synchronous and asynchronous tuning filters, respectively. The synchronous tuning filters are the conventional cascaded filters where the self-resonant frequencies 𝑓 0𝑛 = 𝑓 0𝑚 = 𝑓 𝑐 . Thus, the main diagonal 𝑀 𝑛𝑛 is null and coupling coefficient 𝑀 𝑚𝑛 is simplified to:

𝑀 𝑚𝑛 = ± 𝑓 𝑚 2 -𝑓 𝑛 2 𝑓 𝑚 2 + 𝑓 𝑛 2 2
(2.12)

The asynchronous tuning filters are those with independent control of resonance frequencies, while self-resonant frequencies 𝑓 0𝑛 ≠ 𝑓 0𝑚 . It has two scenarios: i) 𝑀 𝑚𝑛 = 0, if 𝑓 0𝑛 = 𝑓 𝑛 and 𝑓 0𝑚 = 𝑓 𝑚 , which indicates that each mode is controlled independently. ii) 𝑀 𝑚𝑛 ≠ 0, if 𝑓 0𝑛 ≠ 𝑓 𝑛 and 𝑓 0𝑚 ≠ 𝑓 𝑚 . This means all the elements in the CM are not null.

Multi-mode patch filters are naturally asynchronous tuning networks because each mode resonates at a different frequency. So the simplified coupling matrix for a dual-mode patch filters with two independently controlled modes is summarized in (2.13):

𝑀 2 𝑛𝑑 𝑂𝑟𝑑𝑒𝑟 = [ 0 𝑀𝑠1 𝑀𝑠2 𝑀𝑠𝐿 𝑀1𝑠 𝑀11 0 𝑀1𝐿 𝑀2𝑠 0 𝑀22 𝑀2𝐿 𝑀𝐿𝑠 𝑀𝐿1 𝑀𝐿2 0 ] (2.13)
𝑀 12 = 𝑀 21 = 0. As for the FTZ with normalized frequency Ω that can be produced from the dual-mode filter with this scheme, it is provided as follows [77][88]:

Ω = 𝑀 11 𝑀 𝑆1 2 -𝑀 22 𝑀 𝑆2 2 𝑀 𝑆1 2 -𝑀 𝑆2 2 (2.14)
According to (2.14), if 𝑀 𝑆1 < 𝑀 𝑆2 then Ω > 0, thus FTZ is located at upper stopband.

Ideally, the reverse is true, if 𝑀 𝑆1 > 𝑀 𝑆2 then Ω < 0, thus FTZ is located at the lower stopband.

The theoretical curves of the transmission coefficient 𝑆 21 and the reflection coefficient 𝑆 11 for the defined coupling matrix CM, are derived from the loop current equations that are expressed in matrix form and grouped in vector [𝐼], which is summarized in (2.15) [START_REF] Amari | Adaptive synthesis and design of resonator filters with source/load-multiresonator coupling[END_REF].

[-𝑗𝑅 + 𝜔 ′ 𝑊 + 𝐶𝑀][𝐼] = [𝐴][𝐼] = -𝑗[𝑒] (2.15)
Where:

-𝑗 2 = -1 and [𝑅] is a 𝑁 + 2 × 𝑁 + 2 matrix, in which only nonzero entries are 𝑅 11 = 𝑅 𝑖 and 𝑅 𝑁+ 2,𝑁 + 2 = 𝑅 𝑜 , both normalized to 1 (the reference is 50 Ω).

-[𝑊] is a 𝑁 + 2 × 𝑁 + 2 identity matrix, with 𝑊 11 = 𝑊 𝑁+ 2,𝑁 + 2 = 0.

-𝜔′ is the lowpass prototype normalized angular frequency given by (3.16):

𝜔 ′ = 𝜔 𝑐 ∆𝜔 𝜔 𝜔 𝑐 - 𝜔 𝑐 𝜔 (2.16)
where: 𝜔 𝑐 is the center angular frequency of the filter and 𝛥𝜔 is the bandwidth of the filter.

-[CM] is the coupling matrix.

-[𝑒] is a 1 × 𝑁 vector that represents the filter stimulus, in which only nonzero entry is 𝑒 11 = 1.

Then the scattering parameters curves are given by (2.17) and (2.18).

𝑆 21 = -2𝑗[𝐴 -1 ] 𝑁+2,1
(2.17)

𝑆 11 = 1 + 2𝑗[𝐴 -1 ] 11 (2.18)
A Matlab code provided in APENDIX was used to plot the theoretical curves.

Integrated Filter Design Methodology

The design of mm-wave filters is not simple because the behavior of filters at higher frequencies above the sub-wavelength band has more constraints due to parasitics. Also, implementing passive circuits on integrated technologies has a lot of designing rules to be considered and in most cases, they introduce negative drawbacks. In this work a general overview of the proposed design methodology is presented, to be followed in order to successfully implement any future mm-wave filters. To further demonstrate the design approach for an integrated bandpass filter, a summary of thorough step-by-step design procedure is shown in Figure 2.21.

Step 1) Usually at this stage the filter characteristics (center frequency, 𝐹𝐵𝑊 and rejection levels) are chosen according to the intended application. Moreover, the resonator topology should be chosen carefully in order to check its flexibility in responses to build up the filter. It is recommended at this stage to choose the stack from the BEOL of the selected technology, in order to determine the finite 𝑄 of the filter.

Step 2) The filter function (Chebyshev, quasi-elliptic, Butterworth…etc.) is chosen at this stage, including the finite FTZ that could be produced. The initial values of the coupling matrix are extracted from the lowpass prototype parameters using

(2. [START_REF] Miao | A Novel Multilayer Aperture-Coupled Cavity Resonator for Millimeter-Wave CMOS RFICs[END_REF]) and (2.20):

𝑄 𝑒𝑖 = 𝑔 𝑖 𝑔 𝑖+1 𝐹𝐵𝑊 𝑀 𝑠 𝐿 𝑖 = 1 𝑄 𝑒𝑖 ×𝐹𝐵𝑊 for i=1 to n (2.19) 𝑀 𝑖,𝑖+1 = 1 𝑔 𝑖 𝑔 𝑖+1 for i = 1 to n-1 (2.20)
where 𝑛 is the order of the filter, 𝑄 𝑒𝑖 is the external quality factor of a given node at the source or load, 𝑀 𝑠 𝐿 𝑖 is the external quality factor corresponding to the normalized coupling coefficient at the source or load, and 𝑀 𝑖,𝑖+1 is the normalized coupling coefficient between the adjacent nodes. After that the optimization technique in [START_REF] Hong | Microstrip Filters for RF/MicrowaveApplications[END_REF] is used to achieve the intended filter response. Step 3) After the lossless filter response is fixed, the physical dimensions are extracted from the mapping between the coupling matrix and the elements of the design.

The 𝐸𝑀 simulation of the designed filter is conducted (using ANSYS HFSS software in the present work). Then a comparison between the simulated and theoretical results is conducted to make sure that we are still within the filter template specifications.

Step 4) This is a very important stage where the filter design is implemented within the integrated technology framework. All the design rules from the manufacturer's Design Rule Manual (DRM) must be taken into consideration at this step. It includes the minimum and maximum allowed physical dimensions for a strip line at the top metal. In addition to the minimum and maximum allowed metal density on each metallic layer from the BEOL, it is worth to mention that the design rules checker (DRC) may oblige to add metals in undesired zones, where it adds parasitics to the filter. So, modifications to the 3D design is required to compensate the added losses. After a successful post-layout simulation and DRC validation, the layout is ready for fabrication.

Conclusion

In this chapter a full and detailed description of the integrated patch filter design aspects was conducted. It is decomposed into two main parts: square patch design principles and filter synthesis methodology.

Patch resonators with integrated grounded vias allow a great reduction to the overall size, as thoroughly explained, which is an important feature for integrated passive circuits design. Also, an analysis to the effect of different perturbation techniques on the fundamental and higher order modes through exploring their resonance frequencies and fields' distribution, is discussed.

The second part focuses on the filter synthesis methodology, using the adaptive techniques through extracting the coupling matrix elements and with optimization technique, the intended filter can be designed. Dual-mode filters are considered as asynchronous tuned networks, where the resonance modes are independently controlled and different from the center frequency of the filter. Also, the cascaded filter topology is considered as synchronous tuned networks where self-resonant frequency of all the resonators are equal to the center frequency of the filter. Finally, an integrated filter design flow chart, starting from the filter template and passing through 3D design and layout implementation, is presented.

CHAPTER III: MM-WAVE PATCH FILTER DESIGN

Designing a new and novel patch filter is still considered one of the big challenges, because the literature, as presented CHAPTER I, is very rich of ideas and techniques. It is true that our focus in this dissertation is to test bandpass filters based on patch resonators on BiCMOS integrated technology at mm-wave bands, but having a well fashioned design is a key measure. Based on this aim, this chapter thoroughly presents several bandpass filter designs with an original modified patch resonator. It is decomposed into two main parts: i) the first part presents the design and synthesis of dual-mode and dual-band patch filters that operate above 100 GHz and implemented on different stacks from BiCMOS 55nm technology. The duality is rebuild using a hybrid perturbation approach that combines both grounded vias and slots. ii) In the second part a 2 nd order ultra-compact patch-like bandpass filters is developed. Original techniques like Complementary Split Ring Resonator (CSRR) and loading "mushrooms" are integrated along with grounded vias to provide a massive miniaturization to the conventional patch resonator.

Dual-Mode narrowband BandPass Filter above 100 GHz 3.1.1. Grounded Patch Filter with Collinear Feeding

Proposed Patch Resonator with Perturbation

Two techniques are selected from Table 1.1 in order to (i) reduce the dimensions of the square patch resonator, and (ii) flexibly control its modes, which are the grounded vias of size 𝑣𝑖𝑎𝑑 and single vertical slot of length 𝐿 𝑠 , as shown in Figure 3.1 and Figure 3.2, respectively. This hybrid combination can improve the capability to control the modes and increase the miniaturization factor obtained by using only one way. The filter is built up by two steps: first the fundamental modes 𝑇𝑀 01 and 𝑇𝑀 10 are split using grounded vias, which perturb their E field. Afterwards, the vertical slot perturbs the surface current J of 𝑇𝑀 10 with full controllability of its resonance frequency. So, the duality is rebuilt again, but with 𝐿𝐶 -𝑚𝑜𝑑𝑒 and 𝑇𝑀 10 .

To further illustrate on the relationship and the manipulation between modes, perturbations in the resonator are carefully and separately analyzed. vertical slot is in parallel with its surface current flow. While 𝑇𝑀 10 is drastically perturbed by the vertical slot since its surface current has to follow the path around the edges of the slot in order to pass from source to load (I/O feeding), and so its electrical length is increased accordingly. For 𝑇𝑀 11 mode, its surface current flows horizontally and vertically at the four edges of the patch only. When the vertical slot reaches the edges, the top and bottom current flow are affected and slightly perturbed.

In order to deeply analyze the effect of both perturbations on the resonance frequencies of each mode, Figure 3. frequencies are not changed, while 𝑇𝑀 01 resonance frequency is split and shifted upwards.

It is more perturbed when two vias are inserted, where its 𝑓 𝑇𝑀01 shifts from 220 GHz to 245 GHz. Lastly, when vertical slot is inserted, 𝑇𝑀 01 is unchanged as expected and still resonating at 𝑓 𝑐 , while 𝑇𝑀 10 and 𝑇𝑀 11 resonance frequencies are shifted downwards. This confirms the observation carried out in Figure 3.2 (b), e.g. the vertical slot has big impact on 𝑇𝑀 10 with 𝑇𝑀 11 slightly changed, since it perturbs part of its current.

Original Dual-Mode Square Patch Filter their 𝐸 fields are maximal at the edges. This means, the filter is symmetrical across 𝐴𝐴' axis. I/O ports can be deviated from the center by distance 𝐷 𝑡 to realize different strengths of main coupling paths. This ± deviation breaks the filter's symmetry to create transmission zeros (FTZ) provided by higher order modes (𝑇𝑀 01 and 𝑇𝑀 11 ). In that case, asymmetric filter is developed.

Initially, a grounded square patch resonator of 𝐿 𝑝 = 𝜆/2 = 360 μm is designed and simulated using ANSYS HFSS software with two integrated vias of initial size of 𝑣𝑖𝑎𝑑 = 1 μm. A lower resonance due to the 𝐿𝐶 -𝑚𝑜𝑑𝑒 appears at 100 GHz. Then, as a first step, the patch is shrinked to have 𝐿 𝑝 = 200 μm (69% of miniaturization), which in return shifts all its higher resonance frequencies including 𝐿𝐶-mode upwards. Based on the presented analysis, a dual-mode filter can be designed using the first resonance frequencies with an advantage of flexible responses, not only within the pass band but also within the out-of-band. Moreover, 𝑄 𝑒-𝑇𝑀 10 is always greater than 𝑄 𝑒-𝐿𝐶 , i.e. source/𝐿𝐶-mode (𝑀 𝑆2 ) coupling is always greater than source/𝑇𝑀 10 (𝑀 𝑆2 ) coupling, which means only one FTZ can be realized. This will be more elaborated further.

Extracted External Quality Factor and Source-Load Coupling

To verify this analysis, the transmission response (𝑆 21 ) of the proposed dual-mode patch resonator is plotted in manage the upper band rejection, according to the filter specifications. Indeed, by putting the I/O ports near to the edges, higher order modes (𝑇𝑀 01 and 𝑇𝑀 11 ) are excited, which explains why the FTZ appears in the upper band. Then, Source/Load coupling is created and managed by the deviation 𝐷 𝑡 .

Filter Synthesis and Coupling Matrix

Based on the proposed architecture for modified patch resonator and the detailed discussion of the resonance modes behavior, a dual-mode bandpass filter can be designed as a doublet coupling scheme that is shown in Figure 3.4 (b). The two nodes "1" and "2" have a main coupling with source and load, while an indirect coupling between the source and load exists, only with asymmetrical ports feeding, as discussed before. The variations of resonance modes show that asynchronous filter can be designed since its main modes (𝐿𝐶-mode and 𝑇𝑀 10 ) are independently controlled.

Conventionally for any dual-mode patch filter, odd ("1") and even ("2") -modes are naturally coupled. However, in this proposed modified patch, 𝐿𝐶-mode and 𝑇𝑀 10 are uncoupled modes. Yet, based on the previously analyzed 𝐸 fields, 𝐿𝐶-mode can be referred to be the new even-mode since its 𝐸 𝑧 sign changes identically and simultaneously at the source and load, while 𝑇𝑀 10 is still considered as the odd-mode where its 𝐸 𝑧 has opposite signs at the source and load. So, the two different and initiated uncoupled modes are reconfigured to construct the filter. The synthesis methodology presented in CHAPTER II is used. Recalling CM from (2.13), the main diagonal elements 𝑀 11 and 𝑀 22 refer to modes "1" (𝑇𝑀 10 ) and "2" (𝐿𝐶-mode). Since 𝐿𝐶-mode exhibits always the lowest resonance frequency, then 𝑓 𝐿𝐶 < 𝑓 𝑐 , so 𝑀 22 > 0. As for 𝑇𝑀 10 , its 𝑓 𝑇𝑀10 > 𝑓 𝑐 , then 𝑀 11 < 0. Also, both modes are uncoupled, then 𝑀 12 = 𝑀 21 = 0. Moreover, 𝑄 𝑒-𝐿𝐶 < 𝑄 𝑒-𝑇𝑀10 , then 𝑀 𝑠2 > 𝑀 𝑠1 , therefore, according to (2.14), FTZ can be produced in the upper stop band. This is compatible with the variations in Figure 3.7 (b). In addition, 𝑀 𝑠1 = -𝑀 1𝐿 because 𝑇𝑀 10

has odd signs at the source and load, while 𝑀 𝑠2 = 𝑀 2𝐿 , because 𝐿𝐶-mode has even signs at the source and load. 𝑀 𝑆𝐿 is null when there is no coupling between the source and the load (case of asynchronous symmetrical filter) and it is ≠ from zero when there is coupling between the source and load (case of asynchronous asymmetrical filter).

From the presented theory for coupling matrix, and using the initial parameters in [START_REF] Yang | A Low-Loss Bandpass Filter using Edge-Coupled Resonator With Capacitive Feeding in (Bi)-CMOS Technology[END_REF] for Chebyshev response, a 2 nd order asynchronous symmetrical bandpass filter is designed, In both cases, this variation modifies the center frequency and bandwidth. In order to map the achieved coupling matrix for symmetrical bandpass filter to the real dimensions of the patch filter, the optimization technique in [START_REF] Yang | A Low-Loss Bandpass Filter using Edge-Coupled Resonator With Capacitive Feeding in (Bi)-CMOS Technology[END_REF] is used. Also, EM solver from ANSYS HFSS is utilized to extract the self-resonance frequencies of each mode, by weakly coupling the This is mapped to the change of 𝑄 𝑒 when feeding ports are deviated from the origin of the patch. It creates an indirect coupling between S/L supported by the excitation of higherorder modes. For the same defined filter template, the extracted CM for the desired asymmetrical filter with its theoretical 𝑆 21 and 𝑆 11 responses are compared to the achieved simulation results, with infinite 𝑄, and plotted in Figure 3.9 (b). As expected, FTZ is added in the upper-band of the filter, which improves the upper selectivity and the out-of-band rejection.

with

Multiple Filter Designs

The variation of 𝑄, as discussed in CHAPTER I, depends on the chosen stack of the BEOL. The presented results in the synthesis do not take into consideration the losses occurred within the BEOL layers. In order to consider finite 𝑄, the metallic layers are chosen to have copper conductivity of 𝜎 𝑐 = 5.1 • 10 7 s/m. The achieved results for the asymmetrical dual-mode filter are plotted in Figure 3.10 for the same optimized dimensions. The recorded insertion loss is 𝑆 21 = -2.5 dB at the center frequency of 200 GHz. The filter is well matched with a return loss equal to 20 dB and a FBW 20%.

These results are very promising especially at this high frequency which was not targeted before, to our best knowledge. Moreover, the proposed filter has flexible responses where The presented synthesis methodology verifies the EM simulations and the drawn objectives for the proposed patch filter. Based on this, a total of seven patch filters were designed and implemented on B55-8ML, as described here below. for F-Ref2. Conventional patch resonators operating at 120 GHz have not been produced due to their dimensions, which would involve a high silicon cost.

2) Two dual-mode patch filters denoted by F-1 and F-2 operating at 120 GHz have been made on a stack M8U:M1, with symmetrical feeding version and asymmetrical feeding version, respectively.

3) In the same way, two similar dual-mode patch filters operating at 200 GHz were made on the same stack M8U: M1 with symmetrical and asymmetrical versions denoted by F-3 and F-4, respectively. Also, a dual-mode patch filter operating at 200 GHz was realized on AP:M6z stack and denoted by F-5.

In addition to those filters and to improve 𝑄 𝑢 , two filters were designed and implemented on B55-9ML with the configuration as in Figure 3.11. 2) A dual-mode filter operating at 200 GHz with FBW of 10 %, implemented on M9v:M6z stack and denoted by F-6.

All of these configurations allow, (i) to compare the dimensions and performance of the filters at two different frequencies, (ii) to compare the symmetrical and asymmetrical feeding versions, and finally (iii) to compare M8U:M1 stack with an AP:M6z stack from B55-8ML versions and M9v:M6z from B55-9ML version. All possible configurations

were not realized due to technology costs. These filters were synthesized to have return loss of 20 dB and FBW of 20 %. Since the presented synthesis doesn't consider the occurrence of losses (infinite 𝑄), the analysis for the expected losses after the layouts is made in CHAPTER IV along with filter layout and measurement results.

Dual-Band Grounded Patch Filter with Collinear Feeding

The dual-mode filter presented previously shows that it has flexible responses if the self-resonance frequencies of the first four modes are carefully controlled and managed. It could have dual-band dual-mode response with single patch resonator, thanks to multiresonance modes with grounded vias. The proposed patch filter in Figure 3.4 (a) was modified to have both dual-mode asymmetric response and dual-band response as shown in Figure 3.12. The originality of this modified version allows to have multiple response with small modification. In Figure 3.12 (a) a dual-mode asymmetric bandpass filter is designed with two grounded vias aligned horizontally at the edges along the BB' axis, along with couple horizontal slots. This approach turns into dual-band filter response, as in Figure 3.12 (b), if vertical slot is inserted in the middle of the patch along AA' axis. Both filters are fed by collinear two-ports with 180 ° configuration.

Perturbed Square Patch Resonator

In order to explain the effect of vias orientation on the perturbed resonance modes,

Single-Band Dual-Mode Patch Filter

The proposed single-band dual-mode patch filter in Figure 3.12 (a) is designed using the same synthesis methodology presented in section 3.1.1. It is equivalent to the doublet scheme shown in Figure 3.4 (b) with node "1" representing the odd-mode 𝑇𝑀 01 and node "2' representing the even-mode 𝐿𝐶-mode.

Following the same steps, 𝑄 𝑒 of both modes are extracted from (2.6) and its variation is plotted in Figure 3.14 against the ports' deviation 𝐷 𝑡 . As previously explained, 𝑄 𝑒-𝐿𝐶 is always less than 𝑄 𝑒-𝑇𝑀01 , then 𝑀 𝑠2 > 𝑀 𝑠1 , so according to (2.14), one FTZ exists at the upper band rejection. Furthermore, the variation of 𝑄 𝑒 for both modes is changing in a wide interval with values for 𝑇𝑀 01 ranging between 50 to 15, with 𝐷 𝑡 variation between 40 μm 100 μm. In comparison to the previous extracted 𝑄 𝑒 in Figure 3.7, the difference can be explained by observing the 𝐸 field in Figure 3.13, where both modes (𝐿𝐶-mode and 𝑇𝑀 01 )

have non uniform E field distribution along the axis of 𝐷 𝑡 variation. For example, with 𝐷 𝑡 = 40 μm, the feeding ports are partially (low 𝐸 magnitude) exciting 𝑇𝑀 01 mode, which increases 𝑄 𝑒 . Nevertheless, it has good impact on adjusting the matching of the filter, where it is recommended according to this analysis, to place the excitation ports near the edges.

For demonstration, square patch resonator with two grounded vias of initial diameter size 𝑣𝑖𝑎𝑑 = 1 μm, is designed and implemented on M8U:M1 stack using ANSYS HFSS software. Its initial side length is 𝐿 𝑝 = λ/2 = 360 μm. Since its first resonance frequency 𝑓 𝐿𝐶 appears at 100 GHz, the modified patch's size is shrunk by approximately 69% to have 𝑇𝑀 01 mode is mainly controlled by the length 𝐿 ℎ and width 𝑊 ℎ of the horizontal slots.

𝑊 ℎ is fixed to 10 μm, and its impact is the same as 𝐿 ℎ . The maximum number of slots is used, in order to increase the capability of controlling 𝑇𝑀 01 mode, which helps in fine tuning the filter. Figure 3.16 shows the effect of varying 𝐿 ℎ on the resonance frequencies concerning the operating frequency, between 170 GHz and 180 GHz, and the fractional bandwidth, between 15% and 20%, is that a very reduced bandwidth would lead to unacceptable insertion loss, given the quality factor of patch resonators when considering the 8ML BEOL of the B55 technology, even if this quality factor is higher than that of transmission lines made with the same technology.

Dual-Band Dual-Mode Patch Filter

The dual-band filter is made on the same principle as the single-band filter just described, with the addition of a second band using the upper resonance modes 𝑇𝑀 10 and In order to summarize the effect of each element in the proposed layout, Table 3.1 provides a basic design guide for the dual-band dual-mode filter response, i.e. x: significant impact, x: limited impact and -: no impact. Therefore, the presented variations show that the second band can still be modeled as the doublet coupling scheme in In order to consider finite 𝑄, the metallic layers are chosen to have copper conductivity.

The achieved results for dual-band dual-mode filter is plotted in Figure 3.20. The recorded insertion loss (given by 𝑆 21 ) is equal to 2.6 dB for both bands. The filter is well matched with return loss (given by 𝑆 11 ) equal to 15 dB and 𝐹𝐵𝑊 1 = 𝐹𝐵𝑊 2 = 15%. It couldn't be possible with same configuration and same stack to achieve a lower FBW with acceptable The presented synthesis methodology verifies the EM simulations and the drawn objectives for the proposed single-band and dual-band patch filter. Based on this, a total of two filters were designed and implemented on B55-8ML, as described below.

1) A single-band dual-mode bandpass filter operating at 180 GHz and dual-band dualmode bandpass filter operating at 180 GHz and 270 GHz, were developed on the same stack M8U:M1 denoted by F-7 and F-8, respectively. These filters were synthesized to have return loss of 20 dB and FBW of 15 %.

In addition to those filters and to improve 𝑄 𝑢 , two filters were designed and implemented on B55-9ML.

2) A single-band dual-mode bandpass filter operating at 180 GHz and dual-band dualmode bandpass filter operating at 180 GHz and 270 GHz, were developed on the same stack M9v:M6z denoted by F-9 and F-10, respectively. These filters were synthesized to have return loss of 20 dB and FBW of 10 %.

All of these configurations allow, (i) to analyze the performance of the filters at high frequencies, and (ii) to compare M8:M2 stack from B55-8ML version and M9v:M6z from B55-9ML version. Since the presented synthesis doesn't consider the occurrence of losses (infinite 𝑄), the analysis for the expected losses is made in CHAPTER IV along with filter layout design and measurement results.

Selective Grounded Patch Filter with Orthogonal Feeding

Taking the advantage of hybrid perturbations (grounded vias and slots) approach that is just presented with dual-mode filters, and combining it with orthogonal port feedings instead of collinear configuration, a new and original dual-mode bandpass filter design operating at 120 GHz is developed. The new approach improves the selectivity of the filter by creating multiple of transmission zeros at the out-of-band rejection along with better inband filter responses. Also, because we aim in this dissertation to check the potentiality of the BiCMOS 55 nm technology with patch filters at mm-wave, another stack (AP:M6z) from B55-8ML version is used for demonstration.

Patch Resonator with Perturbations

The grounded vias are integrated this time at the TOP/RIGHT edges of the patch resonator as shown in Figure 3.22 (a), in order to perturb both modes simultaneously modified patch is excited by orthogonal ports feeding with 𝐷𝑡 deviation from its center of origin. This configuration, flexibly, allows full excitation of several higher order modes. In this case, the axis of symmetry is rotated by 45° and aligned diagonally at AA' axis due to the boundary conditions created by the inserted vias. Our talk about the orientation of axis of symmetry and ports configuration is very important to determine the splitting technique for fundamental modes and creation of FTZs by upper modes. Without addition of any other perturbation like slots (as in Figure 3.22 (a)), 𝑇𝑀 10 and 𝑇𝑀 01 are still combined and uncoupled, because the symmetry between both modes is unbroken. However, a grounded (a) (b) For demonstration, a conventional patch resonator without any perturbation is designed with 𝐿 𝑝 = 𝜆/2 at the operating frequency 𝑓 𝑐 =120 GHz. Since 𝑇𝑀 10 and 𝑇𝑀 01 are defined diagonally and operate at same 𝑓 𝑐 , 𝐷 𝑡 has to be deviated (> 0 μm) to efficiently and separately excite one of them, along with 𝑇𝑀 11 that is defined at the 4 corners of the patch.

This deviation is mandatory, for the moment, to avoid having zero transmission at 𝑓 𝑐 because fundamental modes are still uncoupled. Our focus in this filter design is to use 𝐿𝐶mode and 𝑇𝑀 10 mode only, while other modes will be used to improve the selectivity. The This configuration of vias and slots shows its efficiency in building dual-mode filter with smaller size and better selectivity. Since it has the ability to bring the higher order modes from very far resonance frequency to operate at the upper-band rejection of the filter, which will create FTZs, as will be seen further.

Bandpass Filter Design

Following the same synthesis methodology presented previously, a dual-mode bandpass filter operating at 120 GHz with FBW of 20 % and return loss of 20 dB is designed. The final design configuration of the proposed filter is shown in Figure 3.26. As observed, 3 slots of lengths, 𝐿 𝑑1 , 𝐿 𝑑2 and 𝐿 𝑑3 , respectively, are added. Actually, when 𝐿 𝑑 is increased to its longest limit (350 μm), the lowest 𝑓 𝑇𝑀10 that could be reached is 140 GHz, as shown in Figure 3. 25 (b). This confines the availability to reach low FBW. So to solve this limitation in frequency shift, 𝐿 𝑑1 and 𝐿 𝑑2 slots are added. Moreover, 𝐿 𝑑3 is added to perturb both 𝐿𝐶-mode and 𝑇𝑀 10 mode concurrently for center frequency control perturbation of both 𝐿𝐶-mode and 𝑇𝑀 10 mode, since the position of 𝐿 𝑑3 is placed where the surface current of vias is high (see Figure 3.23). Also, 𝑇𝑀 10 becomes more sensitive to any added slot, since the path of its current is highly rerouted around all the slots along BB' axis. In this context, it is worth to mention that 𝐿 𝑑3 allows the controllability of center frequency without changing the FBW. Therefore, based on previous works on PCB technology as in [START_REF] Liu | High-selective triple-mode bandpass filter using a new capacitive-loaded patch resonator[END_REF], this filter could be tunable!.

In order to consider finite 𝑄, the metallic layers are chosen to have aluminum conductivity for AP layer and copper for M6z layer. The achieved results for the proposed dual-mode filter is plotted in Figure 3.28. The recorded insertion loss is equal to 2.6 dB.

The filter is well matched with return loss equal to 15 dB and FBW = 20%. In order to improve the performance and make the comparison between B55 8ML and 9ML versions, the same stack AP:M6z from B55 9ML is chosen. An optimization for some of the patch - Based on this design analysis, single resonator was designed and implemented on B55-8ML:

1) A dual-mode bandpass filter operating at 120 GHz was developed on AP:M6z stack and denoted by F-11. It was synthesized to have return loss of 20 dB and FBW of 20 %.

In addition to those filters and to improve 𝑄 𝑢 , 3 filters were designed and implemented on B55-9ML:

2) A dual-mode bandpass filter operating at 120 GHz on AP:M6z and M9v:M6z stacks denoted by F-12 and F-13, respectively. These filters were synthesized to have return loss of 20 dB and FBW of 20 %.

3) A dual-mode bandpass filter operating at 120 GHz on M9v:M6z stack denoted by F-14. It is synthesized to have return loss of 20 dB and FBW of 15 %.

2 nd Order Compact BandPass Filters at sub-wavelength (60 GHz) 3.2.1. Grounded Patch-Like Filter using CSRR

The usage of grounded vias in the middle of the patch (see Figure 2.7) has size reduction capability of approximately 75% (𝐿 𝑝 = 𝜆/4 at its center frequency). It is considered a significant reduce compared to the conventional patch, but it could be more.

Taking a look to its E and J fields distribution in Figure 2.8, it shows that the surface current is radially flows starting from the via to the edges of the patch. So, in order to efficiently perturb it, the complementary split ring resonator (CSRR) is integrated within the patch geometry, as discussed further. To the best of our knowledge, (i) CSRR or patch resonators have never been implemented on CMOS/BiCMOS technology and (ii) it is the first filter study that combines grounded patch resonators with CSRR. The design of compact 2 nd order grounded CSRR bandpass filter operating at 60 GHz and implemented on 55-nm BiCMOS technology is developed and explained in this subsection. It provides a design perspective with intensive size reduction. It is very essential to observe the field distribution of the proposed structure in order to understand how to control the self-resonant frequency later in filter design. The grounded via resonance mode has a uniform electric field distribution across the CSRR surface except at its position, as shown in Figure 3.31 (a). While its surface current flow in Figure 3.31 (b) is directed radially outward/inward from/into via and follows the route through the small metal splits between the concentric etched rings. That means these small metal splits have a significant influence on fine tuning the resonance frequency of the resonator.

Grounded CSRR Structure Analysis

Filter Specifications and Synthesis Procedure

For designing the intended filter, a 2 nd order Chebyshev filter response was chosen with fractional bandwidth (FBW) of 25 % and return loss of 20 dB. Its cascaded coupling scheme is shown in Figure 3.32. Each resonator has its single self-resonant frequency with resonator "1" only coupled to the source and resonator "2" only coupled to the load. There exists an indirect path between the source and the load created by the higher order modes.

The lowpass prototype parameters were selected from [START_REF] Hong | Microstrip Filters for RF/MicrowaveApplications[END_REF] as follows: g0 = 1, g1 = 0.6648, g2 = 0.5445 and g3 = 1.22. In order to build up the normalized coupling matrix of the synthesized filter it is mandatory to determine a set of design parameters such as external quality factor and coupling coefficient that are calculated by (2. [START_REF] Miao | A Novel Multilayer Aperture-Coupled Cavity Resonator for Millimeter-Wave CMOS RFICs[END_REF]) and (2.20), respectively. The computed coupling parameters for the desired filter are: 𝑄 𝑒1 = 𝑄 𝑒2 = 2.66 and 𝑀 12

= 𝑀 21 = 0.42. It is worth mentioning that this kind of filter is of synchronous of tuning, i.e.

the self-resonant frequency of each resonator is equal to the center frequency of the filter.

In this context, the self-coupling parameters 𝑀 11 and 𝑀 22 are null. Also, both resonators are coupled to each other then 𝑀 12 = 𝑀 21 ≠ 0. The chosen filter template, at first stage, is symmetrical, then there is no source-load coupling, i.e. 𝑀 𝑆𝐿 = 0. The extracted normalized general coupling matrix is represented in (3.8).

Filter design and Dimensions Extraction

The proposed 2 nd order bandpass filter was designed and simulated using ANSYS HFSS software. Its design configuration is shown in Figure 3.33. The two resonators are implemented on the M8U:M1 stack from the B55-8ML version. They are electrically coupled by two small strips of length 𝐿 12 on AP and M7 layers. In order to gain flexibility in controlling the external quality factor between the source/load and the resonator, a week coupling feeding aperture of length 𝐿 𝑡 at M7 layer was used. The orthogonal configuration of the feeding ports creates an indirect coupling between source and load, which leads to transmission zero at the upper band. In order to determine the physical length of feeding arm 𝐿 𝑡 , the method presented in CHAPTER II for 𝑄 𝑒 extraction is used. The extracted 𝑄 𝑒 is plotted in Figure 3.34 (a). It varies from 24 to 5 when 𝐿 𝑡 increases from 60 μm to 200 μm.

Similarly, the direct coupling coefficient between the two resonators is determined from

1 S L MS1 2 M2L M12

MSL

(2.12), where 𝑓 01 and 𝑓 02 are the self-resonance frequencies of the two coupled resonators, respectively. The extracted 𝑀 12 is plotted in Figure 3.34 (b). It varies from 0.11 to 0.33 when 𝐿 12 increases from 5 μm to 50 μm. At first stage the simulation results exhibited larger FBW and noticeable passband ripple with bad out-of-band rejection. This is due to the initial values of the coupling matrix, which considers the filter as symmetrical with no source/load coupling. In order to create coupling between source and load, reconfiguration is used as a reference to extract its measured unloaded quality factor. The 2 nd order filter F-16, was synthesized to have return loss of 20 dB and FBW of 20 %.

Ultra-Compact Patch Filter with Loaded "Mushroom"

Integrating shorting vias with patch resonators shows a great advantage to reduce the overall size of the filter. In this subsection an original ultra-compact patch resonator is introduced. Grounded vias are inserted with an extended stub at the corner of the conventional patch resonator. This allows a massive reduction of the patch size according to the analysis presented in CHAPTER II. In addition, the modified patch is loaded with shorted "mushrooms" to control its fractional bandwidth. Those mushrooms can be modeled as loaded capacitance to the patch. For proof of concept, a 2 nd order patch filter is designed at 60 GHz for future 5G/6G applications with FBW of 20 %.

Modified Patch Resonator

The analysis presented previously in section 2.1.2, showed that the lowest resonant frequency of grounded patch resonator is achieved when the via is placed at the corner. In order to decrease it more, the corner is extended by a stub (length 𝐿 𝑠 and width 𝑊 𝑠 ), which is shorted at its end by via of size 𝑣𝑖𝑎𝑑, as shown in Figure 3.36 (a). Orthogonal feeding port structure is used with 𝐷 𝑡 deviation from center of origin.

For demonstration, a conventional patch resonator of initial size 𝐿 𝑝 = 360 μm is implemented on M8U:M1 stack from B55-8ML version, where its fundamental frequency operates at 200 GHz. ANSYS HFSS software is used for design and simulation. When via is inserted at the corner of the patch (without stub extension), the lowest resonance frequency for 𝐿𝐶-mode appears at 𝑓 𝐿𝐶 = 55 GHz, as shown in Figure 3.36 (b). As long as the extended stub is inserted, 𝑓 𝐿𝐶 is impressively decreased. For example, when 𝐿 𝑠 = 100 μm, 𝑓 𝐿𝐶 reached 28 GHz. Then it decreased to 18 GHz when 𝐿 𝑠 is extended to 400 μm.

So, as the extended stub is elongated, the electrical length 𝜃 𝑣𝑖𝑎 of 𝐿𝐶-mode is increased and this decreases 𝑓 𝐿𝐶 as well. Using the eigenmode solver from ANSYS HFSS software, the E field and surface current J distribution of 𝑓 𝐿𝐶 are extracted and shown in Figure 3.37.

As expected, the surface current flows from vias through the extended stub to reach the output port. Also, maximum 𝐸 field occurs at the corners along AA' and BB' axes, where J is null. In this case, 𝐷 𝑡 has to be deviated forward/backward to excite the structure at its corner. Also this will help in improving the out-of-band rejection.

Our interest in this approach is to present a patch resonator that operates at 60 GHz, so the modified patch is resized to have 𝑓 𝐿𝐶 = 60 GHz for 𝐿 𝑝 = 140 μm, 𝐿 𝑠 = 160 μm and 𝑊 𝑠 = 10 μm. Resizing the patch depends on how much miniaturization is needed. In our case, we took the maximum limit. In this context, if a conventional patch of size 𝜆/2 is to be designed at 60 GHz, 𝐿 𝑝 should be set to 1250 μm (𝜆/2). However with our approach, 𝐿 𝑝 is drastically decreased to be of size 𝜆/18. This impressive size reduction allows, approximately, 99 % of overall layout miniaturization according to the methodology used in (2.5). In this case, the proposed modified patch resonator could be comparable to the structures presented in [START_REF] Sun | Design of On-Chip Millimeter-Wave Bandpass Filters Using Multilayer Patterned-Ground Element in 0.13-μm (Bi)-CMOS Technology[END_REF] using microstrip line topologies.

The advantage in size reduction came on the expense of bandwidth enlargement as shown in the simulated results in Figure 3.38. As explained in CHAPTER II, the resonance mode created by the via is modeled as 𝐿𝐶 circuit. In this case, when patch size is decreased, the overall capacitance 𝐶 𝑝 of the patch is decreased as well. For any 𝐿𝐶 circuit, bandwidth is inversely proportional to the capacitance. This is why the FBW is enlarged and reaches 85% at 60 GHz. In order to compensate the increase of bandwidth, the modified patch is loaded with "mushroom". The proposed patch resonator is shown in Figure 3.39. The loaded "mushroom" structure is a metallic floating plate of length 𝐿 𝑚 and width 𝑊 𝑚 connected with vias of size 𝑣𝑖𝑎𝑚 to the ground. It is implemented at M7z layer to create a loading capacitance with the patch. Multiple of "mushrooms" are needed to compensate the lost capacitance and their distribution is controlled by the technology design rules that will be illustrated in the coming chapter. Moreover, 4 etched slots of length 𝐿 ℎ and width 𝑊 ℎ are inserted along the vertical and horizontal axes of the patch in order to control FTZ, that is appeared at 210 GHz. This FTZ is created by the upper modes, which is here the degenerated modes. Since both ports are deviated toward the same corner with 𝐷 𝑡 < 0 μm (𝐷 𝑡 > 0 μm), then the upper excited mode is the even-mode (or the odd-mode).

In order to illustrate more on the reduction of FBW, Figure 3.40 (a) shows the variation Also, the variation of 𝐿 ℎ has no impact on the overall response of the patch resonator. Since both FBW and FTZ can be easily tuned, higher order bandpass filters can be designed.

Second Order ultra-compact bandpass filter

For the proof of concept, and following the same synthesis methodology presented in the previous subsection, a 2 nd order bandpass filter operating at 60 GHz using the proposed "mushroom" loaded patch resonator is designed. The filter is designed to have Chebyshev response with FBW of 25 % and return loss of 20 dB. The overall structure of the proposed filter is shown in Figure 3.41. Two "mushroom" loaded patch resonators are cascaded and coupled to each other. In order to control the couplings between both resonators, two floating metals of length 𝐿 𝑐 and width 𝑊 𝑐 are inserted at AP and M7z layers. After design optimization using ANSYS HFSS software, the achieved results are shown in Figure 4.42.

M8U and M1 layers are set to have copper conductivity. The recorded insertion loss is 3 dB with FBW of 28 %. The filter is well matched with return loss better than 15 dB. Since 𝐷 𝑡 is deviated to the corners, not only this allows to create FTZ in the upper band, but also, an indirect path between 𝑃 1 and 𝑃 2 is occurred and created FTZ in the lower band too. Also, with such kind of resonator it could be possible to design more sophisticated filter with cross-coupled synthesis approach and using the B55-9ML version for better selectivity and FBW. This will be developed in the future.

Based on this design analysis, a total of two filters were designed and implemented on B55-8ML version:

1) 1 st and 2 nd order patch filters at 60 GHz with same patch resonator topology were developed on M8U:M2M1 stack and denoted by F-17 and F-18, respectively. F-17 is used as a reference in order to extract the measured unloaded quality factor of the proposed resonator. The 2 nd order filter F-18 is synthesized to have return loss of 20 dB and FBW of 25 % for the proof of concept.

Conclusion

This chapter presented different kinds of patch filters, which were implemented on different layers of B55 8ML and 9ML integrated technology.

Dual-mode single band and dual-band bandpass filters operating above 100 GHz were thoroughly synthesized and developed. Flexible responses were achieved, thanks to the combination between grounded vias and slots. Following the same synthesis methodology, more selective filter was developed at an operating frequency of 120 GHz. With this type of filters, upper out-of-band rejection was improved through creating multiple FTZs.

Another kind of filters based on conventional cascaded synthesis scheme were developed at 60 GHz. The focus was to present a new approach for patch resonators that can be used for 5G applications at sub-wavelength band with very compact size. The first patch resonator topology combines both CSRR and grounded vias, while the other one is a grounded patch resonator loaded with "mushroom". A massive miniaturization of 99 % was achieved as compared to a conventional patch resonator at the same frequency.

All the presented modified resonators are original and were not designed before on PCB or other technologies. The multi-layering availability within the used technology shows a great interest to develop more sophisticated filters without additional design complexity. The combination of both different versions of B55 with same filters topologies, showed a great interest of the 9ML technology in terms of 𝑄 𝑢 improvement, which leads to better performance. This will be more focused in the coming chapter where measurement results are analyzed.

CHAPTER IV: LAYOUT DESIGN & MEASUREMENT RESULTS

Passive circuit layout is relatively complicated for advanced CMOS/BiCMOS technologies, due to the strict rules enacted by the manufacturer in the Design Rule Manual DRM. During the layout procedure, Design Rule Checker DRC has to be checked more often, mainly for different implementation rules like: metal density, precision dimensions …etc. In this chapter different layout steps, in order to successfully send all the layouts for fabrication, are explained. Also, it is shown the effect of different design rules on the performance of the filters and how it can be compensated. As a second step, measurement results are thoroughly analyzed and comparison with the state-of-art is conducted.

Layout Design and Technology Constraints

For mm-wave IC circuit design, more advanced CAD design tools are required. In order to sketch the layouts of the presented filters, Cadence Virtuoso® software was used and the Process Design Kit (PDK) was supported by STmicroelectronics for BiCMOS 55 nm technology. For confidentiality the design rules values cannot be specified. The layout methodology is driven by three main steps: i) implementation of the filter configuration on its intended layer stack, ii) fulfill the empty and unused metal layers to satisfy DRC and study the losses mechanism, iii) post layout simulation.

During the first step, each filter configuration is implemented on its intended layer, which for our patches are: AP, M8U and M9v layers. These layers share approximately the same precision dimensions rules with less complexity compared to lower layers. Since patch resonators use big strips in size, the first rule to be satisfied is the min/max allowed width for strips. There is no issue with the min limit, though with the max limit. In order to overcome it, small etched slots (with no significant impact) are inserted in specific places (Figure 4.1 (a)) as required by the DRC. Afterwards, the second rule to satisfy is the min/max allowed metal density for the used stack. This rule is only tested when the whole design of a given filter layout is implemented. Taking the example of the filter in Figure 3.39, where there is full metal patch parts that exceed the max allowed limit, it is solved by adding some etched slots as shown in metal density issue can be more highlighted with the implementation of the ground. In all of the presented filter designs, full metal ground is used. In order to satisfy the DRC with less impact on the performance, stacking multiple layers is the solution. Figure 4.2 shows the configuration of a unit cell of a given stack where both layers form an interconnected mesh. In case M1 is selected, M2M1 is stacked instead, and in case M6z is selected, M6zM5x is stacked.

At this layout step, the conductivity of the metals, especially for vias, has to be well extracted due to some technology fabrication constraints. According to the DRM, there exists a contact resistance with by very high resistivity between each metallic/dielectric layer, which drastically reduces the conductivity of the used vias. So, vias were modeled using maxwell-3D solver from ANSYS HFSS to extract its equivalent conductivity to be near to the real fabricated ones. In our case, the equivalent conductivity for vias that are used is 𝜎 𝑣 = 1.6 • 10 6 S/m.

The second step in the layout procedure is to fulfill the unused metal layers with the minimum floating metal possible, which are referred as "dummies". The added dummies "zoom". The size of these dummies was fixed near to the minimum allowed by the technology, in order to reduce eddy current losses. Also, the placement of these dummies was carefully optimized. They have been placed in staggered rows with no overlapping between them in order to minimize the possibility for the electric field to jump from one metallization level to another, with the consequence of reducing the effective height between the patch and the ground plane, thus modifying the patch response. Moreover, the presence of dummies close to the vias leads to high losses, probably linked to the eddy currents induced due to the strong current flowing in the vias and therefore the strong magnetic field around the vias. Therefore, placing dummies in these areas should be avoided if possible. Also, the presence of dummies at the level of the slots leads to a slight modification of the resonant frequencies of the modes. This must therefore be considered when modifying the dimensions of the slots.

Expected Losses Study

Losses mechanism study based on EM simulation using ANSYS HFSS was carried out to recognize the occurrence and identify the dominant losses. For illustration, a dual-mode filter presented in section 3.1.1 is selected. 1) For 𝜎 𝑣 at its nominal value and floating dummies just near the via, 2 dB of losses is added, leading to overall insertion loss of 4.2 dB.

2) For 𝜎 𝑣 at its low value and no floating dummies, the filter records an addition of 3.2 dB of loss. Then when dummies are added the overall insertion loss increases and reaches 7.5 dB.

Therefore, to avoid any additional losses to the designed filter, floating dummies were inserted with no overlapping between them and placed away from the vias as much as the DRC allows. Also vias were thoroughly modeled to reveal actual fabricated via. After that, a post-layout simulation was carried out to verify the desired performance. Since the designed filter's response is fully controllable, acceptable performance was reached, as presented in the next subsections. shows a photo of the Anritsu VectorStar® measurement setup, with the ANRITSU probes and measurement heads above the wafer.

On-wafer measurements of the implemented filters were performed and each time with a first-tier on-wafer TRL calibration. For each stack and with each tape out run, different TRL calibration kits were used. Figure 4.5 shows the "Thru" for the two types of TRL calibrations that were used. M8U:M2M1 and AP:M6zM5x stacks, respectively. The overall size for both resonators is 0.13 mm 2 , particularly with a patch side length of 360 μm. Both patches are the reference designs for all the developed filters. Also, two different stacks were used in order to compare the extracted unloaded quality factor 𝑄 𝑢𝑠 for a single patch resonator, which to our best knowledge will be measured for the first time. 𝑄 𝑢𝑠 is calculated from (4.1) for loaded resonators with single response [START_REF] Hong | Microstrip Filters for RF/MicrowaveApplications[END_REF]:

𝑆 21 = 20 • log 1 + 1 𝐹𝐵𝑊 • 𝑄 𝑢𝑠 (4.1)
where 𝐹𝐵𝑊 is the fractional bandwidth.

The measurement results in comparison to the simulated ones are shown in well match with a return loss greater than 15 dB and FBW of 19%. A transmission zero was expected for asymmetrical feeding. If the transmission response for the filters operating around 200 GHz is observed, it is seen that the rejection is stronger for the asymmetric feeding, but the transmission zero does not appear in measurement. Probably this is related to the calibration that lacks to precision that does not allow measuring low in Figure 4.12(b). Here again, the agreement between simulation and measurement results is very good, because dummies could be fully considered this time in simulation because of less occupied area. The operating frequency is 175 GHz for the first band, same as F-7

for the single-band dual-mode filter, and 267 GHz for the second band. The measured insertion loss is equal to 4 dB, with FBW equal to 17%, for both bands.

Selective Grounded Patch Filter with Orthogonal Feeding

On-wafer chip layout for the dual-mode patch filter F-11 with orthogonal feeding structure operating at 120 GHz is shown in the advantage of increasing the BEOL for passive circuit, especially with the improvement of 𝑄 𝑢 .The overall size for all the filters is 0.07 mm 2 (side length 267 μm).

The on-wafer measurement results for F-11, F-12, F-13 and F-14 filters are shown in

Compact Filters at 60 GHz

Grounded Patch-Like Filter using CSRR On-wafer chip layout for patch-like filters using CSRR, for 1 st order filter F-15 and 2 nd order filter F-16, are shown in The recorded FBW is equal to 23 %. It meets well with the initial conditions set in the filter synthesis. Also, a very good lower out-of-band rejection is achieved, which is interesting given the spectral occupancy of plethora of applications. Generally it is more important to get strong low frequency selectivity for mm-wave filters. A mistake was made with the dimensions when layout was configured, leading to operating frequency of 50 GHz.

Ultra-Compact Patch Filter with Loaded "Mushroom"

On-wafer chip layout for ultra-compact patch filters with loaded "mushroom", for 1 st order filter F-17 and 2 nd order filter F-18, are shown in Figure 4.17 of plethora of applications. Also the upper out-of-band rejection is improved by the addition of FTZ with rejection level of 20 dB for the band above 85 GHz, up to 128 GHz.

Generally it is more important to get strong low frequency selectivity for mm-wave filters.

However, the results show that the upper out-of-band rejection can be improved by using cross-coupled filters.

State-Of-Art Comparison

In order to contextualize the results presented, a comparison with the state-of-art is necessary, as for any scientific work. However, this exercise is complicated in the case of the filters presented in this dissertation, for at least two reasons detailed below. First, very few articles deal with filters designed above 100 GHz. This comes from the fact that the applications are still few over this frequency, but also from a context where researchers working on the synthesis of filters are still relatively far from microelectronics technologies, and its many constraints. However, since applications begin to emerge beyond 100 GHz, with automotive radars but also the back-haul of the future 6G telecommunication standard, and as already mentioned in the introduction, it becomes necessary for our research community to be proactive in demonstrating that it is possible to create filters with acceptable performance that can be integrated into mm-wave frontends. The frequency band beyond 100 GHz is certainly little used today, and one might think that the filtering behavior of amplifiers is sufficient, but this will probably no longer be true when the operating frequency of many systems gradually increases.

Secondly, it always proves dangerous to compare the performance of passive circuits (and even active ones) realized using different technologies from microelectronics. As it was shown earlier, the quality factor of a patch or a transmission line depends enormously on the thickness of the BEOL of the technology, so the performance sometimes turns out to be much more linked to the specificities of the technology rather than to the quality and to the originality of the design.

Nevertheless, and despite the two critical mentioned points, the developed filters in this report are compared to the state-of-art that discussed in CHAPTER I as summarized in Table 4.2. Although the works in [START_REF] Sun | Design of Millimeter-Wave Bandpass Filters With Broad Bandwidth in Si-Based Technology[END_REF] and [START_REF] Sun | Design of On-Chip Millimeter-Wave Bandpass Filters Using Multilayer Patterned-Ground Element in 0.13-μm (Bi)-CMOS Technology[END_REF] are considered among the best published works in 20-30 GHz band, it is still very hard with the extensive use of meandered transmission line topologies to be reproduced to work at higher frequencies. This is especially true when considering technologies like BiCMOS, since the width of the strips increases with the BEOL height, hence limiting the meandering efficiency. So, the focus is on the filters that operate above 60 GHz.

The 𝑄 𝑢 obtained for the developed patch resonator filters are relatively comparable to the most of the one obtained for Transmission line-based "comparable" filters. For example, the filters presented in [START_REF] Franc | High-Performance Shielded Coplanar Waveguides for the Design of CMOS 60-GHz Bandpass Filters[END_REF], carried-out by our research group, have higher 𝑄 𝑢 , due to a realization based on slow-wave transmission lines (S-CPW). Their size is however larger, and they do not allow low frequency rejection, due to the use of a conventional DBR type topology. In addition, as explained in [START_REF] Franc | A Lossy Circuit Model Based on Physical Interpretation for Integrated Shielded Slow-Wave CMOS Coplanar Waveguide Structures[END_REF], the losses of S-CPW increase sharply with frequency beyond 100 GHz, due to the presence of eddy current losses. The advantage provided by S-CPW would therefore be much more mitigated at 120 GHz, and especially 200 GHz. The filter presented in [START_REF] Pokharel | 60GHz-band low loss on-chip band pass filter with patterned ground shields for millimeter wave CMOS SoC[END_REF] presents a very high 𝑄 𝑢 , equal to 26, with good insertion loss of 2.8 dB, in the other hand its size is higher by 100 times as compared to the work presented in F-18. Also, the filters in [5,15-b-38,40,42,43] present a 𝑄 𝑢 above 20, but their size is much higher than what is achieved with F-17 and F-18 for the same operating frequency of 60 GHz. Moreover, the work in F-18 has overall results comparable to those in [START_REF] Lu | Miniaturised 60 GHz rectangular ring bandpass filter in 90 nm CMOS technology[END_REF], but with nevertheless the achieved selectivity (𝑆𝐹 20𝑑𝐵 = 0.39 and 𝑆𝐹 30𝑑𝐵 = 0.27) that is much better, where [START_REF] Lu | Miniaturised 60 GHz rectangular ring bandpass filter in 90 nm CMOS technology[END_REF] is not selective below 15 dB.

For the proposed filters that operate at 120 GHz and above, it is much fair to compare them with the work published in [START_REF] Saadi | Design of Coupled Slow-Wave CPW Millimeter-Wave Bandpass Filter Beyond 100 GHz in 55-nm BiCMOS Technology[END_REF], made within our research group using the same 55-nm BiCMOS (8ML) technology. For more illustration, better than the trend-lines, which makes their contribution higher. Also, the performance of the patch filters are much better than of the transmission line filters in [START_REF] Saadi | Design of Coupled Slow-Wave CPW Millimeter-Wave Bandpass Filter Beyond 100 GHz in 55-nm BiCMOS Technology[END_REF]. For example, the insertion loss of F-11 (4.2 dB) is less than [START_REF] Saadi | Design of Coupled Slow-Wave CPW Millimeter-Wave Bandpass Filter Beyond 100 GHz in 55-nm BiCMOS Technology[END_REF]-a (7.1 dB), for the same FBW. Also, taking the same insertion loss of 4.8 dB like with F-1 and [52]-c, the achieved FBW is 18 % while the other is 28 %. Although the overall selectivity of [START_REF] Saadi | Design of Coupled Slow-Wave CPW Millimeter-Wave Bandpass Filter Beyond 100 GHz in 55-nm BiCMOS Technology[END_REF] is better, it is worth to mention that measured filter F-11 has sharp right selectivity of 0.7. It should be noted, however, that the filters presented in [START_REF] Saadi | Design of Coupled Slow-Wave CPW Millimeter-Wave Bandpass Filter Beyond 100 GHz in 55-nm BiCMOS Technology[END_REF] call for a more complex design based on the use of coupled lines, with the need to properly control parasitic couplings. This last aspect, namely the simplicity of design, argues in favor of patch filters, which are based on simple structures (apart from the problem of taking dummies into account, depending on each technology), and whose design could be described through simple steps usable by mmwave.

(a) (b) Nevertheless, the results achieved in F-12, F-13 and F-14, which are designed on 55-nm BiCMOS 9ML version, are the best among all the presented results. In comparison to the same filter topology used in F-11 and F-12 for the same FBW, but with different BiCMOS versions, 8ML and 9ML, respectively, the recorded insertion loss is 3.6 dB for F-11 and 4.2 dB for F-12. This has a direct impact on 𝑄 𝑢 , that records 22 for F-12 and 28

for F-11. The only reason behind this is due to the significant increase of the BEOL thickness with the 9ML version, which impressively improves 𝑄 𝑢 . So, the achieved unloaded quality factor is the highest among all the referenced filters, thus naturally leading to relatively low insertion loss for a similar FBW to several other articles in the literature.

Therefore, the performance of the integrated filters are not only related to the sophistication of the filter design, but also it is linked to the selected technology.

Conclusion

In this chapter, the main layout challenges for integrated passive filters on the 55-nm BiCMOS technology were described. It highlighted on the main and critical DRC rules like metal densities for unused metal layers below the patch resonator, which drastically influence the fields and leads to power dissipation. As a solution for that, dummy metals were well organized away from high magnetic field areas created by vias. In addition, an empirical analysis for the expected losses was conducted in order to avoid surprises in the measurements.

A full measurement results analysis was carefully carried out. The achieved results meet well with the filters' definitions and can be considered as a promising vision for what can be developed in the future. The comparison with the state-of-art shows that the usage of the 55-nm BiCMOS technology, especially with thicker BEOL as in 9ML version, has a great potential for the development of patch filters. For one of the filters, the recorded 𝑄 𝑢 is 28 which is the highest among all the previously published works.

CHAPTER V: FUTURE PERSPECTIVES-DIPLEXER

Diplexers are fundamental circuits within communication systems, as they allow fullduplex communications to be made possible in a simple way. When considering potential applications in the mm-wave bands, it is very complicated to make high-performance diplexers. SAW or BAW filters, which are available for sub-GHz bands are no longer available, and the realization of waveguide filters becomes critical due to mechanical tolerances. In addition, their connection to the planar parts of the circuits, produced in CMOS technologies, poses a problem.

In this context, we have made a first step toward a diplexer operating at 90 GHz using Both filters are well matched with return loss better that 15 dB. Also, the isolation is better than 35 dB at both 𝑓 1 and 𝑓 2 frequencies.

As a further step after the measurements, a combination of different filter responses based on the results achieved in Chapter VI, especially for F-11 filter, which exhibits better selectivity especially at the upper bands, could be studied. CHAPTER III is the core of this dissertation where different patch filters were thoroughly designed. Following the drawn design methodology, narrowband dual-mode and dual-band filters, operating at 120 GHz and 270/280 GHz, were developed based on a doublet-coupling scheme. After extracting the coupling matrices, theoretical and simulation results were compared to validate the filter definition. In addition to that, cascaded compact 2 nd order patch filters operating at 60 GHz were developed. An original ultra-compact patch resonator using CSRR and loading "mushrooms" structures were designed for that purpose. The combination of these structures with grounded vias allows overall area miniaturization of 99 %. All the developed filters were sent into fabrication through different tape out runs.

The layout circuit design along with measurments results analysis compared with the state-of-art were described in CHAPTER IV. It was a challenge to implement the intended filters on BiCMOS due to some technology constraints. Some design rules asked to remove metals from patch area, which impacted the surface current and others asked to add dummy metals in the unused layers below the patch, which impacted the electric field. Based on the expected losses analysis that were made, one of the recommended solutions was to avoid dummies near to the grounded vias where high magnetic field exists. After the fabricated filters were received, on-wafer measurements were performed. The measurement results came with great agreement with the simulated results. Dual-mode filters operating at 120 GHz achieved an insertion loss of 3.3 dB and 18 % of FBW. In addition to that, great results for dual-band filter at 176/270 GHz with 4 dB of losses and 17 % of FBW were achieved. The comparison with the literature shows that filters implemented on B55-9ML version with AP:M6z stack record the best performance among all the published works with measured 𝑄 𝑢 of 28. This makes the 55-nm BiCMOS 9ML version a promising technology for mm-wave passive circuits design.

Last but not least, diplexer with lower channel at 85 GHz and upper channel at 95 GHz was designed and sent into fabrication based on mushroom loading conventional dualmode filters. The potentiality of this structure makes it possible to design more sophisticated mm-wave diplexers in the future where the demand is notable.

Figure 0 9 Figure 1 . 4 :Figure 3 49 Figure 3 . 3 : 51 Figure 3 . 5 : 52 Figure 3 . 6 : 53 Figure 3 . 7 : 54 Figure 3 . 8 : 61 Figure 3 . 13 : 61 Figure 3 . 14 : 62 Figure 3 . 15 : 63 Figure 3 . 16 : 63 Figure 3 . 17 : 64 Figure 3 . 18 : 68 Figure 3 . 22 : 69 Figure 3 . 23 : 71 Figure 3 . 25 : 72 Figure 3 . 26 : 73 Figure 3 . 28 : 76 ixFigure 3 . 77 Figure 3 . 32 : 78 Figure 3 . 33 : 79 Figure 3 . 35 : 82 Figure 3 . 38 : 83 Figure 3 . 39 :Figure 4 . 7 :Figure 4 . 8 :Figure 5 . 3 :

 091434933513552365337543861313613146231563316633176431868322693237132572326733287637733278333793358233883339474853 Figure 0.1: 6G will unify the experience across physical, digital and human worlds [1]. .............................. 1 Figure 1.1: Microstrip ring resonator disturbed by a notch of width 𝒘 and depth 𝒕 of the structure proposed in [54]……………... ………………………………………………………………………………………………………………………………..8 Figure 1.2: Sketch of a dual mode, four pole, microstrip filter proposed in [55]. .......................................... 8 Figure 1.3: (a) Dual-mode microstrip square loop resonator proposed in [56], (b) Dual-mode microstrip meander loop resonator proposed in [57]. ............................................................................................. 9 Figure 1.4: Geometrical view of a planar dual-mode bandpass filter etched with a pair of asymmetrical crossed slots with built-in control element of mode coupling or perturbation element ∆L proposed in [58]. ....................................................................................................................................................... 9 Figure 1.5: (a) Fabricated tunable filter, (b) Layout [60]. ............................................................................ 10 Figure 1.6: (a) Triple mode wideband filter [73], (b) Cross-coupled 4 th order filter [74]. ............................ 10 Figure 1.7: (a) Triple-mode filter [61], (b) 4 th order 3D filter [62]. .............................................................. 11 Figure 1.8: (a) minimum 𝑺𝟐𝟏 (dB) versus 3-dB 𝑭𝑩𝑾, (b) size (mm 2 ) versus fc, (c) 𝑸𝒖 versus 3-dB 𝑭𝑩𝑾, (d) shape factor versus 3-dB 𝑭𝑩𝑾. ..................................................................................................... 15 Figure 1.9: BiCMOS 55-nm Technology Back-End-Of-Line. (a) 8 Metal Layers, (b) 9 Metal Layers. ...... 18 Figure 1.10: Unloaded quality factor 𝑸𝒖 and size of different patch resonators at 100 GHz and 200 GHz. 19 Figure 1.11: (a) 𝑸𝒖 versus 𝒔𝒖𝒃𝒉 at 𝒇𝒄 = 200 GHz, (b) 𝑸𝒖 at 𝒇𝒄 = 60 GHz, 120 GHz and 200 GHz for selected stacks. ..................................................................................................................................... 19 Figure 2.1: Conventional Patch Resonator……………………………….. ………………………….………..23 Figure 2.2: Electric-Field and Surface-Current distribution of: (a) 𝑻𝑴𝟎𝟏, (b) 𝑻𝑴𝟏𝟎 and (c) 𝑻𝑴𝟏𝟏 modes of rectangular patch resonator. ............................................................................................................. 25 Figure 2.3: Transmission response 𝑺𝟐𝟏 of conventional patch resonator's modes. ..................................... 26 Figure 2.4: Electric model: (a) Conventional patch resonator (𝑻𝑴𝟏𝟎), (b) Grounded patch resonator. ...... 27 Figure 2.5: Transmission coefficient variation of the via electric model. .................................................... 27 Figure 2.6: 𝒇𝑳𝑪 -𝒎𝒐𝒅𝒆 variation with the position of the via along the patch area. ................................ 28 Figure 2.7: Grounded patch resonator with: (a) 𝒗𝒊𝒂𝒎𝒊𝒅𝒅𝒍𝒆, (b) 𝒗𝒊𝒂𝒕𝒐𝒑, and 𝒗𝒊𝒂𝒄𝒐𝒓𝒏𝒆𝒓. ..................... 29 Figure 2.8: E field and J current for: (a) 𝒗𝒊𝒂𝒎𝒊𝒅𝒅𝒍𝒆, (b) 𝒗𝒊𝒂𝒕𝒐𝒑, and 𝒗𝒊𝒂𝒄𝒐𝒓𝒏𝒆𝒓. ................................ 29 Figure 2.9: Square patch resonator with a single feeding port 𝑷𝟏. .............................................................. 30 Figure 2.10: Return loss 𝑺𝟏𝟏 (dB) of square patch resonator with single port 𝑷𝟏 variation. ...................... 31 Figure 2.11: Patch resonators with: (a) collinear configuration and (b) orthogonal configuration. .............. 32 Figure 2.12: E field and surface current distribution with orthogonal port configuration of: (a) 𝑻𝑴𝟎𝟏 and (b) 𝑻𝑴𝟏𝟎. ................................................................................................................................................. 32 Figure 2.13: Phase variation of: (a) 𝑻𝑴𝟏𝟎 and (b) 𝑻𝑴𝟏𝟏. ......................................................................... 33 Figure 2.14: First 4 resonance frequencies of grounded patch with configurations: (a) 𝒗𝒊𝒂𝒕𝒐𝒑 and (b) 𝒗𝒊𝒂𝒄𝒐𝒓𝒏𝒆𝒓. ........................................................................................................................................ 34 Figure 2.15: Grounded patch E fields with via top: (a) 𝑳𝑪 -𝒎𝒐𝒅𝒆, (b) 𝑻𝑴𝟎𝟏, (c) 𝑻𝑴𝟏𝟎 and (d) 𝑻𝑴𝟏𝟏; Grounded patch E fields with via corner: (a) 𝑳𝑪 -𝒎𝒐𝒅𝒆, (b) 𝑻𝑴𝟎𝟏, (c) 𝑻𝑴𝟏𝟎 and (d) 𝑻𝑴𝟏𝟏. .... 35 Figure 2.16: (a) Patch resonator with Edge cut, (b) insertion loss 𝑺𝟐𝟏 variation with 𝑪𝒖𝒕𝒅. ..................... 36 Figure 2.17: Patch resonator with cross slots: (a) symmetrical with collinear feeding, (b) asymmetrical with orthogonal feeding. .............................................................................................................................. 37 Figure 2.18: Patch resonator with symmetric cross slots: (a) Surface current 𝑱 of 𝑻𝑴𝟏𝟎 mode, (b) insertion loss 𝑺𝟐𝟏 variation vs 𝑳𝒔. ..................................................................................................................... 37 Figure 2.19: Patch resonator with asymmetric cross slots: (a) Surface current J of Odd mode, (b) insertion loss 𝑺𝟐𝟏 variation with ∆𝑳. ................................................................................................................. 38 Figure 2.20: Routing and coupling scheme of 𝒏 coupled resonators with source/load-multiresonator coupling. Solid line: direct coupling, dashed lines: bypass or indirect coupling. ................................................ 40 Figure 2.21: Integrated filter design flow chart. ........................................................................................... 44

  the beginning of my thesis work, our mindset has been tuned to welcome a new era of telecommunication, which obeys capabilities to transfer us into the "Metaverse". It is the upcoming promising virtual universe integration that unifies our current experiences across the physical, digital and human world as the diagram in Figure 0.1 shows [1]. Hopefully, it offers more efficient, productive and energy less life. It is not a science fiction, it is what researchers and scientists are promising us after a decade when launching the sixth generation mobile radio (6G).

Figure 0 . 1 :

 01 Figure 0.1: 6G will unify the experience across physical, digital and human worlds [1].It will require development of advanced mobile communication technologies such as cognitive and highly secure data networks with massive sensors. The expected applications will be more relied on Artificial Intelligence (AI) and machine learning such as Augmented /Virtual Reality (AR/VR) with holographic videos, sensory interfaces that feel like real life…etc. Its technological standards are not clear yet, but it will rely on the current fifth generation mobile radio (5G) architecture with new expected frequency allocations at: low bands 460-694 MHz, mid-bands 7-20 GHz for urban outdoor cells enabling higher capacity and sub-THz band for short ranges with peak data rate promising to be up to 1 Terra Byte per second (TB/s).In the meantime, the deployment of 5G radio network or what marketers like to alias, the internet of things (IoT), has just launched. Ericson in its mobility report released in June 2022, mentioned that till now there are 1 billion 5G subscribers and expected to reach

  3(a)) and the other using the meandered loop resonator (Figure 1.3(b)). Both designs achieve the dual-mode characteristics, by splitting the degenerated modes through adding an edge triangular or square perturbation element (capacitive loading). Bandpass filters with two poles and single resonator were presented. Hong and Lancaster mentioned that the behavior of the degenerated modes in the loop resonator are approximately the same as for the full rectangular patch resonator. Later in 1999, Zhu et al. introduced a new technique to split the modes of a rectangular patch resonator [58]. The idea is based on adding diagonal cross etch slots inside the patch. Using asymmetric diagonal etch structure with ∆𝑙 difference as shown in Figure 1.4, the degenerated modes can be split easily to form the dual-mode filter.

Figure 1 . 1 :

 11 Figure 1.1: Microstrip ring resonator disturbed by a notch of width 𝑤 and depth 𝑡 of the structure proposed in [54].

Figure 1 . 2 :

 12 Figure 1.2: Sketch of a dual mode, four pole, microstrip filter proposed in [55].

Figure 1 . 3 :

 13 Figure 1.3: (a) Dual-mode microstrip square loop resonator proposed in [56], (b) Dual-mode microstrip meander loop resonator proposed in [57].

Figure 1 . 4 :

 14 Figure 1.4: Geometrical view of a planar dual-mode bandpass filter etched with a pair of asymmetrical crossed slots with built-in control element of mode coupling or perturbation element ∆L proposed in [58].

Figure 1 . 5 :Figure 1 . 6 :

 1516 Figure 1.5: (a) Fabricated tunable filter, (b) Layout [60].

Figure 1 . 7 :

 17 Figure 1.7: (a) Triple-mode filter [61], (b) 4 th order 3D filter [62].

and

  SF are plot against the 3-dB 𝐹𝐵𝑊, while filter size are extracted against the operating frequency, as shown in Figure 1.8(a), Figure 1.8(c), Figure 1.8(d), Figure 1.8(e) and Figure 1.8(f), respectively. Also, the acquired chip size is plot in Figure 1.8(b). Filters are categorized according to their operating frequency (𝑓 𝑐 < 55 GHz, 55 GHz < 𝑓 𝑐 < 65 GHz and 𝑓 𝑐 > 65 GHz) for fair and better comparison.

Figure 1 . 8 :

 18 Figure 1.8: (a) minimum 𝑆 21 (dB) versus 3-dB 𝐹𝐵𝑊, (b) size (mm 2 ) versus fc, (c) 𝑄 𝑢 versus 3-dB 𝐹𝐵𝑊, (d) shape factor versus 3-dB 𝐹𝐵𝑊.

Figure 1 . 9 :

 19 Figure 1.9: BiCMOS 55-nm Technology Back-End-Of-Line. (a) 8 Metal Layers, (b) 9 Metal Layers.

1. 10 (Figure 1 . 10 :Figure 1 . 11 :

 10110111 Figure 1.10: Unloaded quality factor 𝑄 𝑢 and size of different patch resonators at 100 GHz and 200 GHz.

Figure 1 .

 1 Figure 1.11(a), where M9v:M6z shows higher potential with BEOL height than other because in reality 𝑠𝑢𝑏 ℎ of 11 μm corresponding to AP:M6z, cannot be constructed with the available M9v and M6z layers. Moreover, results in Figure 1.11(b) show that there is a big improvement in performance when using 9ML version with patch resonators (and also TLines). For example, in comparison to AP:M6z for both versions, a difference of 11 in 𝑄 𝑢 is occurred. It is a significant improvement for passive resonators. This will be thoroughly analyzed and compared later when presenting the proposed filters. Next, for more illustration on the potentiality of B55 technology with different BEOL, two 50-Ω mirostrip lines (TL-Metal and TL-AP) were implemented at M8U (from 8ML) and AP (from 9ML) layers with GND at M1 and M6z, respectively. The width 𝑊 𝑇𝐿-𝑀𝑒𝑡𝑎𝑙 and 𝑊 𝑇𝐿-𝐴𝑃 are 7.7 μm and 19 μm for M8U:M1 and AP:M6z stacks, respectively. The achieved results were extracted at 200 GHz, and are shown in Figure 1.11(b). The 𝑄 𝑢

Figure 2 . 1 :

 21 Figure 2.1: Conventional Patch Resonator.both-zero integers 𝑇𝑀 𝑚𝑛 𝑧 mode indices corresponds to x and y axis directions, 𝜔 is the frequency, 𝑘 𝑐 is the wave number, c is the light speed in vacuum, µ 𝑟 is the relative magnetic permeability (µ 𝑟 = 1), 𝜀 𝑒𝑓𝑓 is the effective permittivity and 𝐿 𝑒𝑓𝑓 is the effective length of the patch with:

Figure 2 . 2 :

 22 Figure 2.2: Electric-Field and Surface-Current distribution of: (a) 𝑇𝑀 01 , (b) 𝑇𝑀 10 and (c) 𝑇𝑀 11 modes of rectangular patch resonator.

Figure 2

 2 Figure 2.2 (a). Its 𝐽 flows vertically along the AA' axis with maximum in the middle. It isobvious that when 𝐸 field is maximum, we found 𝐽 as minimum, since for lossless passive circuits, the electrical and magnetic fields are 90° out of phase. In this case, perturbations can be either inserted in the middle of the patch for 𝐽 disturbance, or at the edges for 𝐸 field disturbance, as well. The same behavior is recorded for 𝑇𝑀 10 , but with orthogonal fields distribution defined along BB' axis. This orthogonality between 𝑇𝑀 10 and 𝑇𝑀 01 is due to the symmetry of the square patch resonator. As mentioned before, 𝑇𝑀 11 is defined at the 4 corners of the patch resonator, with 𝐽 flowing at the edges and towards the corners (topleft and bottom-right).

Figure 2 . 3 :

 23 Figure 2.3: Transmission response 𝑆 21 of conventional patch resonator's modes.

Figure 2 . 4 :

 24 Figure 2.4: Electric model: (a) Conventional patch resonator (𝑇𝑀 10 ), (b) Grounded patch resonator.

Figure 2 . 5 :

 25 Figure 2.5: Transmission coefficient variation of the via electric model. and Figure 2.4 (b) shows the electrical model of the same patch but with grounded via in the middle. This model is true only if the via is placed in the middle of the patch along AA' axis, where 𝑇𝑀 10 has null 𝐸 field and is not perturbed. Using the Maxwell 3D tool from ANSYS HFSS, 𝐶 𝑝 and 𝐿 𝑝 were extracted and recorded 0.64 pF and 3.91 pH, respectively. Then the circuit model in Figure 2.4 (b) was simulated using Keysight ADS software to check the effect of tuning 𝐿 𝑣𝑖𝑎 . The transmission coefficient 𝑆 21 (dB) is plot in Figure 2.5 vs frequency from DC to 300 GHz. The resonance mode 𝑇𝑀 01 is fixed and unchanged at 𝑓 𝑐 = 200 GHz, while 𝑓 𝐿𝐶-𝑚𝑜𝑑𝑒 varies from 100 GHz to 50 GHz when 𝐿 𝑣𝑖𝑎 changes from 3 pH to 15 pH, respectively. It indicates that when 𝐿 𝑣𝑖𝑎 is increasing, 𝑓 𝐿𝐶-𝑚𝑜𝑑𝑒 is intuitively decreasing. Therefore, this behavior allows a big reduction of the overall size of the patch if the via is well designed and placed.

Figure 2 . 6 :Figure 2 . 7 :Figure 2 . 8 :

 262728 Figure 2.6: 𝑓 𝐿𝐶-𝑚𝑜𝑑𝑒 variation with the position of the via along the patch area.In order to have a more practical and general view on the effect of different positions of the via, Figure2.6 shows the variation of 𝑓 𝐿𝐶-𝑚𝑜𝑑𝑒 , which is extracted from the EM simulation of a single via inserted simultaneously across the whole area of the patch resonator presented in Figure2.1. It can be noticed that 𝑓 𝐿𝐶-𝑚𝑜𝑑𝑒 varies from 50 GHz to 100 GHz when the via's position is changed along the patch. The lowest resonance frequency is achieved when the via is placed at the corner of the patch while the highest resonance frequency is achieved when the via is placed at its middle. Moreover, 𝑓 𝐿𝐶-𝑚𝑜𝑑𝑒 doesn't change uniformly across the whole area. Its variation across the diagonal axis is different and higher from those along the AA' or BB' axis, accordingly. That means the inductance 𝐿 𝑣𝑖𝑎 is higher when the via is moved along the diagonal axis. Hence, to highlight physicaly about this idea, 3 positions of 𝑣𝑖𝑎 𝑚𝑖𝑑𝑑𝑙𝑒 , 𝑣𝑖𝑎 𝑡𝑜𝑝 , 𝑣𝑖𝑎 𝑐𝑜𝑟𝑛𝑒𝑟 are selected and their configuration with patch resonator is shown in Figure 2.7(a), (b) and (c), respectively. Also, their 𝐸 field and surface current 𝐽 are shown in Figure 2.8(a), (b), and (c) respectively.Generally, a grounded via has a uniform or even 𝐸 field distribution across the patch resonator except at its position where the 𝐸 field is null. On the other hand, 𝐽 flows radially across the patch starting from the via position, where it is maximum because via is purely inductive and shorted, towards the corners where 𝐸 field is maximum. For the 𝑣𝑖𝑎 𝑚𝑖𝑑𝑑𝑙𝑒 ,

Figure 2 . 9 :Figure 2 . 10 :

 29210 Figure 2.9: Square patch resonator with a single feeding port 𝑃 1 .

Figure 2 . 11 :

 211 Figure 2.11: Patch resonators with: (a) collinear configuration and (b) orthogonal configuration.

Figure 2 . 13 :

 213 Figure 2.13: Phase variation of: (a) 𝑇𝑀 10 and (b) 𝑇𝑀 11 .

Figure 2 . 14 :

 214 Figure 2.14: First 4 resonance frequencies of grounded patch with configurations: (a) 𝑣𝑖𝑎 𝑡𝑜𝑝 and (b) 𝑣𝑖𝑎 𝑐𝑜𝑟𝑛𝑒𝑟 .

Figure 2 . 15 :

 215 Figure 2.15: Grounded patch E fields with via top: (a) 𝐿𝐶 -𝑚𝑜𝑑𝑒, (b) 𝑇𝑀 01 , (c) 𝑇𝑀 10 and (d) 𝑇𝑀 11 ; Grounded patch E fields with via corner: (a) 𝐿𝐶 -𝑚𝑜𝑑𝑒, (b) 𝑇𝑀 01 , (c) 𝑇𝑀 10 and (d) 𝑇𝑀 11 .distribution outside the via (Figure2.15 (a) and (e)). In regards to the higher modes, grounded vias affects their 𝐸 field distribution, which shifts upward their resonance frequencies. It is worth to mention that this deformation in the 𝐸 fields will have to be considered for the definition of the feeding ports position for given modes excitation.

  (a) and (b), respectively. Initially without any slot, the patch resonator in

Figure 2 .Figure 2 . 17 :Figure 2 . 18 :Figure 2 . 19 :

 2217218219 Figure2.17 (a) operates at 𝑓 𝑐 = 200 GHz (for 𝑇𝑀 10 and 𝑇𝑀 01 modes). It includes symmetrical cross slots at AA' and BB' diagonal axes with length 𝐿 𝑠 . In order to check the effect of 𝐿 𝑠 variation on the 𝑓 𝑐 of the patch, a single mode 𝑇𝑀 10 is excited through the collinear feeding configuration. Current flow for 𝑇𝑀 10 , as shown before, is maximum at the middle of the patch along x-axis. On the contrary, when slots are inserted, current flow is now maximum at the edges of the slots as seen in Figure2.18 (a), indicating a distortion

  Figure 2.19(a) shows the surface current 𝐽 flow of the odd-mode. Since its 𝐸 field is defined along BB', as shown before in Figure 2.12 (b), its current is obliged to rout around the extended slot from the source to the load. So the electrical length 𝜃 𝑜𝑑𝑑 > 𝜃 𝑒𝑣𝑒𝑛 due to ∆𝐿, then 𝑓 𝑜𝑑𝑑 is split and shifted downward while 𝑓 𝑒𝑣𝑒𝑛 stays unchanged at 200 GHz.Figure 2.19 (b) shows the variation of the insertion loss 𝑆 21 of the degenerated modes with different values of ∆𝐿.When ∆𝐿 = 0 μm, no transmission occurs, which means there is great isolation between the two modes. But when ∆𝐿 is increased, 𝑆 21 rapidly jumps to -4.5 dB and successively, the degenerated modes start to couple and split. For example, with ∆𝐿 = 100 μm, the 𝑓 𝑜𝑑𝑑 reaches 150 GHz while 𝑓 𝑒𝑣𝑒𝑛 is unchanged at 200 GHz. This duality and controllability of the modes allows to design dual-mode patch filters with flexible responses.

Figure 2 . 20 :

 220 Figure 2.20: Routing and coupling scheme of 𝑛 coupled resonators with source/load-multiresonator coupling. Solid line: direct coupling, dashed lines: bypass or indirect coupling.

Figure 2 . 21 :

 221 Figure 2.21: Integrated filter design flow chart.

Figure 3 .

 3 1 (a) shows the configuration of modified patch resonator with two grounded metallic vias at its top/bottom sides along AA' axis. Two vias are used instead of one, in order to increase the

Figure 3 . 1 :Figure 3 . 2 :

 3132 Figure 3.1: (a) configuration of perturbed patch by via. (b) Electric field distribution of first four resonance modes. coupling between the fundamental modes, for upper band rejection improvement. The 𝐸 field distribution of the first four modes (𝐿𝐶 -𝑚𝑜𝑑𝑒, 𝑇𝑀 10 , 𝑇𝑀 01 and 𝑇𝑀 11 ), derived from the eigenmode solution solver in ANSYS HFSS, is shown in Figure 3.1 (b). As discussed before, 𝐿𝐶-mode has a uniform electric field along the surface area of the patch, except at both vias position, where the electric field is null. So, this mode is affected either by changing its 𝑣𝑖𝑎𝑑 or patch 𝐿 𝑝 . Since vias are implemented at the middle of the patch edges, 𝑇𝑀 10 and 𝑇𝑀 11 modes are unaffected, while 𝑇𝑀 01 could be greatly perturbed because its electric field is maximum at the top and bottom edges (in the absence of vias) as shown in Figure 3.1 (b). Next, a vertical slot perturbation element is etched in the middle of the patch along AA' axis, to control 𝑇𝑀 10 and 𝑇𝑀 11 modes, as shown in Figure 3.2 (a). Mainly this slot is intended to control the 𝑇𝑀 10 mode, since its surface current J is maximum in the middle of the patch and flows orthogonally to the slot along BB' axis. The surface current J distribution of the first three eigenmodes: 𝑇𝑀 10 , 𝑇𝑀 01 and 𝑇𝑀 11 , is shown in Figure 3.2 (b). It is clear that 𝑇𝑀 01 mode is almost unchanged since the inserted

Figure 3 . 3 :

 33 Figure 3.3: Transmission response 𝑆 21 of patch resonator with and without perturbations.

Figure 3 .Figure 3 . 4 :

 334 Figure 3.4 shows the proposed configuration for the dual-mode square patch filter with its equivalent coupling scheme. The patch resonator is of length 𝐿 𝑝 and implemented on M8U:M1 stack from BiCMOS 55 nm technology of 8 ML version. The proposed design (Figure 3.4 (a)) combines both perturbations presented previously with two vias of size 𝑣𝑖𝑎𝑑 are inserted along the AA' axis and vertical slot of length 𝐿 𝑠 and width 𝑊 𝑠 inserted in the middle of the patch. The designed filter is desired to have a narrow band dual-mode response with operating frequency 𝑓 𝑐 = 200 GHz, supported by 𝐿𝐶-mode and 𝑇𝑀 10 modes.Its out-of-band rejection is controlled, through creating an indirect path from source to load supported by the higher order modes 𝑇𝑀 01 and 𝑇𝑀 11 . In order to efficiently control these modes, horizontal slots of length 𝐿 ℎ and width 𝑊 ℎ are inserted along the 𝐵𝐵' axis.Consequently, the feeding input/output (I/O) ports are configured collinearly at 180°. The chosen I/O arrangement excites both modes (𝐿𝐶-mode and 𝑇𝑀 01 ) simultaneously, because

Figure 3 . 6 :

 36 Figure 3.6: Resonance frequencies variation vs: (a) vertical slot length 𝐿 𝑠 (𝐿 𝑝 = 200 𝜇m,𝑣𝑖𝑎𝑑 = 4 𝜇m & 𝑊 𝑠 = 10 𝜇m). (b) horizontal slots length 𝐿 ℎ (𝐿 𝑝 = 200 𝜇m, 𝑣𝑖𝑎𝑑 = 4 μm, 𝐿 𝑠 = 190 𝜇m,𝑊 𝑠 = 10 𝜇m & 𝑊 ℎ = 10 𝜇m).The previous variations study shows that there is a wide range of modes controllability for designing the dual-mode filter, if all modes are excited simultaneously. For this purpose, I/O ports are deviated by 𝐷𝑡 from the center of symmetry to vary 𝑄 𝑒 . Using the method presented in CHAPTER II, 𝑄 𝑒 is extracted for 𝐿𝐶-mode and 𝑇𝑀 10 mode and plotted in Figure3.7 (a). When 𝐷 𝑡 = 0 μm, 𝑄 𝑒-𝐿𝐶 and 𝑄 𝑒-𝑇𝑀 10 are almost equal, with 𝑄 𝑒-𝐿𝐶 = 13 and 𝑄 𝑒-𝑇𝑀 10 = 13.78. In this case the proposed structure is symmetrical, so the dual-mode filter can be realized with two poles, but without FTZs. When the absolute value of 𝐷 𝑡 increases, both modes are quietly increased, with more rapid variation for 𝑄 𝑒-𝑇𝑀 10 , because they have almost uniform 𝐸 field distribution at the left and right edges.

Figure 3 .Figure 3 . 7 :

 337 Figure 3.7: Extracted 𝑄 𝑒 factors for 𝐿𝐶-mode and 𝑇𝑀 10 . (b) Transmission response 𝑆 21 variation with 𝐷𝑡.

Figure 3 . 8 :

 38 Figure 3.8: Theoretical filter response with (a) variable 𝑀 22 shifted by x and (b) variable 𝑀 11 shifted by y. patch resonator to the source and load, instead of using electric or magnetic walls technique. For 𝐿𝐶-mode, it is fine-tuned by 𝑣𝑖𝑎𝑑 size, while 𝑇𝑀 10 mode is fine-tuned by the length of the vertical slot 𝐿 𝑆 . Their values are extracted from the variations in Figure 3.5 and Figure 3.6 (a), and mapped to the elements of CM in (3.2). Moreover, for symmetrical filter no FTZ can be produced, then 𝐷 𝑡 is set to 0 μm. The EM simulation results with final patch elements dimensions, and theoretical results from the synthesized CM in (3.3) are shown in Figure 3.9 (a). The achieved responses show a great agreement between simulation for infinite 𝑄 and extracted CM.

3 )Figure 3 . 9 :

 339 Figure 3.9: Comparison between theoretical and simulated responses for: (a) symmetrical filter (𝐿 𝑝 = 200 mm, 𝐿 𝑠 = 188 𝜇𝑚, 𝑊 𝑠 = 10 𝜇𝑚, 𝐿 ℎ = 60 𝜇𝑚, 𝑊 ℎ = 8 𝜇𝑚, 𝐷 𝑡 = 0 𝜇𝑚), and (b) asymmetrical filter (𝐿 𝑝 = 200 mm, 𝐿 𝑠 = 188 𝜇𝑚, 𝑊 𝑠 = 14 𝜇𝑚, 𝐿 ℎ = 60 𝜇𝑚, 𝑊 ℎ = 8 𝜇𝑚, 𝐷 𝑡 = 96 𝜇𝑚).

Figure 3 . 10 :

 310 Figure 3.10: Asymmetrical dual-mode BPF simulated responses with finite Q for 20% and 10 % of FBW.10 % of FBW is possible by changing the self-resonance frequencies of 𝐿𝐶-mode and 𝑇𝑀 10 mode. However, after optimization (𝑣𝑖𝑎𝑑 = 6.3 μm and 𝑊 𝑠 = 22 μm), an insertion loss around 7 dB is occurred for the 10% FBW. In order to improve the performance and compensate the added losses, the B55-9ML version is chosen to check its potentiality with the same filter topology.The proposed patch resonator is implemented on M9v:M6z stack, where 𝑄 𝑢 is 50 for a single patch resonator, which is two times better as compared to M8U:M1 stack (𝑄 𝑢 = 22).At the very beginning the patch wasn't well matched, so we added shorted stubs of length 𝐿 𝑠𝑡𝑢𝑏 = 100 μm and width 𝑊 𝑠𝑡𝑢𝑏 = 10 μm at the input and output ports as shown in Figure3.11 (a). An optimization for the patch resonator elements is required to adjust the responses with 𝐿 𝑝 = 190 μm, 𝑣𝑖𝑎𝑑 = 6.3 μm and 𝐿 𝑠 = 24 μm. The achieved simulated results are plotted in Figure3.11 (b). The recorded 𝑆 21 is really impressive, with maximum insertion loss of 3 dB at center frequency of 200 GHz with great return loss better than 20 dB for narrow FBW of 10%. A big compensation of losses around 4 dB from M8U:M1 stack is achieved, due to the improvement of 𝑄 𝑢 provided by the B55-9ML using the M9v:M6z stack.

Figure 3 . 11 :

 311 Figure 3.11: Proposed BPF: (a) configuration at M9v:M6z stack, (b) simulated responses with finite Q.1) Two patch filters with single order serve as a reference and are denoted by F-Ref1 and F-Ref2. These filters are conventional patch resonators operating at 200 GHz, without any perturbation (via or slot). They have large dimensions of 0.36 μm*0.36 μm (0.13 mm 2 ), but allow an estimation of the quality factor for two combinations of metals: M8U: M1 (patch on M8U and ground on M1) for F-Ref1 and AP:M6z

  conventional patch filter with single response at 200 GHz, implemented on M9v:M6z stack and denoted by F-Ref3.

Figure 3 .Figure 3 . 12 :Figure 3 . 13 :

 3312313 Figure 3.13 shows the 𝐸 field and surface current J distribution of the first four resonance frequencies, 𝐿𝐶-mode, 𝑇𝑀 01 , 𝑇𝑀 10 and 𝑇𝑀 11 , respectively. This time, only 𝑇𝑀 10 is affected by vias, since they shorten part of its 𝐸 field to the ground, while 𝑇𝑀 01 and 𝑇𝑀 11

Figure 3 . 14 :Figure 3 . 15 :

 314315 Figure 3.14: Extracted external quality factors for 𝑇𝑀 01 mode and 𝐿𝐶-mode.

Figure 3 . 16 :

 316 Figure 3.16: Resonance frequencies variation using horizontal slot length 𝐿 ℎ (viad = 3.96 𝜇m). 𝐿 𝑝 ≈ 𝜆/4 = 200 μm. The first four resonance frequencies are: 𝑓 𝐿𝐶 = 165 GHz, 𝑓 𝑇𝑀 01 = 356 GHz, 𝑓 𝑇𝑀 10 = 431 GHz and 𝑓 𝑇𝑀 11 = 509 GHz, respectively. At this stage the interest is in controlling the frequencies of 𝐿𝐶-mode and 𝑇𝑀 01 mode only. 𝐿𝐶-mode is adjusted by varying 𝑣𝑖𝑎𝑑, which modifies the inductance of both vias, as shown in Figure 3.15. When 𝑣𝑖𝑎𝑑 varies from 1 µm to 14 µm, 𝑓 𝐿𝐶 increases linearly from 165 GHz to 233 GHz. Also, 𝑓 𝑇𝑀 10 increases from 431 GHz to 484 GHz. So, 𝑓 𝐿𝐶 and 𝑓 𝑇𝑀 10 are directly affected by via size, while 𝑓 𝑇𝑀 01 and 𝑓 𝑇𝑀 11 are unchanged.

5 )Figure 3 . 17 .Figure 3 . 17 :

 5317317 Figure 3.17. The achieved result shows great agreement between theoretical responses from extracted CM and simulated results, for infinite quality factor. A single FTZ appears at 265 GHz in the upper band rejection. The only specification imposed during the design

𝑇M 11 .

 11 According to the surface current 𝐽 distribution in Figure3.13, 𝑇𝑀 10 has a horizontal current flow along BB' axis, so vertical slot of length 𝐿 𝑣 and width W v is added to reduce its resonance frequency, as presented in Figure3.12 (b).The effect of varying the vertical slot on 𝐿𝐶-mode, 𝑇𝑀 01 , 𝑇𝑀 10 and 𝑇𝑀 11 modes is shown in Figure3.18. It is clear that 𝐿 𝑣 has no impact on 𝑓 𝐿𝐶 and 𝑓 𝑇𝑀01 . When 𝐿 𝑣 increases from 0 to 188 μm, 𝑓 𝑇𝑀10 steeply decreases from 445 GHz to 263 GHz. This "steep" behavior can be explained because, for each variation interval, vertical slot forms a closed loop with couple of horizontal slots. So, the current has to flow around the slots to reach the output. Next, 𝑓 𝑇𝑀11 is affected when 𝐿 𝑣 is greater than 100 μm. It decreases from 343 GHz to 292 GHz, since the slot reached the edges. Hence, it is clear that vertical slot mainly controls the upper band.

Figure 3 . 18 :

 318 Figure 3.18: Resonance frequencies variation using vertical slot length 𝐿 𝑣 (𝑣𝑖𝑎𝑑 = 3.96 𝜇m, 𝐿 ℎ = 177 𝜇m and 𝑊 𝑣 = 8 𝜇m).

Figure 3 . 7 )Figure 3 . 19 .

 37319 Figure 3.19. The achieved results show a great agreement between the simulation and extracted coupling matrix, for infinite 𝑄.

Figure 3 . 19 :

 319 Figure 3.19: Comparison between theoretical and simulated responses for dual-band dual-mode BPF (𝐿 𝑝 = 200 𝜇m, 𝐿 ℎ = 176 𝜇m, 𝑊 ℎ = 8 𝜇m, 𝐿 𝑣 = 170 𝜇m, 𝑊 𝑠 = 16 𝜇m,and 𝐷 𝑡 = 85 𝜇m).

Figure 3 . 20 :

 320 Figure 3.20: Dual-band dual-mode BPF simulated responses with finite 𝑄 for 15% of FBW. s-parameters. So, to improve the performance, the B55-9ML version is chosen to check its potentiality with the same filter topology. As in previous design, the patch wasn't well matched, hence we added shorted stubs of length 𝐿 𝑠𝑡𝑢𝑏 = 100 μm and width 𝑊 𝑠𝑡𝑢𝑏 = 10 μm at the input and output ports as shown in Figure 3.21 (a). An optimization for the patch resonator elements is required to adjust the responses with 𝐿 𝑝 = 190 μm, 𝑣𝑖𝑎𝑑 = 6.3 μm and 𝐿 𝑠 = 24 μm. The achieved results are plotted in Figure 3.21 (b). The recorded 𝑆 21 is -2.8 dB and -2.5 dB at 𝑓𝑐 1 = 185 GHz and 𝑓𝑐 2 = 280 GHz, respectively. A great return loss better than 20 dB and narrow FBW of 10%. The compensation of losses is due to the improvement in the 𝑄 𝑢 provided by the B55-9ML Usage of the M9v:M6z stack.

Figure 3 . 21 :

 321 Figure 3.21: Proposed dual-band BPF: (a) configuration at M9v:M6z stack, (b) simulated responses with finite 𝑄.

Figure 3 . 22 :Figure 3 . 23 :

 322323 Figure 3.22: Proposed grounded patch resonator with TOP/RIGHT vias: (a) without slot, (b) with diagonal slot.

Figure 3 . 24 :Figure 3 . 25 :

 324325 Figure 3.24: transmission response S21 for patch resonator with and without via perturbation. patch resonator is weakly coupled and simulated using ANSYS HFSS software. The extracted transmission response 𝑆 21 is plotted in Figure 3.24 where 𝑓 𝑇𝑀10 = 𝑓 𝑇𝑀01 = 120 GHz and 𝑓 𝑇𝑀11 = 165 GHz. When vias, of 𝑣𝑖𝑎𝑑 = 1 μm, are inserted, a new resonance mode 𝑓 𝐿𝐶 appears at 55 GHz as shown Figure 3.24. 𝑓 𝑇𝑀10 (𝑓 𝑇𝑀01 ) is slightly shifted upward to operate at 128 GHz and 𝑓 𝑇𝑀11 is fixed at 165 GHz. As in the previous filter design methodology, the patch resonator' size is reduced to have 𝐿 𝑝 = 𝜆/4 at the same operating frequency of 𝑓 𝑐 = 120 GHzthanks to the addition of vias. The first 3 resonances, 𝑓 𝐿𝐶 , 𝑓 𝑇𝑀10 (𝑓 𝑇𝑀01 ), and 𝑓 𝑇𝑀11 are shifted upward to re-operate at 106 GHz, 280 GHz and 380 GHz, respectively. For fine tuning and to illustrate more on the effect of vias size on the resonance frequencies, Figure 3.25 (a) shows the variation of the first 3 resonance frequencies versus 𝑣𝑖𝑎𝑑. As previously discussed, the increase of 𝑣𝑖𝑎𝑑 impressively affects and shifts upward 𝑓 𝐿𝐶 and 𝑓 𝑇𝑀10 (𝑓 𝑇𝑀01 ). For instance, when 𝑣𝑖𝑎𝑑 = 4 μm, 𝑓 𝐿𝐶 = 120 GHz and 𝑓 𝑇𝑀10 (𝑓 𝑇𝑀01 ) = 295 GHz. As 𝑣𝑖𝑎𝑑 increases and reaches 24 μm, 𝑓 𝐿𝐶 = 150 GHz and 𝑓 𝑇𝑀10 (𝑓 𝑇𝑀01 ) is shifted to 350 GHz. A slight increase of 𝑓 𝑇𝑀11 occurs, because when the size of vias increase, part of the E field of 𝑇𝑀 11 mode is shorted and so its resonance frequency is shifted upward. After fixing 𝑣𝑖𝑎𝑑 to 4 μm to have 𝑓 𝐿𝐶 = 120 GHz, a diagonal slot of size 𝐿 𝑑 is inserted to mainly perturb the odd-mode 𝑇𝑀 10 . In this case, the degenerated modes are coupled and split.Figure 3.25 (b) shows the variation of the first 4 resonance frequencies versus 𝐿 𝑑 . In

Figure 3 . 26 :Figure 3 . 27 :

 326327 Figure 3.26: Proposed dual-mode patch resonator configuration with TOP/RIGHT edge vias and crossed slots.

Figure 3 . 28 :

 328 Figure 3.28: Comparison between 8ML and 9ML stack versions for dual-mode filter at 120 GHz with finite 𝑄.

  resonator elements is required to adjust the responses: 𝐿 𝑝 = 267 μm, 𝐷 𝑡 = 85 μm, 𝑣𝑖𝑎𝑑 = 10.44 μm, 𝐿 𝑑 = 298 μm, 𝐿 𝑑1 = 70 μm, 𝐿 𝑑2 = 120 μm, 𝐿 𝑑3 = 55 μm and 𝐿 𝑑4 = 130 μm. The width 𝑊 𝑠 of all slots is fixed to 7 μm. The achieved results are plotted in Figure 3.28. The recorded 𝑆 21 is -1.65 dB within the pass band, with return loss better than 20 dB and FBW of 20%. An improvement of 1 dB between B55 8ML and 9ML versions is achieved.

Figure 3 .Figure 3 . 29 :

 3329 Figure 3.29 shows different structures of proposed grounded patch resonators with different CSRR iterations. The conventional patch resonator is of size 𝜆/2 and its

Figure 3 . 30 :Figure 3 . 31 :

 330331 Figure 3.30: Resonance frequencies of grounded patch resonators of: NoCSRR, 1 st iteration CSRR and 2 nd iteration CSRR

Figure 3 . 32 :

 332 Figure 3.32: 2nd order bandpass filter equivalent cascaded coupling scheme (SL: source/load, 1: 𝑓 01 , 2: 𝑓 02 , solid line: main coupling, dotted line: S-L coupling cascaded coupling scheme.

Figure 3 . 33 :

 333 Figure 3.33: Layout configuration of proposed 2 nd order filter.

Figure 3 . 34 :Figure 3 . 35 :

 334335 Figure 3.34: (a) Extracted external quality factor for CSRR resonator at 50 GHz, (b) Extracted equivalent resonator-to-resonator coupling 𝑀 12 .

9 )

 9 of the feeding ports to have 90 degrees between them is required. Then filter synthesis using optimization technique is done. After coupling matrix optimization, 𝑀 12 = 𝑀 21 = 0.18, 𝑄 𝑒1 = 5 and 𝑄 𝑒2 = 5.5 mapping to final dimensions of 𝐿 12 = 15 μm, 𝐿 𝑡1 = 200 μm and 𝐿 𝑡2 = 180 μm, respectively. The optimized normalized coupling matrix with infinite unloaded quality factor is represented in (3.9). The achieved simulated results after taking into consideration the conductivity of all metallic layers are plotted in Figure 3.35. The recorded insertion loss is equal to 4.8 dB at the center frequency of 60 GHz. The filter is well matched with return equal to 28 dB, and fractional bandwidth FBW = 23 %. These results fit well with the defined filter template.Based on this design analysis, a total of two filters were designed and implemented on B55-8ML version:1) 1 st and 2 nd order patch filters at 60 GHz with same patch resonator topology were developed on M8U:M2M1 stack and denoted by F-15 and F-16, respectively. F-15

Figure 3 . 36 :Figure 3 . 37 :

 336337 Figure 3.36: (a) modified patch with extended stub, (b) variation of 𝑆 21 with extended stub length 𝐿 𝑠 .

Figure 3 . 38 :

 338 Figure 3.38: Simulated responses of the modified patch resonator with extended stub at 60 GHz.

Figure 3 . 39 :Figure 3 . 40 :

 339340 Figure 3.39: Proposed ultra-compact patch resonator with extended stub and loaded mushroom.

Figure 3 . 41 :Figure 3 . 42 :

 341342 Figure 3.41: Configuration of 2 nd order ultra-compact patch bandpass filter at 60 GHz with extended stub and loaded "mushroom".

Figure 4 .

 4 1 (b). Those slots are inserted in parallel to the flow of current to minimize their impact. This issue doesn't exist with the filters shown in sections 3.1.1 and 3.1.2 where a lot of etched slots initially exist. The max allowed (a) (b)

Figure 4 . 1 :

 41 Figure 4.1: Layout: (a) filter design in section 4.1.3, (b) filter design in section 4.2.2.

Figure 4 . 2 :

 42 Figure 4.2: stacked ground unit cell.

Figure 3 . 3 :

 33 Figure 3.3: (a) Layout design for filter in section 4.1.2, (b) zoom in to highlight dummies placement. have double drawback, (i) they modify the electric field lines, with a capacitive effect under the patch and under the slots, and (ii) they generate losses by eddy current. For illustration, the layout of the dual-band filter designed in section 3.1.2 is given in Figure 3.3 (a). InFigure 3.3 (b), the dummies that were added in M3x to M7z layers are highlighted in a

  The last step in the IC design is the post layout simulation. In case of performance deficiency, re-optimization of the filter design has to be performed. Afterwards all filters are sent to fabrication. Usually fabrication process takes around 6 months before the measurements. During this dissertation, we had the chance to participate in 4 tape outs: BUKA 2020, BADU 2021, BEAR 2021 and BEQUIA 2022. All tape outs are received except for BEQUIA 2022, which will be available for measurments in March 2023.

  measurement was performed in two different laboratories: CIME-NANOTECH at Grenoble and IEMN at Lille. At CIME-NANOTECH, two different VNAs were used: Anritsu VectorStar® ME7838A4 VNA to cover the band from 70 kHz to 145 GHz, and R&S ZVA VNA to cover the G-band from 140 GHz to 200 GHz. While at Lille R&S ZVA24 VNA was used to cover the band from 220 GHz to 325 GHz.Figure 3.4

  Figure 4.5 (a) "classical" Thru is used with most of the filters with two ports GSG probes.

Figure 4 .

 4 5(b) "specialized" Thru is used with filters discussed in section 3.2.2 where a single GSGSG probe is used due to small gap between the two feeding ports in the design. GSG pads having a pitch equal to 50 µm were used for probes mounting.

Figure 3 . 4 :Figure 3 . 5 :

 3435 Figure 3.4: Anritsu VectorStar® ME7838A4 VNA measurement setup.

Figure 4 .Figure 4 . 6 :Figure 4 . 9 :

 44649 Figure 4.6: On-wafer chip reference single patch resonators at 200 GHz: (a) F-Ref1 stack M8U:M2M1, (b) F-Ref2 stack AP:M6zM5x.

Figure 4 . 10 :

 410 Figure 4.10: Dual-mode patch filters measurement results: (a) F-1, (b) F-2, (c) F-3, (d) F-4, (e) F-5.

Figure 4 . 11 :

 411 Figure 4.11: On-wafer chip patches on M8U:M2M1 stack: (a) F-7 single-band dual-mode at 175 GHz, (b) F-8 single-band dual-mode at 175 GHz.

Figure 4 . 12 :

 412 Figure 4.12: Dual-mode patch filters measurement results: (a) F-7 single-band, (b) F-8 dual-band.

Figure 4 . 13 .Figure 4 . 13 :

 413413 Figure 4.13: On-wafer chip dual-mode patch filter F-11 on B55-8ML AP:M6zM5x stack.

Figure 4 . 14 :

 414 Figure 4.14: Dual-mode patch filters measurement results: (a) F-11, (b) F-12, (c) F-13, (d) F-14.

Figure 4 . 14 .

 414 Figure 4.14. As a first remark, all the measurement and simulated results are with great agreement. A difference in insertion loss, around 1 dB in case of F-13 and F-14, is due to

Figure 4 .

 4 15 (a) andFigure 4.15 (b), respectively. Both filters operate at 60 GHz and were implemented on B55-8ML M8U:M2M1stack. F-15 has an overall size of 0.04 mm 2 (side length 200 μm) and F-16 has a size of 0.08 mm 2 . The achieved measurement results for F-15 and F-16 are shown in Figure 4.16. A very good agreement between measurement and simulation results is obtained. F-15 has a low insertion loss of 1 dB with big FBW of 88 %. It was realized to verify the concept and to extract the measured 𝑄 𝑢𝑠 of the proposed topology, which recorded 10 at 60 GHz. The insertion loss of F-16 is equal to 5 dB at the operating frequency, while the return loss is better than 11 dB. (a) (b)

Figure 4 . 15 :

 415 Figure 4.15: On-wafer chip patch-like filter with CSRR on M8U:M2M1 stack: (a) F-15 Single resonator (b) F-16 2 nd order filter.

Figure 4 . 16 :

 416 Figure 4.16: Patch-like with CSRR filters measurement results: (a) F-15, (b) F-16.

  (a) and Figure4.17 (b), respectively. Both filters operate at 60 GHz and were implemented on B55-8ML M8U:M2M1stack. F-15 has an overall size of 0.04 mm 2 (side length 200 μm) and F-16 is of size 0.08 mm 2 . Those filters are smaller than F-15 and F-16 by 50 %.The achieved measurement results for F-15 and F-16 are shown in Figure4.18. A very good agreement between measurement and simulation results is obtained. F-15 has a low insertion of 1 dB with big FBW of 88 %. It was realized to verify the concept and to extract the measured 𝑄 𝑢𝑠 of the proposed topology, which recorded 12 at 60 GHz. The insertion loss of F-16 is equal to 4 dB at the operating frequency, while the return loss is better than 18 dB. The recorded FBW is equal to 27 %. An improvement of 1 dB was achieved for the insertion loss with this filter topology compared with F-16, which is due to the slight adjustment of the 𝑄 𝑢 and to the slight increase of FBW. A very good lower out-of-band rejection is achieved, especially < 40 GHz. This is interesting given the spectral occupancy

Figure 4 . 17 :

 417 Figure 4.17: On-wafer chip ultra-compact filter with loaded "mushroom" on M8U:M2M1 stack: (a) F-17 Single resonator (b) F-18 2nd order filter.

Figure 4 . 18 :

 418 Figure 4.18: ultra-compact patch filters with loaded "mushroom" measurement results: (a) F-17, (b) F-18.

Figure 4 .

 4 19 (a) andFigure 4.19 (b) show the trend-line variation of insertion loss and 𝑄 𝑢 with respect of FBW. They include all the state-of-art in addition to the proposed filters. The majority of the filters are

Figure 4 . 19 :

 419 Figure 4.19: state-of-art comparison: (a) variation of insertion loss with FBW, (b) variation of 𝑄 𝑢 with FBW.

  55-nm BiCMOS technology with 9ML BEOL version. The difference between channels is set to be 10%. The lower channel Filter1 operates at 95 GHz and the upper channel Filter2 operates at 85 GHz. Both Filters are synthesized to have FBW of 10 % and return loss of 20 dB.Since patch filters show a high flexibility in responses, a conventional dual-mode patch filter with crossed-slots is selected for the study. Its response allows to have FTZs at the lower and upper out-of-band rejection, which will improve the isolation between the channels. The modified configuration for the dual-mode patch filter is shown in Figure5.1.The proposed filter is loaded by mushrooms at the four edges of the patch, where the E field for even-and odd-modes is maximum. The mushrooms play the role of loading capacitance. The diplexer was implemented on B55-9ML AP:M6zM5x stack with square mushroom plates of length 𝐿 𝑐 on M9v layer.

Figure 5 . 1 :

 51 Figure 5.1: Proposed conventional dual-mode patch filter with loading mushrooms.

Figure 5 . 2 :

 52 Figure 5.2: simulated 𝑆 21 variation with 𝐿 𝐶 .

Figure 5 . 3 :

 53 Figure 5.3: Layout configuration for the proposed diplexer at 90 GHz. The variation of the transmission coefficient response with the square mushroom plate 𝐿 𝐶 is shown in Figure 5.2. When 𝐿 𝐶 varies from 0 to 35 μm, the whole response is shifted from 𝑓 𝑐 = 95 GHz to 𝑓 𝑐 = 80 GHz. This allows to have same patch size of 0.2 mm 2 (side length 400 μm) for both channels, which reserves area on the wafer. The final layout of the designed diplexer is shown in Figure 5.3. T-junction of length λ/4 at 𝑓 1 and 𝑓 2 , respectively, was added to connect lower and upper channel branches. For better impedance matching, the input impedance 𝑍𝑖𝑛 𝑥 at the T-junction needs to satisfy the following conditions:

  where 𝑍𝑖𝑛 1 and 𝑍𝑖𝑛 2 are the input impedance of the diplexer at the junction looking into the lower and upper bands filters, respectively. These conditions are easily satisfied by connecting the junction to each filter with a microstrip line, which ensures an open circuit for the other channel. The overall size of the diplexer, with the T-junction, is 0.69 mm² without pads. It was sent to BEQUIA 2022 tape out. The EM simulation of the whole design is shown in Figure5.4. The insertion loss is around 4 dB with a FBW equal to 9%.

Figure 5 . 4 :

 54 Figure 5.4: EM simulation results for the proposed diplexer.

Table 1 .

 1 1: Patch resonator's perturbation techniques. .................................................................................. Table 1.2: State-of-Art for mm-wave filters on BiCMOS/CMOS technologies. ......................................... Table 1.3: Selected BEOL stacks. ................................................................................................................

Table 2 .

 2 1: Extracted 𝐸 field and resonant frequency equations of first 3 pair modes of patch cavity... …………………………………………………………………………………………………………………………………….24 Table3.1: Basic design guide of variable elements effect……… …………………………………………….66 Table4.1: Losses Study For Proposed Patch Filter in section 4.1.1. ………………………………91

Table 4 .

 4 2: Comparison of the Designed mm-wave BPF to works in the State-Of-Art...............................

	LIST OF ABBREVIATIONS
	6G -sixth generation mobile radio
	AI -Artificial Intelligence
	AR/VR -Augmented /Virtual Reality
	5G -fifth generation mobile radio
	IoT -internet of things
	eMBB -enhanced mobile broadband
	xii

FWA -fixed wireless access

ITU-R -International Telecommunication Union Radio Sector

OSI -Open Systems Interconnection

MIMO -Multiple Input, Multiple Output mm-wave -Millimeter-Wave MMIC -Microwave Monolithic Integrated Circuits CMOS -Complementary metal-oxide-semiconductor BiCMOS -Bipolar Complementary metal-oxide-semiconductor PAE -Power Added Efficiency SiGe -Silicon-Germanium BGA -Ball Grid Array PCB -Printed Circuit Board LTCC -Low Temperature Co-fired Ceramics SIW -Substrate Integrated Waveguide GaAs -Gallium Arsenide InP -Indium Phosphide

  The two versions of BiCMOS55 (8 Metal Layers (8ML) and (9ML EVO), are exploited in order to gain margin in comparison between different filter designs performance. The aim is to design the first narrow-band dual-mode bandpass patch filter targeting frequencies above 120 GHz with 10% of fractional bandwidth. The framework collaboration between TIMA Laboratory and STMicroelectronics allowed the availability of participating in different realization tape-out runs in order to design and implement several original 2 nd order and dual-band patch-like filters targeting frequencies at 50 GHz, 60 GHz, 90 GHz, 200 GHz and 270 GHz.

[START_REF] Yeh | A novel ultra-compact and low-insertion-loss 77.GHz CMOS on-chip bandpass filter with adjustable transmission zeros[END_REF]

GHz, using the BiCMOS 55-nm integrated circuit technology that is provided by STMicroelectronics.

Table 1 .1: Patch

 1 resonator's perturbation techniques.

	Perturbation	Types	Functionality
	Edge Cut	Inductive	Split fundamental modes
	Edge Extension	Capacitive	Split fundamental modes
	Shorted VIA	Capacitive Split fundamental modes & adds new 𝐿𝐶 mode
	Slots	Inductive	Split fundamental modes
	Mushroom	Capacitive	Loads resonance mode
	1.2. Integrated Filters' Literature Review
	Filter design at mm-wave bands requires high flexibility in precision, which is currently
	offered by most of integrated technologies as BiCMOS/CMOS, GaAs, and InPs. Passive
	filters that are implemented on GaAs or Integrated Passive Devices (IPD) technologies,

Table 1

 1

	.2 shows the results of mostly designed filters at mm-wave bands covering the
	frequencies from 12.5 GHz up to 120 GHz, which are implemented on either CMOS or
	BiCMOS technologies with different released versions. All filters are compared on the
	following criteria: operating frequency 𝑓 𝑐 (GHz), relative fractional bandwidth % FBW,
	insertion loss (dB), return loss (dB), technology, unloaded quality factor 𝑄 𝑢 , Shape Factor
	SF at 30 dB and 20 dB, and size. Usually, measured 𝑄 𝑢 is calculated using (1.1).
	4.343	1
	3

Table 1 .2: State

 1 -of-Art for mm-wave filters on BiCMOS/CMOS technologies.

	Ref	𝒇 𝒄 (GHz)	𝑭𝑩𝑾 (%)	IL (dB)	RL (dB)	Technology	𝑸 𝒖	𝑺𝑭 𝟑𝟎𝒅𝑩	𝑺𝑭 𝟐𝟎𝒅𝑩	Size (mm²)
	[5]-a	60		2.6	11	0.13 μBiCMOS	28	0.31	0.34	0.14
	[5]-b	60		4.1	11	0.13 μm CMOS	23	0.32	0.37	0.29
	[7]-a	12.5		1.5	16		26	0.13	0.14	0.03
	[7]-b	14		2.5	15	0.13 μm SiGe	23	0.20	0.24	0.07
	[7]-c	17		3.5	15		17	0.19	0.21	0.05
	[8]	31		3.6	15	0.13 μm BiCMOS	7	0.46	0.55	0.05
	[9]	21		5	15	0.13 μm CMOS	17	-	-	0.11
	[11]-a [11]-b	23 27		2.3 2.6	15 13	0.13 μm BiCMOS 0.35 μm CMOS	9 9	-0.61	0.55 0.63	0.15
	[12]-a	23		3.8	20		19	0.13	0.17	0.02
	[12]-b	31		3.2	15	0.13 μm SiGe	34	0.11	0.14	0.02
	[12]-c	31		2.7	23		26	0.16	0.20	0.04
	[15]-a [15]-b	24 60		3.6 2.8	15 10	0.18 μm CMOS	11 22	0.26 0.38	0.34 0.47	0.61
	[16]	25		2.5	20	0.13 μm CMOS	21	0.21	0.31	0.28
	[18]-a [18]-b	27 29		2.5 3.5	13 25	0.13 μm BiCMOS	22 18	--	0.09 0.29	0.03
	[20]	30		1.66	18	0.13 μm BiCMOS	25	-	0.12	0.01
	[21]	31		2.2	15	0.13 μm SiGe	13	-	0.37	0.02
	[22]	31		2.4	15	0.13 μm SiGe	27	-	0.13	0.02
	[23]-a [23]-b	31 35		3.9 3.1	12 20	0.13 μm SiGe	8 11	--	0.44 0.46	0.08
	[24]	33		2.6	15	0.13 μm SiGe	21	0.12	0.15	0.04
	[26]	34		1.5	11	45 nm CMOS	17	-	0.81	0.07
	[27]	35		1.7	18	0.13 μm CMOS	26	-	0.15	0.04
	[28]	35		4.5	12	0.18 μm CMOS	7	0.35	0.41	0.12
	[29]	35		1.6	18.3	0.13 μm CMOS	17	-	-	0.03
	[30]	40		1.7	19	0.13 μm BiCMOS	18	-	0.13	0.01
	[34]	57		3.5	10.2	0.18 μm CMOS	14	-	0.51	0.07
	[35]	60		2.5	25	0.18 μm CMOS	18	-	-	0.16
	[36]	60		2.77	20	0.18 μm CMOS	26	0.18	0.47	0.59
	[37]	60		3.13	11	0.18 μm CMOS	40	-	-	0.03
	[38]	60		5	38	0.25 μm CMOS	22	-	0.18	0.32
	[39]	60		4.7	9	90 nm CMOS	17	0.13	0.18	0.04
	[40]	60		4	20	0.18 μm BiCMOS	27	-	0.17	0.18
	[41]	64		4.9	10	0.18 μm CMOS	18	0.4	0.43	1.71
	[42]	60		3.3	30	0.18 μm CMOS	23	-	-	0.05
	[43]	60		5.9	10	0.13 μm CMOS	20	0.34	0.61	0.35
	[44]	60		4.2	12	90 nm CMOS	16	-	-	0.12
	[45]-a [45]-b	60 77		9.3 9.3	10 10	0.18 μm CMOS	18 18	0.23 0.26	0.40 0.48	0.14 0.11
	[46]	65		2.7	15	0.18 μm CMOS	12	0.02	0.38	0.17
	[47]	62		3.1	10	0.18 μm CMOS	16	-	-	0.13
	[48]	70		3.6	12	0.18 μm CMOS	18	0.44	0.55	0.44
	[49]	77		3.5	10	0.18 μm CMOS	26	0.35	0.42	0.39
	[50]	77		2.9	20	0.18 μm CMOS	21	0.34	0.42	0.02
	[51]	77		3.9	20	0.13 μm CMOS	18	-	0.44	0.08
	[52]-a	115		7.1	20		17	0.32	0.48	0.05
	[52]-b	115		5.2	25	55 nm BiCMOS	17	0.36	0.51	0.07
	[52]-c	125		4.9	10		16	0.41	0.58	0.07

Table 1 . 3 :

 13 Selected BEOL stacks. , thus increasing the losses. The results are plotted in Figure 1.11(b). It shows that 𝑄 𝑢 is linearly increasing with frequency, and that the best achieved results are for the AP:M6z stack from 9ML version with 𝑄 𝑢 values of 28, 35 and 44, respectively.

	M8U:M1	6 μm	7.7 μm
	AP:M6z (8ML)	7 μm	10.5 μm
	M9v:M6z	8 μm	12 μm
	AP:M6z (9ML)	11 μm	19 μm
	been very small

STACK

Approximate Height (𝒔𝒖𝒃 𝒉 ) 50-Ω TLine (𝑾 𝑻𝑳 )

Table 2 . 1 :

 21 Extracted 𝐸 field and resonant frequency equations of first 3 pair modes of patch cavity.

	𝒎 ; 𝒏		𝑬 Field				Resonant Frequency
	𝑚 = 0 ; 𝑛 = 1	𝐴 010 𝑐𝑜𝑠	𝜋 𝐿 𝑒𝑓	𝑦			𝑓 010 =	𝑐 2𝐿 𝑒𝑓 𝜀 𝑟𝑒𝑓𝑓
	𝑚 = 1 ; 𝑛 = 0	𝐴 100 𝑐𝑜𝑠	𝜋 𝐿 𝑒𝑓	𝑥			𝑓 100 =	𝑐 2𝐿 𝑒𝑓 𝜀 𝑟𝑒𝑓𝑓
	𝑚 = 1 ; 𝑛 = 1	𝐴 110 𝑐𝑜𝑠	𝜋 𝐿 𝑒𝑓	𝑥 𝑐𝑜𝑠	𝜋 𝐿 𝑒𝑓	𝑦	𝑓 110 = √2 ×	𝑐 2𝐿 𝑒𝑓 𝜀 𝑟𝑒𝑓𝑓
	𝑚 = 1 ; 𝑛 = 0	𝐴 200 𝑐𝑜𝑠	2𝜋 𝐿 𝑒𝑓	𝑥			𝑓 200 = 2 ×	𝑐 2𝐿 𝑒𝑓 𝜀 𝑟𝑒𝑓𝑓
	𝑚 = 3 ; 𝑛 = 0	𝐴 300 𝑐𝑜𝑠	3𝜋 𝐿 𝑒𝑓	𝑥			𝑓 300 = 3 ×	𝑐 2𝐿 𝑒𝑓 𝜀 𝑟𝑒𝑓𝑓

  𝑀 𝑛 𝑡ℎ 𝑂𝑟𝑑𝑒𝑟 = [ 𝑀 𝑠𝑠 𝑀𝑠1 𝑀 𝑠2 𝑀 𝑠3 ⋯ 𝑀 𝑠𝑛 𝑀 𝑠𝐿 𝑀 1𝑠 𝑀 11 𝑀 12 𝑀 13 ⋯ 𝑀 1𝑛 𝑀 1𝐿 𝑀 2𝑠 𝑀 21 𝑀 22 𝑀 23 ⋯ 𝑀 2𝑛 𝑀 2𝐿 𝑀 3𝑠 𝑀 31 𝑀 32 𝑀 33 ⋯ 𝑀 3𝑛 𝑀 3𝐿

  Thanks to the compactness capabilities of vias, the first four resonance frequencies are: 𝑓 𝐿𝐶 = 155 GHz, 𝑓 𝑇𝑀 10 = 356 GHz, 𝑓 𝑇𝑀 01 = 410 GHz and 𝑓 𝑇𝑀 11 = 503 GHz, respectively. The effect of varying 𝑣𝑖𝑎𝑑, 𝐿 𝑠 and 𝐿 ℎ on the resonance frequencies is checked sequentially. Figure3.5 shows the variation of the intended resonance frequencies versus 𝑣𝑖𝑎𝑑. When 𝑣𝑖𝑎𝑑 varies from 1 μm to 7 μm, 𝑓 𝐿𝐶 is increased from 155 GHz up to 200 GHz. By increasing 𝑣𝑖𝑎𝑑, the equivalent inductance of the via is decreased, thus explaining the increase of 𝑓 𝐿𝐶 . As for 𝑓 𝑇𝑀 10 and 𝑓 𝑇𝑀 11 , they are mostly constant, while 𝑓 𝑇𝑀 01 is shifted upwards from 410 to 446 GHz. So, as expected, 𝑣𝑖𝑎𝑑 is only affecting 𝑓 𝐿𝐶 and 𝑓 𝑇𝑀 01 .Then, fixing 𝑣𝑖𝑎𝑑 to 4 μm, 𝐿𝐶 and 𝑓 𝑇𝑀 10 are constant and not affected by the variation of 𝐿 ℎ , while both 𝑓 𝑇𝑀 01 and 𝑓 𝑇𝑀 11 are significantly decreased. When 𝐿 ℎ is increased from 0 to 60 μm, 𝑓 𝑇𝑀 01 and 𝑓 𝑇𝑀 11 are decreased from 441 GHz and 465 GHz to 390 GHz and 412 GHz, respectively. Here it is good to mention that since horizontal slots are initially inserted at the edges of the patch, 𝑓 𝑇𝑀 11 is directly affected and decreases by the same manner of 𝑓 𝑇𝑀 01 .

	x	A'
	y
	L	VIA
	D t	L p		MS1	1	MS1
	B	L s	B'	S	-MSL	L
			D t	MS2	2	-MS2
		Ws
		A

h Figure 3.5: Resonance frequencies variation vs via diameter 𝑣𝑖𝑎𝑑 (𝐿 𝑝 = 200 𝜇m).

in order to put 𝑓 𝐿𝐶 near 200 GHz, vertical slot is inserted with variable length 𝐿 𝑠 . Figure 3.6 (a) shows the variation of the intended resonance frequencies versus 𝐿 𝑠 , while slot width 𝑊 𝑠 is chosen in way to have enough slot gap to avoid electrical coupling. In this analysis it was fixed to 10 μm. 𝑓 𝐿𝐶 and 𝑓 𝑇𝑀 01 are almost unchanged, a slight shift occurs only when 𝐿 𝑠 reaches the edges of the patch, while 𝑓 𝑇𝑀 10 is drastically decreased from 356 GHz to 212 GHz when 𝐿 𝑠 varies from 0 to 190 μm. Also, 𝑓 𝑇𝑀 11 is constant when 𝐿 𝑠 < 120 μm, and decreases to 465 GHz when 𝐿 𝑠 reaches 190 μm. So the vertical slot is mainly controlling 𝑓 𝑇𝑀 10 , and when it reaches the edges, 𝑓 𝑇𝑀 11 is affected.

Figure 3.6 (b) shows the variation of the intended resonance frequencies when horizontal slots are inserted. The width of all horizontal slots was fixed to 𝑊 𝑠 = 10 μm. 𝑓

  𝑀 11 and 𝑀 22 vary separately by factors 𝑥 and 𝑦, respectively. The theoretical 𝑆 21 and 𝑆 11 responses with the variation of 𝑥 and 𝑦, are plot in Figure 3.8. It is clearly shown that, when 𝑥 or 𝑦 vary separately, 𝑀 11 and 𝑀 22 are modified independently.

	0	0.65	0.7	0
	𝑀 2 𝑛𝑑 𝑂𝑟𝑑𝑒𝑟 -𝑆𝑌𝑀𝑀 = [ 0.65 -0.92 0.7 0	0 0.93	-0.65 0.7	]	(3.1)
	0	-0.65 0.7	0
	Since the desired filter should have flexible responses due to the modes independency, the
	initial coupling matrix is modified to:
	0	0.65	0.7			0
	𝑀 2 𝑛𝑑 𝑂𝑟𝑑𝑒𝑟 -𝑆𝑌𝑀𝑀 = [ 0.65 -0.92 + 𝑦 0.7 0	0 0.93 + 𝑥	-0.65 0.7	]	(3.2)
	0	-0.65	0.7			0
	where coefficients

center frequency 𝑓 𝑐 = 200 GHz, fractional bandwidth (FBW) of 20%, and return loss 𝑆 11 of 20 dB. Its initial coupling matrix for infinite 𝑄 is:

  while fixing 𝑣𝑖𝑎𝑑 to 3.96 𝜇m. It is clear that 𝑓 𝑇𝑀 01 and 𝑓 𝑇𝑀 11 are drastically decreased by the insertion of the horizontal slots. 𝑓 𝑇𝑀 01 decreases from 356 GHz to 184 GHz while 𝑓 𝑇𝑀 11 decreases from 510 GHz to 354 GHz when 𝐿 ℎ increases from 0 to 180 µm. 𝑓 𝐿𝐶 is smoothly unchanged, until the slots are near to the edges (thus perturbing the current around the vias). So, when 𝐿 ℎ is greater than 160 µm, 𝑓 𝐿𝐶 barely decreases from 182 GHz to 165 GHz. 𝑓 𝑇𝑀 11 is unchanged because the horizontal slots are in parallel to its current distribution.The proposed single-band dual-mode square patch filter is synthesized to operate at center frequency of 180 GHz, with FBW of 15% and return loss of 20 dB. Its extracted asynchronous CM after optimization is summarized in(3.5).

		0	0.54 0.63 -0.002
	𝑀 𝑠𝑖𝑛𝑔𝑙𝑒 -𝑏𝑎𝑛𝑑 = [	0.54 0.63	-0.75 0	0 0.68	-0.54 0.63
	-0.002 -0.

Table 3 . 1 :

 31 Basic design guide of variable elements effect

	Design Element 𝐿𝐶-mode	𝑇𝑀 01 𝑇𝑀 10 𝑇𝑀 11
	Via	x	-	x	-
	Horizontal slot	x	x	-	x
	Vertical slot	-	-	x	x

Table 4

 4

.1 summarizes the expected losses for a Dummies

Table 4 . 1 :

 41 Losses Study For Proposed Patch Filter in section 4.1.1. the operating frequency. When perfect metal is used for the patch and vias with no insertion of dummies, the insertion loss is almost null (0.08 dB). This means the loss tangent of 𝑆 𝑖 𝑂 2 dielectric of the BEOL reveals to be negligible, as expected. For nominal patch and via conductivity 𝜎 𝑝 and 𝜎 𝑣 , respectively, and without any floating dummies added, the filter's insertion loss is equal to 2.2 dB. Fixing the patch conductivity to its nominal value, different cases for via conductivity (according to the technology PDK) and presence of floating dummies were studied as follows:

	Patch Conductivity Via Conductivity Floating Dummies IL @ oper. freq (dB)
	∞	∞	none	0.08
	Nominal	Nominal	none	2.2
	Nominal	Nominal	Near via	4.2
	Nominal	Low	none	5.4
	Nominal	Low	Near via	7.5
	different configurations at

  the conductivity of vias, which in reality is tolerated between different limits. The measured insertion loss for F-11 is 4.2 dB with FBW equal to 18 %. The insertion loss was improved with F-12, which recorded 3.3 dB for the same FBW of 18%. Same stack AP:M6zM5x

	was used but with different B55 versions (8ML and 9ML). The recorded insertion loss for
	F-13 is 3.6 dB with FBW of 18 %. Hence, F-12 is slightly better than F-13 because
	AP:M6zM5x is thicker than M9v:M6zM5x. The advantage of B55-9ML version appears
	with the measured results of F-14, which was implemented on M9v:M6zM5x. The
	recorded insertion loss is 4.3 dB, but for FBW of 15 %. This could not be possible with
	same FBW on B55-8ML version. All the filters are well matched with return loss better
	than 15 dB.

Table 4 . 2 :

 42 Comparison of the Designed mm-wave BPF to works in the State-Of-Art.

	Ref	𝒇 𝒄 (GHz)	𝑭𝑩𝑾 (%)	IL (dB)	RL (dB)	Technology	𝑸 𝒖	𝑺𝑭 𝟑𝟎𝒅𝑩	𝑺𝑭 𝟐𝟎𝒅𝑩	Size (mm²)
	[5]-1	60		2.6	11	0.13 μBiCMOS	28	0.31	0.34	0.14
	[5]-2	60		4.1	11	0.13 μm CMOS	23	0.32	0.37	0.29
	[11]-a [11]-b	23 27		2.3 2.6	15 13	0.13 μm BiCMOS 0.35 μm CMOS	9 9	-0.61	0.55 0.63	0.15
	[12]-a	23		3.8	20		19	0.13	0.17	0.02
	[12]-b	31		3.2	15	0.13 μm SiGe	34	0.11	0.14	0.02
	[12]-c	31		2.7	23		26	0.16	0.20	0.04
	[15]-b	60		2.8	10	0.18 μm CMOS	22	0.38	0.47	0.61
	[34]	57		3.5	10.2	0.18 μm CMOS	14	-	0.51	0.07
	[35]	60		2.5	25	0.18 μm CMOS	18	-	-	0.16
	[36]	60		2.8	20	0.18 μm CMOS	26	0.18	0.47	0.59
	[37]	60		3.13	11	0.18 μm CMOS	40	-	-	0.03
	[38]	60		5	38	0.25 μm CMOS	22	-	0.18	0.32
	[39]	60		4.7	9	90 nm CMOS	17	0.13	0.18	0.04
	[40]	60		4	20	0.18 μm BiCMOS	27	-	0.17	0.18
	[41]	64		4.9	10	0.18 μm CMOS	18	0.4	0.43	1.71
	[42]	60		3.3	30	0.18 μm CMOS	23	-	-	0.05
	[43]	60		5.9	10	0.13 μm CMOS	20	0.34	0.61	0.35
	[44]	60		4.2	12	90 nm CMOS	16	-	-	0.12
	[45]-a [45]-b	60 77		9.3 9.3	10 10	0.18 μm CMOS	18 18	0.23 0.26	0.40 0.48	0.14 0.11
	[46]	65		2.7	15	0.18 μm CMOS	12	0.02	0.38	0.17
	[47]	62		3.1	10	0.18 μm CMOS	16	-	-	0.13
	[48]	70		3.6	12	0.18 μm CMOS	18	0.44	0.55	0.44
	[49]	77		3.5	10	0.18 μm CMOS	26	0.35	0.42	0.39
	[50]	77		2.9	20	0.18 μm CMOS	21	0.34	0.42	0.02
	[51]	77		3.9	20	0.13 μm CMOS	18	-	0.44	0.08
	[52]-a [52]-b [52]-c	115 115 125		7.1 5.2 4.9	20 25 10	55 nm BiCMOS (8ML)	17 17 16	0.32 0.36 0.41	0.48 0.51 0.58	0.05 0.07 0.07
	F-1 F-2	115 116		4.8 5.1	20 >15		18 18	0.2 0.22	0.34 0.36	0.08
	F-3	196		3.9	18		19	0.18	0.33
	F-4	200		3.8	18	55 nm BiCMOS	24	0.21	0.34
	F-5	200		3	20	(8ML)	24.2	0.22	0.35	0.037
	F-8	180		4.1	18		25	0.19	0.33
	F-9	176/270		4	>14		25	-	0.4/-
	F-11	120		4.2	>15		22	0.21	0.4
	F-12 F-13 F-14	116 116 119		3.3 3.6 4.3	20 20 20	55 nm BiCMOS (9ML)	28 26 26	---	0.35 0.36 0.36	0.07
	F-16	60		5	>10	55 nm BiCMOS	14.4	-	0.27	0.08
	F-18	60		4	30	(8ML	15.5	0.27	0.39	0.04

For that purpose, it was re-sent to BEQIUA2022 tape out (not received yet) with tolerated amount of dummies. Also, reference single patch resonators operating at 120 GHz couldn't be sent into fabrication due to their big size.

On-wafer chip layout for dual-mode patch filters, F-1 (symmetrical feeding structure)

and F-2 (asymmetrical feeding structure), operating at 120 GHz and implemented on B55-8ML M8U:M2M1, are shown in Figure 4.9 (a) and Figure 4.9 (b), respectively. Also, dualmode patch filters, F-3 (symmetrical feeding structure) and F-4 (asymmetrical feeding As measurement capabilities were limited to 220 GHz, the transmission zero could not be observed. Finally, the measurement results of F-5 operating at 200 GHz and designed on AP:M6zM5x stack, are given in Figure 4.10 (e). Here again, the agreement between measurements and EM simulations is good. The measured insertion loss is about 3 dB, i.e.

the lowest of all the designed filters.

In terms of general conclusion, several remarks can be deduced from all these results.

Firstly, and as expected, the quality factor of the resonators increases with the frequency, thus the insertion loss, for the same bandwidth, decreases. Secondly, the AP:M6zM5x stack makes it possible to obtain slightly higher performance for conventional patches.

Moreover, the advantage of using an AP:M6zM5x stack can be the non-use of the lower layers, which can then be used for routing operations. Active components (diodes, transistors) could also be made under the patch using an AP:M6zM5x stack, because the ground plane completely isolates the patch from the lower layers, neither the magnetic field nor the electric field penetrating through the ground plane.

Dual-Band Grounded Patch Filter with Collinear Feeding

On-wafer chip layout for single-band dual-mode patch filter F-7 operating at 175 GHz Both filters are of overall size 0.037 mm 2 (side length 194 μm). A remark to mention, that filters F-9 and F10 (see Figure 3.21) were sent to BEQIUA2022 tape out, which is not received yet.

The measured and simulated results for F-7 are shown in Figure 4.12(a). The agreement between simulation and measurement results is very good, thanks to the fact that the simulation could be carried out considering the full presence of dummies, which are a lot with this filter. The operating frequency is 175 GHz. The measured insertion loss is equal to 4.1 dB, with FBW equal to 17%. The measured and simulated results for F-8 are shown

GENARAL CONCLUSION

As the mm-wave applications for 5G and future 6G have just emerged, RF filters like any other radio blocks have to be re-designed to operate at mm-wave bands. In this dissertation, a full research study was carried out on building integrated dual-mode bandpass patch filters implemented on the 55-nm BiCMOS technology with its two supported versions of BEOL, 8ML and 9ML. The selection of the technology was made on the interest of combining active and passive circuits on the same chip. The choice of working on the development of integrated mm-wave filters was done since beyond 60 GHz, parasitics from interconnections become significant and the need for using single chip for radio becomes high.

Based on the presented literature, patch filters topology haven't been used in integrated circuits or even at mm-wave bands. In most of the published works, TLines was the dominance due to their small size and good performance. Moreover, it was hard for most of mm-wave filters to have FBW below 20% with acceptable losses. In our study, the challenge with patch filters was first to proof its potentiality to work at very high frequencies and second to present compact versions for its resonator. The performance of conventional patch resonators analyzed in CHAPTER I, shows that 𝑄 𝑢 increases with frequency, which records at 200 GHz with 8ML version a value of 22. Also, it shows that 𝑄 𝑢 increases with the BEOL height, to record with M9v:M6z stack a value of 40. In comparison to TLines, patch filters performance is better. In order to have compact patch resonator, grounded vias were used to reduce the edge of the patch resonator from 𝜆/2 to 𝜆/8. The work of grounded vias is to introduce a new resonance mode that appears below the fundamental modes of the patch, allowing the reduction of overall size.

A full filter theory and synthesis discussion was conducted in CHAPTER II. We used the already published synthesis approaches for dual-mode filters but with some assumptions based on the used resonance modes. In the designed approaches, 𝐿𝐶-mode, which is created by via, is one of the main working modes. It can be considered as the new even-mode of a conventional patch, since it has a uniform E field distribution across the patch area. This is a very important feature to understand in order to define the couplings between the Source/Load with LC-mode and between the working modes itself, according

The Matlab code that is used to plot the theoretical scaterring parameters for the optimized coupling matrix is: clear %-------------------------------------------------------------% % To be completed with the filter specifications: n=; % n is the order of the filter fc=; % Central frequency fc in Hz BW=; % Absolute Bandwidth in Hz %

n+2); % To be complete with the necessary couplings of the coupling scheme % where 1 is related to the source; % 2 to N-1 are related to the modes; % N+2 is related to the load. M(1,2)=; M(1,3)=; M(2,2)=; M(2,3)=; M(3,3)=; % For a symmetrical matrix M: for b=1:n+2 for a=1:n+2 M(a,b)=M(b,a); end end disp(M) %--------------------------------------------------------------------------------------------------% %-----------------------------------------------------------% % To be completed with the graphic definition: points=; % Definition of the curves fi=; % Initial frequency of the graphic ffinal=; % Final frequency of the graphic f=fi:(ffinal-fi)/(points-1):ffinal;

%-----------------------------------------------------------% %----------------------------------------------------------% % S-parameters calculus for a=1:points f1=fc*(f(a)/fc-fc/f(a))/BW; A=M-1j*R+f1*W;