Phase Predistortion of a Class-D Outphasing Linköping University Post Print

Phase Predistortion of a Class-D Outphasing Linköping University Post Print
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
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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.
Postprint available at: Linköping University Electronic Press
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.
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 [1]. Potential solutions are the polar transmitter,
shown for EDGE [2], and the outphasing transmitter [3].
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 [4]. 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:
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 [5], parallel Hammerstein structures [6], or look-up
tables [2], which also can be made adaptive [7].
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) [4]. A gain/phase imbalanceminimization technique was verified in measurements in [8],
and predistortion was used for high power devices in [9].
In [9], 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 [10].
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.
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)
− 1.
e(t) = js(t)
r (t)
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),
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 [4]. 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
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 [4]. 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 [11]. This
also makes Class-D suitable for non-isolating combiners like
transformers, recently demonstrated in [12].
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 [13]. Moreover,
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 [14], 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),
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)),
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 ))
where η1 , η2 are the vectors of polynomial coefficients in
p(ηk , ∆ψ (s1 , s2 )) =
ηk,i ∆ψ (s1 , s2 )i , k = 1, 2. (8)
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 [14] as in
θ̂ = argmin
|y(t) − ŷ(t, θ)|
ŷ(t, θ) = g1 s1 (t)ej p(η1 ,∆ψ (s1 ,s2 ))
+ g2 s2 (t)ej p(η2 ,∆ψ (s1 ,s2 ))
η2T ]T
∈ 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 [15]). The
minimization criterion used was
θ̂DPD = argmin
|s(t) − ŷP (t, θDPD )| ,
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 )
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 ))
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 )),
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.
]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 )
arg(y1,P (t)) = arg(s1 (t)) + h1 (∆ψ ) + f1 (h̃(∆ψ ))
sk,P (t) = sk (t)ej p(ηk,DPD ,∆ψ (s1 ,s2 )) ,
if no phase shift is to occur, and analogously
h2 (∆ψ ) = −f2 (h̃(∆ψ )) + ξ2 (∆ψ ).
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.
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,
← Pout
1.25 1.5 1.75 2 2.25 2.5 2.75
Carrier frequency [GHz]
Measured output power (Pout ), DE and PAE over frequency.
Output power [dBm]
← Pout,max
← Pout,min
DR →
1.25 1.5 1.75 2 2.25 2.5 2.75
Carrier frequency [GHz]
Dynamic range [dB]
Fig. 6.
Fig. 4. Implemented outphasing amplifier with inverters in the output stage.
DE →
PAE, DE [%]
Pout [dBm]
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)).
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
40 001
153 600
80 001
8.67 MHz
153 600
61.44 MHz
34.68 MHz
61.44 MHz
Relative spectral density
for RBW = 30 kHz [dB]
← spectral mask
−0.8 −0.6 −0.4 −0.2
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.
Freq. offset
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).
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).
Relative spectral density
for RBW = 30 kHz [dB]
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.
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 [2] and WCDMA [16] transmitters.
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
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