PA Efficiency and Linearity Enhancement Using External Harmonic Injection

PA Efficiency and Linearity Enhancement Using External Harmonic Injection
PA Efficiency and Linearity Enhancement Using
External Harmonic Injection
Asmita Dani, Student Member, IEEE, Michael Roberg, Student Member, IEEE, and Zoya Popović, Fellow, IEEE
Abstract—This paper presents analysis and experimental
demonstration of a high-efficiency linear power amplifier (PA)
with second-harmonic injection at the output. In this circuit,
the transistor is not driven hard into compression and does not
produce significant harmonic content. External injection at the
output enables voltage and current wave-shaping to achieve high
efficiency. Theoretical analysis of the waveforms shows that the
maximal drain efficiency is 89.9% with, at most, 0.13 dB of reduction in output power compared with the class-A case. The overall
PA efficiency is derived in terms of the injector circuit efficiency.
A harmonically injected prototype GaN HEMT 2.45-GHz PA
demonstrates over 80% efficiency with linearity improved over
the class-AB PA without harmonic injection. Two-tone measurements show a reduction of the third-order intermodulation by 30
dBc in the linear region and greater than 10 dBc in saturation.
Index Terms—Amplifier drain efficiency, Fourier coefficients, harmonics, linearity, microwave power amplifiers (PAs),
third-order intercept, waveform shaping.
large portion of current research in high-power amplification of signals with carriers in the microwave range
focuses on improving efficiency and linearity. There are many
power amplifier (PA) topologies that achieve high efficiency by
driving the active device into a nonlinear region and shaping
voltage and current waveforms across the device via proper selection of the output loading network at harmonic frequencies.
These techniques, such as class-F and
PA topologies, rely
on the nonlinear active device for harmonic current or voltage
generation [1]–[4]. The concept of harmonic injection, however,
refers to architectures in which power at one or more harmonics
of the operating frequency is supplied externally to either the
input, output, or both input and output of the active device.
Analysis of efficiency improvement of tube PAs using harmonic injection into both the grid (input) and plate (output)
has been presented in [5]–[7]. A harmonic-injection scheme
referred to as a harmonic reaction amplifier was presented in
[8]. The harmonic reaction amplifier uses two parallel devices
Manuscript received July 09, 2012; revised September 19, 2012; accepted
September 20, 2012. Date of publication November 15, 2012; date of current
version December 13, 2012. This work was supported in part by the Berrie
Hill research Corporation and the U.S. Air Force under Contract FA8650-10-D1746-0006. This paper is an expanded paper from the IEEE MTT-S International Microwave Symposium, Montreal, QC, Canada, June 17–22, 2012.
A. Dani and Z. Popović are with the Department of Electrical, Computer and
Energy Engineering, University of Colorado, Boulder, CO 80309-0425 USA
M. Roberg is with TriQuint Semiconductor, Richardson TX 75080 USA
Color versions of one or more of the figures in this paper are available online
Digital Object Identifier 10.1109/TMTT.2012.2222918
Fig. 1. Block diagram of a harmonic-injection PA (HI-PA) with second-harmonic injection at the output. A three-port network at the output allows isolaand
between ports 2 and 3, while allowing low
tion between waves at
between ports 1 and 2. The phase of the injected harmonic is critical
loss at
to obtaining high efficiency.
and effectively acts as a push–pull amplifier with respect to
the second harmonic. In 1992, a patent was issued for a harmonic injection amplifier in which the harmonic signal created
using a frequency multiplier is injected into the transistor output
[9]. A class-E VHF PA at 3.5 MHz with a secondary class-E
7-MHz PA injector is presented in [10]. An experiment demonstrating 15.2% efficiency improvement of a 2-GHz GaN PA
using second-harmonic injection at the input is reported in [11].
More recently, a concept for efficiency improvement via injection of harmonics into the output of a class-B/J amplifier was
demonstrated [12]. A novel scheme of efficiency improvement
of a class-E amplifier using input harmonic injection via a feedback loop was shown in [13].
In this paper, we discuss injection of power at the second harmonic, as shown in the block diagram of Fig. 1 and the implications on efficiency and linearity. The approach is valid for any
amplifier mode, not just for class-B/J as in [12] and [14]. The
contributions of this work are organized as follows.
• Section II presents, for the first time, a theoretical Fourierexpansion analysis of output harmonic injection. A relationship between the total efficiency and injected power is
presented for the case of second-harmonic injection. The
analysis gives an insight into the impedance that needs to
be synthesized at the output of the transistor at the fundamental and harmonic frequencies. The effect of efficiency
of the injector circuit on the total efficiency is calculated.
• Section III discusses two prototypes used for experimental
validation, one based on a packaged Cree GaN 10-W 50class-AB PA and the other based on a TriQuint GaN die
with an injection network designed for a non-50- environment.
• Section IV presents measurement results for the relevant
amplifier parameters as a function of the phase and amplitude of the injected harmonic signal for both prototypes.
0018-9480/$31.00 © 2012 IEEE
The experimental results demonstrate an improvement from
58% to 80% in efficiency with an output power of 37 dBm and
over 20-dB gain from a single TriQuint 6-W device. In addition,
the amplifier linearity is shown to be improved with harmonic
injection w.r.t. the class-AB case, which implies significant linearity improvement compared with the same device used in harmonically terminated compressed nonlinear PAs.
The theoretical analysis of a harmonically injected PA
(HI-PA) shown in Fig. 1 is developed based on Fourier expansions of the voltage and current waveforms at the current
source of the transistor, expanding on the approach in [12]
and [15]. First, expressions are derived for injected voltage
which optimizes efficiency, followed by the analysis of total
dissipated power and a discussion of linearity. To obtain an
HI-PA, a linear three-port network is cascaded at the output of
a linear PA, and the required -parameters of that network are
given in [15].
Fig. 2. Optimal drain current and voltage waveforms for second-harmonic injection amplifier, normalized to 1-W output power.
corresponds to a point at which the first derivative of the voltage waveform w.r.t. is equal to zero. Note that
(5) is only valid when
A. Waveform Analysis
Consider the normalized drain voltage and current waveforms at the virtual drain of a linear field-effect transistor (FET)
PA, which are given by
, and the bar indicates a normalized quantity. For instance, when
, the normalized
class-A output power is 1 W, and the waveforms result in 50%
efficiency. If the drain waveforms can be shaped by harmonic
content in a manner such that the overlap of the voltage and
current is minimized for a given fundamental frequency output
power, then drain efficiency will be maximized.
Consider the addition of only the second-harmonic term in
(1) and (2). In order to maintain waveform symmetry, only cosinusoidal components are added. Such a condition will result in
the voltage waveform of the same shape but 180 out of phase
with the current waveform. The waveforms following addition
of a second-harmonic term become
Therefore, the range of
over which (5) is valid is limited to
It remains to be proven which critical points correspond to the
global minima and global maxima. Substituting the critical point
in (5) into the second partial derivative of (3) results in
If is negative in sign, the critical point corresponds to a minimum, while, if it is positive in sign, then it corresponds to a
maximum. Applying the second derivative test to the critical
point described by (6) results in
Therefore, the critical point described by (6) will be an extremum as follows:
is a minimum
is a maximum
as shown in Fig. 2, showing minimal overlap of the voltage and
current waveforms.
From (3) and (4), it can be concluded that the impedance at
is the negative of that at . Effectively, this requires that
power is delivered to the transistor at the second harmonic. An
optimal value of that maximizes the efficiency can be found.
First, the critical points of the drain current and voltage waveforms are expressed as
B. Efficiency Analysis
The normalized total DC power consumed by the amplifier is
expressed as
is the efficiency of the injector circuit. Note that, due
to the symmetry of the current and voltage waveforms,
, the optimal dc supply voltage is that which results in a
drain voltage waveform with minimum of zero. Therefore, from
(3), we have
Fig. 3. Contour plot for
as a function of
and injector circuit efficiency
Fig. 4. Optimal solution for Fourier coefficient
and second-harmonic delivered power relative to fundamental frequency output power versus second
harmonic injector circuit efficiency
The total dc power may now be expanded to the form
Since we use a normalization that sets the fundamental output
power to 1 W, the total efficiency is calculated as the inverse of
the normalized dc power
Fig. 5. Total efficiency
versus injector circuit efficiency
, also shown in Fig. 4. The PA efficiency is determined by inserting
into (15) and (16) to yield
Fig. 3 shows the total efficiency plotted as a function of both
and normalized magnitude of secondinjector efficiency
The value of
is optimized by setting the partial derivative
w.r.t. the Fourier coefficient
to zero and solving for
as follows:
, the optimal
These values minimize
. Given
. A plot of
Fourier coefficient reduces to
which corresponds to the amplitude of the required injected
second-harmonic versus
, is shown in Fig. 4. As one would
expect, the magnitude of the Fourier coefficient decreases as
the injector efficiency decreases. Another interesting parameter
to investigate is the ratio of the delivered fundamental output
power to the required delivered second-harmonic injected
A plot of the total efficiency versus injector circuit efficiency
is shown in Fig. 5 for optimized solution at and a plot for
as a function of
, and is shown in
the total efficiency
Fig. 3. The maximum value is 89.9%, and it rolls off reasonably
slowly with decreasing injector efficiency. This is intuitive because the power required from the injector is significantly lower
relative to 1 W. When
, the output power is only reduced by only 0.13 dB relative to the class-A amplifier.
Also, it is of practical interest to find the supply voltage and
current normalized to class-A:
Fig. 6. Power reduction and normalized supply voltage relative to class-A
versus injector efficiency
than the fundamental output power of the amplifier, as shown in
Fig. 4. As expected, when the amplifier efficiency reaches 50%,
the injector circuit is turned off. In this case, the amplifier degenerates to the canonical class-A mode.
As previously mentioned, the load presented to the transistor
at the second harmonic is the negative of that presented at the
fundamental, so the load resistance normalized to the class-A
fundamental load is 1. To find the output power of the PA
normalized to class-A output power, normalization conditions
corresponding to peak voltage and current constraints are enforced.
are now found, enabling determination of
the maximum instantaneous normalized voltage
and cur, and the output power normalized to the class-A amrent
plifier output power is determined. The normalized dc voltage
is expressed as
Note that, due to the symmetry of the current and voltage wave, the maximum normalized voltage is calcuforms
lated as
The output power normalized to class-A is then given by
Fig. 6 depicts the fundamental frequency output power reduction relative to a class-A amplifier versus the injector efficiency.
This was calculated by computing as a function of
, then
and determining the ratio
computing the output power from
Fig. 6 shows the normalized supply voltage which is approxi.
mately 0.7107 for
A similar analysis can be performed for third-harmonic injection at the output, since symmetric square waveforms can be
achieved using odd harmonics only. In the case of third-harmonic injection, the impedance at the third harmonic is positive
rather than negative, so the ideal waveforms can be realized with
a passive set of output terminations. The analysis shows, however, that the total efficiency given by (22) and (23) is around
65% for injector efficiencies above 40% and does not reach the
high efficiencies of the second-harmonic injection case. Details
of the analysis can be found in [16].
C. Linearity
Transistors exhibit nonlinearities due to various factors such
as input and output device capacitance, transconductance, and
drain–source resistance resulting in a characteristic between
and , which can be represented using the power series
. As seen in (31), the second-order nonlinearity causes an additional dc component and a signal at twice
the fundamental frequency to appear in the output voltage. For a
two-tone signal, the second-order nonlinearity can be easily filtered out and does not cause any in-band distortion of the signal.
However, the third-order nonlinearity results in in-band distortion products. The gain of the fundamental component under
nonlinear operation can be expressed in terms of the fundamental gain and the third-order gain and amplitude, and the
derivation is given in [17]. The analysis in [17] also shows
that the amplitude of the second-harmonic output signal is inversely proportional to the magnitude of the transfer characteristic of the amplifier at the third harmonic, which is referred to in
Section IV. A good discussion on extracting linearity information from a continuous-wave (CW)-fed amplifier by measuring
the third-harmonic output content is presented in [18]. Based on
this theory, in this paper, a CW signal is used for harmonic injection analysis as the device enters saturation. In particular, we
measure second and third harmonic as a function of the injected
power and phase in order to assess the linearity.
Two prototype PAs were used to demonstrate the HI-PA concept. A packaged device in a demo board with class-AB broadband PA configuration is injected through a 50- three-port
injection circuit described in more detail in [12], [14], and [15].
In order to have more design freedom and lower matching network loss, a TriQuint GaN die was used in the second narrowband prototype with a non-50- three-port injector circuit.
Fig. 8. Measured drain efficiency
PA shown in Fig. 7 without injection.
and gain for the class-AB
Fig. 7. Hybrid HI-PA with a 6-W TriQuint TGF2023-01 die. The output
network integrates the harmonic injection three-port network with
matched to 65 and
matched to 71 . The input network does an
impedance transformation from 50 to 10 in order to achieve high gain and
at the fundamental.
A. Packaged Device Prototype PA
is used in a broadA Cree GaN HEMT with 10-W
band (DC-6 GHz) demo board provided by the manufacturer
(CGH40006P-TB) with a packaged device and matched to
as the first prototype. This PA gives
40 dBm
at 2.45 GHz with
12 dBm [15]. The
input power to the fundamental PA is swept from 22 to 34 dBm
(linear to saturation) with the drain bias at 22 and 28 V. The
gate bias was set to 1.6, 1.8, and 2 V for a class AB mode.
The fundamental PA starts compressing at an input power level
of 27 dBm when no harmonic injection is present.
B. Discrete Die Prototype PA
A hybrid class-AB PA is designed using load-pull measurements on the TriQuint TGF2023-01 device at 2.45 GHz, as
shown in Fig. 7. The reference plane for all measurements on
this PA is the virtual drain of the transistor, i.e., the current
source behind the output capacitance of the device. The HI-PA
is designed with the three-port injection network integrated into
the output matching circuit of the amplifier in order to minimize
loss. Design and performance of the injection network is similar
to the one presented in [12] and [15] with the fundamental and
second-harmonic impedances matched close to
as explained in (3) and (4). Due to fabrication tolerances, the
fundamental impedance at the virtual drain of the device was
found to be matched to 65 and the
impedance to 71
(10% higher).
This class-AB PA has 58% drain efficiency with an output
power of 37 dBm without any harmonic injection at a drain bias
voltage of
28 V. Fig. 8 shows the measured drain efficiency
, output power at fundamental
, third harmonic
, and the gain as a function of fundamental
input drive power
The block diagram shown in Fig. 9 shows the measurement
setup for HI-PA prototypes. A portion of the fundamental input
is frequency doubled to create the second harmonic
injection. A voltage-controlled phase shifter and variable gain
Fig. 9. Block diagram of the HI-PA measurement setup. The input signal is split
. A voltage
and frequency doubled to create the injected harmonic,
controlled phase shifter and variable gain amplifier are used to control the am.
plitude and phase of
amplifier (VGA) are used to control the amplitude
and phase at
. All of the measurements are de-embedded to
the virtual drain of the transistor by calibrating the loss in the
output network and taking into account the intrinsic transistor
parasitics, i.e., output capacitance of the device. A bondwire
model in Ansoft High Frequency Structure Simulator (HFSS)
was simulated to consider the inductance loss in the bondwire
transition for the hybrid PA design.
The drain efficiency for an HI-PA takes into account the
amount of second-harmonic power injected into the virtual
drain of the device
as follows:
A. Packaged Device Prototype HI-PA
Fig. 10 compares the measured efficiency, output power, and
gain for the PA with and without harmonic injection. It is seen
that the HI-PA saturates at a higher input power (32 dBm) as
compared with the class-AB PA (27 dBm), resulting in higher
Fig. 11. Comparison of power levels for single-tone and third-order IMD products for HI-PA and class-AB PA without harmonic injection.
phase adjustment. The measured results in Fig. 10 show that
the HI-PA (marked line) saturates at a higher input power than
the PA with no harmonic injection (solid line). At lower input
powers, the IMD3 level is over 30 dB lower for the HI-PA and
remains 10 dB lower after the PA saturates. In Fig. 11, only the
frequency is injected, resulting in a decrease in the
IMD while the
remains unchanged. Symmetrically,
is injected, the
will decrease. Both of the
IMD products will be reduced equally for a signal injected
. This is consistent with measurements obtained
with tube amplifiers in [19] and harmonic injection at input of
solid-state amplifiers in [20], [21].
B. Discrete Die Prototype HI-PA
Fig. 10. Comparison of measured (a) drain efficiency, (b)
, and (c)
22 V, 28 V
gain for the HI-PA to the PA with no harmonic injection at
1.6 V (class-AB). The dashed green line indicates input power at
which the PA becomes nonlinear.
linearity. The gain of the HI-PA is lower by about 1 dB as
compared with the fundamental PA in the linear region, but remains higher in saturation. Harmonic balance simulations using
a nonlinear model provided by the manufacturer show the same
trends for gain as the measured data.
Measured results show that higher efficiency can be achieved
for a constant output power with HI-PA by changing the operating bias point. For instance, the drain efficiency of the PA
improves from 58% with no injection to 75% with injection for
an output power of 40 dBm by changing the drain bias from 28
to 22 V.
A two-tone linearity test is performed at
22 V
1.8 V. The two tones are kept 5 MHz apart
2.45 GHz and third-order intermodulation
(IMD3) products generated at
2.455 GHz
2.46 GHz. Simultaneously,
, or
is injected at the output, each requiring a different
The HI-PA using a TriQuint 6-W GaN discrete high-electron
mobility transistor (HEMT) in a class-AB PA achieves a high
total drain efficiency of 89% with external second-harmonic injection at the output at a bias voltage of
22 V. This
efficiency is very close to the theoretical efficiency of 89.9%
from Fig. 3, though one would expect it to be lower. The reason
being that the theory is derived for an ideal device with ideal
– curves which do not take into account knee voltage of the
transistor and does not generate any odd-order harmonics. In
practice, the PA always generates some harmonic content even
at lower input power levels. The gain of the amplifier reduces
by 1 dB as compared with the amplifier without any harmonic
injection. Fig. 12 shows a comparison of the measured performance for the HI-PA and PA without harmonic injection. These
measurements are optimized for high efficiency and hence the
amplifier is nonlinear at
. It is seen that a better performance is achieved with the discrete device as compared with the
results presented in Fig. 10 for the packaged device, as expected.
As seen in the theoretical analysis (30), harmonic injection
implies a shift in the bias voltage in order to get the optimum
performance from the amplifier. Fig. 13 shows the performance
of the HI-PA at different drain bias voltages for a fundamental
input drive
of 16.2 dBm. The HI-PA is then optimized
in order to get high efficiency along with linearity.
As explained in Section II-C, for a CW amplifier, the values
can give an estimate of the linearity. It is seen
24 V, the drain efficiency of the
from Fig. 13 that, at
HI-PA is improved by over 20% as compared with the class-AB
Fig. 14. Contour plots of (a) measured fundamental output power
dBm and (b) drain efficiency
Fig. 12. Comparison of measured (a)
, (b)
, and (c) gain for discrete die prototype of HI-PA optimized for maximum efficiency.
Fig. 13. Drain efficiency
with the ratio
0.1 and
for different
bias voltages
16.2 dBm.
PA with no injection, and the output power at the third harmonic
is lowered by 30 dB for an input drive level
of 16.2 dBm. At this bias point, conditions for high linearity
and high drain efficiency are obtained with a nominal fundareduction of 0.26 dB over the
mental output power
PA without any injection. Note that, when harmonic injection is
performed, it results in higher fundamental output power due to
reduction in other harmonic content. In order to keep the output
power constant and reduce the dc power dissipation, the drain
supply voltage can be reduced to a certain extent, as shown in
Fig. 13. The supply voltage reduction is only advantageous up
to a device-dependent lower value when the output power starts
decreasing. In the case of packaged prototype, 22 V was found
to be optimal, and, in the case of discrete prototype, this value
was 24 V. Note that the PA with no injection is not designed for
high efficiency, since it is biased in class-AB, and the gate bias
is kept the same for the PA with and without injection. All of
the measurements presented in the remainder of the paper will
be at
24 V.
As discussed in Section II-A, the injected second-harmonic
signal needs to be at a particular phase and amplitude in order to
shape the voltage and current waveforms at the virtual drain of
the amplifier. If the input drive is kept constant, various parameters affecting the performance of the HI-PA such as
drain efficiency
, drain current
, and power at the
vary with the amplitude and
phase of injected second harmonic power
as shown
in Figs. 14 and 15.
Figs. 14 and 15 show that, for
9 dBc and a
phase shift of 80 , high drain efficiency of 79% is achieved
using (32) along with extremely low values of
. Note
that this efficiency takes into account the power of the injected
Fig. 16. Comparison of drain efficiency and gain for HI and PA with no injec.
tion as a function of
Fig. 15. (a) Drain current
(amperes) and (b) third-harmonic output power
in dBm for
16.2 dBm depicting the variation in the
values of these parameters as a function of phase and power level (dBc w.r.t.
) of the injected second harmonic
. Analogous plots can be
obtained for the second-harmonic output power
signal. However, the efficiency of the injector circuit is not included in this proof-of-concept experiment in which the HI-PA
is not fully integrated. The value of
obtained at this
point is approximately 37 dBm, which is only 0.2 dB lower
than the fundamental output power obtained with no injection
(Fig. 8).
The measurements show that, if
is not at the optimum phase and amplitude, the performance of the amplifier
can severely degrade. When the second-harmonic voltage is
out of phase relative to the optimal value, the amplitude of
increases, making the amplifier extremely nonlinear.
The efficiency reduces from 80% to 40% while the output power
drops more than 3 dB. If
is higher than the optimum
value (in this case,
9 dBc), then, even at the optimum phase
of the injected harmonic, the HI-PA is highly nonlinear. This
is due to undesired additional second-harmonic content in the
output voltage and current waveforms generated by the device
under hard drive.
A sweep is performed at
in order to achieve the optimal performance of the HI-PA at various input drive levels.
Since an amplifier undergoes AM–AM and AM–PM distortion,
the optimal phase and amplitude of the injected second-harmonic changes for different input drive levels. Fig. 16 shows a
comparison of the gain and drain efficiency obtained for HI-PA
and PA without harmonic injection as a function of
The efficiency obtained at each input drive level is for an optimal value of amplitude and phase which are also dependent on
Fig. 17. Comparison of
as a function of
HI and PA with no injection. The graph also shows the amplitude of
as a function of
in order to achieve high efficiency and linearity performance for the HI-PA.
. The overall gain of the HI-PA is reduced by 1 dB, and
the 1-dB compression point of the HI-PA is shifted to a higher
of 15.7 dBm, implying improved linearity. The drain efficiency improvement ranges from 8% to 20% as the input drive
level increases.
The comparison of
for the HI-PA and
PA with no injection is shown in Fig. 17 along with
a function of
. As derived in [17], the transconductance
at the third harmonic is inversely proportional to the amplitude
of the second harmonic. The value for gain of an amplifier under
nonlinear operation can be given from (31) as
are values for transconductance at fundamental and third harmonic. Therefore, it is seen that the value
required to lower the value of
for the
HI-PA is exactly equal to
The nominal class-A operation of the PA without harmonic
injection with a 50% drain efficiency is achieved at
13 dBm. Fig. 17 shows that, at this input drive level, the amplitude of
required in order to achieve an optimum
performance in terms of efficiency and linearity for the HI-PA
is 10 dBc. This result matches with the theoretical analysis
presented in Fig. 4 where, for a 100% injector efficiency, the
ratio of
is 0.1 for a class-A bias point.
Fig. 18. Comparison of power at
for HI-PA and PA without harmonic injection as a function of input drive level.
The graph also shows the power injected at the second harmonic tone
achieve lowest
Two-tone measurements with optimization for the amplitude
and phase of the injected second harmonic in order to achieve
lowest IMD3 products in both lower and upper sidebands
are performed. This measurement is similar to
the one presented in Section IV-A for the packaged device
prototype HI-PA where either
are injected at the
output of the HI-PA. Here, the injection of
affects the perat
due to
formance of
active impedance synthesis at the injection port. It is important
to note that the reduction in
results from mixing of
and distortion products caused due to second-order
nonlinearities. It is seen that the reduction in
external second-harmonic injection is greater than 15 dB for
different input drive levels, whereas
remain unaffected. Fig. 18 shows the
reduction in power levels for
achieved for
different fundamental input drive levels along with the amount
of injected
For practical communication signals, the harmonic injection
path needs to be modified in order to inject an exactly doubled spectrum of the signal. As seen in the two-tone measurements, injection at one harmonic tone only affects the distortion
products which are a function of that harmonic tone frequency.
Since, a modulated signal in general is a multitone signal, it will
require a injected signal with twice the modulation bandwidth
and RF carrier. This can be accomplished by baseband signal
The results above show that a PA with harmonic injection
in the output can be both efficient and linear. In the demonstrated results above, we start with a class-AB PA, which is
not perfectly linear. In fact, the theory shown in Section II assumes that some second-harmonic content is generated by the
active device. If the transistor fails to generate second-harmonic
power and presents an impedance other than that of the fundamental frequency output termination, the necessary negative
impedance cannot be synthesized using harmonic injection. In
this case, harmonic injection at both the input and output of the
transistor would be required.
Fig. 19. Minimum
measured at virtual drain of the
16.2 dBm. The minimum for
is obtained with
HI-PA for
17.8 dBc w.r.t.
, whereas minimum for
8.9 dBc.
obtained for
It is of interest to discuss some limitations on linearity and
efficiency that are practically achievable. We have shown that
the third harmonic, which directly affects IMD performance, is
minimized for a specific phase and amplitude of the injected
second harmonic. However, the injected signal also affects the
nonlinear content in the waveform produced by the transistor,
which can be evaluated by measuring the level of the second harmonic at the output. The amount of injected second-harmonic
power that results in a minimum of harmonic content in the
output is shown in Fig. 19. Note that the second and third harmonic have minima for different injected power levels of the
second harmonic. The amplitude of
needed to lower
is approximately 10 dB less than that needed to lower
. Also, the phase shift for
injection differs
by 50 . As seen from Fig. 14, the drain efficiency drops by approximately 10% between these two points in amplitude and
For a modulated input signal, the third-order nonlinearities
have to be minimized since they create in-band distortion which
is extremely difficult to filter. The third-order distortion products are a function of the amplitude of second harmonic produced by the amplifier itself. Hence, a point in the amplitude
and phase of the injected signal needs to be chosen to optimize
linearity by a tradeoff between the second- and third-harmonic
The main practical limitation on efficiency is the implementation of an efficient injector circuit. Fig. 5 shows that an
injector efficiency of 40% or higher, with a power level 10
dB below the output power, is required to obtain an overall
efficiency above 80%. This might present a challenge for very
high-power PAs, but is otherwise not a difficult constraint. In
the prototype characterization presented in this paper, a passive
doubler was used to produce the harmonic. This is not only
inefficient but also impractical for amplifying a real signal,
in which case significant distortion would be introduced. The
linearity tests (Fig. 11) show that a clean doubled frequency
spectrum needs to be injected. Therefore, for signal amplification, a different approach is needed than was done for the CW
tests in this paper. A topic of current research is integration
of an up-converter in the injection circuit with a synchronized
second baseband input. For very broadband signals, the phase
control that achieves linearity might prove to be challenging.
An interesting extension of the concept to a broadband HI-PA
will require a three-port injection network design with good
harmonic isolation and low fundamental frequency loss over a
broad frequency range.
In summary, this paper presents a theoretical Fourier analysis
of PAs with harmonic injection at the output, showing limits
on total circuit efficiency. The theory is experimentally verified
on class-AB 2.45-GHz PAs using both packaged and discrete
GaN HEMTs, resulting in 75% and 80% efficiencies, respectively, at the 1-dB compression points. The linearity of the PA is
shown to be significantly improved for specific phase and amplitude of injected second harmonic, with simultaneous improvement in efficiency. To the best of our knowledge, these are the
first reported efficient linear PAs of this type using solid-state
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Asmita Dani (S’011) received the B.Tech degree
in electronics engineering from the University of
Mumbai, Mumbai, India, in 2008, and the M.S.E.E.
degree from the University of Colorado at Boulder
in 2010, where she is currently working toward
the Ph.D. degree in microwave circuits and system
Her research interests include linearization and efficiency enhancement of power amplifiers using external harmonics, monolithic microwave integrated
circuit design and analysis of communication system
transmitters and receivers.
Michael Roberg (S’09) received the B.S.E.E degree
from Bucknell University, Lewisburg, PA, in 2003,
the M.S.E.E. degree from the University of Pennsylvania, Philadelphia, in 2006, and the Ph.D. degree
from the University of Colorado at Boulder in 2012.
From 2003 to 2009, he was an Engineer with
Lockheed MartinMS2, Moorestown, NJ, where he
was involved with advanced phased-array radar
systems. His current research interests include
high-efficiency microwave PA theory and design,
microwave power rectifiers, monolithic microwave
integrated circuit (MMIC) design, and high-efficiency radar and communication
system transmitters. He is currently with TriQuint Semiconductor—Defense
Products and Foundry Services, Richardson, TX, where he is involved with
wideband high-efficiency GaN MMIC power amplifier design.
Zoya Popović (S’86–M’90–SM’99–F’02) received
the Dipl.Ing. degree from the University of Belgrade,
Belgrade, Serbia, Yugoslavia, in 1985, and the Ph.D.
degree from the California Institute of Technology,
Pasadena, in 1990.
Since 1990, she has been with the University of
Colorado at Boulder, where she is currently a Distinguished Professor and holds the Hudson Moore Jr.
Chair with the Department of Electrical, Computer
and Energy Engineering. In 2001, she was a Visiting
Professor with the Technical University of Munich,
Munich, Germany. Since 1991, she has graduated 44 Ph.D. students. Her research interests include high-efficiency, low-noise, and broadband microwave
and millimeter-wave circuits, quasi-optical millimeter-wave techniques, active
antenna arrays, and wireless powering for batteryless sensors.
Prof. Popović was the recipient of the 1993 and 2006 Microwave Prizes presented by the IEEE Microwave Theory and Techniques Society (IEEE MTT-S)
for the best journal papers and the 1996 URSI Issac Koga Gold Medal. In 1997,
Eta Kappa Nu students chose her as a Professor of the Year. She was the recipient of a 2000 Humboldt Research Award for Senior U.S. Scientists of the
German Alexander von Humboldt Stiftung. She was elected a Foreign Member
of the Serbian Academy of Sciences and Arts in 2006. She was also the recipient
of the 2001 Hewlett-Packard (HP)/American Society for Engineering Education
(ASEE) Terman Medal for combined teaching and research excellence.
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