Linearity of X-Band Class-F Power Amplifiers in High

Linearity of X-Band Class-F Power Amplifiers in High
Linearity of -Band Class-F Power Amplifiers in
High-Efficiency Transmitters
Manoja D. Weiss, Student Member, IEEE, Frederick H. Raab, Senior Member, IEEE, and
Zoya Popović, Senior Member, IEEE
Abstract—Modern communication signals have time-varying
envelopes with significant peak-to-average ratios, resulting in
low average efficiency when amplified by commonly used linear
power amplifiers (PAs). For linear amplification with increased
average efficiency, the Kahn envelope-elimination-and-restoration
method uses a highly efficient saturated PA. In this paper, an
8.4-GHz class-F PA with 55% maximum instantaneous efficiency
at 610-mW output power, is experimentally characterized in
several different biasing modes. Operated in linear mode with
constant drain bias, this PA has 10% average efficiency. The
suppression of two-tone intermodulation products is 27 dBc when
operated at about 0.7 times the peak output power. For the same
PA operated in a modified Kahn mode with drive and bias control,
a comparable linearity (27.7 dBc) can be obtained at peak output
power. Furthermore, the average efficiency increased to 44%, a
factor of 4.4 over the linear fixed bias mode.
N MOBILE and satellite communications, the power amplifier (PA) can consume a large fraction of the total system
power. For example, about 50% of the total power on a communication satellite can be used up by the PA in the transmitter [1].
Therefore, increased PA efficiency considerably reduces total
heat output and prolongs battery lifetime. However, band-limited signals with variable envelopes such as quadrature amplitude modulation (QAM) are typically amplified by linear, but
inefficient PAs, such as class A and class AB. In addition, the PA
is often operated below its maximum power capability in order
to avoid nonlinearities occurring at high output power levels.
This further reduces its efficiency. One method of enhancing
the PA efficiency is a technique known as envelope tracking, in
which the drain bias voltage varies proportionally with the input
signal envelope while maintaining the active device in the linear
regime [2]–[5]. A class-A or class-B PA can also be maintained
in extended saturation and, hence, high efficiency, by providing
optimum drain and gate biases [6]. Alternatively, the Kahn envelope elimination and restoration (EER) technique [7] allows
the use of saturated high-efficiency PAs in linear transmitter
systems. This method, which we refer to as the classical Kahn
Manuscript received March 1, 2000; revised December 1, 2000. This work
was supported by the United States Air Force, Air Force Material Command,
Air Force Research Laboratory, Kirtland Air Force Base under Contract
F29601-99-C-0083 with Green Mountain Radio Research, by the National
Science Foundation under Special Programs in Networking and Communications Grant NCR 9725778, and by by the Army Research Office under
Multidisciplinary University Research Initiative Grant DAAH04-98-1-0001.
M. D. Weiss and Z. Popović are with the Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO 80309 USA.
F. H. Raab is with the Green Mountain Radio Research Company, Colchester,
VT 05446 USA.
Publisher Item Identifier S 0018-9480(01)04438-6.
method, has been successfully demonstrated from HF- through
-bands using saturated class-AB PAs [8], [9].
Dynamic power control in the Kahn technique provides
increased efficiency by conserving RF power consumption at
low-signal envelope levels. This method has been demonstrated
at -band using class-AB PAs [9] and shows promise for use
at higher frequencies. This paper presents an experimental
overview of the efficiency versus linearity performance of an
-band class-F PA in various different modes of operation,
namely, linear with fixed bias, envelope tracking, and Kahn
EER with and without dynamic power control. Switched-mode
class-E and class-F PAs have a theoretical efficiency of 100%
and have been demonstrated with watt-level output powers at
0.5 and 1 GHz with power-added efficiencies (PAEs) of 80%
and 73%, respectively [10]. At 5 GHz, 72% PAE was obtained
[11], dropping to 61% PAE with the same transistor when
scaled to 8 GHz [12]. At 10 GHz, up to 62% PAE was obtained
in an active antenna [13]. However, class-E and class-F PAs
at higher microwave frequencies typically have lower gain,
lower output power [12], and softer saturation characteristics.
Furthermore, they are biased in the linear region because
they have extremely low gain when biased near pinchoff.
Consequently, their efficiency, amplitude modulation (AM)
linearity, and amplitude-modulation-to-phase-modulation
(AM/PM) conversion characteristics are different, and have to
be considered when designing an appropriate dynamic power
control scheme. The goal of the measurements presented here
is to determine the relationship between drain bias and RF
drive level, which gives increased average efficiency without
sacrificing linearity of the PA.
The results presented here are obtained by manually varying
the drain bias and RF drive level according to specific relationships. These control schemes may be implemented, for example,
by using dc–dc converters [3]. For highest linearity, predistortion techniques derived from the signal envelope can be implemented using digital signal processing (DSP).
The basic premise of the Kahn method is that any
narrow-band signal is equivalent to simultaneous AM and
PM of a carrier. As shown in the block diagram of Fig. 1, the
envelope is detected and amplified to high power levels by
an efficient amplitude modulator, such as a class-S modulator
[9]. The class-D, class-E, or class-F PA is operated with high
efficiency by correct choice of the fixed-input RF power level.
The envelope is restored to the carrier through the drain bias.
0018–9480/01$10.00 ©2001 IEEE
Fig. 1. Block diagram of a classical Kahn EER transmitter system. The signal is separated into envelope and phase data, and the phase-modulated carrier drives
the PA. The amplitude is restored by modulation through the drain dc supply.
This gives efficient linear amplification of the RF signal since
the PA gain is proportional to the drain bias.
In the classical Kahn method of Fig. 1, the amplitude of the
phase-modulated drive signal is kept fixed at a large enough
value to ensure optimal PA saturation and high efficiency at
the peak envelope level. However, for lower envelope levels, a
smaller drive signal is sufficient to cause saturation and high
efficiency. Therefore, by regulating the RF drive amplitude in
proportion to the signal envelope, the efficiency of the Kahn
method can be optimized over all envelope levels. Referred to
as Kahn EER with drive modulation, this method conserves RF
drive power while keeping the PA saturated and provides linear
efficient amplification.
In contrast to the Kahn EER method, conventional linear PAs
are not saturated, and the drain bias is kept fixed while the
varying-envelope signal drives the PA. This fixed drain bias is
large enough to allow maximum linear voltage swing for the
highest signal envelope. Since smaller drive levels require less
dc power for the same gain, this amplification method is not efficient at low drive levels. To alleviate this problem, the drain
bias can be made to track the envelope of the input signal in
order to regulate dc power consumption. This dynamic power
control method, known as envelope tracking, allows higher efficiencies for all signal levels while keeping the PA in the linear
voltage (envelope of signal). In practical PAs, the instantaneous
efficiency usually achieves a maximum when the gain is compressed by about 3 dB.
Average efficiency is a good indicator of average power consumption in most communication systems with time-varying envelopes. By increasing the average efficiency of a PA from 30%
to 50% (a factor of 1.7), for the same average output power,
the average input power is reduced 1.7 times, and the battery
lifetime is increased 1.7 times. On the other hand, the average
heat output is reduced by a factor of 2.3. Higher average efficiency [14] is obtained by having increased efficiency over a
large range of signal envelopes and is defined as
is the average output power and
is the average
total input power. The average input power is calculated as the
, and the output power is calculated
expected value of
similarly. If the probability distribution function (PDF) of the
is known, where is the envelope, the average
input and output power can be calculated as
The instantaneous efficiency of a PA is a function of the instantaneous input and output power and the class of operation.
In this paper, the instantaneous efficiency is defined as
is the output RF power and
is the total
input RF and dc power as a function of the signal envelope .
Depending on the class of operation of the PA, the instantaneous efficiency is proportional to the output power or the output
In order to measure the average efficiency of different ampliand
for a sinusoidal input
fier modes, we measure
signal with amplitude . From this measured data, the average
input and output power is then calculated for a signal with any
type of modulation with a known PDF. Note that for the Kahn
modes, is the drain voltage, and for the linear modes, is the
amplitude of the RF input signal.
The PDF of the envelope is a measure of the relative time
corresponding to different levels. The PDFs of some common
can be calculated using (5) and (8). Using a
discrete Fourier transform, the spectrum of the output signal
can then be analyzed. The power ratio between the carrier
and the highest of the third and fifth IMD products is defined
as the IMD. The IMD at peak output power is calculated for the
Kahn modes. For the linear modes, the IMD is calculated at peak
output power and at backed-off power. An acceptable value for
IMD for communication applications is 30 dBc.
Fig. 2. PDFs p(E ) of some common signals. The Rayleigh distribution is
for OFDM (multicarrier) signals and the constant amplitude signal used in
the AMPS is always at peak power. E is the normalized time-varying signal
envelope. is the peak-to-average ratio, given in decibels.
signals are shown in Fig. 2. For frequency modulated (FM)
and other constant-amplitude signals such as the Advanced
Mobile Phone Service (AMPS), the signal is always at peak
output. Shaped-pulse data signals such as QAM have PDFs
with peak-to-average power ratios of 3–6 dB [15]. Multicarrier
signals such as offset frequency division multiplex (OFDM)
have Rayleigh PDFs [16] with typical peak-to-average ratios
from 7 to 13 dB. Such signals are used in cellular communications, multibeam satellite systems, and digital broadcasting.
Varying signal envelope levels give rise to AM and AM/PM
effects, which cause intermodulation distortion (IMD) in
the output signal. In this paper, linearity is represented by
the amount of IMD for a two-tone input signal. Since two
high-power sources at -band were not available to measure
the peak-power IMD, it was calculated based on measurements
of gain compression and phase distortion for a single-tone
excitation to the PA. This input RF signal can be written as
. The output signal as a function of this
input signal amplitude (envelope) is then given by
is the AM characteristic and
is the
AM/PM, both of which are measured for each PA mode.
Using this data, a behavioral model of each PA mode can be
formulated, which is then analyzed under a two-tone excitation.
For the linearity calculation, a two-tone signal such as
is input to the behavioral model. This two-tone signal can also
be represented as
which is a signal of frequency
slowly varying envelope
can be written as
modulated by a
. This expression
A single PA is characterized for operation in five different biasing modes in order to determine the best method of dynamic
bias control for high efficiency and linearity. Two linear modes
of operation, one with fixed and the other with dynamic drain
bias (envelope tracking), are compared with three modes of saturated PA operation, one being the classical Kahn method described in Section II, and the other two being modified Kahn
methods with drive modulation. The following five PA modes
represent specific relationships between the drain voltage and
RF signal amplitude, and are shown graphically in Fig. 3(a).
1) Linear: the signal is fed directly into the RF input and the
drain voltage is fixed. This mode is called the linear mode
because the amplifier is unsaturated.
2) Envelope tracking (ET): linear operation with the dynamic drain voltage proportional to the signal envelope.
3) Kahn: classical Kahn operation, as shown in Fig. 1, with
fixed RF drive.
4) Kahn full-drive modulation (FDM): modified Kahn
mode with dynamic RF input amplitude proportional to
the signal envelope.
5) Kahn partial-drive modulation (PDM): another modified
Kahn mode, which is similar to the Kahn FDM mode, but
has a minimum value for the drive, to increase efficiency
at low envelope levels.
The fixed-bias linear and Kahn modes are not dynamic in that
either the drain is kept fixed or the drive is kept fixed, as can be
seen in Fig. 3(a). The envelope tracking, Kahn FDM, and Kahn
PDM modes are dynamic since both the drain and drive amplitudes change simultaneously. Fig. 3(b) shows the instantaneous
efficiency of the PA used in this study as a function of drain bias
and drive amplitude. It is apparent from this graph that dynamic
control of both values is necessary for maintaining high instantaneous efficiency.
Analogously, variation of the gate bias (quiescent current) in
an RF PA also results in significant savings of dc-input power.
However, minimum drive and gate bias levels are often required
to ensure proper operation of the RF final amplifier and modulator [17]. The minimum drive/gate-bias level ensures saturation of the PA in spite of gain reduction and/or reduces amplitude-to-phase conversion by decreasing the degree of saturation
so that nonlinear capacitance variations are reduced. All five
PA modes listed above were measured with various gate-biasing
schemes. However, there was almost no change in average efficiency between these PA schemes, and the linearity proved to be
low. Therefore, for all measurements described in the following
section, the gate bias is kept fixed.
Fig. 4. Measured instantaneous efficiency of the PA modes. The efficiency is
decreased for low signal levels.
power levels and the phase of the output signal,
, discussed in Section III, are measured for each
is the RF signal amplitude for the linear modes
PA mode.
and the drain voltage for the Kahn modes. The power and
phase are measured using an HP70820A Transition Analyzer.
An HP83020A preamplifier is used to amplify the power levels
from an HP83650A synthesized sweeper so as to saturate the
class-F PA. From this data, the average efficiency and linearity
are calculated for each mode, as described in Section III.
Fig. 3. (a) Five modes of PA operation compared in this paper. Each mode
represents a specific relationship between the drain bias and instantaneous
envelope of the RF input. Two linear modes are compared with three Kahn
modes where the PA is saturated. (b) Instantaneous efficiency as a function
of drain bias and RF input amplitude. By varying both voltages in a dynamic
manner, the efficiency can be optimized for all input envelope levels.
The PA used for this study is an 8.4-GHz class-F PA [12]
designed with a Fujitsu FLK052WG MESFET. At the fundais chosen
mental frequency, the transistor load impedance
in order to maximize power transfer to the load [18], [19], and
is given by
is the maximum drain voltage and
is the maximum
drain current. The load presents the second harmonic at the
switch with a short to increase efficiency by making the
switch voltage waveform approximately a square wave. Higher
harmonics are not considered since the gain decreases with
frequency and is negligible beyond about 30 GHz. The load
filters out the third harmonic, producing a sinusoidal output.
The switch voltage waveform was measured using time-domain optical sampling and class-F operation was confirmed by
observing an approximately square waveform at the drain [20].
The microstrip circuit is fabricated on a 0.508-mm RT5880
) substrate. This PA provides a maximum
Duroid (
instantaneous efficiency of 55% for 610-mW output power and
V and
5.3-dB saturated gain with
Each PA mode is implemented by manually changing the
drain voltage and drive signal amplitude according to the
relationships shown in Fig. 3(a). By monitoring the RF and dc
The effect of dynamic biasing on average efficiency can be
shown by comparing the measured instantaneous efficiency as
a function of output signal amplitude, as illustrated in Fig. 4.
The linear amplifier with fixed bias has very low efficiency at
low power levels. The Kahn method, where the RF drive level is
fixed, has higher efficiency on average than the linear case due
to PA saturation. However, the dynamic biasing schemes (envelope tracking, Kahn FDM, and Kahn PDM) have much higher
efficiency over the entire range of output levels. Kahn PDM has
the best efficiency performance over all other modes. Based on
and the PDFs given in Fig. 2,
measurements of
the predicted average efficiency for multicarrier and QAM signals is calculated as shown in Table I.
Each of the techniques, however, exhibits different AM/PM
, as shown in the measured data in Fig. 5.
The classical and PDM Kahn methods have a large increase in
AM/PM, due to deep saturation of the PA at low envelope levels.
The measured AM linearity, given by the input–output
, is shown in Fig. 6. The peak
transfer characteristic
output level for all modes is about 8 V. The linear modes saturate at high envelope levels and, therefore, must be operated in
backoff for high linearity. The Kahn modes, on the other hand,
have input–output characteristics, which are approximately
straight lines over the entire envelope range. However, the
classical Kahn and Kahn PDM modes suffer from feedthrough,
which occurs in an amplifier when a zero-input signal envelope
on the drain results in a nonzero output due to the feedback
capacitance of the device. This degrades the linearity and also
reduces dynamic range of the output. The Kahn FDM technique
gives no feedthrough and gives the highest AM linearity.
Fig. 5. Measured AM/PM of the PA modes. For the Kahn modes, the envelope
is the drain voltage (0–7 V), and for the linear modes, it is the amplitude of the
RF input (0–4.24 V).
3-dB peak-to-average ratio. Peak power for all modes is about
0.6 W, corresponding to a maximum output envelope of about
8 V. The PDFs of both these signals are shown in Fig. 2. The
overall amplifier linearity is obtained from a combination of the
measured AM and AM/PM effects, as described in Section III.
One would expect the linear mode in backoff to have the
highest linearity, i.e., 27 dBc, with low efficiency, i.e., less than
10%. The FDM Kahn technique, in contrast, gives the same
linearity with a significantly improved average efficiency of
44% (at least a factor of 4.4 improvement).
For QAM signals, the classical Kahn method gives better efficiency than the linear fixed-bias mode, but the dynamic biasing schemes (envelope tracking, FDM, and PDM Kahn) have
much higher average efficiencies and are all comparable. This
is because the PDF for the QAM signal is only 3 dB below
the peak envelope level, where all the dynamic biasing schemes
have similar performances.
A comparison of efficiency and linearity results from the
measurements described in the previous section is summarized
in Table I. The following observations should be pointed out:
1) Kahn EER can be used to linearize highly nonlinear amplifiers such as saturated class-F and E;
2) average efficiency and linearity of Kahn EER can be increased by drive modulation;
3) average efficiency and linearity of a fixed-bias class-F
amplifier can be increased by dynamic drain biasing (envelope tracking);
4) dynamic modes have higher average efficiency and linearity;
5) for approximately the same output power, the saturated
dynamic modes (Kahn FDM, PDM) give higher efficiency and linearity than the dynamic linear method ET;
6) Kahn EER with FDM gives the highest linearity at the
peak output level, while increasing the average efficiency
of the PA by a factor of 4.4 over the case of the unlinearized fixed-bias PA.
Fig. 6. AM linearity of the PA modes. V
is the amplitude of the output
signal, which has a peak value of about 8 V. For the Kahn modes, the envelope
is the drain voltage (0–7 V), and for the linear modes, it is the amplitude of the
RF input (0–4.24 V).
The predicted linearity and average efficiency of the various
techniques are summarized in Table I. The presented data
includes the average efficiency for multicarrier signals with
a 10-dB peak-to-average ratio, and for QAM signals with a
In summary, this paper has discussed the average efficiency
and linearity of an 8.4-GHz class-F nonlinear -band PA
intended for use in transmitters with time-varying signal
envelopes. The class-F amplifier has a high instantaneous
efficiency for high signal amplitudes, but low efficiency for
smaller signals, yielding a poor efficiency when averaged over
time. We show experimentally that several different dynamic
power control techniques can be used to improve the average
amplifier efficiency, and that among these techniques, the
best simultaneous efficiency and linearity are obtained by
a modified Kahn EER technique. For example, the average
efficiency for a Rayleigh distribution of signal amplitudes
(multicarrier OFDM) was improved to 44% for this amplifier at
a peak output power of 0.6 W, with IMD products suppressed to
28 dBc. The same amplifier when operated in linear fixed bias
mode has only 10% average efficiency, with 17-dBc distortion
at the same output power. The techniques we discuss in this
paper are not specific to class-F and class-E amplifiers or to
the signal amplitude distributions we have investigated here.
They are quite general and can be used in conjunction with any
amplifier and a variety of modulation schemes for which the
envelope varies.
The total efficiency of the Kahn method depends not only on
the PA, but also on the amplitude modulator used to amplify
the envelope signal (Fig. 1). The class-S amplitude modulator
at -band [9] has an efficiency of 90% at switching speeds on
the order of 100 kHz. If a 1-MHz dc–dc converter is used instead of a class-S modulator, approximately 90% efficiency can
be obtained [21]. Future work in this area will include design
and integration of the drive and bias control circuits with the
microwave PA.
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Manoja D. Weiss (S’97) was born in Colombo, Sri Lanka. She received the
B.S.E.E degree from the Grove City College, Grove City, PA, in 1993, the
M.S.E.E degree from the Pennsylvania State University, University Park, in
1995, and is currently working toward the Ph.D. degree in electrical engineering
at the University of Colorado, Boulder.
Her research interests include microwave and millimeter-wave high-efficiency amplifiers, distributed transmitters, active antennas, and microwave
semiconductor devices.
Frederick H. Raab (S’66–M’72–SM’80) received
the B.S., M.S., and Ph.D. degrees in electrical engineering from Iowa State University (ISU), Ames, in
1968, 1970, and 1972, respectively.
He is Chief Engineer and Owner of the Green
Mountain Radio Research Company (GMRR),
Colchester, VT, a consulting firm that he founded in
1980. He co-authored Solid State Radio Engineering
(New York: Wiley, 1980) and over 80 technical
papers. He holds seven patents. His professional
activities include RF PAs, radio transmitters, and
radio-communication/navigation systems. He is an extra-class amateur-radio
operator W1FR, licensed since 1961.
Dr. Raab is a member of Eta Kappa Nu, Sigma Xi, the Association of Old
Crows (AOC), the Armed Forces Communications and Electronics Association
(AFCEA), the Radio Club of America (RCA), and the Institute of Navigation
(ION). He was program chairman of RF Expo East’90. He was the recipient of
the 1995 ISU Professional Achievement Citation in Engineering.
Zoya Popović (S’86–M’90–SM’99) received the
Dipl.Ing. degree from the University of Belgrade,
Belgrade, Yugoslavia, in 1985, and the Ph.D.
degree from the California Institute of Technology,
Pasadena, in 1990.
She is currently a Professor of electrical engineering at the University of Colorado, Boulder.
She co-authored Introductory Electromagnetics
(Englewood Cliffs, NJ: Prentice-Hall, 2000) and
co-edited Active and Quasi-Optical Arrays for Solid
State Power Combining (New York: Wiley, 1997).
Her research interests include microwave and millimeter-wave quasi-optical
techniques, microwave and millimeter-wave active antennas and circuits,
RF photonics, high-efficiency microwave circuits, smart antenna arrays, and
antennas and receivers for radio astronomy.
Dr. Popović received the IEEE Microwave Theory and Techniques Society
(IEEE MTT-S) Microwave Prize, the International Scientific Radio Union
(URSI) Young Scientist Award, and the National Science Foundation Presidential Faculty Fellow Award in 1993. She was also the recipient of the URSI Isaac
Koga Gold Medal in 1996, the Eta Kappa Nu Professor of the Year Award from
her students in 1998, and the Humboldt Research Award in 2000 presented by
the Alexander von Humboldt Foundation.
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