Linearity of X-band Class-B Power Amplifiers in Digital Polar Transmitter

Linearity of X-band Class-B Power Amplifiers in Digital Polar Transmitter
Linearity of X-band Class-B Power Amplifiers
in a Digital Polar Transmitter
Narisi Wang, Nestor D. Lopez, Vahid Yousefzadeh, John Hoversten,
Dragan Maksimovic and Zoya Popovic
Department of Electrical and Computer Engineering
University of Colorado, Boulder, Colorado 80309, USA
Abstract- This paper discusses the linearity of a class-E Xband PA in a digital polar transmitter. The PA is nonlinear
since it is compressed by 2.2 dB when achieving a 59% PAE
at 10 GHz. Load-pull is performed under a two4one test and
the resulting optimal efficiency impedance is found to be over
30% different from the single4one load-pull. In addition standard
two4one load-pull measurements indicate that the impedance for
max P0ut coincide with worst nonlinearity (IMD). Surprisingly,
in the two4one polar load-pull, impedance for max P0ut differs
significantly from the impedance corresponding to worst IMD.
Therefore, under polar modulation a different matching circuit
should be designed for optimal linearity and efficiency. The PA
is part of a digital polar transmitter which enables linearization
including phase predistortion, with IMD levels over 11 dB lower
than in the standard two4one test. Load-pull performed on the
polar class-E PA shows that the level of intermodulation products
varies for different signals input into the PA.
Index Terms- Envelope elimination and restoration, polar
modulation, envelope amplifier, class-E amplifier
M/[ ODERN communication systems are forced to continually improve their spectral efficiency in an effort to
achieve higher bitrates in limited bandwidth. This improvement
is typically manifested as a complex scheme in which both
amplitude and phase of the RF carrier are modulated at a high
rate and over a wide dynamic range. Such modulated signals
demand very linear power amplifiers, which are operated
typically in class A or backed-off class AB modes. These linear
operating modes limit the efficiency of the PA to around 30%.
A number of researchers have investigated supply-modulating
techniques that can simultaneously provide high efficiency
and good linearity, and most notable examples are Envelope
Elimination and Restoration (EER), polar modulation and
dynamic biasing [1]-{4]. These types of transmitters are more
complex, and the total transmitter efficiency depends on both
the PA and the supply modulating circuit efficiency.
In this paper, we examine the linearity of a ultra-nonlinear
high-efficiency switched-mode PA in a digital polar transmitter.
The RF carrier is at 10GHz, which is a higher frequency
than most current commercial communication systems, but
is a common frequency in other applications, such as radar.
At carrier frequencies above 2 GHz, the circuit parasitics and
device nonlinearities are more pronounced and difficult to
model. The class-E X-band PA used in this study has been
demonstrated in a two-stage efficient PA [5] and its linearity
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Liner assisted sAitchirg iplifier
Fig. 1. Block diagram of a polar system with FPGA digital control. The
RF PA is a class-E 1O-GHz MESFET amplifier. The envelope signal is split
into a low frequency component which controls a DC-DC converter and a
high frequency component which provides additional envelope AC variations.
Phase variation is achieve with a digitally controlled phase shifter.
Fig. 2. Pout (solid line) and PAE (dashed line) load-pull contours for MESFET
AFM04P2 (Alpha industries). The class-E impedance (27.2 + j31.4Q) is
indicated with 'x'.
and EER operation were investigated in [6]. The class-E mode
of operation lends itself naturally to EER and polar transmitter
architectures. It can be shown, e.g. in [5], that the output
voltage into a fixed resistive (RL) load is proportional to the
supply voltage (VDD):
± (26.
fs * Co RERL
where RE is the real part of the optimal impedance presented
to the device for class-E switched mode operation, fs is the
operating frequency which is also the switching frequency, and
C0ut is the output capacitance of the active device. In addition,
-1 8dBc
30- -- 1
o -40
Input Power [dBm]
Offset Frequency (MHz)
Fig. 3. (a) Single tone power sweep for class-E PA at 10 GHz, (b) two-one output spectrum for 200 kHz offset between tones (carrier frequency is 10 GHz),
and (c) MESFET Pout and worst IMD3 load-pull contours. Class-E impedance is indicated with an 'x'; for this impedance PAE is 45% with +17.5 dBm of
Pout. Optimum PAE of 48% is obtained for 22 + j38Q, 'o' with +17.5 dBm of Pout. Worst IMD3 and maximum Pout contours coincide.
the optimal efficiency and optimal load impedance are ideally
not affected by the bias variation, since the transistor current
and voltage amplitudes only change with bias, but not their
time-domain waveform shapes. The power can theoretically
vary from zero to the maximal available power, but in practice
the lowest power is limited by feedthrough, and the maximal
power is constrained by the power handling of the device.
As a result of the PA property described by Eq. 1, the
output voltage of a class-E PA can be varied proportionally
to variations in the supply voltage, which is required for a
polar transmitter, in which the envelope of the modulated
RF carrier amplitude-modulates the output voltage, while the
phase of the modulated signal is directly input into the PA
through the drive (RF input). This is similar to the analog
EER technique [4], but can be implemented digitally, as shown
with the schematic in Fig. 1. The digitally-controlled drain bias
provides amplitude modulation of the output voltage through
a ultra-efficient slow DC-DC converter in combination with
a fast less efficient linear amplifier which provides the AC
portion of the signal envelope. The signal is generated digitally
and converted from IQ to polar form. The digital control of
the bias allows allocation of the amplitude modulation between
the slow and fast circuits in order to optimize efficiency for
different modulated signals, possibly adaptively.
Practical class-E PAs have achieved 96% drain efficiency in
the low MHz range [9], around 90% at VHF [10] and as high
as 70% at X-band [5]. In [6], class-E PAs are examined and
it is shown they can be linearized to some degree using polar
The class-E PA used throughout this work was designed
using design equations as in [8] and load-pull characterization
of a GaAs MESFET at 10GHz, shown in Fig. 2. The theoretical class-E impedance calculated from the output capacitance
of this device is 24.7 + j28.4Q. The maximum PAE of 59%
at 27.2 + j31.4Q is obtained from load-pull measurements.
P011t, gain, and riD for the PA are + 19.9 dBm, 8.1 dB, and 64%
respectively when the PA is compressed by 2.2 dB. The input
impedance is matched to 8.2 + j27.3Q.
Fig. 3a shows an input power sweep for the amplifier biased
at 4.1 V and 10 mA. The output spectrum for a two-one test
when the tones are offset by 200 kHz and the input power is
+1 IdBm (optimum PAE) is shown in Fig. 3b. The 200 kHz
bandwidth is chosen as an example since it corresponds to the
bandwidth of an EDGE communication signal. The upper and
lower IMD3 levels are -19.5 dBc and -17.8 dBc, respectively.
The PAE for the two-one test with the same total input power
dropped to 45% and the output power dropped to + 17.5 dBm
indicating a gain reduction.
To understand this degradation, load-pull measurements
were taken for a two-one test with the same 200 kHz offset.
Fig. 3c shows Po1ut (solid line) and worst IMD3 contours
(dashed-ine) for the MESFET with +1 1dBm of input power.
It is interesting to observe that there is an overlap between
maximum output power and worst IMDs. The Po1ut and PAE
for the class-E impedance are +17.5 dBm and 45% respectively. Optimum PAE (48%) impedance shifted to 22 + j38Q
(indicated with a 'o') with same Pout.
Digital polar modulation was implemented using a Xilinx
Virtex II FPGA to provide baseband and control signals.
Digital-o-Analog Converters (DAC) are used to control a
phase shifter responsible for modulating the RF carrier and
also to send control signals to the linear portion of the envelope
amplifier. The switching converter is also directly controlled
by the FPGA. Time alignment of these three components is
critical in achieving PA linearity.
The output power level of the envelope amplifier is greater
than that of the RF PA, making it a significant factor in
system efficiency. An efficient wideband envelope amplifier is
realized by taking advantage of the high efficiency of a lowswitching frequency converter and the broad bandwidth of a
linear amplifier. The envelope command is filtered into high
O 14
i12 -
50 =
t 8#8
F -10
Supply Voltage [V]
Time [ps]
Fig. 4. (a) Supply sweep for Class-E PA operated at 10-GHz, (b) envelope and phase control time domain signals for polar two-one test, and (c) polar two-one
output frequency spectrum for 200 kHz offset between tones for a carrier frequency of 1O GHz.
Fig. 5. MESFET Po0t and worst IMD3 polar load-pull contours. The class-E
impedance is indicated with an 'x', for this impedance, the rD of the entire
polar transmitter is 29.5% with Pout of +17.5 dBm. The optimal qD of 30.5%
is obtained for 31.3 + j22.7Q, 'o' with +17.1 dBm of Pout. Worst IMD3 and
maximum Pout contours do not coincide.
and low frequency components which are sent to the linear
amplifier and switching converter respectively. This technique,
referred to as band separation, has the capability to improve
efficiency for various input signal types [11].
In a polar transmitter, the amplifier input power is held
constant and output power variations are achieved by varying
the supply voltage. As previously mentioned, in class-E the
output voltage is nearly proportional to the supply voltage.
Fig. 4a shows how the amplifier parameters (Pout, Gain, riD,
and PAE) change as a function of supply voltage. Since, the
RF input power is held constant throughout this test, it leads
to negative gain and PAE, and drain efficiency higher than
unity at low bias voltage. A maximal PAE of 56% is obtained
for a supply voltage of 3.8 V. The corresponding riD and Pout
are 68.5% and +18.5dBm respectively. The gain under these
conditions is 7.46 dB. As bias voltage varies from 0 V to 5 V
output power varies from +1.4dBm to +18.5dBm.
Polar system linearity measurement requires the two-one
signal to be split into amplitude and phase components, and
fed to the envelope amplifier and phase modulator. Fig. 4b
shows the time domain envelope and phase control signals. For
a polar two-one test the envelope corresponds to a rectified
sinewave and the phase control signal is a squarewave. The
output spectrum for a polar two-one test with tone offset of
200kHz is shown in Fig. 4c. Upper and lower IMD measurements were -24.4 dBc and -23.6 dBc, significantly improved
over the standard two-one conditions class-E PA.
A load-pull was performed under polar two-one excitation.
Po1ut and worst IMD3 contours are shown in Fig. 5. Linearity
improvements observed in the output frequency spectrum of
Fig. 4c are consistent with IMD measurements. There is a
dramatic difference in IMD3 impedance as compared to the
PA tested outside of the polar transmitter under standard
two-one conditions from Fig. 3b. The optimum IMD region
does not coincide with maximum Po1ut. Therefore under polar
modulation a different amplifier matching circuit can be design
for optimal linearity.
The Po1ut and riD for the entire polar transmitter are
+17.5 dBm and 29.5% respectively. Significant reduction in
riD was suffer because the spectral content of the two-one
envelope. The 200kHz tones are too high in frequency for the
high-efficiency DC-DC switching converter to track, limiting
its contribution to only the DC component. Therefore, significant portion of the total envelope power is generated by the
linear amplifier. Additional discussion is given in Section IV.
The maximal rD of the entire polar loop is 30.5% with Po1ut of
+17.1 dBm. The real and imaginary parts of the best-efficiency
load impedance of 31.2 + j22.7Q differ by around 30% from
the single-one load pull value.
A. Distortion and Predistortion
Fig. 6a shows measured AM/AM and AM/PM distortion for
polar class-E PA. The AM/AM distortion describes how the
output voltage to a 50Q load changes as the supply voltage is
varied. The static measurements show that there is significant
phase distortion for voltages below 1 V. Other significant nonidealities are the feedthrough and the roll-off at high voltages.
Baseband predistortion was used to compensate for some
of the polar system nonlinearities by distorting amplitude and
phase information in a manner complimentary to the static
AM/AM and AM/PM characteristics. Baseband distortion was
accomplished using a lookup table (LUT) implemented in the
FPGA. Fig. 6b shows the predistorted baseband amplitude and
phase control signals.
0--- -28dBc
ph~ase -50
Supply Voltage
- - -
Tim1[ s]Ofse frqec [MHz]
Fig. 6. (a) Measured static AM/AM and AM/PM distortion for Class-E PA, (b) predistorted envelope and phase control time domain signals for polar two-tone
test, and (c) polar two-tone output frequency spectrum with predistortion for 200 kHz offset between tones for a carrier frequency of 10OGHz.
Fig. 6c shows the obtained output spectrum for the predistorted polar two-one test with 200kHz spacing between
tones. With predistortion the lower and upper IMD3 levels
are reduced to -28.8dBc and -29.8dBc, for a 4.4dB and
6.2dB improvement, respectively. Table I shows the results
for a two-one test with tone spacing of 20kHz, 200kHz,
625kHz and IMHz offset between tones. It is interesting the
dramatic improvement in two tone performance for 20kHz
case, reducing lower and upper IMD3 levels to -33.2dBc and
-32.9dBc respectively. However, as the separation between
tones increase the effectiveness of the predistortion is degraded
suggesting other types of non-inearities taking place, such as
memory effects. A more complex dynamic PA model which
considers these effects will be required to predistort wideband
signals. Future work in this area includes the implementation
of adaptive predistortion, predistortion of memory effects,
and the elimination of feedthrough using RF drive power
A 10-GHz high-efficiency class-E PA was characterized and
tested in polar modulation under two-one conditions. Linearity
in polar modulation is significantly improved when compared
to the linearity tested under standard two-one conditions.
Load-pull measurements suggest a region where linearity can
be farther enhanced. Therefore, under polar modulation a
different matching circuit should be designed for optimal
linearity and efficiency.
The measured, not optimized, riD for the entire polar classE transmitter in two-one test with 200 kHz offset between
tones is 29.5%. In [11], it is shown that for an envelope signal
with a known amplitude density distribution, an optimum
band-separation frequency fB can be found. Spectrally rich
signals such as EDGE can benefit from the band-separation
optimization technique because significant amount of power
is concentrated at low frequency close to DC. For the case of
EDGE signals, optimal band separation (0.88 ratio of envelope
sent to DC-DC and 0.12 to linear amplifier) estimates efficiencies in the order of 72% for the linear-assisted switching
converter and 50% for the entire transmitter.
This work was supported by the Defense Advanced Research Projects
Agency (DARPA) under the intelligent RF Front Ends (IRFFE) Program under
Grant N00014-02-1-0501. N6stor L6pez and John Hoversten acknowledge Department of Education support under a GAANN Fellowship at the University
of Colorado on Hybrid Signal Electronics (HYSE).
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