Fast Second Harmonic Injection Characterization
for Efficiency Enhancement of RF Power Amplifiers
Haedong Jang
1
, Patrick Roblin
1
, Andr´ es Z´ arate-de Landa
2
and J. Apolinar Reynoso-Hern´ andez
2
1
Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210, USA
Email: roblin.1@osu.edu, Telephone: (614) 292-0998
2
Centro de Investigaci´ on Cient´ ıfica y de Educaci´ on Superior de Ensenada (CICESE), Ensenada B.C., M´ exico
Abstract— A fast characterization method to determine the
optimal second harmonic injection required at the input for
enhancing the efficiency of RF power amplifiers is demonstrated.
The second harmonic is injected with a small frequency offset to
automatically sweep the phase during one modulation cycle. The
power amplifier performance figures of merit are characterized
over the second-harmonic amplitude and phase space. Time
varying voltage and current waveforms are measured using a
large signal network analyzer for a 15 W peak power packaged
GaN device. The constructive second-harmonic injection exhib-
ited improvements in efficiency of 11.7% and 30.5% compared,
respectively, to the cases of (1) no injection with 50Ω termination
and (2) destructive second-harmonic injection.
Index Terms— efficiency, harmonic injection, large signal net-
work analyzer, load-pull, poly-harmonic distortion (PHD) model,
power amplifier, waveform engineering.
I. I NTRODUCTION
RF power amplifier designers have manipulated time do-
main voltage and current waveforms to increase the efficiency
of amplifiers by reducing the overlap between those wave-
forms resulting in minimized dissipated power by devices [1].
The waveforms can be controlled by using a limited number of
dominant harmonics in frequency domain [2]. Conventionally,
harmonic source- and load-pull have been performed to tune
the harmonic matching of the amplifiers [3]. Passive harmonic
matching networks have been commonly used to optimize the
performance.
Beyond passively matching of the harmonics generated by
nonlinear devices, the active injecting of harmonics into the
input or output, specifically the second harmonic which has
dominant effects, have been demonstrated in [4]-[8]. Haynes
et al. used the second harmonic injection in [7] to reduce
the unnecessary input amplitude swing below pinch-off. The
resulting efficiency was even higher than that of the nominal
class-B condition due to the reduced conduction angle as well
as the increase in gain. Dani et al. directly controlled the
output second harmonic in [8] using a three-port injection
circuit. Clearly, these techniques require a wider impedance
coverage (reaching outside the Smith Chart) during the search
of the optimal source and load than can be provided by
conventional passive matching. Additional second harmonic
amplitude and phase tuning were performed experimentally
to optimize the efficiency in [5] but such optimization comes
at the cost of increased measurement time. In the literature
[9]-[11], the automatic phase and amplitude sweep, using
modulated excitations under quasi-static assumption of the
device RF response, were proposed to significantly reduce the
measurement time in real-time active load pull setups.
In this work, the automatic phase sweeping technique is
applied to the second harmonic injection at the transistor
input. For each second-harmonic input-power of interest, a
380
◦
phase sweeping of the second harmonic phase can be
effectively realized by the RF measurement along one full
cycle of the offset modulation frequency. Using 12.5 kHz
frequency offset this corresponds to a minimum 80μs mea-
surement duration. In practice multiple periods are acquired
to reduce the measurement noise but this still results in very
fast measurements. The post processing of the measured data
provides, then, the device figure of merits such as output
power, efficiency, gain and input reflection coefficients over
the second-harmonic amplitude and phase space.
II. AUTOMATIC PHASE SWEEP
A large signal network analyzer (LSNA, MT4463A) pro-
vides vectorial voltage and current information under mod-
ulated signal condition within 20 MHz bandwidth. Slowly
modulated signal can be used for fast RF characterization
under the assumption of a quasi-static device response. The
input excitation includes offset second harmonic as:
A
1
(t)= a
1
(ω)e
jωt
+ a
1
(2ω +Δω)e
j(2ω+Δω)t
. (1)
The second harmonic phase is automatically swept by one
full cycle on every 2π/Δω second. Then, the incident second
harmonic component, slowly varying in time, is expressed in
phase normalized form as:
A
1,2ω
(t)= a
1
(2ω +Δω)e
j(Δω−2
a1(ω))t
, (2)
where, a
1
(ω), a
1
(2ω +Δω) are the measured incident waves
at ω and 2ω +Δω, respectively. However, in the actual
measurements, the nonlinear device induced second harmonic
can be re-injected into the device when the source matching
is not ideal. Therefore, the actually injected second harmonic
is calculated as:
A
1,2ω.actual
(t)=
M
p=−M
a
1
(2ω+pΔω)e
j(pΔω−2
a1(ω))t
, (3)
978-1-4799-2935-1/13/$31.00 ©2013 IEEE