Abstract — This paper discusses a method for improving the
efficiency of linear power amplifiers by externally injecting
power into the output at the second harmonic frequency. An
experimental proof-of-concept PA based on class-A/AB mode
with a 10-W GaN pHEMT at 2.45GHz is presented, and its
efficiency improved from 58% to 75% with –6.5 dBc injected 2
nd
harmonic power. Two-tone measurements confirm improved
linearity with simultaneous increase in efficiency, accompanied
by gain compression at higher input power.
Index Terms—power amplifier, high-efficiency, nonlinear
analysis, GaN pHEMT
I. INTRODUCTION
A large portion of current research in high-power
amplification of signals with carriers in the microwave range
focuses on improving efficiency and linearity [1]. Topologies
such as the Class F and F
-1
achieve high efficiency by driving
the active device into a non-linear region and shaping voltage
and current waveforms across the device via proper selection
of the output loading network at harmonic frequencies [2].
The concept of harmonic injection, however, refers to
architectures in which power at a harmonic of the operating
frequency is supplied to either the input, output, or both input
and output of the active device [3-10]. This paper presents
experimental results of a harmonically-injected power
amplifier (HI PA) at f
0
=2.45GHz showing significant
improvement in the efficiency and linearity over a class AB
PA based on a Cree pHEMT device with an output power of
40dBm. Fig.1 shows a general block diagram of the HI PA
concept with harmonic injection at the output.
Fig. 1. Block diagram of a harmonic-injection power amplifier (HI
PA) with 2f
0
injection at the output. A three-port network at the
output allows isolation between waves at f
0
and 2f
0
between ports 2
and 3, while allowing low loss at f
0
between ports 1 and 2. The phase
of the injected harmonic is critical to obtaining high efficiency.
II. HARMONICALLY-INJECTED PA CONCEPT
To achieve high efficiency, the voltage and current
waveforms should have minimal overlap in time domain. In
harmonically-terminated PAs [11], this is accomplished by
heavily driving the device so that the nonlinear input
capacitance generates harmonics at the output, resulting in a
highly nonlinear PA. In contrast, the PA in Fig.1 is not driven
to generate harmonics; instead harmonic power is injected
externally at the output. A three-port output network satisfying
the following conditions is required when injecting only the
second harmonic at the output of the PA:
=
0 )], ( exp[ 0 , 0 )] 2 ( exp[ , 0
0 , 0 )] 2 ( exp[ , 0 0 )], ( exp[
)] 2 ( exp[ , 0 0 )], ( exp[ 0 , 0
) 2 , (
0 33 0 31
0 22 0 21
0 31 0 21
0 0
f j f j
f j f j
f j f j
f f S
φ φ
φ φ
φ φ
Such a network is implemented in microstrip on a Rogers
4350B 30-mil thick substrate with dielectric constant of 3.66
and loss tangent of 0.0031, similar to the work reported in [9]
at 900MHz and in [10] from 0.6-2.4GHz. Fig. 2 shows the
relevant measured S-parameters extending beyond the second
harmonic of the 2.45GHz fundamental.
Fig. 2: Measured S parameters for the 3 port harmonic injection
circuit at the output of the fundamental amplifier. A photograph of
the 3 port network is shown in the inset.
The analysis of the HI PA concept is performed using
normalized class-A waveforms resulting in an output power of
1W with 50% efficiency. Addition of only cosine terms at the
second harmonic will result in a current waveform consistent
M
in
M
out
2f
0
2f
0
f
0 f
0
f
0
Z(2f
0
)
Z
L
V
DD
v
D
i
D
1 2
3
2.5 3 3.5 4 4.5 5
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
Frequency (GHz)
S parameters (dB)
S
11
S
21
S
31
S
33
Efficiency and Linearity of Power Amplifiers with External
Harmonic Injection
Asmita Dani, Michael Roberg and Zoya Popovic
Department of Electrical, Computer and Energy Engineering, University of Colorado at Boulder
Boulder, CO, 80309-0425
978-1-4673-1088-8/12/$31.00 ©2012 IEEE