A Simplified Broadband Design Methodology For Linearized High-Efficiency Continuous Class-F Power Amplifiers
A Simplified Broadband Design Methodology For Linearized High-Efficiency Continuous Class-F Power Amplifiers
A Simplified Broadband Design Methodology For Linearized High-Efficiency Continuous Class-F Power Amplifiers
6, JUNE 2012
Abstract—This paper describes the design approach employed However, both architectures possess intrinsic bandwidth limi-
for achieving approximated continuous Class-F power amplifier tations that have been only moderately overcome [7], [8].
(PA) modes over wide bandwidths. The importance of the non- PAs operating in the switch-mode domain exploit the non-
linear device capacitance for wave-shaping the continuous Class-F
voltage and current waveforms is highlighted, thus reducing the linear region of the device to impose a highly efficient set of
device sensitivity to second and third harmonic impedance termi- nonoverlapping current and voltage drain waveforms. For ex-
nations. By identifying the high-efficiency regions on the reactance ample, Class-F operation [9] describes an infinite set of fun-
plane for harmonic band placement, the design can be reduced damental and harmonic impedances to present to the device,
to a fundamental matching problem. The distributed simplified which produce nonoverlapping square-wave voltage and half-
real frequency technique synthesis algorithm can then be utilized
to achieve wideband operation. Using a 10-W Cree GaN HEMT sinusoidal current drain waveforms. From practical consider-
device, greater than 70% efficiency has been measured over a ations, only a small number of harmonics can be controlled,
51% bandwidth from 1.45 to 2.45 GHz, with output powers of resulting in a reduction of the maximum obtainable efficiency
11–16.8 W. The nonlinear PA was then linearized using digital from 100%. At RF, the parasitics of the device become signif-
predistortion with 20-MHz long-term evolution and 40-MHz icant and they must therefore be resonated out to present the
eight-carrier W-CDMA excitation signals, to attain adjacent
channel power ratios below 53 and 49 dBc, respectively. To required impedances at the internal current generator plane. Re-
the best of the authors’ knowledge, the measured results represent alization typically involves the use of transmission lines
the best performance obtained from a broadband switch-mode for presenting the precise harmonic impedances. The inclusion
PA, and the best linearized switch-mode performance using 20- of sensitive harmonic resonators then results in an increase of
and 40-MHz modulated signals. the network factor, corresponding to narrowband operation.
Index Terms—Broadband, Class-F, digital predistortion (DPD), The inherent narrowband performance of the Class-F amplifier
high efficiency, power amplifier (PA). restricts its potential for integration within wideband or multi-
band transceivers.
The Class-J amplifier has recently been proposed [10] to alle-
I. INTRODUCTION viate the precise harmonic shorting requirements of the Class-B
(or Class-AB) amplifier. The Class-J principle was then ex-
PA performance can exceed modern Doherty PA results with generalized voltage drain waveform composed of all frequen-
wideband excitation signals at 2.14 GHz. cies up to the fourth harmonic, while ensuring no power is dis-
In this paper, Section II derives the ideal continuous Class-F sipated at the harmonics
amplifier waveforms and impedance conditions. Section III
elaborates on previous work [14] to establish the criteria for ap-
proximated continuous Class-F operation, and the importance (3)
of the nonlinear drain–source device capacitance in waveform
shaping. The high-efficiency regions on the harmonic reactance Noting that the even function given by (2) has two zeros at
plane are identified and the simplified real frequency technique in the range , the Rhodes singularity condition [16] can
(SRFT) [15] synthesis algorithm is employed to design over be exploited to determine the optimum coefficients that satisfy
a wide bandwidth in Section IV. In Section V, measurements (3). This gives rise to a system of linear-dependent equations,
on the fabricated PA reveal greater than 70% efficiency with which can be expressed as follows:
at least 11 W of output power over the 1.45–2.45-GHz band-
width. When the obtained peak efficiency is appropriately
high, Section VI demonstrates the efficient operation of the
switch-mode PA with modulated excitations. Conclusions are
presented in Section VII.
A. Class-F Amplifier
(4)
The Class-F amplifier achieves highly efficient power ampli-
fication by saturating the device and manipulating the gener-
ated harmonics in such a manner as to produce nonoverlapping
drain waveforms. Class-F operation requires open-circuit termi- By computing the row reduced echelon form of (4), system (5)
nations at odd harmonics, with short-circuit terminations at the is found as follows:
even harmonics. By choosing a Class-B bias point, a half-sinu-
soidal drain current waveform is formed, given by (1) as follows
with a resulting square-wave drain voltage waveform:
(5)
(1)
The ideal Class-F waveforms give 100% efficiency in conver- The above under-determined system can then be used
sion of dc to fundamental frequency power, as no harmonic to extract the coefficient values by employing the parame-
power can be generated. In practice, control of up to the third terization . This results in and
harmonic is customary, as the benefit of further harmonic con- . The drain voltage waveform can then be
trol typically produces negligible efficiency improvements. To expressed as a function of the parameter
analyze the Class-F performance, the normalized drain voltage
waveform can be expressed as follows [10]:
(2) (6)
The above equation represents a voltage waveform that Class-F performance is maintained up to , at which point
uniquely delivers maximum power with 90.7% efficiency. the voltage waveform drops below zero, which requires the dc
Imposing this exact waveform at the current generator plane of component to be increased, therefore compromising efficiency.
the device requires precise tuning to compensate for the device This waveform provides a degree of freedom , which can be
parasitics at RF. This sole set of current and voltage waveforms used over a bandwidth to maintain maximum power and effi-
for maximum power and efficiency can usually only be realized ciency. A factorization can be performed to arrive at the form
at a single frequency, resulting in performance degradation presented in [11]
over a broad bandwidth.
(7)
B. Continuous Class-F Amplifier
Continuous Class-F operation describes a range of solutions The tradeoff, in comparison to Class-F, is seen as an increase in
that all deliver the same power and efficiency as in the Class-F the magnitude of the drain voltage waveform (from normalized
case. This family of solutions can be found by starting with a amplitude of 2 to a maximum of 3.37), which is shown in Fig. 1.
1954 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 6, JUNE 2012
Fig. 1. Continuous Class-F waveforms for . Fig. 2. Efficiency as a function of without fourth harmonic voltage compo-
nent.
It is seen from (10) that the fundamental, second, and fourth har-
monic impedances are dependent on the parameter , whereas
the third harmonic remains at a constant open circuit. These [pF]
demanding impedance conditions for continuous Class-F oper-
(11)
ation requires further investigation to understand how perfor-
mance degradation can be minimized with imprecise harmonic
This model offers an approximated large-signal model for the
terminations.
10-W Cree CGH40010FE GaN HEMT device, and assists in un-
derstanding the design tradeoffs for continuous Class-F broad-
III. APPROXIMATED CONTINUOUS CLASS-F MODES band operation. The model also permits convenient access to the
The requirement, given by (10), to present the exact internal drain terminal, which provides the time-domain voltage
impedance terminations over four frequency bands becomes and current waveforms.
unfeasible in practice. It is therefore necessary to devise a By comparing the nonlinear with its linear small-signal
strategy to approximate the continuous Class-F modes over the counterpart, an insight can be obtained into its importance in
band of interest. shaping the drain waveforms, thus reducing the dependency on
TUFFY et al.: DESIGN METHODOLOGY FOR LINEARIZED HIGH-EFFICIENCY CONTINUOUS CLASS-F PAs 1955
(15)
(16)
Fig. 7. Merged output power and efficiency contours representing 80% effi-
The coefficients of the polynomial are initialized and
ciency and 41dBm of output power over the 1.45–2.45-GHz bandwidth. is chosen. The polynomial is then found using (17), which
was determined via the lossless condition [21]
(17)
Fig. 11. Simulated results obtained from the designed distributed amplifier.
Fig. 10. Input and output matching network impedances at the package plane.
impedances and electrical lengths. It is seen that the first line the fundamental band impedance and harmonic band reactance
on the input match is not commensurate, and was incorpo- roll-off occurred. Stability networks were also integrated into
rated to minimize the discontinuity between the device tab the layout to prevent low-frequency oscillations. The layout of
and the circuit. This allows for greater precision in predicting the final amplifier is shown in Fig. 12. Figs. 13 and 14 display
the impedance presented to the device when converted to the measured impedances presented by the input and output mi-
microstrip. The parameter was chosen at 0.38 to produce an crostrip matching networks. The losses over the higher third har-
output harmonic band reactance roll-off, which remains within monic band frequencies in the output match are greater than ex-
the high-efficiency regions. The input harmonic band termina- pected, due to large resonances occurring from the wide lines.
tions were found to have minimal effect on the efficiency so the However, the presented third harmonic terminations lie in the
primary concern was given to accuracy in fundamental input high-efficiency region of the reactance plane while providing
matching. It was also necessary to ensure the characteristic sufficiently high impedance to allow the nonlinearity to
impedance of the lines do not exceed the chosen bounds of shape the waveforms advantageously and maintain high perfor-
. This gave practical dimensions for mi- mance.
crostrip fabrication, based on the RF35 board parameters and The commercially available 10-W Cree CGH40010FE GaN
frequency of operation. Fig. 10 shows the matching network HEMT packaged device was used for implementation. A gate
impedance trajectories on the Smith chart, where the output bias of 3.2 V was chosen, giving a quiescent current of 10 mA
match lies inside the contours across the fundamental band with with the drain bias set at 28 V. A Taconic RF35 board was se-
the harmonic band trajectory remaining in the high-efficiency lected with a board thickness of 1.52 mm, a copper thickness of
region. Thus, the design goals are obtained across the 50% 35 m, and an . The PA was tested with continuous
bandwidth, as shown in Fig. 11. wave (CW) excitation from 1.45–2.45 GHz and the results are
illustrated in Fig. 15. It can be seen that greater than 70% effi-
V. FABRICATION AND EXPERIMENTAL TESTS ciency is obtained from 1.45–2.45 GHz giving a bandwidth of
Firstly, the distributed circuit shown in Fig. 9 was converted 51%. The maximum efficiency measured across the band is 81%
to microstrip for fabrication and testing. Upon transformation at 1.7 GHz with a maximum power-added efficiency (PAE) of
to microstrip, it was necessary to tune the length of the lines 74.6% at 1.6 GHz. Across the band at least 11 W of power is
to compensate for large discontinuities between high and low delivered with a maximum power of 16.8 W, corresponding to
characteristic impedances. Careful monitoring of the second and 40.4–42.2 dBm. Gain between 10–12.6 dB was also measured.
third harmonic band reactance roll-off when tuning ensured they Fig. 16 shows a picture of the final PA. A comparison with sim-
did not enter the low-efficiency regions. Bias networks were in- ilar contemporary state-of-the-art broadband PA results is out-
corporated into the circuit at points where minimal impact on lined in Table I, and it is evident this work surpasses the others
TUFFY et al.: DESIGN METHODOLOGY FOR LINEARIZED HIGH-EFFICIENCY CONTINUOUS CLASS-F PAs 1959
Fig. 15. Measured results of the final amplifier from 1.45 to 2.45 GHz.
TABLE I
COMPARISON WITH STATE-OF-THE-ART BROADBAND PAs
TABLE II
LINEARIZATION PERFORMANCE FOR 1C-LTE SIGNAL
Fig. 19. AM/AM and AM/PM plots for 20-MHz signal carrier LTE signal with
and without DPD.
Fig. 21. AM/AM and AM/PM plots for 40-MHz eight-carrier WCDMA signal
with and without DPD.
[18] P. J. Tasker and J. Benedikt, “Waveform inspired models and the Lei Guan (S’09) received the B.E. and M.E. degrees
harmonic balance emulator,” IEEE Microw. Mag., vol. 12, no. 2, pp. in electronic engineering from the Harbin Institute
38–54, Apr. 2011. of Technology, Harbin, China, in 2006 and 2008, re-
[19] H. J. Carlin and J. J. Komiak, “A new method of broadband equaliza- spectively, and is currently working toward the Ph.D.
tion applied to microwave amplifiers,” IEEE Trans. Microw. Theory degree at University College Dublin.
Tech., vol. MTT-27, no. 2, pp. 93–99, Feb. 1979. He is currently with the RF and Microwave
[20] B. S. Yarman and A. Aksen, “An integrated design tool to construct Research Group, University College Dublin.
lossless matching networks with mixed lumped and distributed ele- His research interests include linearization and
ments,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 39, system-level modeling of RF/microwave PAs with
no. 9, pp. 713–723, Sep. 1992. an emphasis on DPD based on Volterra series and
[21] B. S. Yarman, Design of Ultra Wideband Power Transfer Networks. its field-programmable gate-array (FPGA) hardware
New York: Wiley, 2010. implementation. He also has interests in nonlinear system identification algo-
[22] D. Y.-T. Wu et al., “Design of a broadband and highly efficient 45 W rithms, digital signal processing (DSP), and wireless communication system
GaN power amplifier via simplified real frequency technique,” in IEEE design.
MTT-S Int. Microw. Symp. Dig., Jun. 2010, pp. 1090–1093.
[23] L. Guan and A. Zhu, “Simplified dynamic deviation reduction-based
Volterra model for Doherty power amplifiers,” in IEEE Int. Integr.
Nonlinear Microw. Millimeter-Wave Circuits Workshop, Vienna, Aus- Anding Zhu (S’00–M’04) received the B.E. degree
tria, Apr. 2011, pp. 1–4. in telecommunication engineering from North China
[24] L. Guan and A. Zhu, “Dual-loop model extraction for digital predis- Electric Power University, Baoding, China, in 1997,
tortion of wideband RF power amplifiers,” IEEE Microw. Wireless the M.E. degree in computer applications from the
Compon. Lett., vol. 21, no. 9, pp. 501–503, Sep. 2011. Beijing University of Posts and Telecommunications,
[25] A. Zhu, P. J. Draxler, J. J. Yan, T. J. Brazil, D. F. Kimball, and P. Beijing, China, in 2000, and the Ph.D. degree in elec-
M. Asbeck, “Open-loop digital predistorter for RF power amplifiers tronic engineering from University College Dublin
using dynamic deviation reduction-based Volterra series,” IEEE Trans. (UCD), Dublin, Ireland, in 2004.
Microw. Theory Tech., vol. 56, no. 7, pp. 1524–1534, Jul. 2008. He is currently a Lecturer with the School of Elec-
[26] H. Xu et al., “A high-efficiency class-E GaN HEMT power amplifier trical, Electronic and Communications Engineering,
at 1.9 GHz,” in IEEE Microw. Wireless Compon. Lett., Jan. 2006, vol. UCD. His research interests include high-frequency
16, no. 1, pp. 22–24. nonlinear system modeling and device characterization techniques with a par-
[27] P. Wright, J. Lees, J. Benedikt, P. J. Tasker, and S. C. Cripps, “A ticular emphasis on Volterra-series-based behavioral modeling and linearization
methodology for realizing high efficiency class-J in a linear broad- for RF PAs. He is also interested in wireless and RF system design, digital signal
band PA,” IEEE Trans. Microw. Theory Tech., vol. 57, no. 12, pp. processing, and nonlinear system identification algorithms.
3196–3204, Dec. 2009.
[28] M. P. van der Heijden, M. Acar, and J. S. Vromans, “A compact 12-watt
high-efficiency 2.1–2.7 GHz class-E GaN HEMT power amplifier for
base stations,” in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2009, pp.
657–660. Thomas J. Brazil (M’86–SM’02–F’04) received the
[29] J. Wang, Y. Xu, and X. Zhu, “Digital predistorted inverse class-F GaN B.E. degree in electrical engineering from Univer-
PA with novel PAPR reduction technique,” in IEEE MTT-S Int. Mi- sity College Dublin (UCD), Dublin, Ireland, in 1973,
crow. Symp. Dig., Jun. 5–10, 2011, pp. 1–1. and the Ph.D. degree in electronic engineering from
the National University of Ireland, Dublin, Ireland, in
1977.
He was subsequently involved with microwave
subsystem development with Plessey Research,
Caswell, U.K., prior to rejoining UCD in 1980. He
is currently a Professor of electronic engineering
and Head of the School of Electrical, Electronic and
Communications Engineering, UCD. His research interests are in the fields
Neal Tuffy (S’12) received the B.E. degree in elec- of nonlinear modeling and characterization techniques at the device, circuit,
tronic engineering from University College Dublin, and system levels. He also has interests in nonlinear simulation algorithms
Dublin, Ireland, in 2006, and is currently working to- and several areas of microwave subsystem design and applications. He has
ward the Ph.D. degree at University College Dublin. authored or coauthored numerous publications appearing in international
He is currently with the RF and Microwave scientific literature.
Research Group, University College Dublin. His Prof. Brazil is a Fellow of Engineer Ireland. He is a member of the Royal Irish
research interests include waveform engineering Academy. From 1998 to 2001, he was an IEEE Microwave Theory and Tech-
techniques, particularly for the design and fabrica- niques Society (MTT-S) Worldwide Distinguished Lecturer in high-frequency
tion of high-efficiency broadband PAs. computer-aided design (CAD) applied to wireless systems. He is currently a
member of the IEEE MTT-1 Technical Committee on CAD.