Multi-Frequency Measurements for Supply Modulated Transmitters

Multi-Frequency Measurements for Supply Modulated Transmitters
Multi-Frequency Measurements for Supply
Modulated Transmitters
Scott Schafer, Student Member, IEEE, and Zoya Popović, Fellow, IEEE
Abstract—Transmitters for high peak-to-average power ratio
communication are increasingly using supply modulation to
improve efficiency. In addition to a dc component, the dynamic
supply may contain ac components up to 500 MHz. The low-frequency (LF) dynamic impedance of the supply terminal of a power
amplifier (PA) is often unknown and available nonlinear transistor models are unable to predict dynamic LF effects required
for design of wideband efficient supply modulators (SMs). This
paper describes a technique to calibrate and measure multi-port
multi-frequency parameters of a transistor and PA under supply
modulation conditions. The measurement setup is used to characterize the complex drain impedance of GaN transistors and PAs in
large-signal operation at X-band with 1–500-MHz LF excitation
on the drain terminal, over a range of input power levels. In addition, the LF drain impedance of a 10-GHz monolithic microwave
integrated circuit PA with 4-W output power and 60% peak
power-added efficiency is measured when the PA is connected to a
simple switched resonant SM. The main motivation for this work
is to obtain knowledge of the dynamic supply-port impedance that
can enable improved PA and SM co-design.
Index Terms—Drain impedance, envelope tracking (ET), highefficiency transmitters, microwave power amplifiers (PAs), transition characterization.
IRELESS systems have increasingly complex modulation schemes and increasing signal bandwidths in order
to improve capacity [1]. Such signals have high peak-to-average
power ratios (PAPRs) and it is a challenge to design an efficient transmitter that meets linearity requirements, especially
for signal bandwidths exceeding a few tens of megahertz. A
common transmitter power amplifier (PA) that addresses this
problem is the Doherty amplifier [2], which suffers from bandwidth limitations, although there have been recent demonstrations with increased bandwidth operation [3]. Other solutions
for amplifying high PAPR signals include outphasing [4] and
various forms of supply modulation [5]. Additionally, supply
modulation has also been shown to be beneficial to Doherty [6]
and outphasing PAs [7].
Manuscript received February 05, 2015; revised June 25, 2015; accepted
July 11, 2015. Date of publication August 05, 2015; date of current version
September 01, 2015. This work was funded by the Office of Naval Research
(ONR) under the Defense Advanced Research Projects Agency (DARPA)
Microscale Power Conversion (MPC) Program N00014-11-1-0931.
The authors are with the Department of Electrical, Computer and Energy
Engineering, University of Colorado, Boulder, CO 80309-0425 USA (e-mail:
Color versions of one or more of the figures in this paper are available online
Digital Object Identifier 10.1109/TMTT.2015.2458962
Fig. 1. Simplified block diagram of a supply-modulated transmitter. The baseband signal is expressed in envelope and phase form, where most of the envelope signal is input to the drain of the PA through an efficient SM. The phase
and a portion of the envelope are unconverted to the carrier that drives the PA
input. In this configuration, the device is under multi-frequency excitation and
can be viewed as a three-port (ports 1 and 2 are RF, while port 3 is LF). The
) variation is shown for static
, however, this variation of PAE is
not necessarily true for a variation in supply voltage (
Efficiency improvement by supply modulation comes from
decreasing wasted dc power when the output power of the RF
power amplifier (RFPA) is reduced. Various forms of supply
modulation include envelope elimination and restoration (EER)
[5], envelope tracking (ET) [8], and polar [9]. Fig. 1 shows
a general block diagram of a supply-modulated transmitter
with an illustration of power-added efficiency (PAE) versus
output power (
, and its dependence on supply
voltage ( ). The supply modulator (SM) needs to provide
sufficient power while following the signal envelope, which for
high bandwidth signals implies high supply slew rates [10]. In
addition, common stability capacitors in the supply dc circuit
have to be eliminated because the supply has high-bandwidth
signal content [11], [12]. A problem rarely addressed in the
literature is the dynamic envelope-frequency impedance that
the PA presents to the SM.[13]1 Additionally, most commercial
nonlinear RF transistor models are not designed to predict
low-frequency (LF) dynamic behavior at the drain supply
port, where the drain supply port is considered the third port.
Multi-frequency three-port measurements are therefore very
useful for supply-modulated RFPA transmitter co-design.
Related previous work can be found in papers on LF measurements for device characterization [14]–[21], baseband
impedance investigation for linearity [22]–[26], and bias line
instabilities [12], [27]. Very few systems have been designed
to characterize transistors under drive while simultaneously
measuring or monitoring baseband ( 500 MHz) performance
or properties. However, [28] creates a basic mixer-like transfer
function to model inter-modulation products mixed from a
1This paper is an expanded version from the IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, May 17–22, 2015
0018-9480 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See for more information.
Fig. 2. Simplified diagram of measurement setup for a transistor. The RF path uses power sensors to measure the performance of a DUT under normal operating
conditions. The tuners present RF loads to the DUT and are approximately short 50- transmission lines at low frequencies ( 1 GHz). The LF path generates
an LF signal and includes biasing for the drain of the DUT. A coupler with an oscilloscope measures the forward and reverse wave parameters of the LF path.
The RF and LF paths are split with a special bias tee that differentiates the RF and LF signals (diplexer). A similar bias tee is used on the gate to terminate the LF
impedances in 50 and provide bias. The DUT shown in the figure is a transistor, but can also be a PA.
baseband injection at the drain. Also, efforts have been made to
measure and model the nonlinear current source of a transistor
by simultaneously exciting LF ( 10 MHz) and RF on the gate
of the device and measuring response at LF and RF [29], [30].
For literature in device characterization, device behavior at
frequencies less than 1 MHz is important for accurate transistor
modeling that takes into account thermal and trapping effects.
In [14], it is shown that LF 5 Hz to 1 GHz -parameters of GaN
transistors can be used to separate trapping from thermal effects.
In [15] and [16], active bias tees with very high LF impedances
were implemented from about 5 Hz to 1 MHz to measure LF
dispersion. Another application of LF in device characterization
is the use of the baseband signal to control the RF impedance of
a load–pull setup [18]. Here the baseband in-phase/quadrature
(I/Q) are used as the feedback in a closed-loop active load–pull
setup. More advance setups involve active envelope frequency
load–pull to present a constant impedance across the baseband
frequencies [19], [31].
To investigate baseband effects on linearity, a time-domain
measurement on a 835-MHz class-B PA under two-tone excitation showed that there is an optimal IF impedance for linearity [22]. Gate voltage dependence and tone separation was
investigated in [23], while [24] implements a control circuit to
change the baseband impedance. A six-port reflectometer was
developed in [25] so that the baseband impedance can be varied
with variable gate and drain biases. While [22]–[25] showed
useful data for linearity investigations, the results are usually
limited to a single-tone RF excitation and no injected power into
the drain/collector (the third port) of the transistor. In contrast,
our work presents measurements of the broadband drain supply
impedance while the PA is under normal large-signal operating
conditions, possibly with modulation, and with LF power injected into port 3 to model supply modulation.
A few papers monitor and control the LF stability of a transistor by varying capacitance and/or resistance values on the
bias line [12], [27]. The methods presented in these papers accurately measure and account for bias line instabilities, but are
specific to the measured PA module and do not give any information on the LF parameters of the transistor themselves.
In this paper, both a single transistor and an amplifier are
tested in a three-port configuration under excitation on all
ports. The RF impedance and LF impedance are measured in a
nominal operating condition under multi-frequency excitation,
which is an important difference from previous reported work.
The measurement system from Fig. 2 is a system to simultaneously measure the LF drain impedance and dynamics of a
transistor while in large-signal RF operation with modulated
signals. The carrier frequency in this case is 10 GHz while the
LF excitation covers 1–500 MHz. The work in this paper is an
extension of [13].
Section II details the measurement setup and calibration.
Sections III – V present measured data on an X-band GaN
transistor, monolithic microwave integrated circuit (MMIC)
PA, and PA with a resonant SM, respectively.
The test system shown in Fig. 3 was developed to measure
LF impedances over a wide bandwidth ( 1–500 MHz) while
simultaneously measuring the large-signal RF performance of
a device-under-test (DUT). The RF path uses a spectrum analyzer to distinguish multiple tones at RF frequencies. Fundamental frequency tuners are used to adjust the RF loading of
the transistor. In the LF path, an oscilloscope is used to acquire the time-domain waveform. The oscilloscope is the National Instruments NI PXIe-5162, which has 10 bits of vertical resolution with 2.5-GS/s simultaneous sampling on two
channels. The sample rate is controllable with an external clock
input and internal rate multipliers and dividers. The two coupled voltage waveforms ( , ) are digitized and the Fourier
transform taken to find the voltage wave, which can then be converted to pseudo-wave parameters ( , ) [32]. The LF signal
is ac coupled onto the dc drain voltage. This allows an RF signal
generator to provide a LF signal up to the bandwidth of the bias
tee. The entire dc LF block can be replaced with an SM that
Fig. 3. Photograph of setup with labeled: 1) RF source, 2) gate tuner, 3) probe
station with DUT, 4) drain tuner, 5) bias tee, 6) LF coupler, 7) oscilloscope, and
8) LF source.
simultaneously supplies the dc and LF signals without re-calibration.
The RF carrier frequency used in this paper is 10 GHz, which
is far from the LF of
500 MHz. This allows simpler filter
design of the bias tee to differentiate the RF and LF signals.
A. Bias Tee
The bias tee is of particular interest for wide-bandwidth signals as it must be designed to pass the LF content to the transistor while blocking the same content from leaking out to the
RF load. The function of the bias tee is similar to a diplexer,
but somewhat simpler. For the measurements presented in this
paper, the circuit is a parallel combination of a small dc blocking
capacitor (in the RF path) and a seventh-order low-pass filter
(in the LF path). The bandwidth of the low-pass filter is 1 GHz,
which is adequate to pass large bandwidth envelope signals. A
small blocking capacitor is necessary to restrict the LF signal
from passing to the RF load. As the low-pass filter requires large
inductance and capacitance values, parasitics of the elements
causing resonances in the RF band are non-negligible and the
primary limitation for a wide bandwidth bias tee. Additional elements (an inductor and capacitor) were used in the RF path
to help flatten the frequency response in the RF band. A photograph of the bias tee used is shown in Fig. 4 along with its
measured -parameters. There is 1 dB of insertion loss through
the RF path and 0.3-dB loss through the LF path. The match
is better than 40 dB at LF and 10 dB at 10.7 GHz.
B. Calibration
The goal of the setup is to acquire the absolute voltages and
currents at the DUT at low frequencies ( 500 MHz). In brief,
the thru-reflect-line (TRL) calibration method is performed
at RF frequencies with -parameter measurements of the
high-frequency couplers to determine the power meter offsets.
At LF frequencies, a short-open-load (SOL) with an absolute
power calibration is performed coaxially at the LF coupler (as
shown by and in Fig. 2) before connecting to the load tuner
probe station. De-embedding to the DUT requires an additional
SOL calibration using an impedance substrate standard (from
Cascade Mircotech). The sampling frequency and number of
points used in the fast Fourier transform (FFT) is kept constant
throughout the calibration and measurement giving a discrete
frequency grid. The LF calibration is described in more depth
in the remainder of this section.
Fig. 4. (a) Photograph and circuit diagram of wideband bias tee, which operates
as a diplexer. (b) Measured performance of the bias tee.
The -parameter matrix from the coupler to the DUT is
are measured from the oscilThe raw digitized parameters
loscope and converted into the frequency domain with an FFT.
Using the SOL, three of the four -parameters can be found. To
facilitate this computation,
is assumed to be 1 and a scaling
factor, , is used for the absolute power calibration. The reflection coefficient can be written as
is the known reflection coefficient of a calibration
standard. Using three different standards gives three equations
is the measured value with the calibration standards SOL (as denoted in the subscript) connected to the reference plane. Equation (3) is solved for the three -parameters.
Next, a calibrated power meter is connected to the same
coaxial plane as the SOL for the power calibration. The
calibrated power meter measures the absolute power at the
reference plane regardless of the reflection coefficient mismatch: the power measured is the incident power
In the setup, the measured power directly gives
. The reflection coefficient of the power meter can be found using the
-parameters solved for in (3), which allows the computation
of the scaling parameter, . Computation of the calibrated
Fig. 5. Nonlinear device model is not valid under dynamic operation at
low frequencies, as expected. Comparison between simulated and measured
V and
LF impedance at 10 MHz for the 10 90 m device at
mA mm.
pseudo-waves at the DUT from the raw measured values is
easily performed by using (1). Note that the phase of is still
unknown (ultimately three complex standards were used plus
one scalar standard, giving a total of seven parameters versus
eight unknowns).
To find the relative phase of
between frequencies, a multisine signal is generated and measured (similar to the method
presented in [33]). The Schroeder method is used to synthesize
a low peak-to-average ratio multisine waveform with a 10-kHz
tone spacing and an arbitrary waveform generator (ARB) generates the signal [34]. First, the relative phase of the tones are
measured directly by connecting a calibrated oscilloscope to the
output of the ARB. The ARB is attached to the LF coupler on
the port closest to the bias tee and the multisine waveform is
digitized by the oscilloscope. Since the relative phases between
the frequency components are known, the phase of
can be
computed by
where is known within a linear phase shift,
are measured,
are known from the SOL calibration.
The above calibration method allows determination of the
voltage, current, and impedance at the LF port of the DUT while
the other two ports are measured with standard RF instruments.
Before investigating the behavior of a PA, it is instructive
to investigate the transistor alone. Test devices of 10 90 m
were fabricated in the TriQuint 0.15- m GaN process on a 4-mil
system-on-chip (SiC). These devices are used in the MMIC PAs
in the following sections.
Most nonlinear device models are not extracted at low frequencies. Fig. 5 shows a comparison between measurement and
simulation of the complex impedance of the drain port over
swept baseband input power (or LF input power, ) at 10 MHz.
The model is Angelov based and was extracted with 10-GHz
load–pull (original application frequency) at multiple drain voltages with a bias point of 100 mA/mm. The device was measured at 100 mA/mm with a 20-V drain with 14-dBm input RF
Fig. 6. - curves for 10 90 m device. At each point, the LF impedance is
measured. The device is kept under 3.0-W power dissipation to avoid damage
to the device.
power. The simulation was performed under the same parameters as the measurement. The simulation result has roughly
the same impedance at low input powers, but as the LF input
power increases, the trend is opposite of measurement: the LF
real part of the impedance decreases by only about 50 starting
at 15-dBm input while the measurement starts an increasing at
2-dBm input with a total increase of 110 . Another example is
shown in [13, Fig. 6], simulation for one of the MMICs shows
nonphysical behavior near compression, although RF simulations with the same model accurately predict carrier-frequency
behavior. These examples highlight the need to characterized
the device for supply modulation purposes under high multi-frequency drive.
A. Static Drain Impedance
The – curves of the 10 90 m device were measured
and are shown in Fig. 6. At each bias point, the small-signal
drain impedance was measured. The device is kept under 3.0-W
power dissipation to avoid breakdown or device failure as our
measurement bench is not capable of pulsed measurements. The
measured LF impedance at 1 MHz is shown in Fig. 7(a). Other
frequencies (up to 100 MHz) have nearly identical results because of the very small reactance under static measurements.
The measured impedance is not the same as the small signal
bias point resistance (
) because of dispersive effects [16],
[35], [36]. Since the measurement frequency is above the typical
transition frequency for dispersion (e.g., 100 kHz in [16]), the
measured impedance is closer to the -parameters at the particular bias point instead of the dc resistance. The trends shown in
Fig. 7(a) can be thought of as a bias dependent switch; at low
, the device is off and presents a high impedance, while when
the channel is open (high ), there is only the resistance of the
channel itself. The saturation of the device can be seen as the
increase of resistance for higher
V is not saturated, Fig. 6, and so the impedance still decreases for larger
). Plotting the impedance versus gate voltage in Fig. 7(b), the
turn-on voltage can be clearly seen at various
as a large decrease in drain resistance.
The frequency variation of the static bias point can easily be
fit by a parallel RC circuit. However, the higher current bias
points have a distinct series inductive part that indicates other effects besides a bias-dependent resistance and capacitance. This
Fig. 9. (a) Measured RF load–pull performance on 10 90 m transistor at
V, and RF
dBm. (b)
at 10 MHz
10 mA/mm,
plotted versus RF impedance at various input powers.
Fig. 7. (a) Measured real part of the drain impedance at 1 MHz with no RF
input. While the partial derivative of the – curves gives a rough approximation in trends of the drain impedance, there is a significant magnitude difference
V. (b) Real part of the measured drain impedance
above approximately
plotted versus gate bias clearly shows the turn-on voltage for the device at various drain voltages.
Fig. 8. Complex impedance from 10 to 500 MHz of a few bias points of the
10 90 m transistor plotted on a 50- admittance grid. The lower gate bias
voltage curves can easily be fit by a parallel RC circuit. The higher gate biases
( 1 and 2 V) have an inductive part in addition to the RC indicating other
effects under high current.
can be seen in Fig. 8 where the higher current bias points ( 1
and 2 V) have a slant toward the left instead of following the
constant admittance circles.
B. Dynamic Impedance
Source–pull and load–pull were performed on the
10 90 m device to find the optimum fundamental frequency
RF terminations for maximum PAE at 10 GHz and
The peak PAE RF load is
. Measured output power
and efficiency contours are shown in Fig. 9(a). Over various
RF input powers and at each load–pull point, the LF impedance
is measured [see Fig. 9(b)]. The value of the real impedance
varies not only with the RF load, but with the RF input power
as well. For example, at the peak power RF impedance in
Fig. 9(a), at low power the drain impedance is high around
300 and decreases to 150 at maximum power with 22-dBm
input power.
Under supply modulation, the envelope can be considered in
the frequency domain as a signal with power over a bandwidth.
It is reasonable to expect that the impedance seen by the SM will
be dependent on the power that it supplies,
. Figs. 10 and
11 show the variation in real and imaginary parts of the drain
impedance versus RF and LF baseband input power for an optimum PAE RF load. When the transistor is biased in class B
[see Fig. 11(a)], the impedance generally increases with baseband input power, , and decreases with RF input power,
At RF saturation for both 10 and 100 mA/mm,
is at a
minimum and roughly uniform across
at 150 . However,
at 100 mA/mm [see Fig. 10(a)], there is a second impedance
minimum for low RF and LF input power. Note that
also varies significantly over input powers and bias point [see
Figs. 10(b) and 11(b)].
The MMIC chosen for measurements is a single-stage
class-B PA on 0.15- m GaN. The PA combines two
10 100 m (number of fingers
length of finger) devices
at the output for 2 mm of output stage gate periphery and
4 W of output power at saturation, and is shown in Fig. 12(a).
The MMIC was mounted as in [37] with the off-chip drain
Fig. 10. Measured: (a) real and (b) imaginary drain impedance at 10 MHz and
V versus input RF and LF power at
mA mm.
capacitances removed. The measurement setup for a PA is
simpler than the transistor setup as a bias network is already
integrated on the MMIC. In this case, the bias tee was not
specially designed to diplex the LF and RF frequencies. In
addition to finding the impedance that the PA will present to the
modulator, the purpose of the measurements here is to quantify
how wide of an LF modulation bandwidth injected through the
drain bias line is achievable with a pre-built PA.
The LF equivalent circuit in Fig. 12(b) shows integrated capacitors and resistors on the MMIC and the interconnection
to the measurement setup. The PA was designed to work near
pinch-off in class-B operation with 5 mA of quiescent current.
The drain impedance of the PA was measured under RF operating conditions at 10.1 GHz. The PAE is shown in Fig. 13 and
is highest at the nominal drain voltage bias of 20 V and high
compression. Simultaneously, impedance was measured across
the baseband frequency de-embedded to the off-chip end of the
bondwire connected to the MMIC dc bias pad. Fig. 14(a) shows
the impedance at 1 MHz. At this frequency, the real part of the
impedance decreases and the reactance (not shown) increases
with RF input power.
Fig. 15(a) and (b) shows the impedance across frequency
when the amplifier is compressed (approximately 34.5-dBm
output power with
V). The high bias line capacitance
of 87.8 pF causes the impedance to be very low and roughly
Fig. 11. Measured: (a) real and (b) imaginary drain impedance at 10 MHz and
V versus input RF and LF power at
mA mm.
Fig. 12. Layout of MMIC PAs used for drain impedance measurements.
(a) X-band GaN 4-W PA. Two 10 100 m devices are combined as a
single-stage amplifier (2.3 2 mm). (b) LF equivalent lumped-element
schematic. The shunt RC of 29.4 pF and 14 is for LF stability of the MMIC.
The effective shunt capacitance on the MMIC is 87.8 pF.
constant above 80 MHz. At a particular drain voltage, the
impedance variation looks like a parallel RC for low frequencies. At higher baseband frequencies, the impedance looking
into the bias line becomes inductive, as seen in Fig. 15(b),
caused by the wirebond to the die. The equivalent parallel
RC of the PA (for frequencies under 100 MHz) is shown in
Fig. 16. Over input power and drain voltage, the equivalent
capacitance is very close to 88 pF; the bias line capacitance is
the dominating factor for the reactive impedance. The resistive
part of the impedance, however, depends on the drain voltage
Fig. 13. Measured PAE of the amplifier shown in Fig. 12(a) versus output
power and drain voltage.
Fig. 15. (a) Real and (b) imaginary impedance of the PA bias line across frequency and drain voltage at 26-dBm input RF power. Due to the large bias line
capacitance on chip, the impedance above 80 MHz is nearly zero. The area at
250 MHz at 10 V had a measured negative real impedance indicating possible
bias line instabilities.
Fig. 14. (a) Real and (b) imaginary part of the PA bias line impedance
at 1 MHz. At low input power, the PA is pinched off and presents a large
impedance to the drain modulator. As the RF drive power increases, the real
impedance decreases below 100 .
and input power, generally increasing with
and decreasing
Some of the conclusions that can be drawn from the measured
data are as follows.
• From Fig. 14(a), it is seen that the real part of the drain
impedance for a supply modulated PA varies substantially
over drain voltage and output power. The imaginary part
also varies significantly at the nominal drain voltage
of 20 V. Therefore, the design of the signal-split from
Fig. 1 will have a large impact on not only the PAE, but
on the SM efficiency, which varies with loading.
• From Fig. 15, most of the frequency variation of the drain
impedance is below 100 MHz. This is due to the on-chip
Fig. 16. Extracted resistance and capacitance of the PA over drain voltage and
input power. The bias network capacitance overwhelms the small reactance of
the transistors giving nearly constant equivalent capacitance over input power
and drain voltage. The real part of the impedance, however, increases with
and decreases with
agreeing with the transistor measurements [see
Figs. 7(a) and 9].
Fig. 17. Block diagram of transmitter with MMIC PA and resonant modulator.
There are two bias line capacitors on the MMIC fixture totaling 0.011 F.
Fig. 18. Time-domain drain voltage and current measured at RFPA bias pad. The RFPA is biased at: (a)
V for both plots.
supply voltage is
capacitance. The SM bandwidth, efficiency, and possibly
stability would be compromised in this case.
• Even when there are no off-chip drain bias capacitors such
as was done for these measurements, there is a large frequency variation in the impedance. With a more conventional PA design, the bandwidth would be even more limited and stability a possible issue.
These measurements are representative of only one PA design
and will be different for other designs. However, class-B
was focused on here because it has the same bias point as
other high-efficiency modes of operation (class-E, class-F,
class-F ). Class-A PAs will have less impedance variation as
shown in the transistor measurements [see Fig. 10(a)], however,
under supply modulation are limited to an efficiency of 50%.
High-efficiency mode PAs designed for supply modulation
must take the bias network and transistor drain impedance
variation into account.
V and (b)
V while the modulator
Fig. 19. RF average output power and drain efficiency over a pulse. By lowering the RFPA gate voltage, the efficiency can be increased with approximately
the same output power.
The measurement setup described here can also monitor performance of and interaction between a PA and SM. The PA from
Section IV is next connected to an SM and the system measured
with the LF coupler placed between the RFPA and modulator.
The modulator in this case is not a standard dc–dc converter
assisted with a linear amplifier commonly used for communication signals, e.g., [6], but rather a resonant modulator for AM
radar pulses. Radar supply modulation has been explored by
other authors and the primary benefit includes reduced radiated
spectral emissions. The resonant modulator is a simple design
based on a damped LC resonant circuit and has been shown to
reach efficiencies
90 [38], [39]. A simplified diagram of
the resonant modulator designed for a resistive load of 220 is
shown in Fig. 17. The inductance and capacitance are switched
(using switches SW1, SW2, and SW3) into the circuit to charge
and discharge, giving an approximate Gaussian output waveform shape. Since the waveform of interest is no longer a continuous wave as the previous sections of the paper have been,
it is more useful to use time-domain voltages and currents. For
the measurements, the RF input power is kept constant to keep
the load variation of the transistor separate from the modulator
PA dynamic interaction.
The transmitter example in this paper uses a resonant modulator because it has a smooth and slow envelope that is well
Fig. 20. Simulated efficiency of the resonant modulator and example buck converter versus a static resistive load.
known and has a large voltage variation, going from 0 V to the
nominal voltage of the amplifier. In addition, the PA/SM combination is complete and is used as it would be in a system.
The de-embedded voltage and current at the MMIC bias
pad (off-chip capacitances were de-embedded) are shown in
Fig. 18 for two different gate bias voltages. In the first case
[see Fig. 18(a)], the modulator switching times were adjusted
for an optimum Gaussian shape for an input power of 24 dBm
(red line in online version). As the input power decreases from
24 dBm down to 16 dBm, the load that the modulator sees
increases, giving a higher peak voltage and increasing the
optimum discharging time for the capacitor causing a negative
voltage at the end of the Gaussian pulse. The current follows
the same Gaussian shape as the voltage, but there is current
Fig. 21. (a) Waveform and (b) Bode plot simulation of Buck converter with fourth-order output filter designed for a 30- purely real load. The converter tracks
the envelope of a 20-MHz LTE waveform. The envelope is accurately tracked for the designed load of 30 . However, with the measured load of the PA in
V and 23.8-dBm RF input power), the higher resistance and capacitance cause distortion and significant drain voltage overshoot.
Section IV (at
ringing at the peak of the pulse caused by SW1 turning off in
the modulator.
In the second case [see Fig. 18(b)], the modulator switching
times were adjusted for an optimum Gaussian shape in the
voltage for an input power of 0 dBm (black line) at a bias
V. The voltage has Gaussian shape, however,
the modulator is supplying very little power to the PA, as the
current is very low. As the RF input power increases, the modulator sees a decreasing load, decreasing the peak voltage of
the modulator. Additionally, the optimum charging time for the
capacitor is decreased, giving the upswing in the voltage at the
end of the Gaussian pulse for high RF input powers. However,
it is evident the modulator is not designed for such a high load,
as there is no current into the PA even at the optimum input
power of 0 dBm: there would be no efficiency improvement of
the transmitter using an SM because of the very low power that
the resonant modulator supplies. This means that the resonant
modulator would need to be redesigned if an input power of
0 dBm is desired with a very pinched off PA.
The average RF output power and drain efficiency of the
RFPA is shown in Fig. 19. There is a clear tradeoff between
RFPA efficiency and modulator distortion (which translates to
distortion of the RF output pulse). With a more adequate load
for the resonant modulator (
V)m the RFPA only
reaches 31% drain efficiency. The efficiency can be increased to
38% by pinching the device off, however, large distortions are
apparent in the current waveforms from the modulator. Moreover, the resonant modulator works best for a particular load, in
this case about 50 , as shown in Fig. 20. Under pinch-off, the
resonant modulator is far from the optimum load impedance, as
the transistor has a very high impedance.
The LF measurement setup is used as a diagnostic tool
for investigating and optimizing the performance of the resonant modulator when connected to the RFPA. By observing
the voltage and the current at the RFPA bias line, distortion
and SM/RFPA interactions can easily be seen. The two plots
illustrate a tradeoff between RFPA efficiency and linearity
performance of the modulator. In this case, to keep a Gaussian
shape for different loads, the modulator switching times can be
adjusted for the load variation of the RFPA by a simple lookup
table. The more optimum solution for output power control is
by adjusting the resonant modulator supply voltage directly
decreasing the amplitude of the Gaussian pulse. As shown in
previous sections, the impedance variation over drain voltage
is smaller than the impedance variation over RF input power.
The measurements presented in this paper highlight the need
to understand the RF transistor impedances at baseband over all
operating conditions for optimal design of the SM. The baseband impedance can vary dramatically over input powers and
bias conditions.
For the resonant pulse transmitter example in Section V, it is
clear the modulator cannot handle the load variation of the PA
caused by RF input power changes with a variable amplitude
Gaussian pulse. Instead, the drain supply voltage on the modulator must be changed to minimize the load variation and give
variable output powers. This complicates the system implementation of such a modulator requiring another variable voltage
supply, albeit one that can be considerably slower than the resonant pulse modulator. In short, for this example, the modulator
should be designed to supply power under a higher resistive load
or the PA design should be changed to provide a more uniform
impedance over RF/LF input powers. Communication transmitters commonly use a switching dc–dc converter assisted with a
linear amplifier [6]. The dc–dc converter creates a large amount
of noise at baseband and needs a low-pass LC filter to block
switching noise from the modulator [40] and some authors have
expanded the modulator output reactances to higher order filters
[41]. However, even with a filter, the modulator load is determined by the transistor dynamic impedance. As an example, a
Buck converter was simulated in Simulink by MathWorks with
a fourth-order output filter optimized for a 30- load [42]. The
output voltage waveform for a 20-MHz LTE envelope is shown
in Fig. 21(a). There is good tracking with the static 30- load.
However, with a baseband load extracted from Section IV (
pF from Fig. 15) at a static
RF input power, the waveform becomes greatly distorted with
large voltage swings, which may cause damage to the amplifier. The large resistance change causes the bulk of the distortion. Fig. 21(b) shows the frequency transfer function for the
converter with various loads. The amplitude shows the need for
linearization. This simulation does not include the variation in
baseband impedance due to drain voltage, which would create
even more distortion. With the potential variation in baseband
impedance, the buck converter would no longer be at an optimal load (Fig. 20), decreasing the efficiency of the transmitter
system. This further highlights the need to consider the variation in baseband impedance of a transistor or PA for different
RF input powers and bias points.
These measurements would be very useful for creating a
model and potential implementations for supply modulation
[17], [28]. The LF ability of the measurement setup can be
applied directly to modeling LF phenomena including trapping
effects in the small-signal regime [14], and the nonlinear regime
[17], [20], [21], [43]. The goal of this paper is to quantify the
dynamic supply-terminal impedance towards the understanding
of the interaction of a PA with a wideband ( 10 MHz) SM. If
one considers the impedance contours in Fig. 11, the impedance
seen by an SM is roughly constant when the transistor is under
RF compression. If a transmitter is operated in this region,
the output power dynamic range must come entirely from the
variation of voltage on the drain (also known as EER) and
allows high-efficiency PA operating modes (class-E, class-F,
class-F ). If a transmitter trajectory includes a combination
of RF and LF input power (partial drive modulation), the
impedance variation can be minimized by operating the RF
transistor in class-A. For the device in this paper, a 50variation is observed for a 100-mA/mm bias point compared to
200 for partial drive modulation. However, partial drive
modulation limits the maximum efficiency of the PA to 50%
and system to 50 depending on the efficiency of the SM.
In summary, a measurement system is developed to characterize static and dynamic supply port impedances from 1 to
500 MHz, while the transistor/PA is under large-signal operation in X-band. The LF port is calibrated to measure the absolute
voltage and current. The setup is versatile in that it can measure
bare die transistors for modeling and design, PAs for co-design
with an SM, and transmitters to inspect interactions between the
PA and SM.
The authors are very grateful for the donation of equipment
from National Instruments (Dr. T. Inoue and Dr. Truchard).
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Scott Schafer (S’06–A’10–GSM’11–M’15), photograph and biography not
available at time of publication.
Zoya Popović (S’86–M’90–SM’99–F’02), photograph and biography not
available at time of publication.
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