Phase Predistortion of a Class-D Outphasing RF Amplifier in 90 nm CMOS Jonas Fritzin, Ylva Jung, Per Niklas Landin, Peter Handel, Martin Enqvist and Atila Alvandpour Linköping University Post Print N.B.: When citing this work, cite the original article. ©2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Jonas Fritzin, Ylva Jung, Per Niklas Landin, Peter Handel, Martin Enqvist and Atila Alvandpour, Phase Predistortion of a Class-D Outphasing RF Amplifier in 90 nm CMOS, 2011, IEEE Transactions on Circuits and Systems - II - Express Briefs, (58), 10, 642-646. http://dx.doi.org/10.1109/TCSII.2011.2164149 Postprint available at: Linköping University Electronic Press http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-71781 1 Phase Predistortion of a Class-D Outphasing RF Amplifier in 90nm CMOS Jonas Fritzin, Student Member, IEEE, Ylva Jung, Per Niklas Landin, Student Member, IEEE, Peter Händel, Senior Member, IEEE, Martin Enqvist, Member, IEEE, and Atila Alvandpour, Senior Member, IEEE Abstract—This paper presents a behavioral model structure and a model-based phase-only predistortion method suitable for outphasing RF amplifiers. The predistortion method is based on a model of the amplifier with a constant gain factor and phase rotation for each outphasing signal, and a predistorter with phase rotation only. The method has been used for EDGE and WCDMA signals applied to a Class-D outphasing RF amplifier with an on-chip transformer used for power combining in 90nm CMOS. The measured peak power at 2 GHz was +10.3 dBm with a drain efficiency and power-added efficiency of 39 % and 33 %, respectively. For an EDGE 8-PSK signal with a phase error of 3 ◦ between the two input outphasing signals, the measured power at 400 kHz offset was -65.9 dB with predistortion, compared to -53.5 dB without predistortion. For a WCDMA signal with the same phase error between the input signals, the measured ACLR at 5 MHz offset was -50.2 dBc with predistortion, compared to -38.0 dBc without predistortion. Index Terms—outphasing, CMOS, amplifier, linearization. I. I NTRODUCTION T O meet the increasing demand for higher data rates, wireless systems target larger bandwidths and higher bandwidth efficiency. For more efficient use of the limited frequency spectrum, non-constant envelope modulation schemes are used, which require high linearity in the transmitter circuits in order to comply with spectral and modulation requirements. To benefit from the CMOS scaling in terms of power consumption and silicon area, a highly “digital” transmitter is desirable in the development of mobile multistandard RF transceivers . Potential solutions are the polar transmitter, shown for EDGE , and the outphasing transmitter . In the outphasing transmitter, the original non-constant envelope-modulated signal is used to create two constantenvelope signals, separately amplified by two highly efficient switched amplifiers, like Class-D, and then recombined in a power combiner. In practice the two amplifier stages and signals will experience gain and phase imbalances, creating nonlinearities and spectral distortion . Previous predistortion methods of RF power amplifiers (PA) include modelManuscript received February 2, 2011; revised April 29, 2011; accepted July 8, 2011. This work has been supported by the Swedish Foundation for Strategic Research (SSF), the Excellence Center at Linköping-Lund in Information Technology (ELLIIT), the Swedish Research Council (VR), and Ericsson Research, Kista, Sweden. This paper was recommended by Associate Editor Gwee Bah Hwee. J. Fritzin, Y. Jung, M. Enqvist, and A. Alvandpour are with the Department of Electrical Engineering, Linköping University, SE-581 83 Linköping, Sweden, phone: +46(0)13-282671, e-mail: firstname.lastname@example.org. P.N. Landin and P. Händel are with the Signal Processing Lab, ACCESS Linneaus Center, Royal Institute of Technology, Stockholm, Sweden, and with the Center for RF Measurement Technology, University of Gävle, Sweden. P.N. Landin is also with the Dept. ELEC, Vrije Universiteit Brussel, Belgium. based predistorters using model structures such as Volterra series , parallel Hammerstein structures , or look-up tables , which also can be made adaptive . With the increased interest in linearized switched amplifiers, like the outphasing amplifier, suitable amplifier models and predistortion methods are necessary. A number of methods have been presented, but only a few have been verified in measurements. Phase-predistortion was evaluated for Chireix combiners in simulations and by using signal generators in measurements (no PA was used) . A gain/phase imbalanceminimization technique was verified in measurements in , and predistortion was used for high power devices in . In , the predistorter separately compensates for gain and phase imbalances, where the gain imbalance is eliminated by changing the amplitudes of the input outphasing signals. The gain imbalance can also be eliminated by adjusting the voltage supplies in the output stage . This paper presents a behavioral model structure and a model-based phase-only predistortion method suitable for outphasing RF amplifiers. The predistorter proposed in this paper compensates for both amplitude and phase distortion by changing only the phases of the two input outphasing signals. The proposed predistortion method has been used for EDGE and WCDMA signals applied to a Class-D outphasing RF amplifier with an on-chip transformer used for power combining in 90nm CMOS. The predistortion method is applicable at the baseband level and has not been implemented in hardware. The outline of the paper is as follows. In Section II, the outphasing concept is explained. In Section III, the behavioral model and the phase predistortion method are described. The implemented amplifier is described in Section IV. In Section V, the measured RF performance and the performance for modulated signals with and without phase-predistortion are presented. In Section VI, the conclusions are provided. II. O UTPHASING C ONCEPT Fig. 1(a) shows the outphasing concept, where a nonconstant envelope-modulated signal s(t) = r(t)ejα(t) = rmax cos(ϕ(t))ejα(t) , 0 ≤ r(t) ≤ rmax (1) where rmax is a real-valued constant, is used to create two constant-envelope signals, s1 (t) and s2 (t), as s1 (t) = s(t) + e(t) = rmax ejα(t) ejϕ(t) s2 (t) = s(t) − e(t) = rmax ejα(t) e−jϕ(t) s 2 rmax − 1. e(t) = js(t) 2 r (t) (2) 2 (a) (a) (b) (c) Fig. 1. (a) Outphasing concept and signal decomposition. (b) Ideal power combining of the two constant-envelope signals. The two constant-envelope signals contain the original signal, s(t), and a quadrature signal, e(t), and are suitably amplified by switched amplifiers like Class-D. By separately amplifying s1 (t) and s2 (t), and combining the outputs of the two individual amplifiers, the original signal is reconstructed and amplified as in Fig. 1(b). In the sequel, PA refers to the complete outphasing amplifier and amplifier refers to the switched amplifiers A1 and A2 . Letting g1 and g2 denote two real valued gain factors, on s1 (t) and s2 (t), and δ a phase mismatch in the path for s1 (t), then it is clear from y(t) = g1 ejδ s1 (t) + g2 s2 (t) = [g1 ejδ + g2 ]s(t) + [g1 ejδ − g2 ]e(t), (b) (3) that besides the amplified signal, a part of the quadrature signal remains. The quadrature signal has a larger bandwidth than the original signal, s(t), and degrades Adjacent Channel Leakage Ratio (ACLR) and reduces the margins to the spectral mask, unless canceled in the power combiner . In order not to allow a residual quadrature component to distort the spectrum or limit the Dynamic Range (DR) |g1 + g2 | | max(y(t))| = 20 log10 (4) DR = 20 log10 | min(y(t))| |g1 − g2 | of the PA, the phase and gain mismatches between s1 (t) and s2 (t) must be minimized . The DR sets limits on which output amplitudes can be achieved with the PA, but within the DR the PA can achieve all amplitudes by changing the phases of the outphasing signals. The constant gain, g1 and g2 , approximations are especially suitable for Class-D amplifiers, where the output can be considered as an ideal voltage source whose output voltage is independent of the load . This also makes Class-D suitable for non-isolating combiners like transformers, recently demonstrated in . III. P REDISTORTION A digital predistorter (DPD) has been designed to predistort the input of the implemented PA to cancel the nonlinearities, and is ideally the inverse of the PA transfer function. Models describing the behavior between the PA input and output as well as the PA inverse, the DPD, have been estimated using estimation data sets (EDGE and WCDMA signals). The DPD was applied to a second data set, validation input data, and the DPD output was applied to the PA. The DPD was estimated in cascade with the PA model, as in Fig. 2(c), to assure that the pre-inverse is obtained, which is not necessarily the same as the post-inverse in the general case . Moreover, (d) Fig. 2. The inputs and outputs of (a) the PA, (b) the PA model, (c) the DPD and PA model (d) the DPD and PA. (c) illustrates the DPD estimation setup and (d) the intended use of the DPD. most system identification methods assume additive noise on the output , whereas an estimation of the post-inverse, from the output y(t) to the input s(t), would have the noise at the estimation input signal y(t). The largest amplitude of the input signal and the measured output signal were normalized to 1, thus g1 + g2 was normalized to 1 during modeling. Despite the fact that the PA is analog and the baseband model is time-discrete, the notation t is used for indicating the dependency of time. Based on the context, t may thus be a continuous or discrete quantity. A. PA model The PA model was estimated from the input s(t) and the measured output y(t) of the PA as in Fig. 2(a). With the gain mismatch between g1 and g2 and a time delay τ , a first model structure, Model structure A, was suggested as yA (t) = g1 s1 (t + τ ) + g2 s2 (t), (5) where τ is a real valued constant. Applying this model to estimation input data, the phase error appeared to be dependent on the amplitude of the input; the phase shift increases with an increasing input amplitude. Fig. 1(a) shows that the amplitude information of the original input signal s(t) can be found in the angle between s1 (t) and s2 (t), ∆ψ (s1 , s2 ) = arg(s1 (t)) − arg(s2 (t)), (6) where ∆ψ = 2ϕ in Fig. 1(a). Here, the phases are assumed to be unwrapped. To model the amplitude dependent phase shift without changing the constant amplitude of the signals s1 (t) and s2 (t), a model structure with an exponential function with a polynomial of order n in the exponent was used. This model, referred to as Model structure B, can be described by yB (t) = g1 s1 (t)ej p(η1 ,∆ψ (s1 ,s2 )) + g2 s2 (t)ej p(η2 ,∆ψ (s1 ,s2 )) (7) where η1 , η2 are the vectors of polynomial coefficients in n X p(ηk , ∆ψ (s1 , s2 )) = ηk,i ∆ψ (s1 , s2 )i , k = 1, 2. (8) i=0 Model structure B with the additional constraint η1,i = η2,i , i = 1, 2, . . . , n is referred to as Model structure C. The model parameters in a given model structure are estimated by minimizing a quadratic cost function  as in θ̂ = argmin θ N X t=1 2 |y(t) − ŷ(t, θ)| (9) 3 ŷ(t, θ) = g1 s1 (t)ej p(η1 ,∆ψ (s1 ,s2 )) + g2 s2 (t)ej p(η2 ,∆ψ (s1 ,s2 )) η1T η2T ]T (10) 2n+4 ∈ R , y(t) is the meawhere θ = [g1 g2 sured output data and ŷ(t) is the modeled output, compare Fig. 2(a) and 2(b). This structure leads to a nonlinear and possibly nonconvex optimization problem, so the minimization algorithm might find a local optimum instead of a global. B. DPD model When identifying the DPD model, the model structure was assumed to be the same as for the PA model, motivated by the Stone-Weierstrass theorem (Theorem 7.26 ). The minimization criterion used was N X 2 θ̂DPD = argmin |s(t) − ŷP (t, θDPD )| , (11) θDPD t=1 ŷP (t, θDPD ) = ĝ1 s1,P (t)ej p(η̂1 ,∆ψ (s1,P ,s2,P )) + ĝ2 s2,P (t)e j p(η̂2 ,∆ψ (s1,P ,s2,P )) k = 1, 2, h1 (∆ψ ) = −f1 (h̃(∆ψ )) + ξ1 (∆ψ ) (14) and hk (v) be the (ideal) predistorter working on input sk (t), yP (t) = g1 s1,P (t)ej f1 (∆ψ (s1,P ,s2,P )) + g2 s2,P (t)ej f2 (∆ψ (s1,P ,s2,P )) (15) Defining f˜(v) = v + f1 (v) − f2 (v) and h̃(v) = v + h1 (v) − h2 (v), and requiring no output amplitude change leads to ∆ψ (y1,P , y2,P ) = f˜(h̃(∆ψ )) = ξ(∆ψ ) h̃(∆ψ ) = f˜−1 (ξ(∆ψ )), (17) (13) y(t) = y1 (t) + y2 (t) k = 1, 2. where ξ(∆ψ ) = ∆ψ + ξ1 (∆ψ ) − ξ2 (∆ψ ). The phase change can be calculated as and requiring arg(y1,P (t)) = arg(s̃1 (t)) = arg(s1 ) + ξ1 (∆ψ ) leads to C. Theoretical motivation of the DPD Model At the output of the combiner, the perfect predistorter should lead to a (normalized) output which is a copy of the input, i.e. no amplitude or phase alteration should occur. This holds if the signals y1 (t), y2 (t) from Fig. 1 are equal to s1 (t), s2 (t) from (2) except for the gain. Nonidentical gain factors result in a scaling and an added phase shift, and yk (t) should instead be compared to s̃k (t) (the input signal s(t) decomposed as y(t) with gain factors g1 and g2 ), so that s̃1 (t) + s̃2 (t) = s(t), |s̃k (t)| = gk , k = 1, 2 and arg(s̃1 (t)) ≥ arg(s̃2 (t)). The phase shifts ξk = arg(s̃k (t)) − arg(sk (t)), k = 1, 2, depend only on g1 and g2 and |s(t)|, or ∆ψ , where ∆ψ = ∆ψ (s1 , s2 ). Let fk (v) be the (perfect) model of the phase shift in the PA defined as sk,P (t) = sk (t)ej hk (∆ψ (s1 ,s2 )) , Fig. 3. (a) The deviation from the ideal phase difference at the output without predistortion (line 1) and with predistortion (line 2), for Model structure B identified for EDGE input. (b) The deviations from the ideal phase of the signals y1 and y2 without predistortion (y1 line 3 and y2 line 4) and with predistortion (y1 line 5 and y2 line 6, lines 5 and 6 reach a value of 1.06). The measurements with ∆ψ > 2.8 (right of the vertical line) represent 0.6 % of the data. (12) T T η2,DPD ]T ∈ R2n+2 . The signal ŷp (t) is and θDPD = [η1,DPD the output from the PA model, using a predistorted input, as in Fig. 2(c). The resulting estimated parameter vector θ̂DPD contains the DPD model parameters. With these parameters the signals s1,val,P (t) and s2,val,P (t) were created using the validation data and applied to the PA as in Fig. 2(d). The measured results are presented in Section V. = g1 s1 (t)ej f1 (∆ψ ) + g2 s2 (t)ej f2 (∆ψ ) (b) arg(y1,P (t)) = arg(s1 (t)) + h1 (∆ψ ) + f1 (h̃(∆ψ )) where sk,P (t) = sk (t)ej p(ηk,DPD ,∆ψ (s1 ,s2 )) , (a) (16) (18) if no phase shift is to occur, and analogously h2 (∆ψ ) = −f2 (h̃(∆ψ )) + ξ2 (∆ψ ). (19) Choosing predistorters according to (18) and (19) used as in (15), it is possible to achieve a perfect compensation in the PA described by (14). Two independent predistorters are used, one for each signal s1 (t) and s2 (t). Though the predistorters used are not ideal but estimated using measured data, the same requirements of no phase shift and no amplitude change are valid. The resulting deviation from the ideal phase difference leads to a change in output amplitude with and without predistortion for EDGE as shown in Fig. 3(a), for Model structure B, and is clearly reduced by the DPD. The deviations from the ideal phase in each signal path should be zero and the DPD reduces the deviations in a large part of the working area, as seen in Fig. 3(b). The output phase deviation is also improved, shown by the small deviation from the ideal phases of y1 (t) and y2 (t) after predistortion. IV. I MPLEMENTATION OF THE C LASS -D O UTPHASING RF A MPLIFIER Fig. 4 shows the implemented Class-D outphasing amplifier with an inverter-based output stage and an on-chip transformer as power combiner. Fig. 5 shows the chip photo. The chip was bonded on a FR4 printed circuit board and connected with bond-wires. The NMOS, T1 and T3 , and PMOS, T2 and T4 , transistor widths in the output stage were 60 µm and 180 µm, respectively. An off-chip capacitor (Ctune ) was used to set the frequency characteristics, optimized at 2 GHz. The buffers of the output stage were tapered buffers with tapering factor λ = 3. A 4:3 turns ratio was used in the transformer for a high coupling factor and a high bandwidth, but constrains the output power to levels suitable for transceivers and low-power PAs. The self-inductances of the galvanically isolated primary, 4 12.5 50 ← Pout 5 20 2.5 10 1 1.25 1.5 1.75 2 2.25 2.5 2.75 Carrier frequency [GHz] 3 0 Measured output power (Pout ), DE and PAE over frequency. Output power [dBm] 20 50 10 45 ← Pout,max 0 40 −10 35 −20 30 −30 ← Pout,min −40 −50 0.75 1 25 DR → 1.25 1.5 1.75 2 2.25 2.5 2.75 Carrier frequency [GHz] 20 3 Dynamic range [dB] Fig. 6. 30 PAE → 0 0.75 Fig. 4. Implemented outphasing amplifier with inverters in the output stage. 40 DE → PAE, DE [%] Pout [dBm] 10 7.5 15 Fig. 7. Measured maximum output power, Pout,max , and minimum output power, Pout,min , and dynamic range, DR, over frequency. Fig. 5. Photo of the chip with size 1x1mm2 . Lp , and secondary, Ls , windings were 3.7 nH and 2.5 nH, respectively. The windings were implemented in the top three metal layers and had a total thickness of 2 µm. The quality factors, Qp and Qs , were 10 and 8 at 2 GHz, respectively. Onchip resistors were used for an equivalent input impedance of 50 Ω at the chip edge for each RF input (s1 (t) and −s2 (t)). V. M EASUREMENT R ESULTS A. Measured RF Performance Fig. 6 shows the measured maximum output power (Pout ) with the drain efficiency (DE) and power-added efficiency (PAE) over frequency for the amplifier only (the predistortion method has not been implemented in hardware). VDD and Vbias were 1.3 V and 0.65 V, respectively. The 3 dB bandwidth was 2 GHz (1-3 GHz). At 2 GHz, the output power was +10.3 dBm with a DE and PAE of 39 % and 33 %, respectively. The gain was 23 dB from the buffers to the output. The minimum and maximum output power and DR of the PA are plotted in Fig. 7, where Pout,max = Pout in Fig. 6. In simulations at 2 GHz, the DR was ∼30 dB for a large number of load impedances (RL ). Thus, the predistortion method is expected to give similar ACLR performance as reported in Section V-B even if the load is changed. B. Measured Performance of Modulated Signals The Peak-to-Average Power Ratios (PAPR) of the EDGE and WCDMA signals were 3.0 dB and 3.2 dB, respectively. The spectrum of the estimation data sets are shown in Fig. 8(d) and Fig. 9(d). The signal generator was an SMU200A with two phase-coherent RF outputs and an arbitrary waveform generator where s1 (t) and s2 (t) were stored. For the computation of the model parameters a variety of algorithms are available to solve the nonlinear optimization problem. In this paper, the Matlab routine fminsearch, based on the Nelder-Mead simplex method, was used. The estimation and validation data sets contain Nid and Nval samples, respectively. The input and output sampling frequencies are denoted fs and fs,out , respectively. To minimize the influence of measurement noise, the signals were measured K times, and a mean was calculated. The data collection parameters are shown in Table I. Measurements with two amplitude-matched signal generators, i.e. g1 = g2 = 0.5, show that phase errors of 12 ◦ and 4 ◦ are acceptable for WCDMA and EDGE to meet the ACLR and 400/600 kHz offset requirements. Thus, a predistortion implementation would require a phase resolution of at least 7 bits, i.e. 360 ◦ /27 = 2.81 ◦ . For each bit of increased phase resolution, the ACLR and margins to the spectral mask improve by ∼3 dB. The measured performance of the amplifier for modulated signals are summarized in Table II and Table III. For the EDGE signal at 1 GHz, the phase offset between s1 (t) and s2 (t) in the baseband was adjusted to minimize phase mismatch (ideally 180 ◦ between the two RF inputs for nonmodulated s1 (t) and −s2 (t) in Fig. 4, i.e. maximum output power for a continuous signal). The margins to the spectral mask were 4.0 and 7.0 dB at 400 and 600 kHz offset from the carrier, and no predistortion was applied. At 2 GHz, including phase adjustments, the margins to the mask have disappeared as shown in Fig. 8(a). As the phase error cannot be assumed to be 0 ◦ in a transceiver, a phase error of 3 ◦ was added and led to a violated spectral mask as in Fig. 8(b). The estimation output data y(t) were used in the predistortion method to extract the model parameters, using EDGE WCDMA Nid 40 001 153 600 TABLE I DATA COLLECTION Nval fs 80 001 8.67 MHz 153 600 61.44 MHz fs,out 34.68 MHz 61.44 MHz K 150 200 5 EDGE Relative spectral density for RBW = 30 kHz [dB] 0 −10 ← spectral mask −20 −30 −40 −50 −60 ←c ←d ←a −70 b ↓ −80 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 Offset from carrier frequency [MHz] at 2 GHz Fig. 8. Measured EDGE output spectrum at 2 GHz. (a) Without phase error between s1 (t) and s2 (t). (b) With 3 ◦ phase error between s1 (t) and s2 (t). (c) When DPD is applied to (b). (d) Spectrum of estimation signal. Spectrum of validation signal was similar. TABLE II M EASURED SPECTRAL PERFORMANCE OF THE EDGE SIGNAL Freq. Freq. offset Spec. Meas. (a) Meas. (b) Meas. (c) 2 GHz 400 kHz -54 dB -54.4 dB -53.5 dB -65.9 dB 600 kHz -60 dB -60.3 dB -59.9 dB -68.2 dB (a) With no phase error and no DPD. (b) For a 3 ◦ phase error and no DPD. (c) When DPD is applied to (b). TABLE III M EASURED SPECTRAL PERFORMANCE OF THE WCDMA SIGNAL Freq. ACLR Spec. Meas. (a) Meas. (b) Meas. (c) 1 GHz 5 MHz -33 dBc -40.6 dBc -39.4 dBc -53.6 dBc 10 MHz -43 dBc -59.8 dBc -56.2 dBc -60.3 dBc 2 GHz 5 MHz -33 dBc -43.4 dBc -38.0 dBc -50.2 dBc 10 MHz -43 dBc -53.9 dBc -50.9 dBc -52.2 dBc See Table II for description of (a)-(c). WCDMA Relative spectral density for RBW = 30 kHz [dB] 0 DPD proved to be successful and improved the margin to the EDGE spectral mask at 400 kHz and the WCDMA ACLR at 5 MHz offset by 12.2-12.4 dB. −10 −20 −30 −40 −50 −60 −70 ←a ←b ←c ←d −80 −10.0 −5.0 0.0 5.0 10.0 Offset from carrier frequency [MHz] at 2 GHz Fig. 9. Measured WCDMA spectrum at 2 GHz. (a)-(d) as in Fig. 8. Model structure B with n = 5. The predistorted input signals, s1,val,P (t) and s2,val,P (t), were computed for the validation input signal, resulting in an output spectrum as shown in Fig. 8(c). The measured power at 400 and 600 kHz offsets were -65.9 and -68.2 dB, respectively. The average power at 2 GHz was +7 dBm with 22 % PAE and RMS EVM of 2 %. Fig. 9(a) shows the measured WCDMA spectrum at 2 GHz, with minimized phase mismatch and no predistortion. Adding 3 ◦ of phase error, a distorted spectrum as in Fig. 9(b) was measured. The phase predistortion method, using Model Structure C with n = 4, for the validation signal, improves the measured ACLR at 5 MHz offset to -50.2 dBc, with a spectrum shown in Fig. 9(c). At 1 GHz, similar performance was achieved as seen in Table III. The channel power at 2 GHz was +6.3 dBm with PAE of 22 % and RMS composite EVM of 1.4 % (0.6 % after DPD). The RX noise floor after predistortion, assuming a 45 MHz offset, was -140 dBc/Hz and limited by the signal generator phase noise, not the outphasing amplifier. Before predistortion, the noise floor was -138 dBc/Hz. The measured spectral performance at 400 kHz offset and the ACLR at 5 MHz is comparable to state-of-the-art EDGE  and WCDMA  transmitters. VI. C ONCLUSIONS This paper presents a behavioral model structure and a model-based phase-only predistortion method suitable for outphasing RF amplifiers. The predistortion method is applicable at the signal generation level in the baseband, and it has been used for EDGE and WCDMA signals applied to a Class-D outphasing RF amplifier with an on-chip transformer for power combining in 90nm CMOS. In measurements at 2 GHz, the R EFERENCES  X. He and J. van Sinderen, “A 45nm WCDMA Transmitter Using Direct Quadrature Voltage Modulator with High Oversampling Digital FrontEnd,” in ISSCC Dig. Tech. Papers, Feb. 2010, pp. 62–63.  J. Mehta, V. Zoicas, O. Eliezer, R. Staszewski, S. Rezeq, M. Entezari, and P. 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