Power amplifiers and transmitters for RF and microwave

Power amplifiers and transmitters for RF and microwave
Power Amplifiers and Transmitters for RF
and Microwave
Frederick H. Raab, Senior Member, IEEE, Peter Asbeck, Fellow, IEEE, Steve Cripps, Senior Member, IEEE,
Peter B. Kenington, Senior Member, IEEE, Zoya B. Popović, Fellow, IEEE, Nick Pothecary, Member, IEEE,
John F. Sevic, Member, IEEE, and Nathan O. Sokal, Life Fellow, IEEE
Invited Paper
Abstract—The generation of RF/microwave power is required
not only in wireless communications, but also in applications such
as jamming, imaging, RF heating, and miniature dc/dc converters.
Each application has its own unique requirements for frequency,
bandwidth, load, power, efficiency, linearity, and cost. RF power is
generated by a wide variety of techniques, implementations, and
active devices. Power amplifiers are incorporated into transmitters in a similarly wide variety of architectures, including linear,
Kahn, envelope tracking, outphasing, and Doherty. Linearity can
be improved through techniques such as feedback, feedforward,
and predistortion.
Index Terms—Amplifier, Chireix, class A, class B, class C, class
D, class E, class F, Doherty, envelope tracking, feedback, feedforward, HF, Kahn, microwave, outphasing, power, predistortion,
transmitter, UHF, VHF.
power amplifier (PA) is a circuit for converting dc-input
power into a significant amount of RF/microwave output
power. In most cases, a PA is not just a small-signal amplifier driven into saturation. There exists a great variety of different PAs, and most employ techniques beyond simple linear
amplification. A transmitter contains one or more PAs, as well
as ancillary circuits such as signal generators, frequency converters, modulators, signal processors, linearizers, and power
supplies. The classic architecture employs progressively larger
PAs to boost a low-level signal to the desired output power.
However, a wide variety of different architectures in essence
disassemble and then reassemble the signal to permit amplification with higher efficiency and linearity.
Manuscript received August 10, 2001; revised September 13, 2001.
F. H. Raab is with Green Mountain Radio Research, Colchester, VT 05446
P. Asbeck is with the Department of Electrcial and Computer Engineering,
University of California at San Diego, La Jolla, CA 92093-0407 USA.
S. Cripps is with Hywave Associates, Somerset Chart TA20 3JS, U.K.
P. B. Kenington is with Wireless Systems International Ltd., Bristol BS16
1EJ, U.K.
Z. B. Popović is with the Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO 80309-0425 USA.
N. Pothecary is with IT Systems Ltd., 0047 Marino, Italy.
J. F. Sevic is with Tropian Inc., Cupertino, CA 95014 USA.
N. O. Sokal is with Design Automation Inc., Lexington, MA 02420-2404
Publisher Item Identifier S 0018-9480(02)01963-4.
In the early days of wireless communication (1895–mid1920s), RF power was generated by spark, arc, and alternator
techniques. With the advent of the DeForest audion in 1907, the
thermoionic vacuum tube offered a means of generating and
controlling RF signals, and vacuum-tube PAs were dominant
from the late 1920s through the mid-1970s. Discrete solid-state
RF-power devices began to appear at the end of the 1960s
with the introduction of silicon bipolar transistors such as the
2N6093 [(75-W HF single sideband (SSB)] by RCA. Their
dominance in the 1980s brought about the use of lower voltages, higher currents, and relatively low load resistances. The
1990s saw a proliferation of a variety of new solid-state devices
including HEMT, pHEMT, HFET, and HBT, using a variety
of new materials such as InP, SiC, and GaN. These devices
offer amplification to 100 GHz or more and are in many cases
grown to order in MMIC form. The combination of digital
signal processing (DSP) and microprocessor control allows
widespread use of complicated feedback and predistortion
techniques to improve efficiency and linearity.
Modern applications are highly varied. Frequencies from
VLF through millimeter wave (MMW) are used for communication, navigation, and broadcasting. Output powers vary from
10 mW in short-range unlicensed wireless systems to 1 MW
in long-range broadcast transmitters. Almost every conceivable
type of modulation is being used in one system or another.
PAs and transmitters also find use in systems such as radar, RF
heating, plasma generation, laser drivers, magnetic-resonance
imaging, and miniature dc/dc converters. No single PA or
transmitter technique suits all applications. Many techniques
that are now coming into use were devised decades ago, but
only recently made possible by advances in signal-processing
and control technology.
The need for linearity is one of the principal drivers in the
design of modern PAs. Signals such as CW, FM, classical
FSK, and GMSK (used in GSM) have constant envelopes
(amplitudes) and, therefore, do not require linear amplification. Full-carrier amplitude modulation is best produced by
high-level amplitude modulation of the final RF PA. Linear
amplification is required when the signal contains both amplitude and phase modulation. Examples include SSB voice,
0018–9480/02$17.00 © 2002 IEEE
Fig. 1. RF waveforms for SRRC and multicarrier signals.
vestigal-sideband television (both NTSC and HDTV), modern
shaped-pulse data modulation (QAM, QPSK, CDMA), and
multiple carriers (OFDM).
The requirements for both high data rates and efficient utilization of the increasingly crowded spectrum necessitates the use
of shaped data pulses in modern digital signals such as QPSK,
QAM, and CDMA. Most systems use raised-cosine shaping,
which eliminates intersymbol interference during detection and
allows the spectrum to be shaped arbitrarily close to rectangular
[1]. This requires the transmission of square-root–raised-cosine
(SRRC) data pulses that look much like truncated sinc functions.
The resultant modulated carrier (Fig. 1) has simultaneous amplitude and phase modulation with a peak-to-average ratio of
3–6 dB.
Applications such as cellular base-stations, satellite repeaters, and active phased arrays require the simultaneous
amplification of multiple signals. The signals can, in general,
have different amplitudes, different modulations, and irregular
frequency spacing. In a number of applications including HF
modems and digital broadcasting, it is more convenient to use a
large number of carriers with low data rates than a single carrier
with a high data rate. Orthogonal frequency division multiplex
(OFDM) [2] employs carriers with the same amplitude and
modulation, separated in frequency so that modulation products
from one carrier are zero at the frequencies of the other carriers.
The resultant composite signal (Fig. 1) has a peak-to-average
ratio in the range of 8–13 dB.
Distortion of the amplified signal can be caused by both amplitude nonlinearity (such as a variable gain) or amplitude-tophase conversion (produced, for example, by a voltage-variable
capacitance). The result is splatter into adjacent channels and
impairment of detection. Linearity is characterized, measured,
and specified by various techniques, depending upon the specific signal and application.
The carrier-to-intermodulation (C/I) ratio, compares the amplitude of the desired output carriers to the intermodulation-distortion (IMD) products [3]. Noise-power ratio (NPR) is the ratio
of the notch power to the total signal power when a PA is driven
by noise with a spectral notch. Adjacent channel power ratio
(ACPR) compares the power in an adjacent channel to that of
the signal (Fig. 2). It is currently the most widely used measure
of linearity, but defined differently for each application. Error
vector magnitude (EVM) is the distance between the desired
and actual signal vectors.
Efficiency, like linearity, is a critical factor in PA design.
Three definitions of efficiency are commonly used. Drain efficiency is defined as the ratio of RF-output power to dc-input
Fig. 2. ACPR offsets and bandwidths.
Fig. 3.
Envelope PDFs.
power, i.e.,
. Power-added efficiency (PAE) incorporates the RF-drive power by subtracting it from the output
. PAE gives a reasonable indication of
power, i.e.,
PA performance when gain is high; however, it can become negative for low gains. An overall efficiency such as
is usable in all situations. This definition can be varied to include
driver dc-input power, the power consumed by supporting circuits, and anything else of interest.
The instantaneous efficiency is the efficiency at one specific
output level. For most PAs, the instantaneous efficiency is
highest at the peak output power (PEP) and decreases as output
decreases. When amplifying signals with time-varying amplitudes, a useful measure of performance is the average efficiency,
which is defined [4] as the ratio of the average outuput power
to the average dc-input power, i.e.,
The probability-density function (PDF) gives the relative
amount of time an envelope spends at various amplitudes
(Fig. 3). The PDF of an SRRC signal must generally be determined by simulation or measurement. Multiple carriers produce
random-phasor sums and, therefore, have Rayleigh-distributed
envelopes. The average input and output powers are found by
integrating the product of the variable of interest and the PDF
of the envelope over the range of the envelope.
Fig. 4. Power-output PDFs.
Fig. 6. Waveforms for ideal PAs.
Fig. 7.
Fig. 5.
Single-ended PA.
The need to conserve battery power and to avoid interference
to other users operating on the same frequency necessitates the
transmission of signals whose peak amplitudes are well below
the PEP of the transmitter. Since peak power is needed only
in the worst-case links, the “backoff” is typically in the range
of 10–20 dB. For a single-carrier mobile transmitter, backoff
rather than envelope PDF is dominant in determining the average power consumption and average efficiency. The PDF of
the transmitting power (Fig. 4) depends not only upon the distance, but also upon factors such as attenuation by buildings,
multipath, and orientation of the mobile antenna [5].
RF PAs are commonly designated as classes A–F [3]. Classes
of operation differ in the method of operation, efficiency, and
power-output capability. The “power-output capability” (“transistor utilization factor”) is defined as output power per transistor normalized for peak drain voltage and current of 1 V and
1 A, respectively. The basic single-ended topology (Fig. 5) includes an active device, dc feed, and output filter/matching network. Transformer-coupled and complementary topologies are
also used. The drain voltage and current waveforms of selected
ideal PAs are shown in Fig. 6.
A. RF-Power Transistors
RF PAs utilize a wide variety of active devices, including
bipolar-junction transistors (BJTs), MOSFETs, JFETs (SITs),
GaAs MESFETs, HEMTs, pHEMTs, and vacuum tubes [6],
Efficiency as a function of output (CW).
[7]. The power-output capabilities range from tens of kilowatts
for vacuum tubes to hundreds of watts for Si MOSFETs at HF
and VHF to hundreds of milliwatts for InP HEMTs at MMW
frequencies. Depending upon frequency and power, devices
are available in packaged, chip, and MMIC form. Virtually all
RF-power transistors are n-p-n or n-channel types because the
greater mobility of electrons (versus holes) results in better
operation at higher frequencies. While the voltages and currents
differ considerably, the basic principles for power amplification
are common to all devices.
B. Methods of Amplification
Class A: In class-A amplification, the transistor is in the active region at all times and acts as a current source controlled
by the gate drive and bias. The drain–voltage and drain–current
waveforms are sinusoids. This results in linear amplification
, where output voltage
with an output power of
. The dc-power input
load cannot exceed supply voltage
is constant, hence, the instantaneous efficiency (Fig. 7) is proportional to the power output and reaches 50% at PEP. The average efficiency is inversely proportional to the peak-to-average
ratio (e.g., 5% for 10 dB) and backoff (Fig. 8). For amplification of amplitude-modulated signals, the quiescent current can
be varied in proportion to the instantaneous signal envelope. The
utilization factor is 1/8. Class A offers high linearity, high gain,
and operation close to the maximum operating frequency of the
Class B: The gate bias in a class-B PA is set at the threshold
of conduction so the transistor is active half of the time and
the drain current is a half-sinusoid. Since the amplitude of the
Fig. 8. Efficiency as a function of backoff (SRRC OQPSK).
drain current is proportional to drive amplitude, class B provides
linear amplification. The instantaneous efficiency varies linearly
(78.5%) at PEP
with the RF-output voltage and reaches
for an ideal PA. For low-level signals, class B is significantly
more efficient than class A, and its average efficiency can be
several times that of class A at high peak-to-average ratios (e.g.,
dB). The utilization factor is the
28% versus 5% for
same 0.125 of class A. Class B is widely used in broad-band
transformer-coupled PAs operating at HF and VHF. It is finding
increasing use in microwave PAs, including experimental PAs
using complementary devices.
Class C: The gate of a classical (true) class-C PA is biased
below threshold so that the transistor is active for less than half
of the RF cycle. Linearity is lost, but efficiency can be increased
arbitrarily toward 100% by decreasing the conduction angle toward zero. Unfortunately, this causes the output power (utilization factor) to decrease toward zero and the drive power to increase toward infinity. A typical compromise is a conduction
angle of 150 and an ideal efficiency of 85%. When driven
into saturation, efficiency is stabilized and the output voltage
is locked to supply voltage, allowing linear high-level amplitude modulation. Classical class C is widely used in high-power
vacuum-tube transmitters, but is generally impractical for solidstate PAs.
Class D: Class-D PAs use two or more transistors as
switches to generate square drain–voltage (or current)
waveforms. A series-tuned output filter passes only the fundamental-frequency component to the load, resulting in a
for the transformer-coupled
power outputs of
configuration. Current is drawn only through the transistor
that is on, resulting in a 100% efficiency for an ideal PA. The
is the highest of any PA. If
utilization factor
the switching is sufficiently fast, efficiency is not degraded by
reactance in the load.
Practical class-D PAs suffer from losses due to saturation,
switching speed, and drain capacitance. Finite switching speed
causes the transistors to be in their active regions while conducting current. Drain capacitances must be charged and discharged once per RF cycle, resulting in power loss that is propor[8] and increases directly with frequency. Class-D
tional to
PAs with power outputs of 100 W to 1 kW are readily implemented at HF, but are seldom used above lower VHF because of
losses associated with the drain capacitance. Recently, however,
experimental class-D PAs have been tested with frequencies of
operation as high as 1 GHz [9].
Class E: Class E employs a single transistor operated as a
switch [10]. The drain–voltage waveform is the result of the
sum of the dc and RF currents charging the drain-shunt capacitance. In optimum class E, the drain voltage drops to zero and
has zero slope just as the transistor turns on. The result is an
ideal efficiency of 100%, elimination of the losses associated
with charging the drain capacitance in class D, reduction of
switching losses, and good tolerance of component variation.
Optimum class-E operation requires a drain shunt susceptance
and a drain series reactance
. It delivers a
for an ideal PA with a utilization
power output of
factor of 0.098. Variations in load impedance and shunt susceptance cause the PA to deviate from optimum operation, but the
degradations in performance are generally no worse than those
for classes A and B.
The capability for efficient operation in the presence of significant drain capacitance makes class E useful in a number of applications. High-efficiency HF PAs with power levels to 1 kW can be
implemented using low-cost MOSFETs intended for switching
rather than RF use [11]. Class E has been used for high-efficiency
amplification at frequencies as high as -band [12].
Class F: Class F boosts both efficiency and output by using
harmonic resonators in the output network to shape the drain
waveforms. The voltage waveform includes one or more odd
harmonics and approximates a square wave, while the current
includes even harmonics and approximates a half sine wave. Alternately (“inverse class F”), the voltage can approximate a half
sine wave and the current a square wave. As the number of harmonics increases, the efficiency of an ideal PA increases from
the 50% (class A) toward unity (e.g., 0.707, 0.8165, 0.8656,
0.9045 for two, three, four, and five harmonics, respectively)
and the utilization factor increases from 1/8 toward
The required harmonics arise naturally from nonlinearities and
saturation in the transistor. While class F requires a more complex output filter than other PAs, the impedances at the “virtual
drain” must be correct at only a few specific frequencies.
A variety of modes of operation in-between classes C, E, and
F are possible. The maximum achievable efficiency [13] depends upon the number of harmonics. The utilization factor depends upon the harmonic impedances and is highest for ideal
class-F operation.
C. Load–Pull Characterization
RF-power transistors are characterized by breakdown voltages
and saturated drain currents. The load impedance for maximum
power results in drain voltage and current excursions from near
zero to nearly the maximum values. The load impedances corresponding to delivery of a given amount of RF power with a specified maximum drain voltage lie along parallel-resistance lines on
the Smith chart. The impedances for a specified maximum current analogously follow a series-resistance line. For an ideal PA,
the resultant constant-power contour is football shaped [14].
In a real PA, the “virtual drain” is embedded behind the drain
capacitance and bond-wire/package inductance. Transformation of the ideal drain impedance through these elements causes
Fig. 10.
Fig. 9. Example load–pull contours for 0.5-W 836-MHz PA (courtesy Focus
Microwave and dBm Engineering).
the constant-power contours to become rotated and distorted.
With the addition of second-order effects, the contours become
elliptical. As shown in the example of Fig. 9, the power and efficiency contours are not necessarily aligned, nor do maximum
power and maximum efficiency necessarily occur for the same
load impedance. Sets of such “load–pull” contours are widely
used to facilitate design tradeoffs.
Load–pull analyses are generally iterative in nature, as
changing one parameter may produce a new set of contours. A
variety of different parameters can be plotted during a load–pull
analysis, including not only power and efficiency, but also
gain, distortion, and stability. Harmonic impedances as well as
drive impedances can also be varied. The variable impedance
required for load–pull testing can be obtained by mechanical,
electrical, or active techniques.
D. Microwave PAs
At microwave frequencies, lumped elements (capacitors, inductors) become unsuitable as tuning components and are used
primarily as chokes and bypasses. Matching, tuning, and filtering at microwave frequencies are, therefore, accomplished
with distributed (transmission-line) networks. Proper operation
of PAs at microwave frequencies is achieved by providing the
required drain–load impedance at the fundamental and a number
of harmonic frequencies.
Class F: Typically, a transmission line between the drain and
load provides the fundamental-frequency drain impedance of
the desired value. A stub that is a quarter-wavelength at the harmonic of interest and open at one end provides a short circuit
at the opposite end. The stub is placed along the main transmission line at either a quarter or a half-wavelength from the drain
to create either an open or short circuit at the drain [15]. The
supply voltage is fed to the drain through a half-wavelength line
bypassed on the power-supply end or alternately by a lumped-element choke. When multiple stubs are used, the stub for the
highest controlled harmonic is placed near the drain. Stubs for
lower harmonics are placed progressively further away and their
lengths and impedances are adjusted to allow for interactions.
X -band class-E PA.
Typically, “open” means 3–10 times the fundamental-frequency
impedance, and “shorted” means no more 1/10 to 1/3 of the fundamental-frequency impedance [13]. Dielectric resonators can
be used in lieu of lumped-element traps.
A wide variety of class-F PAs have been implemented at UHF
and microwave frequencies. Generally, only one or two harmonic impedances are controlled. In one -band PA [16], for
example, the output circuit provides a match at the fundamental
and a short circuit at the second harmonic. The third-harmonic
impedance is high, but not explicitly adjusted to be open. The
3-dB bandwidth of such an output network is about 20%, and
the efficiency remains within 10% of its maximum value over a
bandwidth of 15%.
Class E: The drain–shunt capacitance and series inductive
reactance required for optimum class-E operation result in a
at the fundamental frequency,
drain impedance of
at the second harmonic, and proportionately
smaller capacitive reactances at higher harmonics. At microwave frequencies, class-E operation is approximated by
providing the drain with the fundamental-frequency impedance
and preferably one or more of the harmonic impedances [17].
An example of a microwave approximation of class E that
provides the correct fundamental and second-harmonic impedances [16], [17] is shown in Fig. 10. The stub immediately to the
right of the FET is a quarter-wavelength long at the second harmonic so that the open circuit at its upper end is transformed to a
short at its lower end. The line at the drain in combination with
drain capacitance and inductance is also a quarter-wavelength
to translate the short on its right end to an open at the virtual
drain. The remaining lines provide the desired impedance at the
fundamental. This circuit uses an FLK052 MESFET to produce
0.68 W at -band with a drain efficiency of 72% and PAE of
Methods exist for providing the proper impedances through
the fourth harmonic [18]. However, the harmonic impedances
are not critical [13], and many variations are, therefore, possible. Since the transistor often has little or no gain at the higher
harmonic frequencies, those impedances often have little or no
effect upon performance. A single-stub match is often sufficient
to provide the desired impedance at the fundamental while simultaneously providing an adequately high impedance at the
second harmonic, thus eliminating the need for an extra stub
Fig. 12. Thick-film hybrid S -band PA amplifier module (courtesy UltraRF).
Fig. 11. Internal view of dual-band (GSM/DCS) PA module for
cellular-telephone handset (courtesy RF Micro Devices).
and reducing a portion of the losses associated with it. Most
microwave class-E amplifiers operate in a suboptimum mode.
Demonstrated capabilities range from 16 W with 80% efficiency
at UHF (LDMOS) to 100 mW with 60% efficiency at 10 GHz
[10], [17], [19].
Comparison: Classes AB and F have essentially the same
saturated output power, but class F has about 15% higher efficiency and class E has the highest efficiency [19]. Gain compression occurs at a lower power level for class E than for class
F. For a given efficiency, class F produces more power. For the
same maximum output power, the third-order IMD products are
about 10 dB lower for class F than for class E. Lower power PAs
implemented with smaller RF-power devices tend to be more efficient than PAs implemented with larger devices [16].
E. Examples
The PA for a 900-MHz CDMA handset is typically a single
GaAs-HBT RFIC that includes a single-ended class-AB PA. Recently developed PA modules also include a silicon control IC
that provides the base-bias reference voltage and can be commanded to adjust the output-transistor base bias to optimize efficiency while maintaining acceptably low amplifier distortion
over the full ranges of temperature and output power. A typical
PA module (Fig. 11) produces 28 dBm (631 mW) at full output
with a PAE of 35%–50%.
The thick-film-hybrid PA module shown in Fig. 12 uses four
140-mm LDMOS FETs operating from a 26-V drain supply.
The individual PAs have 11-dB power gain and are quadrature-combined to produce a 100-W PEP output at -band. The
average output power is 40 W for EDGE and 7 W for CDMA,
with an ACPR of 57 dBc for EDGE and 45 dBc for CDMA.
Solid-state PAs for MMW frequencies (30–100 GHz) are
-band PAs are based upon
predominantly monolithic. Most
-band PAs are based upon
pHEMT devices, while most
InP HEMTs. Some use is also made of HBTs at the lower
MMW frequencies. Class A is used for maximum gain. Typical
Fig. 13.
Linear transmitter architecture.
performance characteristics include 4 W with 30% PAE at
-band, 250 mW with 25% PAE at -band, and 200 mW
-band. Devices for operation at MMW
with 10% PAE at
are inherently small so large power outputs are obtained by
combining the outputs of multiple low PAs in corporate or
spatial power combiners.
Transmitters use as building blocks not only PAs, but a variety
of other circuit elements including oscillators, mixers, low-level
amplifiers, filters, matching networks, combiners, and circulators. The arrangement of building blocks is known as the architecture of a transmitter. The classic transmitter architecture
is based upon linear PAs and power combiners. More recently,
transmitters are being based upon a variety of different architectures including stage bypassing, Kahn, envelope tracking, outphasing, and Doherty.
A. Linear Architecture
The conventional architecture for a linear microwave transmitter consists of a baseband or IF modulator, an up-converter,
and a power-amplifier chain (Fig. 13). The amplifier chain consists of cascaded gain stages with power gains in the range of
6–20 dB. If the transmitter must produce an amplitude-modulated or multicarrier signal, each stage must have adequate linearity. This generally requires class-A amplifiers with substantial power backoff for all of the driver stages. The final amplifier (output stage) is always the most costly in terms of device
size and current consumption, hence, it is desirable to operate
the output stage in class B. In applications requiring very high
linearity, it is necessary to use class A in spite of the lower efficiency.
Fig. 14.
Corporate architecture with Wilkinson combiners.
B. Power Combiners
Whether to use a number of smaller PAs versus a single larger
PA is one of the most basic decisions in selection of an architecture [14]. Even when larger devices are available, smaller devices often offer higher gain, a lower matching factor (wider
bandwidth), better phase linearity, and lower cost. Heat dissipation is more readily accomplished with a number of small devices, and a soft-failure mode becomes possible. On the other
hand, the increase in parts count, assembly time, and physical
size are significant disadvantages to the use of multiple, smaller
In the corporate architecture (Fig. 14), power is split and
combined in steps of two. Hybrid combiners isolate the two
PAs from each other and allow one to continue operating if the
other fails. Quadrature combiners insert a 90 phase shift at the
input of one PA and a 90 phase shift at the output of the other.
This provides a constant input impedance, cancellation of odd
harmonics, and cancellation of backward-IMD (IMD resulting
from a signal entering the output port). In addition, the effect of
load impedance upon the system output is greatly reduced (e.g.,
to 1.2 dB for a 3 : 1 SWR). The Wilkinson combiner is fabricated
using quarter-wavelength lines and can be extended to include
more than two inputs or outputs.
C. Stage Bypassing and Gate Switching
Stage-bypassing and gate-switching techniques reduce power
consumption and increase efficiency by switching between large
and small amplifiers (e.g., the driver) according to peak signal
level. This can significantly increase the transmitter efficiency
when operating well into backoff, as shown in Fig. 8 (“GS”) for
ideal class-B PAs. These techniques are particularly effective
for mobile handsets that operate over a large dynamic range,
and improvement of the average efficiency from 2.1% to 9.5%
has been demonstrated [20].
D. Kahn Technique
The Kahn envelope elimination and restoration (EER) technique (Fig. 15) combines a highly efficient, but nonlinear RF
PA with a highly efficient envelope amplifier to implement a
high-efficiency linear RF PA. In its classic form, a limiter eliminates the envelope, allowing the constant-amplitude phase modulated carrier to be amplified efficiently by class-C, class-D,
class-E, or class-F RF PAs. Amplitude modulation of the final
RF PA restores the envelope to the phase-modulated carrier creating an amplified replica of the input signal.
EER is based upon the principle that any narrow-band signal
can be produced by simultaneous amplitude (envelope) and
phase modulations. In a modern implementation, both the
Fig. 15.
Kahn-technique transmitter.
Fig. 16. Class-S modulator.
envelope and phase-modulated carrier are generated by a DSP.
In contrast to linear amplifiers, a Kahn-technique transmitter
operates with high efficiency over a wide dynamic range and,
therefore, produces a high average efficiency for a wide range
of signals and power (backoff) levels. Average efficiencies three
to five times those of linear amplifiers have been demonstrated
from HF to -band [21].
Transmitters based upon the Kahn technique generally have
excellent linearity because linearity depends upon the modulator rather than RF-power transistors. The two most important
factors affecting the linearity are the envelope bandwidth and
alignment of the envelope and phase modulations. The envelope bandwidth must be at least twice the RF bandwidth and the
misalignment must not exceed one-tenth of the inverse of the
RF bandwidth [22]. In practice, the drive is not hard limited and
follows the envelope, except at low levels [23]. At higher microwave frequencies, the RF-power devices exhibit softer saturation characteristics and larger amounts of amplitude-to-phase
conversion, necessitating the use of predistortion.
The most widely used high-level modulator is class S
(Fig. 16). A transistor and diode or a pair of transistors act as
a two-pole switch to generate a rectangular waveform with a
switching frequency several times that of the output signal.
The width of pulses is varied in proportion to the instantaneous
amplitude of the desired output signal, which is recovered
by a low-pass filter. Class S is ideally 100% efficient and, in
practice, can have high efficiency over a wide dynamic range.
The switching frequency must typically be six times the RF
bandwidth. A switching frequencies of 500 kHz is readily
achieved with discrete components, and 10 MHz is achievable
in IC implementations. Class-G and split-band modulators can
be used in wide-band applications.
E. Envelope Tracking
The envelope-tracking architecture is similar to that of the
Kahn technique. The supply voltage is varied dynamically to
conserve power, but with sufficient excess (“headroom”) to
allow the RF PA to operate in a linear mode. The RF drive
contains both amplitude and phase information, and the burden
of providing linear amplification lies entirely on the final RF
Typically, the envelope is detected and used to control a dc–dc
converter. While both buck (step-down) or boost (step-up) converters are used, the latter is more common as it allows operation
of the RF PA from a supply voltage higher than the dc-supply
voltage. This configuration is also more amenable to the use of
n-p-n or n-channel transistors for fast switching. The result is a
corresponding to the dc-supply voltage and
tracking of larger envelopes with a fixed headroom. If the RF PA
is operated in class A, its quiescent current can also be varied.
The efficiency is significantly better than that of a linear RF
PA operating from a fixed supply voltage, but lower than that
of the Kahn technique. The efficiency of a system based upon
an ideal converter and class-B RF PA with headroom that is
10% of peak is included in Fig. 7 (“ET”). In practice, power
consumption by the converter and other circuits further reduces
the efficiency at lower output amplitudes.
A high switching frequency in the dc–dc converter allows
both a high modulation bandwidth and the use of smaller inductors and capacitors. Converters with switching frequencies of
10–20 MHz have recently been implemented using MOS ASICs
[24], GaAs HBTs [25], and RF-power MOSFETs [26]. The average efficiency for CDMA signals is typically increased from
that of a conventional linear amplifier by a factor of 1.5–2.
F. Outphasing
Outphasing was invented by Chireix during the 1930s as a
means of obtaining high-quality AM from vacuum tubes with
poor linearity and was used through about 1970 in RCA “ampliphase” AM-broadcast transmitters. In the 1970s, it came into
use at microwave frequencies under the name LINC (i.e., linear
amplification using nonlinear components). An outphasing
transmitter (Fig. 17) produces an amplitude-modulated signal
by combining the outputs of two PAs driven with signals of
different time-varying phases. Basically, the phase modulation
causes the instantaneous vector sum of the two PA outputs
to follow the desired signal amplitude. The inverse sine of
phase modulates the driving signals for the two
PAs to produce a transmitter output that is proportional to .
In a modern implementation, a DSP and synthesizer produce
the inverse-sine modulations of the driving signals.
Virtually all microwave outphasing systems in use today employ hybrid combiners to isolate the two PAs from each other
and to allow them to see resistive loads at all signal levels. However, both PAs deliver full power all of the time. Consequently,
the efficiency of a hybrid-coupled outphasing transmitter varies
with the output power (as in a class-A PA), resulting in an average efficiency that is inversely proportional to peak-to-average
ratio (as in class A). Recovery of the power from the dump port
Fig. 17.
Chireix-outphasing transmitter.
of the hybrid combiner offers some improvement in the efficiency.
Summation of the out-of-phase signals in a nonhybrid combiner inherently results in variable reactive PA-load impedances.
If the combiner is untuned, the current drawn from the PAs is
proportional to the transmitter-output voltage, resulting in an efficiency characteristic that varies with signal amplitude, as in a
similar class-B PA. The Chireix technique uses shunt reactances
on the inputs to the combiner to tune out the drain reactances at
a particular amplitude, which, in turn, maximizes the efficiency
in the vicinity of that amplitude. In the classic implementation,
the efficiency is maximized at the level of the unmodulated AM
carrier and remains high over the upper 6 dB of the output range
(Fig. 7) and for about 8 dB into backoff (Fig. 8). With judicious
choice of the shunt susceptances, the average efficiency can be
maximized for any given signal [27]. For example, the average
efficiency for a multicarrier signal with a 10-dB peak-to-average
ratio can be boosted from the 28% of class B to 52.1%. Simulations suggest that nonhybrid combining of microwave PAs increases both efficiency and distortion [28].
G. Doherty Technique
The classical Doherty architecture (Fig. 18) combines two
PAs of equal capacity through quarter-wavelength lines or networks. The “carrier” (main) PA is biased in class B, while the
“peaking” (auxiliary) PA is biased in class C. Only the carrier
PA is active when the signal amplitude is half or less of the PEP
amplitude. Both PAs contribute output power when the signal
amplitude is larger than half of the PEP amplitude.
Operation of the Doherty system can be understood by
dividing it into low-power, medium-power (load-modulation),
and peak-power regions [29]. In the low-power region, the
peaking PA remains cut off and appears as an open circuit.
The carrier PA, therefore, sees a 100- load and operates as
an ordinary class-B amplifier. The instantaneous efficiency
increases linearly with output, reaching the 78.5% of ideal class
B at saturation of the carrier PA at 6 dB from transmitter PEP.
As the signal amplitude increases into the medium-power region, the peaking PA becomes active. The additional current
sent to the load by the peaking PA causes the apparent load
to increase above the 25 of the low-power
impedance at
region. Transformation through the quarter-wavelength line results in a decrease in the load presented to the carrier PA. The
Fig. 18.
Doherty transmitter.
carrier PA remains in saturation and acts as a voltage source. It
operates at peak efficiency and delivers an increasing amount
of power. At PEP output, both PAs see 50- loads and each delivers half of the system output power. The PEP efficiency is
ideally the 78.5% of class-B PAs.
The classical power division approximately maximizes the
average efficiency for full-carrier AM signals, as well as modern
single-carrier digital signals. The use of other power-division
ratios allows the lower efficiency peak to be shifted leftward so
that the average efficiency is increased for signals with higher
peak-to-average ratios. For example, a transition at 36 percent of
PEP voltage results in a 60% average efficiency for a Rayleighenvelope signal with a 10-dB peak-to-average ratio, which is a
factor of 2.1 improvement over class B. Doherty transmitters
with unequal power division can be implemented by using different PEP load impedances and different supply voltages in the
two PAs [30].
Much recent effort has focused on accommodating nonideal
effects (e.g., nonlinearity, loss, phase shift) into a Doherty architecture [31]. In a modern implementation, DSP can be used
to control the drive and bias to the two PAs, resulting in more
precise control and higher linearity. The power consumed by
the quiescent current of the peaking amplifier is also a concern.
Nonetheless, -band Doherty LDMOS transmitters exhibit an
average efficiency nearly twice that of a quadrature-combined
PA with the same ACPR. It is also possible to use three or more
stages to keep the instantaneous efficiency relatively high over
a larger dynamic range [32]. The average efficiency of a threestage Doherty with ideal class-B PAs is 70% for a Rayleigh-envelope signal with 10-dB peak-to-average ratio [29].
Linearization techniques are used both to improve linearity
and to allow more efficient, but less linear methods of operation.
The three principal types of linearization are feedback, feedforward, and predistortion.
A. Feedback
Feedback linearizes the transmitter by forcing the output to
follow the input. It can be applied either directly to the RF amplifier (RF feedback) or indirectly to the modulation (envelope,
phase, or and components).
In RF feedback, a portion of the RF-output signal from the
amplifier is fed back to and subtracted from the RF-input signal
without detection or down-conversion. The delays involved
must be small to ensure stability, and the loss of gain at RF
is a more significant design issue. The use of RF feedback in
discrete circuits is usually restricted to HF and lower VHF
frequencies, but it can be applied within MMIC devices well
into the microwave region [33].
Envelope feedback reduces distortion associated with amplitude nonlinearity. It can be applied to either a complete transmitter or a single PA [33]. The RF input signal is sampled by
a coupler and the envelope of the input sample is detected. The
resulting envelope is then fed to one input of a differential amplifier, which subtracts it from a similarly obtained sample of the
RF output. The difference signal, representing the error between
the input and output envelopes, is used to drive a modulator in
the main RF path. This modulator modifies the envelope of the
RF signal, which drives the RF PA. The envelope of the resulting
output signal is, therefore, linearized to a degree determined by
the loop gain of the feedback process. For a VHF BJT amplifier
in which amplitude nonlinearity is dominant, two-tone IMD is
typically reduced by 10 dB.
The polar loop overcomes the fundamental inability of envelope feedback to correct for AM-PM distortion by adding a
phase-locked loop to the envelope feedback system. Envelope
detection and phase comparison generally take place at the IF.
For a narrow-band VHF PA, the improvement in two-tone IMD
is typically around 30 dB. The envelope bandwidth must be at
least twice the RF bandwidth, but the phase bandwidth must be
at least ten times the RF bandwidth.
The Cartesian-feedback technique overcomes the problems
associated with the wide bandwidth of the signal phase by applying modulation feedback in and
(Cartesian) compocomponents are the natural outputs
nents. Since the and
of a modern DSP, the Cartesian loop is widely used in mobileradio systems. Two identical feedback processes operate independently on the and channels (Fig. 19). The inputs are applied to differential integrators (in the case of a first-order loop)
and the resulting difference (error) signals are quadrature-upconverted to drive the PA. A sample of the output from the PA
is attenuated and down-converted in quadrature and synchronously with the up-conversion process. The resulting quadrature
feedback signals then form the second inputs to the input differential integrators, completing the two feedback loops. The phase
shifter shown in the up-converter local-oscillator path is used
to align the phases of the up- and down-conversion processes.
The use of Cartesian feedback with a class-C PA amplifying an
IS-136 (DAMPS) signal improves the first ACPR by 35 dB and
the allows the signal to be produced with an efficiency of 60%
B. Feedforward
The very wide bandwidths (10–100 MHz) required in multicarrier applications can render feedback and DSP impractical.
In such cases, the feedforward technique can be used to reduce
distortion by 20–40 dB. In its basic form (Fig. 20), a feedforward amplifier consists of two amplifiers (the main and error
amplifiers), directional couplers, delay lines, and loop control
Fig. 19.
Cartesian-loop transmitter.
Fig. 21.
Fig. 20. Feedforward transmitter.
networks [34]. The directional couplers are used for power splitting/combining, and the delay lines ensure operation over a wide
bandwidth. Loop-control networks, which consist of amplitudeand phase-shifting networks, maintain signal and distortion cancellation within the various feedforward loops.
The input signal is first split into two paths, with one path
going to the high-power main amplifier, while the other signal
path goes to a delay element. The output signal from the main
amplifier contains both the desired signal and distortion. This
signal is sampled and scaled using attenuators before being
combined with the delayed portion of the input signal, which
is regarded as distortion free. The resulting “error signal”
ideally contains only the distortion components in the output
of the main amplifier. The error signal is then amplified by the
low-power high-linearity error amplifier, and then combined
with a delayed version of the main amplifier output. This
second combination ideally cancels the distortion components
in the main-amplifier output while leaving the desired signal
Successful isolation of an error signal and the removal of
distortion components depend upon precise signal cancellation
over a band of frequencies. For a 30-dB cancellation depth, the
amplitudes must be matched within 0.22 dB and the phases
Predistortion concept.
within 1.2 [34]. For manufactured equipment, realistic values
of distortion cancellation are around 25–30 dB. The limiting
factor is nearly always the bandwidth over which a given accuracy can be obtained.
The outputs of the main and error amplifiers are typically
combined in a directional coupler that both isolates the PAs from
each other and provides resistive input impedances. For a typical 10-dB coupling ratio, 90% of the power from the main PA
reaches the output. For the same coupling ratio, only 10% of the
power from the error amplifier reaches the load, thus the error
amplifier must produce ten times the power of the distortion in
the main amplifier. The peak-to-average ratio of the error signal
is often much higher than that of the desired signal, making amplification of the error signal inherently much less efficient than
that of the main signal. As a result, the power consumed by the
error amplifier can be a significant fraction (e.g., one-third) of
that of the main amplifier. In addition, it may be necessary to
operate one or both amplifiers well into backoff to improve linearity. The overall average efficiency of a feedforward transmitter may, therefore, be only 10%–15% for typical multicarrier
Since feedforward is inherently an open-loop process,
changes in device characteristics over time, temperature,
voltage, and signal level degrade the amplitude and phase
matching and, therefore, increase distortion in the transmitter
Fig. 22.
Constant-gain predistorter.
output. An automatic control scheme continuously adjusts
the gain and phase to achieve the best signal cancellation and
output linearity. The first step is to use FFT techniques, direct
power measurement, or pilot signals to determine how well the
loop is balanced. Both digital and analog techniques can be
used for loop control and adjustment.
C. Predistortion
The basic concept of a predistortion system (Fig. 21) involves
the insertion of a nonlinear element prior to the RF PA such that
the combined transfer characteristic of both is linear. Predistortion can be accomplished at either RF or baseband.
An RF predistorter typically creates the expansive predistortion characteristic by subtracting a compressive transfer function (such as that of a diode) from a linear transfer function.
Improvements in the ACPR by 10 dB are typical. As with feedforward, the operating bandwidth is limited by the gain and
phase flatness of the predistorter itself and of the RF PA. In
addition, memory effects in the PA and the predistorter limit
the degree of cancellation. Better performance can be achieved
with more complex forms of RF predistortion such as Adaptive
Parametric Linearization (APL), which is capable of multiorder
correction [33]. Most RF-predistortion techniques are capable
of broad-band operation with practical operational bandwidths
similar to, or greater than, those of feedforward.
D. Digital Predistortion
Digital predistortion techniques exploit the considerable processing power now available from DSP devices, which allows
them both to form and to update the required predistortion characteristic. They can operate with analog-baseband, digital-baseband, analog-IF, digital-IF, or analog-RF input signals. Digitalbaseband and digital-IF processing are most common. The two
most common types of digital predistorter are termed “mapping
predistorters” and “constant-gain predistorters.”
A constant-gain predistorter (Fig. 22) requires only a singledimensional lookup table, indexed by the signal envelope to
generate the expansive predistortion characteristic. It is simple
to implement and requires only a modest amount of memory for
a given level of performance and adaption time. A mapping predistorter utilizes two lookup tables, each of which is a function
of the and components of the input. This type of predistorter is capable of excellent performance. However, it requires
a significant storage and/or processing overhead for the lookup
tables and their updating mechanism, and has a low speed of
An example of linearization of a PA with two 3G W-CDMA
signals by a digital baseband-input predistorter is shown in
Fig. 23. The linearized amplifier meets the required spectral
mask with a comfortable margin at all frequency offsets. The
noise floor is set by the degree of clipping employed on the
waveform, which limits the ACPR improvement obtained. It
clearly demonstrates, however, that digital predistortion can
be used in broad-band, as well as narrow-band applications.
Fig. 24 shows an example of a commercial 3G transmitter with
digital predistortion.
The ever-increasing demands for more bandwidth, coupled
with requirements for both high linearity and high efficiency
create ever-increasing challenges in the design of PAs and transmitters. These problems are especially acute in base-station and
satellite transmitters, where multiple carriers must be amplified
simultaneously, resulting in peak-to-average ratios of 10–13 dB
and bandwidths of 30–100 MHz. A number of emerging techniques may prove useful in these applications in the near future.
Fig. 23. Linearization of 3G W-CDMA PA signal by digital baseband-input
predisorter (courtesy WSI).
the carrier frequency. The polarity is toggled by a quantizer so
that the average carrier amplitude is the desired value. The quantizer forces most of the quantizing noise to fall outside of the
signal band where it can be removed by a narrow-band output
Carrier PWM drives the RF PA with bursts of the RF carrier frequency. The width of the bursts is varied in proportion to
the instantaneous output amplitude. A narrow-band output filter
passes the desired average carrier amplitude and rejects the sidebands associated with the burst frequency. While the process is
analogous to that in a class-S modulator, the burst frequency can
be 100 MHz or more to accommodate wide-band signals.
Electronic tuning [36] allows frequency agility, matching
of unknown and variable loads, and amplitude modulation.
Components for electronic tuning include p-i-n diode switches,
MEMS switches, MEMS capacitors, semiconductor capacitors,
ceramic capacitors (e.g., BST), and bias-controlled inductors.
“Load modulation” uses an electronically tuned output filter to
vary load impedance and thereby the instantaneous amplitude
of the output signal. The modulation bandwidth can be quite
wide, as it is limited only by the bias feeds to the tuning components. With judicious choice of the impedance locus used in
the modulation process, the efficiency remains high over most
of the dynamic range, resulting in average efficiencies three
times those of a class-B PA.
Fig. 24.
S -band
transmitter with digital predistorter (courtesy
RF pulsewidth modulation (RF PWM) varies the duty ratio of
a class-D RF PA to produce an output signal with a time-varying
envelope. The amplitude of the output is proportional to the inverse sine of the pulsewidth. The spurious products associated
with PWM are located in the vicinity of the harmonics of the
carrier and, therefore, do not limit the modulation bandwidth.
Delta-sigma modulation also directly modulates the carrier
produced by a class-D RF PA [35]. The PA is driven at a fixed
clock rate (hence, fixed pulsewidth) that is generally higher than
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Frederick H. Raab (S’66–M’72–SM’80) received the B.S., M.S., and Ph.D.
degrees from Iowa State University, Ames, in 1968, 1970, and 1972, respectively.
He is Chief Engineer and Owner of Green Mountain Radio Research
(GMRR), Colchester, VT, a consulting firm that provides research, design, and
development of RF PAs, transmitters, and systems.
Dr. Raab was the recipient of the 1995 Professional Achievement Citation in
Peter Asbeck (M’75–SM’97–F’00) received the B.S., M.S., and Ph.D. degrees
from the Massachusetts Institute of Technology (MIT), Cambridge.
He was with the Sarnoff Research Center, Philips Laboratory, and Rockwell
Science Center, where he helped develop high-speed devices and circuits using
III–V compounds and heterojunctions. In 1991, he became a Professor at the
University of California at San Diego (UCSD), La Jolla.
Steve Cripps (M’81–SM’90) received the B.A., M.A., and Ph.D. degrees from
Cambridge University, Cambridge, U.K., in 1971, 1974, and 1975, respectively.
He has held engineering and management positions at Loral and Celeritek,
both in the U.S. In 1996, he returned to the U.K. and is currently an independent
consultant specializing in microwave and RF power-amplifier design.
Peter B. Kenington (M’99–SM’02) received the B.Eng. and Ph.D. degrees
from Bristol University, Bristol, U.K., in 1986 and 1989, respectively.
In 1990, he became a Lecturer in Communications Engineering and jointly
founded Wireless Systems International Ltd., Bristol, U.K., in 1995. In 1997, he
joined the company full-time as Head of Advanced Development, and became
the Chief Technology Officer in 2000.
Zoya B. Popović (S’86–M’90–SM’99–F’02) received the Ph.D. degree from
the California Institute of Technology, Pasadena, in 1990.
She is current a Full Professor at the University of Colorado, Boulder. She has
authored books on introductory electromagnetics spatial power combining. Her
research interests are in high-efficiency microwave circuits, active and smart
antenna arrays, and RF photonics.
Nick Pothecary (M’99) received the B.Eng. and Ph.D. degrees from the University of Bristol, Bristol, U.K., in 1990 and 1994, respectively.
He is currently an international consultant specializing in RF linear power
and electromagnetics. He has taught many courses in both industry and
academia. He authored Feedforward Linear Power Amplifiers (Norwood, MA:
Artech House, 1999).
John F. Sevic (S’87–M’90) received the B.S.E.E. degree from the Michigan
Technological University, Houghton, in 1989, and M.S.E.E. degree from the
Illinois Institute of Technology, Chicago, in 1992.
He possesses experience in designing RF/MW PAs that ranges from transistor
die to correction algorithm development. He has also been involved in device
modeling and load-pull analysis. He is currently the RFIC PA Manager and Staff
Engineer at Tropian Inc., Cupertino, CA.
Nathan O. Sokal (S’50–A’51–M’56–SM’56–F’89–LF’94) received the B.S.
and M.S. degrees in electrical engineering from the Massachusetts Institute of
Technology (MIT), Cambridge, in 1950.
In 1965, he founded Design Automation Inc., Lexington, MA, a consulting
company performing electronics design review, product design, and technology
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