Geneviève Baudoin
email: g.baudoin@esiee.fr

Martine Villegas
email: m.villegas@esiee.fr

Martha Suarez
email: suarezm@esiee.fr

Antoine Diet
email: antoine.diet@lss.supelec.fr

Fabien Robert
email: robertf@esiee.fr

Performance Analysis of Multiradio Transmitter with Polar or Cartesian Architectures Associated with High Efficiency Switched-Mode Power Amplifiers

Keywords: Multiradio transmitter, high-efficiency RF transmitter, polar transmitter architectures, Cartesian transmitter architectures, class E power amplifier,  coding, PWM coding, WiMAX, LTE

This paper deals with wireless multi-radio transmitter architectures operating in the frequency band of 800 MHz -6 GHz. As a consequence of the constant evolution in the communication systems, mobile transmitters must be able to operate at different frequency bands and modes according to existing standards specifications. The concept of a unique multiradio architecture is an evolution of the multistandard transceiver characterized by a parallelization of circuits for each standard. Multi-radio concept optimizes surface and power consumption.

Transmitter architectures using sampling techniques and baseband  or PWM coding of signals before their amplification appear as good candidates for multiradio transmitters for several reasons. They allow using high efficiency power amplifiers such as switched-mode PAs. They are highly flexible and easy to integrate because of their digital nature. But when the transmitter efficiency is considered, many elements have to be taken into account: signal coding efficiency, PA efficiency, RF filter. This paper investigates the interest of these architectures for a multiradio transmitter able to support existing wireless communications standards between 800 MHz and 6 GHz. It evaluates and compares the different possible architectures for WiMAX and LTE standards in terms of signal quality and transmitter power efficiency.

Introduction and Context

Wireless communications systems including cellular communications, personal area networks (PANs), local area networks (LANs) and metropolitan area networks (MAN) have presented a considerable development in recent years and keep evolving constantly. Coexistence of different wireless standards on a same device is necessary to satisfy the users who expect mobility, ubiquitous connection and high data rates at the same time. This coexistence should not increase the size of the device or reduce its battery life. The goal of this evolution is to reduce the number of external components and to increase the integration in the low-cost CMOS technology. Another stage which pursues the evolution towards the cognitive radio and implies flexibility of each stage of the communication chain is the cognitive Multi-Radio. Instead of including an independent architecture for each standard, universal transmitter architecture capable of generating all the different standards waveforms seems to be the best solution (especially in terms of consumed power and surface occupation). This concept is known as multi-radio transmitter. Cognitive Multi-Radio has the capability of the multistandard concept and moreover it is capable to perform an efficient environment spectrum scanning and react to the environment conditions choosing the appropriated communication standard. At present, we envisage a cognitive multi-radio able to support existing wireless communications standards between 900 MHz and 6 GHz. Principal parameters to consider in a multi-radio signal for each standard are bandwidth, power dynamic range and envelope magnitude range (expressed by the Peak to Average Power Ratio -PAPR) which depend on the modulation type. From the mobile multi-radio transmitter point of view, key aspects to consider are power efficiency and linearity. Moreover, transmitted signal is limited to the frequency band assigned by local regulation and must respect established limits of adjacent channel power ratio (ACPR) and power spectrum emission mask. If required, transmitter must be able to adjust its output power over a defined range. Multi-radio architecture should handle variations of previously enounced parameters respecting all standards requirements.

To overcome the implementation design complexity, linearization methods or highly linear non-constant envelope architectures able to transmit high PAPR signals must be investigated. In this context, different constant envelope Invited paper architectures (CEAS) have been proposed. In these architectures, the input of the power amplifier (PA) is a constant envelope signal even if the useful signals at the input and output of the transmitter have a time varying envelope. The potential interest of such architectures is to allow the use of high efficiency power amplifiers such as switched-mode PAs. But in order to regenerate the original varying envelope signal, an RF filter is most of the time necessary at the output of the PA. Therefore when efficiency is considered, many elements have to be taken into account: signal coding efficiency, PA efficiency, RF filter.

Among the CEAS transmitter architectures, we can distinguish at least 3 kinds of approaches. In the first one, the signal envelope (i.e. its magnitude) is used to modulate in amplitude the PA power supply such as EER (envelope elimination and restoration) [START_REF] Kahn | Single sideband transmission by envelope elimination and restoration[END_REF], [START_REF] Raab | RF and microwave power amplifier and transmitter technologies[END_REF], envelope tracking [START_REF] Staudinger | High efficiency CDMA RF power amplifier using dynamic envelope tracking technique[END_REF], [START_REF] Raab | RF and microwave power amplifier and transmitter technologies[END_REF] and the different kinds of dynamic power supply techniques [START_REF] Raab | RF and microwave power amplifier and transmitter technologies[END_REF] or polar lite architectures [START_REF] Lie | TZU-YIN YANG Design of highly-efficient wideband RF polar transmitters using Envelope-Tracking (ET) for mobile WiMAX/Wibro applications[END_REF]. In the second one such as LINC (Linear amplification with non-linear component) [START_REF] Cox | Linear amplification with nonlinear components[END_REF] or CALLUM (Constant Amplitude Locked Loop Universal Modulator) [START_REF] Cox | A high-efficiency RF transmitter using VCO-derived synthesis: CALLUM[END_REF], the original signal with time varying envelope is decomposed in a sum of 2 constant envelope signals that are amplified by two identical PA and recombined at the output of PAs. In the third one, the time varying original signal is sampled and coded into a 2-level signal [START_REF] Cox | Linear amplification by sampling techniques: A new application for delta coders[END_REF] to generate a constant envelope signal. These different approaches can be combined such as in EER-LINC architectures [START_REF] Diet | EER-LINC RF transmitter architecture for high PAPR signals using switched power amplifiers[END_REF].

In this paper, we focus on RF Transmitters with switched-mode PA and CEAS architectures using sampling techniques and baseband  or PWM coding of signals and we analyze their interest for multiradio transmitters. In section 2, we present the principles of polar and cartesian sampled CEAS architectures with baseband  or PWM coding. In section 3, we describe the results obtained by simulation for the different architectures and compare the different approaches from the point of view of signal quality and power efficiency. This section is split in 2 parts: the first one analysis the quality of the reconstructed signal in the case of an ideal PA and the second one presents the results with a switched class E PA.

Principles of Constant Envelope Architectures using Sampling Techniques

In the following, we will call "original signal" the signal at the input of the transmitter that has potentially a time varying envelope. CEAS architectures using sampling technique (that we will note CEAS) rely on the coding of the original signal into a constant-envelope signal that is usually a two-level signal from which the original signal can be restored by a filtering operation. We will call this signal the "coded signal". The coding operation is sometimes called modulation. The most frequent coding techniques are PWM (Pulse Width Modulation) and  modulation (or coding). These coding techniques take profit of an oversampling operation before the two-level coding.

Historically, the first CEAS architecture using sampling techniques is the LIST architecture (Linear amplification using sampling technique) that was proposed by Cox [START_REF] Cox | Linear amplification by sampling techniques: A new application for delta coders[END_REF]. The LIST architecture is described in Fig. 1.

G 0° 90°R F output signal OL à f c zI(t) zQ(t) GI RF (t) GQRF(t)  Coder  Coder I(t) IRF(t) Q(t) QRF(t) G f f f fS f fRF-fS fRF fRF-fS f fRF-fS fRF fRF-fS Q f fRF-fS fRF fRF-fS I f fRF-fS fRF fRF-fS

Image signal

Fig. 1. LIST architecture proposed by Cox [START_REF] Cox | Linear amplification by sampling techniques: A new application for delta coders[END_REF].

The real and imaginary parts of the complex envelope of the original signal are oversampled and coded by delta coders. These two coded signals modulate in amplitude two carriers in quadrature. The resulting frequency transposed signals have a constant envelope. They are amplified by two high efficiency PAs whose output are summed. Finally, the signal is filtered by a pass-band filter to regenerate the amplified original signal. One of the critical point of the LIST architecture is the efficient combining of the outputs of the two PAs.

The signal to noise ratio (SNR) after the signal reconstruction depends on the oversampling ratio. Typically with the LIST approach, for an SNR of 55 dB, it should be greater than 200B where B is the signal bandwidth.

A general question for CEAS architectures is the bandwidth B of the output RF bandpass filter signal to consider. In a multi-channel system, the bandwidth B should be the total bandwidth of the system and not the bandwidth of a single channel. This allows using the same RF bandpass filter whatever the channel but of course it increases the necessary oversampling frequency.

New CEAS architectures have been proposed in the literature using PWM or  modulation. We can distinguish two approaches, depending on whether the RF or the baseband signals are coded. Fig. 2 illustrates the case where the RF signal is coded [START_REF] Wagh | High-efficiency switched mode RF power amplifier[END_REF]. In this architecture the RF modulated signal is directly coded by a bandpass  or PWM modulator. This approach is based on a 1 bit quantization of the RF modulated signal. Resulting constant envelope signal drives a Switched mode PA followed by a band-pass filter in order to reduce  noise. The main difficulty of this approach is the necessary sampling frequency that is typically equal to 4 times the carrier frequency for the bandpass modulator. In the case of high frequency carrier (typi-cally above 2 GHz) it is still very difficult or impossible to realize coders at such high frequencies. There are several possible baseband approaches depending on how the complex envelope is processed. They differ in particular on whether cartesian or polar coordinates are processed and on whether PWM or  coders are used. We can therefore distinguish: polar , Cartesian  polar PWM and Cartesian PWM architectures. And for each of these architectures, different electronic implementations can be proposed. In the following, we will note z(t) the complex envelope, z I (t), z Q (t) its Cartesian coordinates and t(t) its polar coordinates, with the following relation:

  ( ) ( ) ( ) ( )exp ( ) I Q z t z t jz t t j t      . ( 1
)

Principles of Polar  or PWM CEAS Architectures

Two approaches have been originally proposed for polar   or PWM CEAS transmitters [START_REF] Berland | A transmitter architecture for Nonconstant Envelope Modulation[END_REF], [START_REF] Jeong | A Polar Delta-Sigma Modulation (PSDM) scheme for high efficiency wireless transmitters[END_REF]. In this paper we focus on the first one, which uses a "±a 1-bit   or PWM coder" (2 opposite level output). It is presented in Fig. 3 extracted from [START_REF] Berland | A transmitter architecture for Nonconstant Envelope Modulation[END_REF]. In the figures of this section, we represent a 1-bit  coder but it can be replaced by a PWM coder. In this architecture, envelope and phase restoration is carried out in baseband before the power amplifier.

In a polar CEAS architecture, data are mapped following a given modulation to generate the complex envelope z(t). The resulting complex envelope is decomposed in its polar coordinates and the baseband envelope and phase signals t cos((t)), sin((t)) are constructed. Then, the envelope signal t is coded by a low-pass  or PWM modulator and the output of the bit coder is a two-level constant envelope signal noted  coded t with  coded t = ± a. We will call coded envelope, the signal  coded t. Phase signal exp(jφ(t)) and coded envelope are recombined to form a constant envelope signal  coded t exp(jφ(t)). This signal is frequency up-converted with at the carrier frequency f c (with ω c = 2πf c to form the RF modulated signal x(t):

                  ( ) ( )exp ( ) exp , ( ) cos ( ) cos sin ( ) sin , ( )cos ( ) . coded c coded c c c x t t j t j t t t t t t t t t                   (2)
The RF modulated signal x(t) is sent to the power amplification. As x(t) is a constant envelope signal, linearity requirements are relaxed for the PA and a switched mode PA can be used. Delay mismatch is not as severe issue as in the classical EER [START_REF] Baudoin | Influence of time and processing mismatches between phase and envelope signals in linearization systems using Envelope Elimination and Restoration, application to hiperlan 2[END_REF] architecture. Amplified signal is finally filtered.

To keep  modulator stability, an input level controller must be included at the input of the  modulator.

Different electronic implementation can be applied for this architecture. We can generate the two signals A second possible implementation of the architecture is presented in Fig. 5. The output of the low-pass  or PWM modulator is analog. The digital phase (or instantaneous frequency) signal is converted to analog and then modulated to the carrier frequency with a modulated PLL. Finally constant envelope and phase signals are recombined.

The advantage of this approach compared to the first one is that it requires only one DAC. Furthermore, DAC frequency requirements are mitigated. But the bandwidth of the phase signal can be a challenge for the modulated PLL. In that case, the modulated PLL can be replaced by an IQ modulator but two DAC are necessary to generate cos(φ(t)) and sin(φ(t)). In the first architecture, modulation to the carrier frequency is performed by the IQ modulator block with help of an analog mixer. Similarly, the second architecture makes use of an analog multiplier to recombine envelope and phase.

A third possible architecture (see Fig. 6) proposes to generate a digital carrier and then to replace the analog mixer by a digital one, like an AND gate for example. We will refer in that case to digital mixed signal. We consider that digital mixing is advantageous for polar sigma delta architecture, not only it offers all the typical advantages of a digital signal treatment but it also offers IC integration. Synchronization between envelope and phase signals is a critical aspect in polar architectures. To overcome this problem, it is suggested in this third approach to use the same frequency generator for the ADPLL reference and for the  or PWM modulator. This is a practical implementation because only one frequency generator is needed in the architecture.

Some studies on a fully digital implementation based on a radio-frequency DAC are presented in [START_REF] Gutierrez | BiCMOS Implementation of a full-digital linearized system for complex modulation transmitter[END_REF].

Principles of Cartesian  or PWM CEAS Architectures

Instead of using polar coordinates, we have proposed to separate base-band modulated signal into its In-Phase and Quadrature components leading to a "Cartesian" CEAS transmitter architecture [START_REF] Suarez Penaloza | A Cartesian Sigma-Delta transmitter architecture[END_REF].

In the proposed Cartesian ΣΔ or PWM transmitter CEAS architecture data are mapped and treated in base-band according to the chosen modulation requirements. Resulting signal is separated in its In-Phase (I) and Quadrature (Q) components. I and Q components are non constant envelope signals, so two 1-bit lowpass ΣΔ or PWM modulators are used to code and transform them in signals varying between +/-a. Resulting I and Q coded signals have constant envelope, they are RF modulated and recombined before power amplification. The PA input is then a constant envelope signal. Finally, amplified signal is filtered by a bandpass filter centered at the carrier frequency (Fig. 8).

Simulation and Comparison of CEAS Polar and Cartesian Architectures

The polar and cartesian CEAS architectures have been simulated and compared with WiMAX and LTE input signals. Simulations and comparisons have been done first with an ideal PA to evaluate the influence of the sampling frequency on the quality of the reconstructed signal and secondly with a class E switched-mode PA to evaluate the efficiency of the full transmitter. All the simulations were conducted using the Agilent Advanced Design Software (ADS).

Input Signals Used for the Tests

Mobile WiMAX and LTE standards have been adopted for simulations because they support a very demanding modulation in terms of envelope PAPR and bandwidth.

According to the WiMAX forum implementation profiles, four primitive parameters characterize the OFDMA symbol: channel bandwidth (BW), number of used subcarriers including data and DC subcarriers (N used ), sampling factor (n) and cyclic prefix to useful time ratio (G) [START_REF]Air Interface for Fixed and Mobile Broadband Wireless Access Systems Amendment 2: Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed[END_REF]. One of the implementation profiles proposed by the Wi-MAX Forum was selected for mobile WiMAX simulations: a 10 MHz channel -1024 FFT size, "n" factor and cyclic prefix to useful time ratio G were fixed to 57/50 and 1/32 respectively. A 64-QAM modulation is considered in simulations to achieve the highest PAPR signal. Obtained symbol rate is 11 Msymb/s. WiMAX standard defines a power spectral mask for unlicensed bands (10 and 20 MHz channels), even if mobile WiMAX only can be deployed in licensed bands, this mask can be taken as a reference: for the 10 MHz channel -50dBc must be reached at 14.5 MHz from carrier. Furthermore, ETSI has defined masks for the channel bandwidths that were originally proposed in 802.16d. Adapting the ETSI mask for the 10 MHz channel, -50dBc must be reached at 20 MHz from carrier. We have considered one of the frequency bands proposed by the WiMAX Forum for mobile WiMAX with a bandwidth of 100 MHz.

LTE is a multi-carrier standard specified by the 3GPP consortium. It is an evolution of the cellular phone standards that targets high data rates, up to 70 Mbps in uplink and up to 300 Mbps in downlink for a 20 MHz channel and a 4x4 MIMO configuration. LTE disposes of the same frequency bands as those allocated to UMTS [START_REF]Technical Specification 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); User Equipment (UE) radio transmission and reception (Release 8)[END_REF]. It uses OFDMA (Orthogonal Frequency Division Multiple Access) in the downlink direction, while the uplink is based on SC-FDMA (Single Carrier Frequency Division Multiple Access). LTE output power limits may vary depending on the frequency band, nevertheless maximal value is 23 dBm. The minimum requirements for the Error Vector Magnitude (EVM) are 17.5% for QPSK, 12.5% for 16-QAM and 8% for 64-QAM [START_REF]Technical Specification 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); User Equipment (UE) radio transmission and reception (Release 8)[END_REF].

For the simulations, we used Uplink SC-FDMA signals generated using the LTE source provided by the ADS software. The 1920 -1980 MHz frequency band (E-UTRA Band number 1) has been chosen for this study. A 10 MHz channel bandwidth has been selected; it defines 50 resource blocks, 600 useful data sub-carriers and an FFT size of 1024. Each sub-carrier is modulated by QPSK. Normal cyclic prefix is used for symbol generation and hence there are 6 symbols per slot. The total bandwidth of LTE is 60 MHz.

Antenna Filter

Antenna filter should guarantee minimal ripple over the targeted bandwidth and also present enough stopband attenuation in order to respect power emission mask. Ripple of 1 dB and out of band attenuation of 51 dB were fixed for the filter conception. Elliptic type filter was considered because its transfer function is quite similar to that of Bulk Acoustic Wave (BAW) filters [START_REF] Suarez Penaloza | Front-end filtering requirements on a mobile cognitive multi-radio transmitter[END_REF]. BAW filters are designed associating Film Bulk Acoustic Resonators (FBARs). We envisage BAW filters as good candidates for Multiradio applications because they handle high power levels and offer significant band rejection and high operation frequency. Moreover, they can be integrated "above IC", which means size reduction and package simplicity [START_REF] Suarez Penaloza | Front-end filtering requirements on a mobile cognitive multi-radio transmitter[END_REF].

Characteristics of the ΣΔ Modulator

Envelope ΣΔ modulators used in the polar and the Cartesian architectures have the same transfer function.

This ΣΔ modulator has been synthesized using the Matlab Delta-Sigma Toolbox [START_REF] Schreier | Understanding Delta-Sigma Data Converters[END_REF]. The choice of the sampling frequency f  is a critical point. Choosing a high f  improves the signal to noise ratio (SNR) for the reconstructed signal but increases the power consumption of the  coder. It can be shown that to minimize  noise folding and to improve the SNR, f  must verify the following conditions, where f c is the carrier frequency and m an integer:

, 2 2 . c c f f f f m          (3)
For the WiMAX and LTE cases of the simulations, we have chosen f  f c which give the best possible oversampling ratio (OSR). For the simulation we have chosen f c =3.7 GHz for WiMAX and f c = 1.96 GHz for LTE. The OSR is equal to 18 for WiMAX and to 16 for LTE.

With these input parameters, the noise transfer function (NTF) obtained with the "synthetizeNTF" toolbox function is:

2657 . 0 8396 . 0 ) 1 ( 2 2     z z z NTF .
A feedback ΣΔ structure (Fig. 9) has been selected instead of a feedforward structure because of its response flatness, less overvoltage risk and better stability. Using the "realizeNTF" function a, b, c, and g coefficients are obtained.

Characteristics if the PWM Modulator

In the different CEAS architectures, a PWM modulator can be used instead of a ΣΔ modulator. There are different ways to realize a PWM modulator. In analog PWM modulators, a periodic reference signal with a frequency (f pwm ) is compared with the input signal and the 2-level value of the coded output depends on the result of the comparison. Different reference signals can be used such as symmetrical triangular or sawtooth signals. The original input signal is regenerated by applying a low-pass filter to the PWM modulator output. The SNR between the original and regenerated signals depends on the frequency of the reference signal. Typically, PWM modulator frequency (f pwm ) is not as elevated as the ΣΔ modulator frequency. For simulations purposes and aiming to compare results with both architectures, f pwm has been chosen to be a sub-multiple of the ΣΔ sampling frequency f  . We have chosen: f pwm = f  /10. It is therefore equal to 370 MHz for the WiMAX case and to 196.6 MHz for the LTE case. A sawtooth reference signal has been used. PWM minimum time (T pwm ) has been initially fixed to be the same as the ΣΔ output minimum time (T  ). The PWM modulator output signal varies between [-A, A].

Simulation Results and Comparison with an Ideal Power Amplifier

The results of this section are obtained with an ideal PA.

Simulation results for the Cartesian ΣΔ architecture: Fig. 10 shows the power spectral densities (psd) of the signals before and after the RF filter for the Cartesian ΣΔ architecture. Power mask is respected as it can be verified in Fig. 11 which is a zoom of Fig. 10 around the carrier frequency. In order to estimate EVM transmitter contribution, an ideal receiver was simulated. EVM is found to be 0.38%.

Simulation results for the Polar ΣΔ architecture:

This section presents the results obtained with a Polar ΣΔ transmitter architecture as described by Fig. 3. Simulation parameters are the same as those used for the Cartesian ΣΔ architecture simulation.

Envelope bandwidth is higher than I and Q signals bandwidth (about 30 MHz instead of 5 MHz). Fig. 12 shows transmitter output spectrum before and after filtering (using the same filter as for the Cartesian architecture). Transmitted signal also respects the power mask and EVM is found to be 0.46%. Comparison of the Cartesian and the Polar ΣΔ architectures: In conclusion, the polar and Cartesian architectures give similar results from the point of view of signal quality (spectrum and EVM) but the Cartesian architecture is slightly easier to implement.

One advantage of the Cartesian architecture in comparison to the polar architecture is that for the same sampling frequency, OSR can be higher because I and Q signals bandwidth is narrower than envelope bandwidth. Furthermore, in polar ΣΔ architecture a Digital to Analog Converter (DAC) is necessary for the phase signal (an ideal one was considered in the simulation). Cartesian architecture doesn't need this extra component because conversion is directly performed by the ΣΔ modulators (I and Q signals). Besides, a digital mixing architecture as proposed before with a digital carrier and a digital mixer (like an AND gate for example) instead of an analog one, can be directly implemented with the Cartesian architecture. Finally, because I and Q paths in the Cartesian architecture are symmetrical, the Cartesian ΣΔ architecture is less sensible to mismatching effects than the Polar one.

The results of this comparison are valid only for an ideal PA and do not take into account efficiency aspects that are considered in the next section. In particular it is interesting to analyze the influence of the envelope coding on the PA efficiency in the case of a switched mode PA.

Comparison of the Architectures with a Switched-Mode PA

In order to characterize the architecture with a switched-mode PA, we have designed an amplifier operating in class E. First, we recall the advantages and principles of switched mode amplifiers.

Switched-mode PA:

Switched-mode power amplifier (Sw PA) topology has been chosen for efficiency improvement [START_REF] Jayaraman | Linear high-efficiency microwave power amplifiers using bandpass deltasigma modulators[END_REF]. There are different classes of Sw PAs (D, S, E and F), based on different transistor behavior and reactive elements of the load network. Class D and S are used in pulsed and lowpass applications like audio, and do not provide a bandpass filtering of the signal as needed in wireless communications. Class E and F are suitable for RF applications [START_REF] Raab | RF and microwave power amplifier and transmitter technologies[END_REF], [START_REF] Nielsen | Transmitter architecture based on ΔΣ modulation and switched power amplification[END_REF]. Class F PA is based on several resonating networks with high Q factors which are difficult to implement. Class E PA uses an inductor and a shunt capacitor to balance the parasitic output capacitance of the transistor. The topology used to design the amplifier is described below (Fig. 13) and is named "serial inductor". A high efficiency PA is based on maximum voltage at zero current and vice versa, without any DC power dissipation. From this theoretical hypothesis, it is possible to calculate the optimum value of Class E output network element. In this case, the output of the transistor is supposed to be a short or an open circuit and the quality factor (Q) of C 0 -L 0 is considered as infinite (perfect filtering conditions). In the signal provided by the architecture, information appears around the fundamental frequency and most of the power is spread over a wide spectrum including the two first lobes. A finite value of Q (Q = 8) guarantees good switching conditions. The load has been set to 50 Ω (R 1 ) considering emission filter and antennas as ideal. The calculation for Class E network components is: 0

G D S V pinch-off V drain V DC I drain C 1 L 1 (+L 0 ) C RF (or C 0 ) R 1 RF in RF out Z p Z s Z ch G D S V pinch-off V drain V DC I drain C 1 L 1 (+L 0 ) C RF (or C 0 ) R 1 RF in RF out Z p Z s Z ch
0 ) 15249 . 1 ( 1      Rload Q C , 2 0 0 0 1  C L  , (4) DS shunt C Rload C    0 1836 . 0  , (5) 0
.15249 1

   Rload L serial . (6)
In this study we use a GaAs E-PHEMT, Avago ATF50189 transistor.

It is a high linearity and medium power FET (29dBm output power at 1dB gain compression). The class E amplifier has been designed to work at LTE frequency band. Input matching network has been designed keeping in mind that it should not filter the wide spectrum signal provided by the architecture. The goal is to preserve constant envelope property while mainly amplifying the information. Simulated amplifier performances show drain efficiency (η D ) of 92%, overall efficiency (η 0 ) of 89% and 14dB of gain for 5 dBm 1-tone input signal.

From the amplifier results, it is possible to analyze the performances of each architecture.

The performances are evaluated by the EVM and the efficiency. For the EVM, Tab. 1 gives the value in the case of a WiMAX signal characterized by a channel bandwidth of 10 MHz, 64 QAM modulation, and sampling frequency equal to three times of carrier frequency [START_REF] Robert | Study of a polar sigma-delta transmitter associated to a high efficiency switched mode amplifier for mobile WiMAX[END_REF].

Conclusion

This paper concentrates on flexible multi-radio architectures. This kind of architectures could be used in the future for cognitive radio applications. Three architectures have been analyzed and compared: the polar architecture with envelope modulator, the polar architecture with pulse width modulator and the cartesian architecture. Validation is accomplished with the most critical signals in terms of power dynamics and frequency bandwidth; these are the LTE and mobile WiMAX.

PWM architecture shows better power efficiency. But, it was shown that although the global efficiency of  polar architecture was lower than PWM architecture, performance in the band of interest around the carrier was better. The polar  architecture provides an output power lower than the PWM architecture but slightly degrades the emitted signal. Cartesian  architecture is that which has the lowest output power and efficiency. The final choice of architecture is a compromise between required perform-ances and reconfigurability. Moreover, taking into account the emission filter in an integrated technology involves a co-design.

Fig. 2 .

 2 Fig. 2. Principle of CEAS architecture with coding of the RF signal showing the spectrum shapes (psd power spectral density) of signals.

Fig. 3 .

 3 Fig. 3. Polar CEAS architecture.



  coded t cos(t)) and  coded t sin((t)) in a digital way.Therefore, two digital-to-analog converters are necessary before the RF IQ modulator as depicted in Fig.4. DACs sampling frequency is chosen according to the  or PWM frequency. It has to be high enough to avoid  or PWM noise overlapping. Targeted communication standards in new cellular systems and wireless local area network require high  or PWM frequencies and therefore significant sampling frequency for DACs.

Fig. 4 .

 4 Fig. 4. Polar CEAS architecture with digital I and Q signals.

Fig. 5 .

 5 Fig. 5. Polar architecture with modulated PLL.

Fig. 6 .

 6 Fig. 6. Polar architecture with digital mixing.

Fig. 8 .

 8 Fig. 8. Cartesian transmitter architecture.

Fig. 9 .

 9 Fig. 9. Cartesian transmitter architecture.

Fig. 10 .

 10 Fig. 10. Signal psd before and after the RF band-pass filter for the Cartesian architecture.

Fig. 11 .

 11 Fig. 11. Transmitted signal spectrum (zoom).

Fig. 12 .

 12 Fig. 12. Signal spectrum before and after the band-pass filter for the polar architecture.

Fig. 13 .

 13 Fig. 13. Serial inductor topology of a Class E amplifier.

  EVM value for the WiMAX case with a class E PA.It may be noted that the EVM values in the case of LTE signal are of the same order.We evaluated the efficiencies in the case of the LTE signal in Tab. 2. Efficiency results for the LTE case with a class E PA.

		PWM	Polar Δ	Cartesian ΣΔ
	EVM	5,1%	1.4%		3.3%
	Tab. 1. Parameters		PWM	Polar 	Cartesian 
	Pin		6 dBm	6 dBm	6 dBm
	Pout		16,6 dBm	13,9 dBm	12 dBm
	Drain Efficiency	79,2 %	61 %	34,8 %
	PAE		72,3 %	51,1 %	26,1 %
	Global Efficiency	74 %	55,5 %	32 %
	Global Gain	10,6 dB	7,9 dB	6 dB
	PAE_BW (60 MHz)	22,2 %	30,2 %	4,6 %
	Tab.2.

Acknowledgements

This research was partially supported by the French Research program CROLLES II "nano 2008" and "nano 2012".

About Authors

Geneviève BAUDOIN Martine VILLEGAS graduated from the "Ecole Nationale Supérieure de l'Electronique et des ses Applications" (ENSEA), Paris, France, in 1981. In 2007 she received the Qualification as PHD Supervisor (HDR), from the University of Marne-la-Vallée. After an experience of some years in the industry as designer of microwave monolithic integrated circuits, she joined the world of education & investigation (ESIEE-Paris). She developed the activities in the area of the circuits and systems in radio-frequency and microwaves fields, then in the digital radio communications. She is presently Professor at ESIEE in the Telecommunications Department.


Antoine Diet

Martine Villegas

Geneviève Baudoin

Fabien Robert

A Methodology for multi-band class E RF PA design

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A Methodology for multi-band class E RF PA design A. Diet 1 , M. Villegas 2 , G. Baudoin 2 , F. Robert 2 1 UMR 8506, L2S-DRÉ. Supélec, F-91192 Gif Sur Yvette, France. antoine.diet@lss.supelec.fr 2 Université Paris-Est, ESYCOM, EA 2552; Groupe ESIEE, Noisy-Le-Grand 93162, France.

Abstract -This paper presents a simple methodology for the design of a highly efficient PA in the context of multiradio devices. This PA belongs to the radiofrequency reconfigurable part within a transmitter. Our goal is to improve the PA efficiency over the bandwidth. The method is based on the extraction of the transistor's non-linear output parameters and the optimisation of a given class E topology to an ideal impedance load. Herein, the method is illustrated by an integrated design using between 2 and 4 GHz and the results of the simulations (in terms of efficiency) agree well with the transient simulation and the S-Parameters optimisation. Considerations are given for the complete development of this design and the interest for future multiband front end designs.

Index Terms -RF architecture, multi-radio, class E PA.

I. THE MULTI-RADIO CONTEXT

Wireless communications are widely used for our daily needs. There are numerous examples which use between 2 and 4 GHz and standard names like BLUETOOTH, WiFi, WiMAX, UMTS and LTE are well-known. An important aspect of today's applications is the increasing data rate need, especially in connectivity standards (WiFi, WiMAX), because of the user's high Quality of Service (QoS) demands. To increase the data rate, we tend to use wideband or multi-standard architecture [START_REF] Baudoin | Radiocommunications Numériques : Principes, Modélisation et Simulation[END_REF] [START_REF] Diet | Flexibility of Class E HPA for Cognitive Radio[END_REF]. The concept of software radio includes a self-reconfigurable radio link. While focusing on the radiofrequency (RF) part, the term multi-radio is preferred. A multi-radio RF device is supposed to use different RF flexible blocks, whose parameters are the centre/carrier frequency, bandwidth, modulation scheme and average power, see figure 1.

figure 1 : Multi-radio front-end challenges

Also, the signal dynamics (represented by the Peak to Average Power Ratio) should not decrease the transmitter's performance. Due to the different PAPRs of the standard signals (OFDM for example), the transmitter has to be linearised, because the power amplifier (PA) introduces crippling non-linear effects (NL) [START_REF] Sokal | Class E, A new Class of high efficiency Tuned switching PAs[END_REF] [START_REF] Diet | EER architecture specifications for OFDM transmitter using a class E PA[END_REF]. The present challenge is to linearise the RF architecture while keeping high efficiency, because this is related to batterylife (especially in our context of nomadic transceiver design). Lots of linearization techniques were proposed [START_REF] Baudoin | Radiocommunications Numériques : Principes, Modélisation et Simulation[END_REF] and recent works made EER/polar-based architecture very popular [START_REF] Diet | Radio Communications Architectures" chapter of Radio Communications[END_REF]. The envelope information can be coded by a Pulse Width Modulation or a Sigma Delta (ΣΔ) process in order to present a constant power property which is beneficial for the architecture efficiency. This coding enables its recombination by a multiplication with the carrier signal, which is modulated by the phase information. This multiplication can be achieved before the PA or by supply modulation, if the PA is in a switched (SW) class [START_REF] Diet | EER architecture specifications for OFDM transmitter using a class E PA[END_REF] such as class D, S, E or F [START_REF] Cripps | Advanced techniques in RF Pas design[END_REF].

As RF blocks are flexible, the size of the transmitter is optimized and the system efficiency is directly dependant on the different configurations. Moreover, a major design challenge is to keep a highly efficient PA for the different bands specified by the standards (carrier frequency and bandwidth). The idea of the front end design is an optimization (frequency sweeping) of a Class E PA. The Class E was chosen for its high efficiency performance and for the small number of reactive components needed, whatever the topology is [START_REF] Cripps | Advanced techniques in RF Pas design[END_REF] As was discussed in [START_REF] Colantino | Multi-band PA architectural solutions[END_REF], PAs for multi-radio can be of three types: (i) broadband, (ii) reconfigurable (for example: [START_REF] Diet | Flexibility of Class E HPA for Cognitive Radio[END_REF]) or (iii) multi-band matching PAs. We present in this paper a simple methodology based on previous studies of Class E and optimisation processing. A slight increase in the number of reactive components can improve the bandwidth of such a PA and drive us to a dual band PA optimisation.

II. PROPOSED DESIGN METHOD

The proposed design method is summarized in figure 2. Once the given transistor and frequency bands are chosen, the idea is to first extract the non-linear (NL) output of the transistor in switched mode of operation, in part one of the method. In that order, we performed a transient simulation where the transistor input voltage implies a hard switching behaviour (a FET is supposed here). This hypothesis is achieved by a closed loop on the gate-tosource voltage that maintains the saturation of device whatever the frequency is, see figure 2. Thanks to this simulation, we calculated the frequency-dependant gate-to-source voltage, and the resulting input power Pin (unmatched case). A Large Signal S-Parameters (LSSP) frequency simulation, including the parametric input power Pin, computes the LSSP output matching coefficient (S22 NL) of the transistor. In part two of the method, we model the real transistor as an ideal switch with its S22 NL (impedance) in parallel: a transistor and a capacitor, as is drawn in figure 2 and confirmed by the Smith chart. This supposes that we consider the unilaterality (S12 = 0).

At this point, we can compute the load facing the ideal switch, made up of the S22 NL, the output network (to be designed) and the antenna, as seen in Figure 2. and [START_REF] Mury | Series-L/Parallel-Tuned Class-E Power Amplifier Analysis[END_REF], we focused on parallel-based topologies with finite DC feed inductor. The ideal load that must face the ideal transistor (the "perfect switch" part) of this type of topology [START_REF] Diet | Flexibility of Class E HPA for Cognitive Radio[END_REF] [START_REF] Mury | Series-L/Parallel-Tuned Class-E Power Amplifier Analysis[END_REF] is Z opt (ω RF ) = 0.8265 R load e j34°, where R load is the reactive part of the antenna (radiating part) and ω RF the centre/carrier frequency. The optimisation process goals are to match the impedance of the circuit (S22 NL + output network + antenna) to the optimal class E load Z opt . We compute the matching coefficient Г classE according to this criteria (50 Ohms is replaced by Z 0 = Z opt = 0.8265 R load e j34°) . Once the optimisation process meets the goals, the network is incorporated into the final transient simulation in order to evaluate the resulting efficiency over the bandwidth.

We applied this method with the model of a MESFET Avago ATF50189 and a designed antenna (Vivaldi type). Results of the S22 NL (Z out ) extraction are reported in Figure 2 (left) and the antenna impedance is drawn in the left, middle smith chart. Three networks are computed: for 2 to 2.5 GHz (LTE, UMTS band), 3.2 to 3.8 GHz (WiMAX) and for both frequency bands. Figure 3 shows the results of the optimisation for the three networks, by computing the matching coefficient Г classE . We reported the result of the final transient simulation only with the network matching both frequency bands. This networks uses one DC feed inductor of 1 nH, two grounded shunt inductors of 1.62 and 2.36 nH, two series capacitors of 0.8 and 0.9 pF and two shunt capacitors of 0.4 and 1 pF. The efficiency and output power are drawn in Figure 3. We notice high theoretical drain efficiency in the range of 90%, corresponding to the goal parameters of our optimisation process. In practice, this will be lowered by the practical loss of the circuit. Maximum efficiencies agree well with matched frequency bands predicted by the S-Parameters simulation.

Drain to source voltages and currents are drawn for 2.3 and 3.5 GHz, in order to demonstrate the class E operation of the amplifier. We notice the negative current due to the importance of the output transistor capacitance (intrinsic) at these frequencies of operation. The drain-to-source voltage is varied from 1 to 3 V and shows the independence of the efficiency and the quasilinear variation of the output power, characterizing the saturation of the transistor. These results are shown in figure 4. It is important to evaluate this efficiency of the dual band PA over the voltage and the frequency because the multi-radio idea implies a power control whatever the signal parameters are.

III. CONCLUSION

We presented a simple methodology for class E efficiency optimisation over frequency. This method helps drive the study of broadband or multi-band PA for multiradio. Results based on a real transistor model reach almost a one octave class E PA with reactive element values in an acceptable range for integrated design. The small number of reactive component is attractive for the design of a dual-band PA, as presented. The possibility of output power variations are simulated for slow (average power) or fast (envelope information) amplitude control. We will extend the number of frequency bands according to multi-radio front end needs.

  [START_REF] Grebennikov | Class E high efficiency PA: Historical aspects and prospects[END_REF] [8][START_REF] Kazimierczuk | Class E tuned PA with shunt inductor[END_REF] [10][START_REF] Mury | Series-L/Parallel-Tuned Class-E Power Amplifier Analysis[END_REF] [12][START_REF] Sokal | Class E, A new Class of high efficiency Tuned switching PAs[END_REF].

Figure 2 :

 2 Figure 2: Proposed design method Based on numerous theoretical developments concerning class E topologies, [13] [12] [7] [8] [9] [10]and[START_REF] Mury | Series-L/Parallel-Tuned Class-E Power Amplifier Analysis[END_REF], we focused on parallel-based topologies with finite DC feed inductor. The ideal load that must face the ideal transistor (the "perfect switch" part) of this type of topology[5] [11] is Z opt (ω RF ) = 0.8265 R load e j34°, where R load is the reactive part of the antenna (radiating part) and ω RF the centre/carrier frequency. The optimisation process goals are to match the impedance of the circuit

Figure 3 :

 3 Figure 3 : Switched mode simulation of the transistor (transient) for three types of NT : (i) single band WiFi, (ii) single band WiMAX and (iii) dual band WiFi/WiMAX with transient drain to source voltage and current at 2.3 and 3.5 GHz. Efficiency (ETA in purple) and Output power (red) are reported on the same figure. Matching coefficient for 50 Ohms (blue) and Zopt (red) are draw with frequency alignment.

Figure 4 :

 4 Figure 4 : Results of transient simulation with the transistor and the optimized dual-band network: efficiency and output power in function of the frequency and for Vds = 1, 2 and 3 V


Fabien Robert

Antoine Diet

Martine Villegas

Epifano Fabio

Cathelin Philippe

Triaire Pascal

Geneviève Baudoin

Architecture

Architecture and Filtering Requirements for Fully Digital Multi-radio Transmitters

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Architecture and Filtering Requirements for Fully

Digital Multi-radio Transmitters F.Robert #*1 , A.Diet ∆ , M.Villegas 2* , F.Epifano # , Ph.Cathelin # , P.Triaire # , G.Baudoin Abstract-This paper gives filtering requirements for an alldigital transmitter and identifies technical and technological challenges. Herein, we highlight trade-offs implied by such a transmitter. This work targets a flexible and low power consumption transmitter, taking into account advantages of submicron CMOS technologies. We focused on a multi-radio transmitter for cellular standards such as GSM, WCDMA and LTE for mobile applications. Simulation results point out the mandatory frequency replicas management caused by upsampling process and the so needed filtering before emission to be dimensioned. Specifications of the filter to be design are given after an overall fully digital architectures study.

I. CONTEXT

For the last years, wireless applications increased their demand on low power consumption and high data rate transfer in the frame of WLAN and WPAN mobile communications. To satisfy this demand, mobile terminals must be able to address different communication standards such as GSM, WCDMA and brand new LTE. The increasing number of cellular standards highlights the challenging development of multi-radio concept, for coexistence constraints. Coexistence implies the transmitter to be able to generate all different standard waveforms without over-sizing and increasing overall power consumption. In multi-radio the goal is to avoid transmitters parallelization, providing the ability to adapt a unique transmitter to several standards. This implies high flexibility at each stage of transmitter architecture. A classical direct conversion transmitter for mobile applications is shown in figure 1. To design such a transmitter we must consider several parameters of the signal. Some parameters depend on the standard itself [1] [2] (and so modulation schemes) like bandwidth, power dynamic or envelope amplitude variation (also known as peak to average power ratio, PAPR). Other parameters directly depend on architecture like spectral purity, linearity or power efficiency. In a coexistence context, in the same terminal, spectral purity is a very important feature since emissions must respect standards limits and limit desensitization of other radio engines.

Theses limits are defined through adjacent channel power ratio (ACPR), adjacent channel leakage ration (ACLR) and transmit cellular spectrum emission masks setting coexistence with connectivity standards RX or duplex FDD cellular reception. Considering WCDMA standard as an example, we must respect at least -33 dBc ACLR1 and -43 dBc ACLR2. Consequently, the architecture in figure 1 leads to use "Digital to Analog Converters" (DAC) with more than 7 bits of resolution at hundred MHz clock rate.

Nowadays sub-micron technologies allow to design challenging solutions at a few GHz rate. Higher sampling frequencies lead to a larger frequency offset between LO and replicas. It then relaxes constraints on filtering key blocks along the signal path.

The goal of this study is to demonstrate the ability and benefit in pushing the Digital to Analog (D/A) frontier towards mixing or even power amplifying blocks. In the following part, we present three kinds of digitally based transmitter architectures. Theses examples are classified depending on their growing digitization degree, from the less digitized to the most digitized.

Then, we study main blocks of an all digital architecture: up-sampling, digital mixing and D/A conversion. Finally, we propose some solutions to improve replicas management due to up-sampling and we specify the most important characteristics of the filtering block.

II. DIGITAL TRANSMITTER ARCHITECTURES

Innovating baseband processors performances and research improvements on high speed DACs lead to integrate more and more transmitter key blocks in the digital domain. In this part we detail the evolution of the digital part in transmitter architectures from baseband toward power amplifier (PA).

A. Digital Mixing Architectures

Mixing is the first block, we can observe after up-sampling stage and FIR-IIR filters in a classical transmitter. The first architecture we present includes the mixing stage in the digital domain. Mixing an up-sampled baseband signal at GHz frequency implies transistors with a high cut-off frequency. Using 90 nm CMOS technology addresses this challenge. The architecture presented [START_REF] Eloranta | A multimode transmitter in 0.13 µm CMOS using direct-digital RF Modulator[END_REF] [4] [START_REF] Eloranta | Direct Digital RF Modulator: a multi-function architecture for a system-independent radio transmitter[END_REF] is based on a classical direct conversion architecture. This architecture is digitized the closest possible to the PA. Frequency synthesis and power amplification stage are still analog blocks in this system. Figure 2 shows this architecture. Digitization of the mixing block limits process imperfections such as biasing path isolation leading to LO (Local Oscillator) leakage. It reduces the importance of using heavy calibration loops and so improves the overall system stability. It also reduces occupied area of the chip. In this architecture, mixing and D/A conversion are operated in a single block, the "RF Digital to Analog Converter" (RFDAC) (figure 2). It is important to note that up-sampling frequency and converter frequency must be chosen so that zeros of the SINC filter function (zero order hold: ZOH) match with baseband signal harmonics due to up-sampling. This architecture can be seen as a basis towards fully digital architectures although it still depends on analog frequency synthesis and power amplification. Power consumption implied by this new block can be highlighted as a drawback. This will be discussed in part III.

B. Digital Mixing and Frequency Synthesis Architecture

The second architecture [START_REF] Pozsgay | A Fully Digital 65nm CMOS Transmitter for the 2.4 to 2.7 GHz WiFi/WiMAX bands using 5.4GHz Sigma Delta RF DACs[END_REF] is also based on direct conversion architecture. It has been developed by a STMicroelectronics team for WiFi/WiMAX signals at 2.4 GHz. Compared to previous architecture many improvements were made. The "Sigma-Delta RFDAC architecture" (figure 3) presents the advantage of using digital blocks from baseband to the PA including an all digital phase lock loop. As in the previous architecture, baseband signal is upsampled with filtering of oversampling replicas through FIR and IIR filters. As an improvement the signal gain control is performed throughout the overall transmission chain. The first power control appears just after up-sampling stage with a 12 dB "low speed" dynamic control. This is done by multiplying IQ signals with a 10 bits control word. A second control "high speed" appears, with an additional range of 18 dB (using 6 dB steps). Until then, the signal is up-sampled to half the desired carrier frequency. MASH multi-bits Σ∆ modulators oversample both I and Q signals to twice the carrier frequency. Sub-microns technologies such as 65 nm CMOS allow this, since we need high speed (5 GHz) multi-bits modulators.

IQ signals are then separated: IQ and I'Q' paths. A delay is applied to I'Q' path. The combination of both mixed IQ and I'Q' after RFDACs generates notches in the spectrum noise shaping area. It helps reducing the TX shaping noise in a close-in RX band. Moreover, an additional 6 dB gain control is possible by shutting down the I'Q' RFDACs. The drawback is the suppression of the advantage of notches. It is possible only if shaping noise is below spurious emission limits in narrow bands.

C. Fully Digital Architecture

The last architecture [START_REF] Vk | A fully digital architecture for wideband wireless transmitters[END_REF] (figure 4) is the most digitized one. The "Digital Quadrature RF Modulator" (DQRM) is based on a digital IQ approach architecture. As well as in [START_REF] Eloranta | A multimode transmitter in 0.13 µm CMOS using direct-digital RF Modulator[END_REF] and [START_REF] Pozsgay | A Fully Digital 65nm CMOS Transmitter for the 2.4 to 2.7 GHz WiFi/WiMAX bands using 5.4GHz Sigma Delta RF DACs[END_REF], IQ signals are up-sampled and filtered. This is done in order to place spectral re-growths (ZOH) far enough from the carrier frequency. This is possible, setting notches at multiples of the oversampling frequency. Two signals are created "abs(I+Q)" and "abs(I-Q)". This two signals are coded through a thermometer coder and alternatively fed at the input of a Digitally-driven Power Amplifier (DPA) at twice the LO frequency. It can be seen as an oversampling by four of the envelope signal. Moreover signs of "I+Q" and "I-Q" are calculated to estimate the phase information, and to create four phases control digital words. Theses words activate at each change of IQ symbol, one of the four 90° phase shifted clock signal at the carrier frequency. Thus, each time IQ symbols change, the phase of the carrier frequency changes. Phase and amplitude are recombined through the DPA comparable to a RFDAC. Taking the example of an 8 bits binary to thermometer coding, this will lead to use 256 pairs of transistors, each providing a unit current source.

Amplitude takes two values at 2 x RF frequency, and the clock alternates positive and negative current sources in the DPA at RF frequency. It results in the following samples at each symbol: abs(I-Q) abs(I+Q) -abs(I-Q) -abs(I+Q). Bandpass filtering at the output helps to restore the initial signal. As we obtain a NZR signal, filtering is less stringent than when using a classical IQ modulator. DPA behaviour will be detailed in part III. This architecture has the advantage of frequency flexibility although up-sampling ratio must be adapted to the carrier frequency. This depends on the targeted band at the emission due to proximity of other RX standards bands. The principal issue in frequency reconfigurability is to find a filtering solution associated to the DPA. It is also well power flexible thanks to the biasing of each unit current source transistor. In [START_REF] Vk | A fully digital architecture for wideband wireless transmitters[END_REF] an example is given at 5.8 GHz for a WiMAX signal of 10 MHz (64-QAM) which is very tough. Resulting spectrum re-growths in theses conditions are less than -50 dBc/Hz.

III. KEY FUNCTIONS OF A DIGITAL TRANSMITTER

This paragraph will detail the main functions we have to deal with in the design of a fully digital transmitter. These are the digital up-sampling stage, and the digital mixing D/A conversion and power amplification stage.

A. How up-sampling impacts on filtering?

Every partially or fully digital transmitter has an upsampling stage to increase SNR before carrier mixing. As we show below a trade-off must be done between up-sampling frequency, IQ quantization number of bits and post mixing filtering. Up-sampling replicas appear in the spectrum. We can define a ratio (UF) between Transmit frequency (F RF ) and up-sampled baseband frequency (F upsampling ). As an illustration of number of bits impact on close band noise, the architecture was simulated using 7 bits (red) and 15 bits (blue) resolution for IQ. In the case of a GSM 900 signal replicas level decreases to -81 dBc which is lower than the standard requirements of -69 dBc. In a multi-radio context large bandwidth standards (LTE, WCDMA) will be a constraint over replicas level.

This table shows the impact of up-sampling on spurious emission at a frequency offset corresponding to F upsampling . As a second step we simulate the impact on close band noise while moving quantization resolution from 5 to 15 bits. On figure 5, we plot a comparison of architecture signal output spectrum between 7 bits and 15 bits resolutions to observe the impact in quantization number of bit. Looking at figure 6, we observe a reduction of close noise level as the number of bits increases. It exists some solutions to artificially increase signal resolution up to 13 bits [START_REF] Vk | All Digital Quadrature Modulator Based Wideband Transmitters[END_REF]. Finally the third mean leading to an optimisation of replicas is the ratio UF between F RF and F upsampling . The higher is F upsampling , the lower is UF and further apart are replicas, thus relaxing filtering.

Sub-micron technology now helps to up-sample at hundred MHz rates. Simulations were done to estimate performances while increasing F upsampling (case of GSM 900), and are reported in figure 7. As UF decreases, replicas are pushed away from the emission band. This helps to reduce complexity of the final filtering stage. Looking at each TX band spectrum emission mask, we must be careful with spurious emissions that could desensitize Rx band (FDD case) and also other standards Rx such as GPS in the same terminal.

The most stringent coexistence band is the GPS limiting emissions of other standards to -168 dBm/Hz. To be sure every replica is filtered enough we have to characterize the worst case. Our simulations showed the worst case (if UF=10) is for WCDMA TX band 4 with 66dB attenuation needed at 129MHz from the carrier. This is quite difficult to obtain, so we need to optimize replicas placement in spectrum to relax filtering constraints. This will be detail in part IV.

B. Digital to analog mixing toward power amplification

As the signal is up-sampled at the right frequency to minimize level of replicas, it must be mixed around the carrier. This digital signal must be D/A converted using DACs of at least 7 bits resolution (see previous paragraph). In fully digital transmitter this two steps can be done in the same block using an RFDAC [START_REF] Eloranta | A multimode transmitter in 0.13 µm CMOS using direct-digital RF Modulator[END_REF]

[4][5][6] .
The principle is the parallelization of weighted or unit Gilbert cells activated by the amplitude signal codeword. The data is coded by an N-bits word depending on the expected DAC resolution. Figure 8 represents an example for a 4 bits coded signal. At the LO rate, switches activate the parallelized unit cells, providing unit current sources depending on the codeword. Final current is then proportional to amplitude level of I or Q up-sampled signal. The linearity and the resolution of the signal increase as parallelized cells increase. Parallelization smooths IQ imbalance and results from the average cells imbalances. Power control of the structure can be done by a variation on the bias current, resulting in a reduced output current of each unit cell. Some realizations show 9 bits RFDAC able to perform 45 dB power control [START_REF] Vk | A fully digital architecture for wideband wireless transmitters[END_REF].

RFDAC design depends on the kind of signal to transmit. In nowadays cellular context we transmit high PAPR signals in HSUPA (7.3 dB on RF, 9.6 dB on IQ path) so we need to adapt current cells weight. As an example if baseband signal is on 10 bits, the 4 LSB bits are coded into a 16 values thermometer code to control 16 unit current (I) cells. On the other side the 6 MSB are coded into a 64 values thermometer codeword to drive the 64 weighted (16 x I) current cells. A major issue of RFDAC is the RF power they are able to provide. If targeting standards such as GSM, transmitter must emit up to 33dBm. Recent work [START_REF] Gutierrez | A 1.4GS/s 9-bits 45dB Power Control RFDAC for Digital Radio Transmitters[END_REF] shows RFDAC providing a maximum of 2.7 dBm. This introduces the question of how providing more power while keeping advantages of RFDACs.

The concept of DPA for Digital Power Amplifier appears. This can be seen as a digitally modulated PA. Instead of parallelizing current cells, DPA parallelizes unit PAs. Depending on an amplitude codeword, amplifiers are fed by the phase modulated signal to be amplified. The maximum power obtained with this solution, reaches 25 dBm peak [START_REF] Pornpromlikit | A 25-dBm High-Efficiency Digitally Modulated SOI CMOS Power Amplifier for Multi-standard RF Polar Transmitters[END_REF]. A weakness of this concept is to dynamically match the DPA impedance with the antenna load while switching unit PAs (load pull effect).

IV. IMPROVEMENT

In the previous paragraph we showed two main drawbacks of fully digital transmitters. First one is the quantization noise close to the emission bandwidth, second are replicas due to up-sampling. At less than Fupsampling offset from TX band, the most limiting factor is the quantization noise polluting RX band. This can be corrected by increasing the number of bits up to 7 to satisfy at least -90 dBc as presented in figure 6. At more than Fupsampling from TX band, main spurious contributors are replicas from up-sampling. From this hypothesis we first evaluate filtering requirements, trying to respect both WCDMA and LTE spectrum emission masks. DQRM architecture was simulated assuming an output power of 10dBm which is the targeted power in nowadays fully digital architecture. We show below on table II, requirements at the antenna for the two most stringent bands (band 1 and 4). Band 4 is very stringent due to GPS band. For the replicas not to desensitize simultaneously operating receivers, we must set replicas power level at the minimum power level admitted in theses bands. If looking at band 1 we must be careful to set out of band emissions to target a maximum level of -140 dBc/Hz in own FDD cellular Rx band and -125.8 dBm/Hz spurious emission level at antenna elsewhere. If transmitting WCDMA with UF=10, this leads to a 29 dB filtering at 40MHz from the carrier frequency. Looking at band 4, to respect co-existence with GPS band (-168 dBm/Hz) we must assure a 66 dB filtering at 129 MHz from the carrier. This is very difficult to implement.

This implies very stringent and quite impossible filtering at the output of the architecture before the last stage of power amplification. Assuming that the most limiting parameters for replicas power level are other standards Rx bands we can imagine a replicas management process. The main idea is to evaluate the optimal up-sampling frequency for each cellular Tx band avoiding to place replicas in other standards Rx bands. Thus replicas power levels are only defined by the spectrum emission mask of the emitted standard. Below on figure 9 is represented the example of LTE band 1 using a 5 MHz bandwidth. We have chosen a clever up-sampling frequency placing the first replica far from band 33 and just below the GPS band thus drastically reducing filtering requirements. The same process was applied to all cellular standards Tx band. As we must keep in mind that this architecture has to be designed we choose optimal up-sampling frequencies that are integer multiples of dedicated carrier frequency. This leads to re-evaluate the previous table filtering requirements. Looking at band 1 and 4 WCDMA the most difficult case is to obtain 23 dB attenuation at 360 MHz from LO. Now we can define a precise filter design goal to achieve requirements for every cellular Tx standard considering all digital transmitter architecture. Moreover if we want to address all theses bands, we must have a certain frequency tuning agility. We can split the problem in two different agile filters. The first one would address low frequencies from 698 MHz to 915 MHz (bands 5, 8, 12, 13, 14, 18, 19) and the second would address high frequencies from 1710 MHz to 1980 MHz (bands 1, 2, 3, 4, 9, 10).

For both filters goal were set as follow:

-23dB attenuation at 360MHz from center frequency -3dB bandwidth of at least 60MHz First obtained results in filtering topologies synthesis leads us to use high quality factor elements (Q > 500).

V. FUTURE WORKS In the multi-radio context, we identified some limitations if using fully digital transmitter architectures for cellular standards. We demonstrated some keys to meet cellular standards requirements.

This can be achieved if respecting above given system specifications and filtering requirements. This method can be applied for all fully digital architectures since replicas management is a global issue for this kind of architecture. In our cellular multi-radio context the most challenging specifications to address are high resolution DACs at GHz frequencies and architecture output filtering. Managing replicas level through a clever choice in up-sampling frequency help to relax filtering specifications.

We showed the most challenging case for WCDMA Transmit band 4 (23 dB attenuation need at 360 MHz from LO) using a 7 bits resolution. After these simulated results, a solution is currently in development for reconfigurable high band and low band filters addressing Transmit bands from LTE band 12 (698 MHz) to WCDMA band 1 (1980 MHz) using high Q elements.

Fig. 1

 1 Fig. 1 Classical direct conversion transmitter This transmitter architecture can be split into three different areas: digital baseband, analog baseband to RF and analog RF front-end. In this study we consider a cellular multi-radio

Fig. 2

 2 Fig. 2 Digital mixing architecture

Fig. 3

 3 Fig. 3 Sigma-Delta RFDAC architecture

Fig. 4

 4 Fig. 4 DQRM architecture

  Several parameters related to the architecture and signal affects replicas behaviour. These are the signal bandwidth, the up-sampling factor and the number of bits used to quantify I and Q signals.

Figure 5

 5 illustrates the spectrum obtained at the output of an all digital architecture. Signal is a 20 MHz LTE (64-QAM) at F RF =2 GHz. Up-sampling frequency is set to 200MHz.

Fig. 5

 5 Fig. 5 All digital architecture output spectrum We observe in this figure notches at the centre of replicas frequencies implied by the convolution of signal with SINC² interpolation function of the up-sampler (ZOH). The lower the signal bandwidth, the lower are replicas level. We made simulation for LTE 20, 10 and 5 MHz bandwidth (still 2 GHz F RF and UF = 10).

Fig. 6

 6 Fig. 6 Impact of IQ resolution on Tx band close noise

Fig. 7

 7 Fig. 7 Impact of up-sampling frequency on replicas level

Fig. 8

 8 Fig. 8 RFDAC example

Fig. 9

 9 Fig. 9 Spurious Emission Mask for 5MHz LTE band 1 versus DQRM Tx Spectrum at 10dBm output power (normalized in dBm/Hz)

TABLE . I

 . Impact of signal bandwidth on replicas level

	Signal Bandwidth	1st replicas (dBc)	2 nd replicas(dBc)
	20MHz	-33,7	-39,8
	10MHz	-40,4	-46,4
	5MHz	-47,7	-53,4

TABLE . II

 . Filtering requirements at antenna function of UF

TABLE . III

 . Filtering requirements at antenna after replicas management for the same study case


Antoine Diet
email: antoine.diet@lss.supelec.fr

Ajib Bahi
email: a.bahi@esiee.fr

Martine Villegas
email: m.villegas@esiee.fr

Geneviève Baudoin
email: g.baudoin@esiee.fr

Class E dual band PA performances with PAPR repartition in the context of nomadic multi-radio architecture

Keywords: RF architectures, multi-radio, class E PA

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. NOMADIC MULTI-RADIO FRONT END

Due to the user increasing demand in high data rate and mobility, some concept such as cognitive radio are attractive and promising in wireless communications. Nowadays, the context of cognitive radio includes nomadic communications and the adaptability to any specifications of cellular and connectivity standards such as UMTS, LTE, WiMAX, WiFI and so on. This flexibility of "the RF part" in a transceiver is known under the concept of "multi-radio", and drives it to consider the design of a transmitter that must:

-Adapt to any of the modulation schemes (power or spectral efficient modulation). Orthogonal Frequency Division Multiplex (OFDM) is a good representative of high data rate wideband signals used (ex. WiMAX and WiFI).

-Provide different bandwidths and carrier frequencies, in the idea of opportunism spectrum allocation (1 to 100 MHz).

-Present a low average efficiency, due to the interest in battery lifetime. This is mandatory for the transmitter part where the Power Amplifier (PA) is responsible for a major part of the current consumption.

-Guarantee the linearity of the transmitter whatever the modulation, bandwidth, mean power and carrier frequency are. This includes power scale-ability, because the transmitter is not supposed to operate at its maximum power all the time. In fact, it is often necessary to operate at a lower level.

-Do not produce crippling spectral re-growths that could disturb other transceivers (co-existence). This implies a severe filtering selectivity at the different "carrier frequency and bandwidth" possibilities.

Herein, we focus on the design of the transmitter front-end for the above-mentioned goals of the multi-radio. The challenge of such a transmitter is to provide the enumerated requirements while realizing frequency transposition, power amplification and filtering before feeding the antenna. The front-end must adapt to any characteristic of the signal, for example the amplitude variation. This variation can be slow for average power control or fast, for dynamic amplitude information (also called dynamic envelope information). The PAPR (Peak to Average Power Ratio) characterizes the importance of the signal dynamic for a given modulated signal. For example, the PAPR in the case of OFDM signal can reach more than 10 dB, depending on the number of subcarriers [START_REF] Robert | Study of a polar ∆Σ transmitter associated to a high efficiency switched mode amplifier for mobile Wimax[END_REF].

High PAPR causes crippling non-linearities at the PA stage. This is a difficulty that implies linearization techniques (feedback, feed-forward, pre-distortion) or linear architecture (Envelope Elimination and Restoration EER, Envelope Tracking/Following ET, LINC, CALLUM…) [START_REF] Kahn | Single Sideband Transmission by Envelope Elimination and Restoration[END_REF]. Polar based linear architectures, such as EER and ET, have known a great success these years with the challenging possibilities of reducing the PAPR by envelope coding (PWM, Σ∆) [START_REF] Choi | A Σ∆ digitized polar RF transmitter[END_REF] [START_REF] Nielsen | Transmitter Architecture Based on ∆Σ Modulation and Switch-Mode PA[END_REF]. In such architecture, the use of a switched high efficiency PA is interesting for an efficiency maximization of the amplification, and the coded envelope can provide the necessary constant power signal for driving such PAs [START_REF] Choi | A Σ∆ digitized polar RF transmitter[END_REF][13][14] [START_REF] Robert | Study of a polar ∆Σ transmitter associated to a high efficiency switched mode amplifier for mobile Wimax[END_REF] [START_REF] Suarez Peñaloza | Influence of the Envelope coding on a Class E Amplifier Efficiency in Polar Architecture[END_REF]. The efficiency of such architecture is favored by the choice of a switched PA in class E, whose theory has been studied in [START_REF] Sokal | Class E, A new Class of high efficiency Tuned switching PAs[END_REF]

[3][4][5][6][7][8][9][10].
These solutions show a new technical lock that is filtering requirement. Due to the important spectral re-growths generated by the envelope coding (still remaining after the amplification), the overall efficiency is impacted by its coding efficiency and need a mandatory filtering, to respect standards requirements [START_REF] Robert | Study of a polar ∆Σ transmitter associated to a high efficiency switched mode amplifier for mobile Wimax[END_REF]. This results in a linear but not so efficient solution. The multi-radio front-end must be designed with the idea of a reconfigurable and/or multiple pass-band profile (multi-band) while power amplification is performed [START_REF] Colantino | Multi-band PA architectural solutions[END_REF][15] [START_REF] Diet | A Methodology for multi-band class E RF PA design[END_REF]. Our idea is to demonstrate the feasibility of managing high PAPR signal for suitable multi-radio frontend: high average efficiency, linearity and multi-band possibility. We present in the part II of this paper the design of a dual-band PA in class E, following a sub-optimal design method, whose principle was presented in [START_REF] Diet | A Methodology for multi-band class E RF PA design[END_REF]. The technology at these frequencies is integrated because we choose a transistor in the idea to adapt to LTE (2-2.2 GHz) and WiMAX (3.6 -3.8 GHz). Signals of such standards are typically OFDM, and that is why the power scale-ability is studied in part III (slow and fast variation) by supply or driving signal amplitude variation.

The novelty of this paper is to demonstrate the efficient amplification of amplitude information (modulated signal) with a switched mode PA (class E), at two frequency bands of interest. The methodology used can be extended for multiple bands of operation and the importance of PAPR repartition (supply and driving signal) is underlined as a new way of optimization in polar based architectures.

II. DUAL-BAND CLASS E PA: NEW METHOD AND DESIGN

The design of the dual-band PA is based on the methodology exposed in [START_REF] Diet | A Methodology for multi-band class E RF PA design[END_REF], as figure 1 resumes the different steps: by defining the power capability of the transistor and extracting the major part of its output nonlinearities, a sub-optimum design in frequency is possible, if the output network has sufficient degrees of freedom (number of L and C). The efficiency is computed in transient simulation by extracting the real power dissipated by the transistor and delivered to the load. Herein, the load is simulated with wideband antenna measurements (Vivaldi type designed for 1.8 to 6 GHz) as in [START_REF] Diet | A Methodology for multi-band class E RF PA design[END_REF]. This method takes into account the transistor switching limit, and its output non-linear behavior, rather than idealizing it. As the hard switching is difficult in practice, we worked with integrated transistor model, here the AVAGO ATF 50189. This component can be scaled for 0.3W in switched mode, due to the class E factor of use which is 10.1816 (peak drain current/voltage, 3.56*2.86 [2][4]). Taking into account the maximum drain-to-source voltage of almost 10V, we supplied the drain with V DC = 3V. This yields to a DC current of I DC = 0.1 A, and a "supply resistance" R DC = 30 Ohms. The optimum resistance for the load is R load = 16.8 Ohms [START_REF] Raab | Idealised operation of the class E tuned PA[END_REF]. We scaled the loading network input impedance with this value of R load . Once these parameters fixed, we performed a transient simulation where the transistor is hardly switched and identified the driving power in function of the frequency, P in (f). With P in (f), we simulated a Large Signal S-Parameters (LSSP) simulation in order to extract the major contribution of transistor output non-linearity: S 22 NL, as the principle is drawn in figure 3. Figure 2 represents the following step of "network optimization", with the integration of the antenna load measurements and S 22 NL. The optimization goal is to present the optimal load impedance at the LTE and WiMAX bands while rejecting other spectral components for linearity improvements (high impedance, helping in filtering the signal [START_REF] Raab | Idealised operation of the class E tuned PA[END_REF][9] [START_REF] Diet | A Methodology for multi-band class E RF PA design[END_REF]). The criterion used is the matching coefficient, modified for the optimal class E load value rather than 50 Ohms, see [START_REF] Kahn | Single Sideband Transmission by Envelope Elimination and Restoration[END_REF]. Optimization results are draw in figure 2, where G ADAPT shows two bands of class E mode of operation. The optimized network is reintroduced in a transient simulation where the transistor is hardly switched at different frequencies, in order to evaluate the class of operation and performance. Figure 3 summarizes the topology used for the PA, and results reported for drain voltage and drain current showed typically switched mode load line behavior. Imperfections in the switching trajectory are due to the intrinsic S 22 NL of the transistor: mainly non-linear C DS and R DS . At the two wanted frequency bands, the class E "drain waveforms" are observed and the efficiency is reported on figure 4.

Transient simulations are processed with sinusoidal and square signal. Results are reported on figure 4 where real powers (mean of voltage*current) dissipated in the transistor and delivered to the antenna are computed in the two cases.

Also the input power is computed for evaluating the PAE (Power Added Efficiency). Figure 4 demonstrates that high efficiency (80 to 90%) can be reach in the two wanted bands of operation, and that the 0.3W targeted power is attained. The PAE is interestingly high at the same frequencies. This part has shown that it is possible to design a "dual-band profile" class E PA. Next part will focus on the amplitude modulation possibilities.

III. PAPR REPARTITION

The PAPR causes crippling non-linearity (PA) without a linearization process. This is the challenging lock in the design of front-end for multi-radio because we want a high average efficiency and linearity at the same time. To explore the amplitude modulation possibilities of our dual band PA, we swept the supply drain voltage (Vds) and the high level of the switching driving signal (command signal on Vgs). Results are reported in figure 5 Figure 5 showed an important dependency of the output power with Vds and Vgs (VHI is the maximum value of Vgs). The efficiency is less sensitive with Vds variation, as the transistor is highly saturated. VHI reduction drives it to an important decrease in efficiency and we can identify a limit of the transistor switching behavior around VHI = 0.6 V. In the idea of PAPR repartition, the amplitude modulation can be done on both voltages, but Vgs will affect more the efficiency performance than Vds. These simulations were DC variations, and we introduced, in a second step, sinusoidal modulation on both Vds and Vgs signals. These variations are about 100 MHz for Vgs and 60 MHz for Vds, representing a potential signal bandwidth. Figure 6 shows the variations at the two frequencies (LTE/WiMAX) and its resulting amplitude information delivered to the load (top). Also the spectrum of figure 6 shows that the only spectral re-growth to deal with is the second harmonic. Efficiencies (drain and PAE) are computed for modulated signals with the same parameters, at different carrier frequencies. Figure 7 shows performance of 60 to 70% drain efficiency, attained by the dual-band PA for amplitude modulated signal. The ability to restore an amplitude modulation by supply modulation and/or driving signal modulation has been explored for our high efficient dual band class E PA. Efficiencies computed are promising for the use of such structures in multi-radio front-ends (50 % PAE).

IV. CONCLUSION AND PERSPECTIVES

A dual-band class E PA for multi-radio applications has been studied and showed its ability to amplify efficiently modulated signal at two frequency bands of interest, with the same device. The design methodology enables this type of PA to be used in multi-radio architectures, characterised by important PAPR, while considering good performances in output power, efficiency, and power control.

These new results allow to reconsider the transmitter architectures design approaches and give a possibility to solve the tricky problem of power emission in multi-standards or multi-radio.

  OPTIMISATION, With Z opt (R load ) Simulation of the transistor in switched mode over the bandwidth and computation of the corresponding input power (transient) Characteristics Vgs, Ids, Vds of the transistor R load and P RF Definition of the gate voltage for switched mode at each frequency Pin Simulation in fct(Pin) Large Signal S-Parameter (LSSP) S22 Extraction of S22, and definition of a LC topology, loaded by the antenna. (S-Parameter) Simulation of the optimum LC network with the transistor in switched mode (transient simulation). Computation of the efficiency and FOM. OPTIMISATION, With Z opt (R load ) Simulation of the transistor in switched mode over the bandwidth and computation of the corresponding input power (transient) Characteristics Vgs, Ids, Vds of the transistor R load and P RF Definition of the gate voltage for switched mode at each frequency Pin Simulation in fct(Pin) Large Signal S-Parameter (LSSP) S22 Extraction of S22, and definition of a LC topology, loaded by the antenna. (S-Parameter) Simulation of the optimum LC network with the transistor in switched mode (transient simulation). Computation of the efficiency and FOM.

Fig. 1 :

 1 Fig. 1 : Methodology for class E multi-band design[START_REF] Diet | A Methodology for multi-band class E RF PA design[END_REF]

Fig. 2 :

 2 Fig. 2 : Optimization of loading network, with extraction of transistor S22NL, polarization inductance and antenna load. Resulting GADAPT.

Fig. 3 :

 3 Fig. 3 : Topology of the dual-band PA and simulated dynamic load line

Fig. 4 :

 4 Fig. 4 : Real power for sinus and square driving signal (top) and drain/PAE efficiency (bottom).

F1 = 2 Fig. 5 :

 25 Fig. 5 : At F1 and F2, variation of Vds (4 top figures) and Vgs (4 bottom figures). Real power (in, RF, dissipated) and efficiency results.

Fig. 6 :

 6 Fig. 6 : Dynamic modulation of Vgs (100 MHz) and Vds (60 MHz) for F1 and F2. Spectrum at F2 (bottom) with and without modulation

in Real power in Watt Efficiency

		1 .1 1 .1	Real power in Watt
		1 .0 1 .0		P DISS P DISS
		0 .9 0 .9
		0 .8 0 .8
	PRF PRF	0 .5 0 .6 0 .7 0 .5 0 .6 0 .7								P RF P RF
		0 .4 0 .4
		0 .2 0 .3 0 .2 0 .3						P in P
		0 .1 0 .1
		0 .9 1 .0 0 .0 0 .9 2.0E9 Efficiency 2.2E9 2.4E9 1 .0 2.2E9 2.4E9 2.0E9 0 .0	2.6E9 2.6E9	2.8E9 2.8E9	3.0E9 3.0E9	3.2E9 3.2E9	3.4E9 3.4E9	3.6E9 3.6E9	3.8E9 3.8E9	4.0E9 4.0E9
		0 .8 0 .8								η η η η η η η η
		0 .6 0 .7 0 .6 0 .7					square square		η η η η PAE η η η η PAE
		0 .5 0 .5
		0 .4 0 .4
		0 .3 0 .3						sinus sinus
		0 .2 0 .2
		0 .1 0 .1	2.0E9 2.0E9	2.2E9 2.2E9	2.4E9 2.4E9	2.6E9 Frequency in GHz 2.8E9 3.0E9 3.2E9 3.4E9 2.6E9 2.8E9 3.0E9 3.2E9 3.4E9 Frequency in GHz	3.6E9 3.6E9	3.8E9 3.8E9	4.0E9 4.0E9

  .

	Pdiss Pdiss Pdiss	PRFin PRFin PRFin	PRF PRF PRF	0.10 0.15 0.20 0.25 0.30 0.35 0.35 0.35 0.10 0.15 0.20 0.25 0.30 0.10 0.15 0.20 0.30 0.25	F1 = 2.1 GHz							ETA_PAE ETA_PAE ETA_PAE	ETA ETA ETA	0.7 0.8 0.9 1.0 1.0 1.0 0.7 0.8 0.9 0.9 0.7 0.8	F1 = 2.1 GHz
							0.05 0.05 0.05																		0.6 0.6 0.6
							0.00 0.00 0.00																		0.5 0.5 0.5
								0.6 0.6 0.6	0.8 0.8 0.8	1.0 1.0 1.0	1.2 1.2 1.2	1.4 1.4 1.4	1.6 1.6 1.6	1.8 1.8 1.8	2.0 2.0 2.0	2.2 2.2 2.2	2.4 2.4 2.4	2.6 2.6 2.6	2.8 2.8 2.8	3.0 3.0 3.0				0.6 0.6 0.6	0.8 0.8 0.8	1.0 1.0 1.0	1.2 1.2 1.2	1.4 1.4 1.4	1.6 1.6 1.6	1.8 1.8 1.8	2.0 2.0 2.0	2.2 2.2 2.2	2.4 2.4 2.4	2.6 2.6 2.6	2.8 2.8 2.8	3.0 3.0 3.0
							0.6 0.6 0.6																			1.0 1.0 1.0
							0.5 0.5 0.5	F2 = 3.6 GHz												0.9 0.9 0.9	F2 = 3.6 GHz
	Pdiss Pdiss Pdiss	PRFin PRFin PRFin	PRF PRF PRF	0.2 0.3 0.4 0.2 0.3 0.4 0.2 0.3 0.4															ETA_PAE ETA_PAE ETA_PAE	ETA ETA ETA	0.7 0.8 0.7 0.8 0.7 0.8
							0.1 0.1 0.1																			0.6 0.6 0.6
							0.0 0.0 0.0																			0.5 0.5 0.5
							0.6 0.6 0.6	0.8 0.8 0.8	1.0 1.0 1.0		1.2 1.2 1.2	1.4 1.4 1.4	1.6 1.6 1.6	1.8 1.8 1.8	2.0 2.0 2.0	2.2 2.2 2.2	2.4 2.4 2.4	2.6 2.6 2.6	2.8 2.8 2.8	3.0 3.0 3.0				0.6 0.6 0.6	0.8 0.8 0.8	1.0 1.0 1.0	1.2 1.2 1.2	1.4 1.4 1.4	1.6 1.6 1.6	1.8 1.8 1.8	2.0 2.0 2.0	2.2 2.2 2.2	2.4 2.4 2.4	2.6 2.6 2.6	2.8 2.8 2.8	3.0 3.0 3.0
															VdsDC VdsDC VdsDC										VdsDC VdsDC VdsDC
							0.35 0.35 0.35																			1.0 1.0 1.0
	Pdiss Pdiss Pdiss	PRFin PRFin PRFin	PRF PRF PRF	0.05 0.10 0.15 0.20 0.25 0.30 0.05 0.10 0.15 0.20 0.25 0.30 0.05 0.30 0.10 0.25 0.15 0.20	F1 = 2.1 GHz								ETA_PAE ETA_PAE ETA_PAE	ETA ETA ETA	0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8	F1 = 2.1 GHz
							0.00 0.00 0.00																			0.0 0.0 0.0
							0.6 0.6 0.6	0.40 0.40 0.40		0.45 0.45 0.45		0.50 0.50 0.50	0.55 0.55 0.55	0.60 0.60 0.60	0.65 0.65 0.65	0.70 0.70 0.70	0.75 0.75 0.75	0.80 0.80 0.80				1.0 1.0 1.0	0.40 0.40 0.40	0.45 0.45 0.45	0.50 0.50 0.50	0.55 0.55 0.55	0.60 0.60 0.60	0.65 0.65 0.65	0.70 0.70 0.70	0.75 0.75 0.75	0.80 0.80 0.80
							0.5 0.5 0.5	F2 = 3.6 GHz												0.8 0.9 0.8 0.9 0.8 0.9	F2 = 3.6 GHz
	Pdiss Pdiss Pdiss	PRFin PRFin PRFin	PRF PRF PRF	0.2 0.3 0.4 0.2 0.3 0.4 0.2 0.3 0.4															ETA_PAE ETA_PAE ETA_PAE	ETA ETA ETA	0.4 0.5 0.6 0.7 0.4 0.5 0.6 0.7 0.4 0.5 0.6 0.7
							0.1 0.1 0.1																			0.2 0.3 0.2 0.3 0.2 0.3
							0.0 0.0 0.0																			0.1 0.1 0.1
							0.40 0.40 0.40		0.45 0.45 0.45	0.50 0.50 0.50	0.55 0.55 0.55	0.60 0.60 0.60	0.65 0.65 0.65	0.70 0.70 0.70	0.75 0.75 0.75	0.80 0.80 0.80				0.40 0.40 0.40	0.45 0.45 0.45	0.50 0.50 0.50	0.55 0.55 0.55	0.60 0.60 0.60	0.65 0.65 0.65	0.70 0.70 0.70	0.75 0.75 0.75	0.80 0.80 0.80
															VHI VHI VHI											VHI VHI VHI

Drain and PAE average efficiencies for modulated signals

		0.8
		0.7
		0.6
	ETA	0.4 0.5
		0.3
		0.2
		0.1
		2.0E9	2.2E9	2.4E9	2.6E9	2.8E9	3.0E9	3.2E9	3.4E9	3.6E9	3.8E9	4.0E9
						VgsFREQ
	Fig. 7 :