IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 5, MAY 2006 1969
Analysis and Experiments for High-Efficiency
Class-F and Inverse Class-F Power Amplifiers
Young Yun Woo, Youngoo Yang, Member, IEEE
, and
Bumman Kim, Senior Member, IEEE
Abstract—This paper presents analytic and experimental com-
parisons for high-efficiency class-F and inverse class-F amplifiers.
The analytic formula of the efficiencies, output powers, dc power
dissipations, and fundamental load impedances of both amplifiers
are derived from the ideal current and voltage waveforms. Based
on the formula, the performances are compared with a reasonable
condition: fundamental output power levels of class-F and inverse
class-F amplifiers are conditioned to be identical. The results show
that the inverse class-F amplifier has better efficiency than that of
class-F amplifiers as the on-resistance of the transistor increases.
For experimental comparison, we have designed and imple-
mented the class-F and inverse class-F amplifiers at 1-GHz band
using a GaAs MESFET and analyzed the measured performances.
Experimental results shows 10% higher power-added efficiency
of the inverse class-F amplifier than that of the class-F amplifier,
which verifies the waveform analysis.
Index Terms—Class-F amplifier, harmonics control circuit, high-
efficiency amplifier, inverse class-F amplifier, power amplifier.
I. INTRODUCTION
A
GROWING popularity of the wireless communication
systems makes the high-efficiency RF power amplifiers
very important RF components. The class-F amplifier, which
has short load termination at even-order harmonics (current
peaking) and open load termination at odd-order harmonics
(voltage peaking), has become a representative of the high-ef-
ficiency amplifier [1]–[3]. Very recently, the inverse class-F
amplifier has started to draw attention due to its superior
performance. It is commonly known that the inverse class-F
amplifiers, which have open load at even-order harmonics
(voltage peaking) and short load at odd-order harmonics
(current peaking), can deliver higher efficiency than class-F
operation. Some papers with partial analyses, simulations, or
experiments, which demonstrated advantages of the inverse
class-F amplifier, have been reported [4]–[6]. However, there
have been no reports treating fully analytic and experimental
comparisons for the clear explanation of the better efficiency of
the inverse class-F amplifier.
Manuscript received November 24, 2005; revised February 1, 2006.
This work was supported in part by the Korean Ministry of Education
under the BK21 Project and by the Center for Broadband OFDM Mobile
Access (BrOMA) at the Pohang University of Science and Technology
(POSTECH) under the ITRC Program of the Korean MIC, supervised by IITA
(IITA-2005-C1090-0502-0008).
Y. Y. Woo and B. Kim are with the Department of Electrical Engineering,
Pohang University of Science and Technology, Pohang 790-784, Korea (e-mail:
w0yun@postech.ac.kr).
Y. Yang is with the School of Information and Communication,
Sungkyunkwan University, Suwon 440-746, Korea (e-mail: yang09@skku.
edu).
Digital Object Identifier 10.1109/TMTT.2006.872805
Fig. 1. Ideal current and voltage waveforms according to the load line on tran-
sistor’s I–V plane. Class-F (solid line). Inverse class-F (dotted line).
The purpose of this paper is to provide the quantitative and
clear explanation of better efficiency, and the design guide for
optimizing the output power or efficiency of the inverse class-F
amplifiers in comparison to the class-F amplifiers. For that pur-
pose, the efficiency equations of the inverse class-F and con-
ventional class-F amplifiers are derived using ideal time-domain
waveforms. The analytic comparisons are then carried out using
the equations under the condition that the fundamental output
power of both amplifiers are identical around where they have
maximum PAE.
For an experimental comparison, the class-F and inverse
class-F amplifiers at 1-GHz band are designed and imple-
mented. The analysis and experimental results clearly show
why the inverse class-F amplifier has higher efficiency than the
class-F amplifier.
II. A
NALYTIC APPROACH
A. Representation of Parameters
Fig. 1 shows the ideal time-domain current and voltage
waveforms of the class-F and inverse class-F amplifiers, when
they have the same fundamental output power under the same
drain biases. The class-F amplifiers have half-sinusoidal current
and square-wave voltage signals. On the contrary, the inverse
class-F amplifiers have square-wave current and half-sinusoidal
voltage signals. These ideal waveforms of the class-F and
inverse class-F amplifiers can be analyzed using Fourier series
0018-9480/$20.00 © 2006 IEEE
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1970 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 5, MAY 2006
expansion, which gives expressions for the various parameters,
such as a dc power dissipation, a fundamental RF output
power, and a required fundamental load impedance to obtain a
proper RF output power. The calculation is summarized in the
Appendix. For the class-F amplifiers, they are presented using
the variables shown in Fig. 1 as follows:
(1)
(2)
(3)
In the same way, parameters of the inverse class-F ampli-
fiers can be calculated as in the following equations using
,
, and :
(4)
(5)
(6)
where
.
Using (1), (2), (4), and (5), the efficiencies of the class-F and
inverse class-F amplifiers can be easily calculated as follows:
% (7)
% (8)
where
and are the efficiencies of the class-F and inverse
class-F amplifiers, respectively. From (7) and (8), if
is zero,
the efficiencies of the class-F and inverse class-F amplifiers are
100%. The efficiencies could be differentiated from each other
due to the different knee voltages originated from the different
peak current levels.
B. Performance Comparison
To compare the performances of the class-F and inverse
class-F amplifiers, we take the condition of the same output
power at the same drain bias voltage. Since the same transistors
are used in the design, other design parameters may need to
be adjusted in order to satisfy the above conditions for both
amplifiers.
Using the condition of
from (2) and (5), we
can get a second-order equation of
for a fixed drain bias
and
as follows:
(9)
Fig. 2. Performances of the class-F and inverse class-F amplifiers for the iden-
tical fundamental RF output power condition with varying
R
from 0 to 2
.
(a) Efficiency and fundamental load impedance. (b) DC power dissipation and
fundamental RF output power.
The solution of (9) can be represented as
(10)
Selecting a reasonable value of
from (10) and adding the
case, (10) is rewritten as
for
for
(11)
If (11) is substituted to the inverse class-F formula of (4)–(6)
and (8), we can easily obtain the analytic forms of dc power
dissipation, RF output power, load impedance, and efficiency
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WOO et al.: ANALYSIS AND EXPERIMENTS FOR HIGH-EFFICIENCY CLASS-F AND INVERSE CLASS-F POWER AMPLIFIERS 1971
Fig. 3. Harmonic control circuits for: (a) class-F amplifier and (b) inverse
class-F amplifier.
of the inverse class-F amplifier as functions of not ,but
, where the RF output power is identical with that of the
class-F amplifier. The resulting equations are not presented in
this paper because of complexity. The calculation is numerically
performed using M
ATLAB.
The comparison results of performances between the class-F
and inverse class-F amplifiers are presented in Fig. 2. For the
calculation, we assumed a
supply of 5 V and of 1 A
with a uniform transconductance.
The efficiency of the inverse class-F amplifier is better than
that of the class-F amplifier with increasing
due to the
higher
to ratio to maintain an identical ,as
shown in Fig. 2(a). Fig. 2(b) shows a significantly decreasing
dc power consumption of the inverse class-F amplifier for the
same RF output power, as
increases. From the analysis re-
sults and Fig. 1, we can expect that the inverse class-F amplifier
delivers superior efficiency when the amplifiers are not limited
by the breakdown voltage, but by the bias voltage, which is the
normal operation condition of handset power amplifiers.
III. D
ESIGN AND EXPERIMENTS FOR THE VERIFICATION
For experimental comparison of the class-F and inverse
class-F amplifiers, we have designed 1-GHz-band class-F
and inverse class-F amplifiers using OKI’s 0.1-W MESFET
KGF1284. The simulation of the two amplifiers is performed
using Agilent’s Advanced Design System (ADS) with an
in-house MESFET large-signal model [7].
Fig. 4. Simulated root-mean-square values of drain voltage and current signals
in frequency domain for: (a) class-F amplifier and (b) inverse class-F amplifier.
The designed class-F and inverse class-F amplifiers have the
same input matching networks and the same dc bias (class-B
bias point with
V and V), except op-
eration modes (class-F versus inverse class-F). The second and
third harmonic components are terminated properly in the de-
sign for circuit simplicity.
In order to control the two harmonic components, we have
constructed the output harmonic control networks, as illustrated
in Fig. 3. Fig. 3(a) and (b) shows the harmonic control circuits
for class-F and inverse class-F amplifiers, respectively. The con-
trol circuits include both arm shunt stubs for better harmonic
trap and tuning lines (gray lines in Fig. 3) for compensating de-
tuning effects of the device’s parasitic passive components.
Output matching networks of the two amplifiers are designed
for optimum performance with these harmonic control circuits.
We have simulated the two designed amplifiers and probed
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1972 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 5, MAY 2006
Fig. 5. Simulated time-domain voltage and current waveforms for: (a) class-F
amplifier and (b) inverse class-F amplifier.
voltage and current signals. The results are shown in Figs. 4
and 5, which are the drain voltages and currents of the two
amplifiers in the frequency and time domains, respectively.
As expected, the class-F amplifier has third-order voltage
peaking with third-order load impedance of 252.26
and second-order current peaking with second-order load
impedance of 1.05
, while the inverse class-F amplifier
has second-order voltage peaking with second-order load
impedance of 419.5
and third-order current peaking with
third-order load impedance of 3.00
, as shown in Fig. 4.
Time-domain signals also show that the class-F amplifier has a
square-like voltage signal and a current signal close to half-sine
wave, while the inverse class-F amplifier has the opposite (see
Fig. 5).
The photographs of the implemented class-F and inverse
class-F amplifiers are shown in Fig. 6. We have measured output
powers and power-added efficiencies (PAEs) of the two ampli-
fiers using a 1-GHz one-tone signal. Fig. 7 shows the simulated
and measured power responses and PAEs of the class-F and
inverse class-F amplifiers. As shown in Fig. 7(a), the inverse
class-F amplifier has approximately 1-dB lower gain because
the square-wave drain current needs more input drive than the
half-sinusoidal drain current for the same output power level.
The maximum PAE of the class-F amplifier is approximately
64% at an output power of 22.5 dBm. The maximum PAE of
the inverse class-F amplifier is approximately 74% at the same
output power level, which is 10% higher than that of the class-F
amplifier. The superior PAE performance of the inverse class-F
Fig. 6. Implemented: (a) class-F amplifier and (b) inverse class-F amplifier.
Fig. 7. Simulated and measured performances of the class-F and inverse
class-F amplifiers. (a) Output power levels. (b) PAEs.
amplifier at the same output power level supports the analysis
results well.
IV. C
ONCLUSION
We have analyzed and compared the time-domain waveforms
of the class-F and inverse class-F amplifiers. The analysis results
show that, under the operation condition of the same drain bias,
the inverse class-F amplifier has superior PAE to the class-F
amplifier when on-resistance
of the transistor exists. As
gets larger or the drain bias voltage gets lower, the perfor-
mance difference also increases. For experimental comparison,
we have designed and implemented 1-GHz class-F and inverse
class-F amplifiers. The implemented inverse class-F amplifier
has a maximum PAE of approximately 74% at 22.7-dBm output
power, which is 10% higher than that of the class-F amplifier.
This result clearly validates our analysis.
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WOO et al.: ANALYSIS AND EXPERIMENTS FOR HIGH-EFFICIENCY CLASS-F AND INVERSE CLASS-F POWER AMPLIFIERS 1973
Fig. 8 Ideal current and voltage waveforms for: (a) class-F amplifier and
(b) inverse class-F amplifier.
From the analysis and experiment for the comparison of the
two amplifiers, the inverse class-F amplifier is expected to be
useful to the power amplifiers for the base-stations or handsets
requiring high efficiency. This study also provides a good de-
sign guide for the inverse class-F amplifier to extract higher ef-
ficiency.
A
PPENDIX
A. Class-F
Fig. 8 shows the ideal current and voltage waveforms of the
conventional class-F amplifiers. To extract each frequency com-
ponent, the current and voltage waveforms of Fig. 8 are ex-
panded using a Fourier series as follows:
(A.1)
(A.2)
where
and are the time-domain current and voltage
waveforms including dc and RF components, respectively.
can be substituted for the knee voltage (see
Fig. 1).
The current and voltage waveforms can then be rearranged
with each harmonic’s component. The dc and fundamental RF
components of (A.1) and (A.2) are separated as the functions of
peak current, dc voltage, and
as
(A.3)
(A.4)
(A.5)
B. Inverse Class-F Amplifiers
Fig. 8 shows the ideal current and voltage waveforms of the
inverse class-F amplifiers. The current and voltage waveforms
are expanded using the Fourier series as follows:
(A.6)
(A.7)
can be substituted to the knee voltage . From
(A.7),
can be written using dc supply voltage as follows:
(A.8)
Here, the current and voltage waveforms can be rearranged
with each harmonic’s component. The dc and fundamental RF
components of (A.6) and (A.7) are separated as the functions of
peak current, dc voltage, and
as
(A.9)
(A.10)
(A.11)
R
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Young Yun Woo received the B.S. degree in elec-
trical and computer engineering from Han-Yang
University, Seoul, Korea, in 2000, and is currently
working toward the Ph.D. degree in electronic and
electrical engineering from the Pohang University
of Science and Technology (POSTECH), Pohang,
Korea.
His current research interests include RF power
amplifier design, linear power amplifier (LPA)
system design, and digital predistortion (DPD)
techniques for linearizing high power amplifiers.
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