Karan Gumber
email: karan.gumber@u-bordeaux.fr

Simon Hemour
email: simon.hemour@u-bordeaux.fr

C Dejous

Keywords: Backscatter radio, harmonic reflection amplifier, RFID, self-interference, tunnel diode. Harmonic Reflection Amplifier for Widespread Backscatter Internet-of-Things, Member, IEEE, Corinne Dejous, Member, IEEE

published or not. The documents may come

Harmonic Reflection Amplifier for Widespread Backscatter Internet-of-Things

Karan Gumber, Corinne Dejous, Simon

I. INTRODUCTION

ITH the emergence of the fifth generation (5G) technologies, the year 2020 came across 30 billion connected devices, or 5.1 connected devices per person on average [START_REF]Red Pixie -The World of Data infographic Black and Blue[END_REF], which anticipates a proliferation of Internet-of-Things (IoT) platforms that could range from small portable electronics devices such as smartphones and sensors to large electric vehicles. Backscatter communication is a promising technology towards true ubiquitous IoT, as it simplifies the many "thing" complexity [START_REF] Gu | Reconfigurable nonlinear circuit for wireless power harvesting and backscattering[END_REF]. In this asymmetric communication scheme, RF signal is generated on one side only (the reader), whereas the tag backscatters the modulated signal to the reader with identification and other preferred information [START_REF] Ramos | Semi-Passive Time-Domain UWB RFID System[END_REF].

Most readers work in monostatic configuration where a transmitter (Tx) and receiver (Rx) share the same antenna. The low Tx to Rx isolation resulting from contiguous intra-band operation leads to self-interference (SI) or self-jamming signal leakage. Unfortunately, the anti-jamming interference circuits and/or high dynamic radio front end that have to be used to circumvent SI are expensive [START_REF] Boaventura | Perfect isolation: Dealing with self-jamming in passive RFID systems[END_REF]. Self-jamming mitigation can either use interference from directional coupler [START_REF] Kim | A passive circulator with high isolation using a directional coupler for RFID[END_REF] or quasicirculator [START_REF] Kuo | Near-field power transfer and backscattering communication to miniature RFID tag in 65 nm CMOS technology[END_REF]. Substantial methods have been employed, including LNA post-distortion [START_REF] Safarian | RF identification (RFID) reader front ends with active blocker rejection[END_REF], feed-forward cancellation [START_REF] Jung | A novel carrier leakage suppression front-end for UHF RFID reader[END_REF], and impedance tuning [START_REF] Jung | A reconfigurable carrier leakage canceler for UHF RFID reader front-ends[END_REF].

In [START_REF] Lee | Compact antenna module with optimized TX-to-RX isolation for monostatic RFID[END_REF], the mitigation of SI in monostatic configuration is done by using a directional coupler with impedance mismatch reflector incorporated into the antenna. Similarly, the antijamming signal in [START_REF] Forouzandeh | Self-interference cancelation in frequency-domain chipless RFID readers[END_REF] has been achieved with the combination of power divider, combiner and vector multiplier. However, the performance of this method is entirely dependent on the dynamic range of vector multiplier. To cancel the leakage signal in [START_REF] Forouzandeh | Application of wideband differential phase shifters with wide phase range in chipless RFID readers[END_REF], a compensation signal was generated using an ultra-wideband poly-phase power divider, which is added vectorially before the receiver front end. Signal conditioning has been used in [START_REF] Sajid | Canceling self-jammer and interfering signals in an RFID system[END_REF], in which a sample of Tx signal is combined with an Rx signal with opposite phase to counter the SI. The adaptive SI cancellation algorithm was discussed in [START_REF] Rimini | Method and apparatus for adaptive non-linear self-jamming interference cancellation[END_REF] that automatically alters the self-jamming signal depending upon the changes in the tag environment.

All these methods provide rejection of the Tx leakage, but at the cost of increased reader Rx complexity. These solutions are also bulky in physical size and simultaneously limit the sensitivity of the system.

An alternative technique to reduce self-jamming is separating the Tx/Rx frequencies, similar to the frequencydivision duplex system. The Tx leakage that influences the Rx frequency is filtered at Tx output, conversely, the leakage outside the Rx frequency is filtered at Rx input. Therefore, in the recent years, alternative solutions have been exploiting passive transponders/tags [START_REF] Ma | Accurate indoor ranging by broadband harmonic generation in passive NLTL backscatter tags[END_REF], [START_REF] Ma | Harmonic-wisp: A passive broadband harmonic RFID platform[END_REF] to generate harmonics for enabling communication that greatly reduces direct reflections and self-interference. The idea has even been proposed for active [START_REF] Amato | The harmonic tunneling tag: a dual band approach to backscattering communication[END_REF] circuit. However, dual-band operation is not new and have been explored for the RFID transponder [START_REF] Gu | Analysis and exploitation of diplexer-based fully passive harmonic transponder for 5G applications[END_REF]- [START_REF] Gu | Novel diplexer-based harmonic transponder for 5G-compatible IoT applications[END_REF], but the generation of harmonics comes at a cost of conversion loss that significantly impact the link budget, and thus the communication distance. Table I and Fig. 1 compare the proposed outcome with the previously reported reflection amplifier in terms of power consumption, gain and power added efficiency (η) (PAE) etc. [START_REF] Khaledian | Two-way backscatter communication tag using a reflection amplifier[END_REF]- [START_REF] Chung | A novel bi-directional amplifier with applications in active Van Atta retrodirective arrays[END_REF], while Table II compares the performance of the proposed harmonic backscatterer with previously reported harmonic tags [START_REF] Gu | Diplexer-Based Fully Passive Harmonic Transponder for Sub-6-GHz 5GCompatible IoT Applications[END_REF], [START_REF] Ma | Accurate indoor ranging by broadband harmonic generation in passive NLTL backscatter tags[END_REF]- [START_REF] Lazaro | A passive harmonic tag for humidity sensing[END_REF].

A harmonic tunneling tag concept is illustrated in Fig. 2, where the tunnel diode is employed as a nonlinear element. The signal illuminates the tag at the fundamental frequency (f0), and the non-linear element in the tag generates and re-radiate the signal back to the reader, both at the fundamental frequency (f0) and at the second harmonic (2f0).

The present study is an expanded version of [START_REF] Gumber | Nonlinear negative resistance-based harmonic backscatter[END_REF], which proposed a topology based on a non-linear, negative resistance based tag that can completely overshadow the SI and also provide a conversion gain of around 18 dB at 2f0 with power consumption of 144 µW, measured at an excitation signal of -50 dBm. In addition, the HRA allows simultaneous use of both the frequency bands to enable legacy compatibility with nonharmonic readers. It also increases the throughput in a crowded frequency spectrum and thus it has emerged as a potential solution in a cluttered environment for long-range RFID tags. The originality of the work lies in stability analysis of the proposed HRA. The concept of stability in negative resistance devices is explained theoretically and supported by simulation as well as measurement results. The capacity of the HRA to perform binary phase-shift keying (BPSK) is also elaborated in the expanded version. In addition, the effect of the incident Fig. 2. The harmonic tunneling RFID dual-band communication system that is able to communicate at fundamental and harmonic frequency.

power on the reflection gain, conversion gain and input impedance of the HRA are experimentally demonstrated. The impedance characterization of the AI301A bare tunnel diode in the simulations and measurements has been carried out.

The paper is organized in five sections: Section II provides the details on the characterization of bare tunnel diode, while Section III and IV demonstrate the measurement results based on static and dynamic-bias modulation, respectively. Finally, based on analysis and preceding results, conclusions are made in Section V.

II. CHARACTERIZATION OF A BARE TUNNEL DIODE

The first step before fabricating any prototype based on tunnel diode is to determine the dc current-voltage (IV) characteristic of the bare tunnel diode. The dc IV characteristics of the three tunnel diodes (AI301A, 3I101D and 3I306E) are shown in Fig. 3, they were measured over a bias voltage (Vb) ranging from 0 mV to 300 mV. The differential resistance and current responsivity [START_REF] Hemour | Towards low power high efficiency RF and microwave energy harvesting[END_REF] of AI301A are also shown in Fig. 3. Table III shows a comparison of these three diodes based on spice parameters, each with its biasing voltage and the corresponding negative.

As depicted from the IV curve, the tunnel diode AI301A shows a negative differential resistance (NDR) region from 110 mV to 300 mV, where the output current starts reducing with the increase in Vb. When biased in the NDR region, the tunnel diode can operate as an amplifier. For a given dc bias (meaning dc power loss), a positive differential resistance would dissipate RF power (RI 2 ), while a negative differential resistance would increase RF power (-RI 2 ) and this property makes it different from other diodes.

For these measurements, the E3648A high precision biasing supply from Keysight is used to bias the diode, which was controlled using the Command Expert, Standard Commands for Programmable Instruments. For high precision extraction of voltage and current consumption of AI301A tunnel diode, 34410 and 34401 digital multi-meters (DMM) are employed. The number of power line cycles (PLC) of 34410 DMM is set at 10 and 34401 DMM is set at 6 digits slow, which corresponds to 100 PLC integration time and 6.5-digit resolution. The biasing voltage across the diode is varied from 1mV to 300mV at a step of 1mV, and the delay between two consecutive steps is set to 3 sec. The 7 th order polynomial fitting was extrapolated [START_REF] Chp Lorenz | Breaking the efficiency barrier for ambient microwave power harvesting with heterojunction backward tunnel diodes[END_REF]: 𝐼(𝑣) = -5.83𝑣 7 + 14.12𝑣 6 -12.87𝑣 5 + 5.10𝑣 4

𝐼(𝑣) = ∑ 𝑎 𝑖 𝑣 𝑖 , 𝑖=𝑁 𝑖=0 𝑁 𝜖 ℕ. (1
- 0.53𝑣 3 -0.18𝑣 2 + 0.04𝑣 -1.47 • 10 -5 (2)
Over the negative Rtd region (Fig. 3) the device exhibits a peak-valley voltage (ΔV) and current (ΔI) difference of around 190 mV and 1.62 mA, respectively, which sets the maximum RF "output" power of the diode to about -12 dBm, as calculated from [START_REF] A-Khalidi | Resonant tunneling diode terahertz sources with up to 1mW output power in the J-band[END_REF]:

max 3 16 P V I    (3)
Frequency multiplication can be obtained when the NDR varies nonlinearly with the voltage. The optimum doubler efficiency can be obtained, when the diode is biased at the edge of the NDR region, as the IV characteristic is almost symmetrical at the bias point [START_REF] Hwu | Negative differential resistance frequency conversion with gain[END_REF] and the current responsivity is high. Alternately, biasing the device at the NDR midrange, anti-symmetrical around the bias point, with a constant value of Rtd and lower responsivity absolute value, would lead to highest tripling efficiency. In this work, aiming a doubler amplifier, the bias point was chosen as 144 mV, |-Rtd|= 147 Ω. Operating on the peak current, Vb = 110 mV, |-Rtd| >1500 Ω, offers no advantage as suggested in [START_REF] Barner | An ideal harmonic generator[END_REF].

Z antenna Z circuit-parasitics -R Matching Circuit Z diode Z circuit Z input -R V bias

Cparasitics Rparasitics Lparasitics

Lbias-tee Cbias-tee Fig. 4. A fundamental block diagram and fabricated prototype of a harmonic reflection amplifier.

III. HARMONIC TUNNELING TAG STATIC MEASUREMENT

The measurement campaign aimed to experimentally validate the capacity of harmonic tunneling tag in terms of achievable reflection gain at the fundamental frequency and conversion gain at the second harmonic. The basis of any measurement relies on its simulation framework, which is elaborated first.

A. Simulation framework

The simulation work of the proposed design is carried out in the Advance Design System (ADS) by building the Symbolically Defined Device (SDD) model of tunnel diode from its IV characteristics. The transient simulations are performed to make sure that the HRA does not start to oscillate at any biasing voltage. The matching network was built to obtain the desired output signal at the frequency of interest. The matching network includes a dual-band LC resonator indicated in Fig. 2. The matching network performs two functions (a) make sure that the negative impedance of the diode is successfully transformed into antenna impedance (b) ensure the selectivity of desired dual-frequency band. The negative resistance seen towards the diode is -147 Ω, and the input impedance of the HRA is approx. -49 Ω, when the incident power is -60dBm. This impedance transformation is carried by the matching circuit to ensure stability as well as to transfer maximum power.

The simulated S-parameters of the full circuit (excluding diode) are shown in Fig. 5. The circuit has been optimized to exhibit negative resistance at only 450 MHz and 900 MHz frequencies. Simulation is then compared to S1P (one-port S parameter) measurements of the physical tunnel diode at the optimum bias point.

The performance of the overall HRA is characterized by reflection gain, which is given as:

2 diode circuit in diode circuit ZZ ZZ    ( 4
)
where Zcircuit is the load impedance connected to the reflection amplifier. Note that the Zcircuit should also consider the antenna impedance at the input port; Zdiode is the input impedance of the tunnel diode (Fig. 4). The reflection gain of HRA must exceed unity as the input resistance of tunnel diode is negative [START_REF] Zhao | Negative resistance based electronic impedance tuner[END_REF]. If Zdiode approaches -Zcircuit, then │Гin│ 2 tends to infinity. Oscillations can start if the magnitude of negative impedance of the diode exceeds the magnitude of the positive load impedance of the circuit [START_REF] Hoffins | Conditions of oscillation for waveguide mounted tunnel diodes[END_REF], [START_REF] Kidner | Power and stability limitations of resonant tunneling diodes[END_REF]:

    Re Re circuit diode ZZ  (5)
where Re[Zdiode] < 0. To avoid such uncontrolled oscillations, the load impedance magnitude of the circuit designed must be always greater than the negative impedance magnitude of diode, which is given by:

    Re Re 0 circuit diode ZZ  (6)
where In order to achieve high gain at the frequency of interest, the impedance of matching network is tuned very close to the negative input impedance of tunnel diode, while respecting the non-oscillation conditions.

B. Experimental setup

For prototyping and testing, the AI301A soviet tunnel diode is used which is cheap, rugged and easily available. It is also important to mention that more efficient tunnel diodes can operate at a lower biasing point. The experimental prototype of the proposed circuit can be seen in Fig. 4(b). It was fabricated using Rogers RO3010 substrate with thickness 1.28mm, dissipation factor 0.0022 and relative permittivity 10.2. The fabricated hardware was composed of AI301A tunnel diode, variable capacitances from Vishay, and inductors from Coilcraft.

The various components of the HRA are tuned and optimized using harmonic balance and transient simulation in ADS to ensure maximum reflection and conversion gain at fundamental and 2 nd harmonic frequency, while at the same time disabling the oscillatory conditions. The working operation of HRA is summarized in Fig. 7.

The type of operation performed by the HRA depends on the input signal. With a single frequency band at f0, which can either be centered at 414.6 MHz or 829.2 MHz, the amplifier performs a dual-band operation, by boosting the signal at fundamental frequency f0, and at the second harmonic frequency. For such characterization, a one-port network analysis with frequency offset is performed (Fig. 8). Since one-port conversion gain is usually not available on vector network analyzer, it has to be computed from the raw fn a wave (measurements @ fn with source at fn), and the 2. fn b wave (measurements @ 2fn with source at fn). Note that special care should be given in the calibration and error coefficient handling, as forward error term should be taken into account at fn, while reverse wave error term should be considered at 2fn. Conversion gain for higher harmonics follow the same methodology. Practically, these measurements are done with Keysight E5080 vector network analyzer (VNA), for incident power ranging from Pin, min = -90 dBm to Pin, max = -20 dBm.

Input

C. Tuning the negative differential resistance and the conversion gain

The negative resistance of tunnel diode is exploited with respect to biasing voltage. The change in the biasing voltage tunes the negative differential resistance of tunnel diode, which in turn produces the reflection and conversion gain. The gains as a function of biasing voltage is shown in Fig. 9. As depicted from Fig. 9, one can easily achieve the desired gain just by tuning the biasing voltage. This experiment is conducted to show the reproducibility of the measurement results across different tunnel diodes (same part number). If any other diode with the same part number is employed it can produce similar results, but may be with change in bias point.

D. Frequency behavior and stability conditions

The optimum behavior of the proposed HRA is found for a bias voltage of Vb=144 mV. Under this dc condition, the measured input impedance of the bare AI301A tunnel diode is:

27 44 @ 0=414.6 MHz 8 4 @ 2 0=829.2 MHz diode jf Z jf            
To assess the overall stability of the circuit, the input impedance has to be measured as seen from the antenna to verify that there is no frequency for which it goes to the instability region. The stability test is conducted in Fig. 10, where the real impedance of the HRA is plotted against incident power. As shown in Fig. 10, when the incident power approaches near -50dBm, the HRA impedance reduces from -50 Ω towards the instability region. It can also be confirmed from the Fig. 11 that shows the measured real part of the HRA impedance for an incident power of -50 dBm before final tuning. It is observed two sharp resonances with values below -50 Ω at f0, approximately -48 Ω at 2f0. Under such condition free-running oscillation would occur at f0, while an incident signal at the vicinity of f0 would trigger an injection locked oscillation [START_REF] Saavedra | Self-oscillating mixers: a natural fit for active antennas[END_REF]- [START_REF] Toker | Self-oscillating tunnel diode mixer having conversion gain[END_REF].

E. Antenna impedance impact on the operation

The antenna impedance mostly varies in practical case towards higher real impedance value because equivalent series resistance increases with the added loss of the surrounding antenna. Therefore, there is no risk for instability if the surrounding happened to impact the antenna impedance. Fig 12 shows the impact of antenna impedance on the stability of the proposed HRA. It can be observed from the contour plot, that the HRA always remains stable if the antenna impedance is higher than 50 Ω. If the antenna impedance is close to 50 Ω, it yields the maximum reflection gain (as high as 30dB)

F. Influence of the incident power on stability

As the HRA is designed to operate at a negative impedance very close to the antenna impedance, it is also necessary to verify the stability versus incident signal RF power level. It can be explained by considering Fig. 10 and Fig. 13, where Fig. 10 represents the variation of real and imaginary parts of the HRA input impedance at both frequencies as a function of the incident power level. This can be observed in Fig. 13, which depicts the reflection gain (S11) and conversion gain of the HRA as a function of the incident power. From very low incident power (-90 dBm) to -50dBm, the equivalent (linear) resistance seen by the input signal is very close to -50Ω, related to a high and constant value of S11. Note that in the case of unstable behavior, the S11 would keep rising as the incident power increases.

Furthermore, it can be observed in Fig. 13 that near -50 dBm, the reflection gains at f0 and 2f0 are maximum, as well as the conversion gains at both frequencies. It happens because

Magnitude (dB)

Input Power (dBm) S11@f0 @414.6MHz S11@2f0 @ 829.2MHz CG @ 829.2MHz>414.6MHz CG @1658.4MHz>829.2MHz

Fig. 13. Measured input reflection coefficient (S11) at fundamental frequency f0 (green), and at 2f0 (brown), and 2 nd harmonic conversion gains with respect to f0 (blue) and 2f0 (orange) as a function of incident RF power.

│Re[Zdiode]│comes very close to Re [Zcircuit], that provides high reflective gain │Гin│ as indicated in (4). Beyond -50 dBm incident power level, the real part of the impedance at f0 and 2f0 increases from -50 Ω and mismatch takes place, (shown in Fig. 10 and Fig. 11). The higher the mismatch of real impedance, the lower the reflection and conversion gains. Both reflection and conversion gains originate from different physical mechanisms of the tunnel diode. The conversion gain results from the fast varying input impedance, which is linked to the second order I(V) curve variation, i.e. the dc current responsivity represented in Fig. 3. Thus, the nonlinearity of tunnel diode generates the inter-modulation product and higher harmonics, which is power dependent, since more incident RF power will lead to greater impedance variation, hence more conversion. The negative input impedance of the circuit (linked to the differential resistance of the tunnel diode) is responsible for amplification of every existing signal, i.e. for the incident wave (reflection gain) as well as the generated harmonics (conversion gain).

Of course, as the frequency increases, the signal is more subject to parasitic losses which lead to lower conversion gain, as it is the case for 829.2 MHz to 1658.4 MHz conversion gain. The measurements reported in Fig. 13 are used to investigate the P1-dB and P3-dB compression points. The measured P1-dB incident power Pin-1 dB of -43 dBm at f0 and 2f0 corresponds to a maximum linear Pout of -13 dBm and -23 dBm respectively.

The one port analysis of the HRA consistent with 'a', 'b' waves at the frequency band f0 = 414.6 MHz and exploiting the frequency offset mode with a multiplicative factor of 2 is shown in Fig. 14. The 'a' and 'b' wave centered at f0 = 414.6 MHz are measured in Channel I corresponding to Fig. 8, whereas 'b' wave centered at 2f0 = 829.2 MHz is measured in the Channel II by exploiting frequency offset mode. The data extracted from these three waves help to find the reflection and conversion gains as depicted in Fig. 15. Both 'a' and 'b' shows a very linear behavior from very low incident power (-90 dBm) to -50dBm, that imply constant reflection gain (S11) in this region. The conversion efficiency is given as the ratio of b@2f0/ a@f0. As it is shown in Fig. 14 when 'b' wave at 2f0 starts increasing from 'a' wave at f0, it is marked as the region of positive conversion gain for second harmonic that lies at 829.2 MHz. This region starts originating when the incident power impinging on the HRA comes close to -65 dBm, and it continues up to -22 dBm incident power. Similarly, this positive region of conversion gain for the 829.2 MHz fundamental frequency that corresponds to the second harmonic at 1658.4 MHz is shown in Fig. 13. This region is very small, it is only restricted to the incident power ranging from -47 dBm to -43 dBm, where the conversion gain at the second harmonic that lies at 1658.4 MHz goes above 0 dB. Indeed, when the incident power is large enough, (here from -50 dBm), the tunnel diode ceases to operate in "small signal", the input signal starts flowing over the positive resistance part of the curve and does not benefit further from the ideal (nonlinear & negative) response. This in turn modifies both the gain and input impedance of the HRA that pushes HRA into saturation and leads to a decrease of the gains.

It was observed that the HRA exhibits a reflection gain over the dual frequency band. The measured reflection and conversion gains for three incident powers are shown in Fig. 15. It is observed a peak reflection gain of 25 dB or even greater over both the frequency bands (f0 and 2f0) at incident power of -50 dBm. At the same incident power, it provides a controllable conversion gain at the second harmonic of approximately 18 dB and -16.5 dB at 829.2 MHz and 1658.4 MHz, respectively.

G. Selection of device

The selection of device is of concern for the fabrication of amplifier, where stability is of paramount importance. Three different diodes are shortlisted for the purpose of fabricating an amplifier, which has very similar IV characteristics as depicted in Fig. 3. After fabricating the three prototypes with three different diodes, we found the 3I101D provides excellent reflection as well as conversion gain. While, conducting the stability test, it is unstable starting from very low power to -40dBm, which can be observed from Fig. 16. The other diode 3I306E passed the stability test as shown in Fig. 16, but was unable to provide good reflection and conversion gain. Therefore, the AI301A was chosen that has combination of both stability and efficiency. To verify the reproducibility of measurement results across different AI301A tunnel diodes (using same part number), two additional prototypes were tested using AI301A. All the prototypes tested using AI301A were very stable and produced good reflection and conversion gain.

H. Power link budget

The link budget is a method to diagnose the entire system. It determines the gain and losses in a system by calculating the RF power level at each point [START_REF] Lazaro | Radio link budgets for UHF RFID on multipath environments[END_REF]. It governs the margin in system performance and can locate point of failure. The evaluation of the proposed system is performed in two cases shown in Fig. 17. In Case I (shown in Fig. 17 (a)), the reader and tag both transmit and receive fundamental frequency i.e. 414.6 MHz. However, in case II (shown in Fig. 17 (b)), the reader illuminates the tag at the fundamental frequency, while the tag re-radiates the second harmonic, i.e. 829.2 MHz, to the reader. The power link budget of the entire system in both cases is shown in Fig. 18, which is given as: Pread= PT + GR + GT -LT -Pmod -LFS + GHRA (7) all the above terms are explained in Table IV, where the value of the first five terms are assumed, the sixth term LFS is calculated using free-space path loss (FSL) equation provided in Table IV, and the value of last term is extracted from Fig. 13. The fifth term, modulation loss (Pmod) occurs due to the change in circuit impedance from state '0' (Z= 5.6-j×0.2 Ω) to state '1' (Z= -51.6-j×3.2 Ω), which defines how the tag modulates the reader signal back to reader. The last term, gain provided by the HRA also depends upon the type of operation. If the system is operating as Case I (Fig. 17 Above equation ( 7) is used to calculate the maximum read range of complete system, which also depends on the readers receive sensitivity. The reader sensitivity is good enough so that the signal reflected by the tag must be successfully detected by the reader. For the proposed link budget, we assume readers receive sensitivity is around -90 dBm. The maximum theoretical read range of active HRA is around 150m and 35m, which is shown in

IV. HARMONIC TUNNELING TAG DYNAMIC MODULATION

The inherent negative resistance of tunnel diode enables HRA to be employed as a high gain modulator in backscattered low powered RFID systems. We introduced dual-band reflection amplifier in the previous section, it can modulate the backscatter signal by ON-OFF keying (OOK). It is more spectrally efficient than Frequency Shift Keying, as no energy is spent on the transmission of zero, but it is more prone to noise and interferences [START_REF] Lee | An on-off mode RTD oscillator operating at extremely low power consumption[END_REF], [START_REF] Wang | 5-Gb/s 50-cm wireless link using a high power compact III-V 50-GHz transmitter[END_REF].

In the proposed HRA, both the frequency bands are either ON or OFF simultaneously, leading to a compatibility with legacy system that do not operate using harmonic backscatter communication. The response of the HRA to the arbitrary waveform 0101101011101100 OOK modulation is shown in Fig. 19 with an incident wave power of -50dBm. It can be seen that the reflected power at fundamental frequency alternates between 0 dBm and 28 dBm, which leads to a more than 25 dB contrast between the ON-OFF states. Moreover, the wave generated from the fundamental at the second harmonic alternates at -20 dBm and 10 dBm, which means that even higher contrast is obtained. More contrast means the signal offers higher immunity to noise and interfering signals. Phase Shift Keying (PSK) modulation can also be considered allowing constant power to be transferred to the transponder regardless of modulation state [START_REF] Khaledian | A power efficient implementation of in-band full-duplex communication system (ReflectFX)[END_REF]. More specifically, BPSK is guaranteed with this circuit, as two phases responses are obtained for the same gain. The phase of the backscatter signal and reflection gain at f0 for the incident power of -50dBm is shown in Fig. 20.

For Fig. 20, since the VNA could not control the dc bias, indirect measurement was performed. The bias generator was set to bias the HRA with slow ramp function from 0 to 300 mV, while VNA measurements have been done in time domain (thus on exact time corresponds to an exact bias). It is shown that a gain of 16.8 dB can be obtained for two different bias (ϕ=-97° when Vb =142 mV and ϕ=83°, when Vb =146 mV).

The phase stability as a function of the incident power is also measured to evaluate the impact of backscattering resilience to channel variation (Fig. 21). It is seen that the phase is quite stable at both frequencies. V. CONCLUSION This work describes the design and testing of a harmonic reflection amplifier using a tunnel diode that can amplify, backscatter and modulate the incident RF power in legacy RFID applications. It also operates in dual-band for transmitting information using the inherently generated 2 nd harmonic. Its ability to operate in dual-band improves the sensitivity of a communication link by avoiding the self-jamming leakage and also acts smartly in a crowded frequency spectrum. The demonstrated HRA is ideally suited for RFID applications that deserve high data rates with improved read range. The conversion gain as high as +18 dB at the 2 nd harmonic opens the way to integrate the proposed tunneling tag with inter-band mobile communication. The low power consumption and considerable reflection/conversion gains make the proposed HRA an idyllic candidate for RFID and inter-band 5G communication.

Fig. 1 .

 1 Fig. 1. Comparing the various state-of-the-art reflection amplifiers in terms of efficiency and output power vs dc power consumption.

Fig. 3 .

 3 Fig.3. Measured dc characteristics of the tunnel diodes AI301A, 3I101D and 3I306E. The 7 th order polynomial fitting of the measured dc IV characteristic allowed to estimate the differential resistance of AI301A |-Rtd|= 147 Ω and the responsivity ℜ= 11.9 A/W that are highlighted, for biasing at 144 mV. Shaded region represents linear characteristics, where ℜ ≤│7.5 │A/W.

Fig. 5 .

 5 Fig. 5. Simulated S parameter of circuit without tunnel diode, representing two resonances at the desired frequency band.

2

 2

  Re[Zdiode] < 0, and the highest reflective gain is obtained only if |Re[Zdiode]| is kept different from Re[Zcircuit] by a very small margin. The simulated real and imaginary impedance of the tunnel diode SDD model at different bias points is shown in the upper graph of Fig. 6 (a) and Fig. 6 (b), respectively. A quite good agreement is observed with the measured real and imaginary impedance of the AI301A tunnel diode represented in the lower graph of Fig. 6 (a) and Fig. 6 (b).

Fig. 6 .

 6 Fig. 6. (a). Real and (b) imaginary impedance of the tunnel diode at various biasing using the simulated SDD model, and measured AI301A bare diode.

Fig. 7 .Fig. 8 .

 78 Fig. 7. The basic working principle of the harmonic reflection amplifier.

Fig. 9 .

 9 Fig. 9. Measured reflection and conversion gain as a function of the bias voltage for an input frequency of 414.6MHz and an input power of -50 dBm.

Fig. 10 .

 10 Fig.10. Measured real (brown) and imaginary parts (green) of the HRA impedance at both frequencies f0 (=414.6 MHz) and 2f0 (=829.2 MHz) for various incident powers, when optimum bias of 144 mV is applied.

Fig. 11 .

 11 Fig.11. Measured input impedance of the HRA before final biasing for an incident power of -50 dBm, when optimum bias of 144 mV is applied. Under such conditions, self-injection locking would be expected at f0, because the impedance of the HRA falls below -50 Ω. The shaded portion represents the unstable region, if the antenna impedance (Zantenna) = 50 Ω.

Fig. 12 .

 12 Fig.[START_REF] Forouzandeh | Application of wideband differential phase shifters with wide phase range in chipless RFID readers[END_REF]. Contour chart of the reflection gain (eq. 4) and stability criteria (eq.5) for a source-pull calculation of any possible antenna impedance considering the input impedance (47-j×1.3 Ohm) of the circuit at 414MHz for power below -60dBm.

Fig. 14 .

 14 Fig.[START_REF] Rimini | Method and apparatus for adaptive non-linear self-jamming interference cancellation[END_REF]. One port analysis of the HRA to find reflection and conversion gains from 'a', 'b' waves at fundamental frequency f0=414.6 MHz.

Fig. 16 .

 16 Fig. 16. Measured real impedance of the HRA for three different prototypes (employing different tunnel diodes at frequency f0 (=414.6 MHz) for various incident powers.

  (a)), HRA provides reflection gain, whereas, if system is operating as Case II (Fig.17

Fig. 15 .

 15 (b)), HRA provides conversion gain. Simulated (green) and measured (brown) reflection gain at fundamental frequency and measured conversion gain (purple) at the second harmonic frequency for the incident power (Pin) of (a) -30 dBm, (b) -40 dBm, and (c) -50 dBm. In the conversion gain graph, the frequency in x-axis is the frequency of the output signal

Fig. 17 .Fig. 18 .

 1718 Fig. 17. Complete system for calculating the power link budget in the forward and reverse path (a) Case I: reader transmits f0 (414.6 MHz) and tag re-radiates f0 (414.6 MHz), where tag provides reflection gain (b) Case II: reader transmits f0 (414.6 MHz) and tag re-radiates 2f0 (829.2 MHz), where tag provides conversion gain. Transmit Power

  (a), (b) corresponds to Fig. 17 (b).

  Fig 18 (a) and Fig. 18(b), corresponding to Case I (Fig. 17

  (a)) and case II (Fig.17

  (b)), respectively.

Fig. 19 .

 19 Fig.[START_REF] Gu | Diplexer-Based Fully Passive Harmonic Transponder for Sub-6-GHz 5GCompatible IoT Applications[END_REF]. Relative output power (reflection gain) corresponding to an arbitrary bit sequence OOK modulation at f0=414.6 MHz, the '0' state corresponds to circuit impedance Z= 5.6-j×0.2 Ω, whereas the '1' state corresponds to Z= -51.6-j×3.2 Ω (upper graph) and relative output power at 2f0= 829.2 MHz (conversion gain) where the '1' corresponds to the input power at the fundamental being converted to the second harmonic frequency (lower graph). The '0' state corresponds to no bias voltage, whereas the '1' state corresponds to 144 mV.

Fig. 20 .

 20 Fig. 20. Capability of the HRA to perform BPSK by maintaining the magnitude symmetry of 16.8 dB, but with a phase difference of 180°, at two different biasing points Vb1= 142 mV (T1=1.262 ms) and Vb2= 146 mV (T2=1.277 ms), respectively.

Fig 21 .

 21 Fig 21. Measured phase of the HRA at both frequency bands, f0 =414.6 MHz (wine) and at 2f0 =829.2 MHz (green) for various incident power, when optimum bias of 144 mV is applied.

TABLE II

 II

		: COMPARISON OF STATE-OF-THE-ART HARMONIC BACKSCATTER
	Ref.	Type	2 nd Harmonic Freq. (GHz)	CG (dB)
	This	Active	0.414>0.829	-24 to +29
	work
	[19]	Passive	7	-17
	[41]	Passive	1.6	-26
	[42]	Passive	0.929	-15 (without amplifier)
		Active		-8 (with amplifier)
	[43]	Semi-	1.8	-23
		passive
	[44]	Passive	2.4	-26.5
	[45]	Passive	2	-19.9
	[46]	Passive	1.736	-30

TABLE I :

 I COMPARISON OF STATE-OF-THE-ART REFLECTION AMPLIFIERS AVAILABLE IN LITERATURE Ref.

		Year	Device	Freq. (GHz)	Vdc (V)	Idc (mA)	Pdc (mW)= Vdc*Idc	Pin(dBm) or P-1 dB	Gain (dB)	Pout(dBm)= Pin+Gain	 	out dc P P
	This	2020	AI301A GaAs Tunnel Diode	0.4146	0.144	1	0.144	-43	30	-13	34.79
	work			0.8292					20	-23	3.479
				CG**					16	-27	1.385
	[21]	2019	NE3509M04 GaAs FET	2.45	1	--	--	--	11.5	--	--
	[22]	2018	MBD5057-E28 Ge Tunnel Diode	5.8	0.09	0.5	0.045	-75	40	-35	0.702
	[23]	2018	MBD5057-E28 Ge Tunnel Diode	5.8	0.06	0.34	0.0204	-81	35	-46	0.123
	[24]	2017	NE3509M04 (Renesas) GaAs FET	1.8	1	2.4	2.4	-24.9	21.9	-3	20.87
				2.4				-24.8	13	-11.8	2.7525
	[25]	2017	AI301A GaAs Tunnel Diode	0.89	0.2	1	0.2	-30	17	-13	25.055
	[26]	2017	AI201A GaAs Tunnel Diode	0.915	0.117	1.5	0.178	-30	13	-17	11.2
	[27]	2017	2um Resonant Tunnel Diode	5.8	2*0.47	0.46	0.42	-34	8.6	-25.4	0.68
	[28]	2015	MBD5057-E28 Ge Tunnel Diode	5.45	0.08	0.566	0.045	-70	34.4	-35.6	0.612
	[29]	2014	BFT25A Bipolar Junction Transistor	0.915	0.755	0.431	0.325	-50	10.2	-39.8	0.0327
								-40	7.7	-32.3	0.143
								-30	4.9	-25.1	0.9508
	[30]	2014	Bipolar Junction Transistor	0.9	0.83	0.73	0.605	-50	30	-20	1.65
								-30	14.92	-15.08	5.13
	[31]	2014	BFT25A Bipolar Junction Transistor	0.9	0.83	0.8	0.664	-50	29	-21	1.196
								-20	9	-11	11.96
	[32]	2014	InP 0.9um Resonant Tunnel Diode	5.7	0.36	0.173	0.125	--	10.4	--	--
	[33]	2013	BPF405 (Infineon) Si BJT	5.25	2.5	0.8	2	-25	13	-12	3.15
	[34]	2013	CFY30 MESFET	4.5	3	6	18	--	10.2	--	--
	[35]	2013	Josephson junction	2.685	--	0.054	--	-117	30	-87	--
	[36]	2012	MOSFET	4	0.8	0.15	0.12	-71.9	22.3	-49.6	0.00933
	[37]	2011	NE32584 HJFET	5.8	0.7	9	6.3	--	11.48	--	--
	[38]	2008	pHEMT	21	2.3	91	209.3	-75	14	-61	0
	[39]	2006	pHEMT-MMIC DOIPH process	21	3	110	330	-45	14	-31	0.00024
	[40]	2003	NE32584C HJFET	6.26	--	--	--	--	8.1	--	--
	CG**= Conversion Gain @ 2f0:414.6MHz to 829.2MHz

Tunnel Diode Matching Network L 2 C 1 L 1 DC Block RF in@f0 RF out@f0 RF out@2f0 RF block C 2 Vbias DC Biasing and Stabilization L 3 Cancellation circuit-less reader (separate Tx and Rx frequency)

TABLE III :

 III PERFORMANCE COMPARISON OF THREE DIFFERENT TUNNEL DIODES

	Parameters	Circuit I-	Circuit II-	Circuit III-
		AI301A	3I101D	3I306E
	Vbias (mV)	144	214	164.5
	I(Vbias) (mA)	1	0.68	1.073
	Power consumed (uW)	144	145.5	176.5
	Negative resistance	-147	-158	-137
	Peak current @25°C	1.6 -2.4 mA 1.7 -2.4mA	1.8 -2.2mA
	Voltage at peak current	<180mV	<160mV	<170mV
	Parasitic capacitance	< 12 pF	2.5 -10pF	4 -12pF
	Parasitic inductance	<1.5nH	<1.3nH	NA
	technology	GaAs	GaAs	GaAs

TABLE IV :

 IV DESCRIPTION OF VARIOUS LINK BUDGET COMPONENTS

	Link	Budget component	Term.	Value
	Forw	Power transmit by reader	PT	15dBm
	ard	Reader antenna gain	GR	4dBi
		Free space loss @ 414.6 MHz =	LFS@414.6MHz
		-27.55+20log(MHz)+20log(metre)
		Power incident at tag (Pinc)= PT + GR -LFS@414.6MHz
	Reve	Tag antenna gain	GT	2dBi
	rse	Miscellaneous Loss at tag	LT	1dB
	(Tag	Modulation Loss	Pmod	6dB
	to	Case I: Reflection gain provided by	GHRA@414.6MHz	Fig. 13
	read	the HRA @ 414.6 MHz		(green)
	er)	Case II: Conversion gain provided	GHRA@829.2	Fig. 13
		by the HRA @ 829.2 MHz	MHz> 414 MHz	(blue)
		Case I: Free Path loss @ 414.6 MHz	LFS@414.6MHz
		Case I: Free Path loss @ 829.2 MHz	LFS@829.2MHz
		Case I:

Power back to reader (Pread) @ 414.6 MHz Pread = Pinc + GT -LT -Pmod -LFS@414.6MHz + GHRA@414.6MHz(RG) Case II: Power back to reader (Pread) @ 829.2 MHz Pread = Pinc + GT -LT -Pmod -LFS@829.2MHz + GHRA@829.2MHz>414.6MHz(CG)

	Reader Antenna Gain		Tag Antenna Gain
	GR=4dBi		GT=2dBi
	Initial Power	Free Path Loss LFS@414.6MHz	Modulation Loss Pmod=6dB
	PT=15dBm
	Reader	Miscellaneous	HRA Tag
		loss (LT)= 1dB	Reflection Gain
				GHRA@414.6MHz
	Reader Antenna Gain		Tag Antenna Gain
	GR=4dBi		GT=2dBi
		Free Path Loss
		LFS@414.6MHz	Modulation Loss
			Pmod=6dB
	Initial Power PT=15dBm	Free Path Loss LFS@829.2MHz
	Reader			HRA Tag
				Conversion Gain
			GHRA@829.2MHz>414.6MHz

This work was supported in part from the French State in the frame of the "Investments for the future" Programme IdEx Bordeaux, reference ANR-10-IDEX-03-02, and LabEx AMADEus (ANR-10-LABX-0042-AMADEUS).