IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS, VOL. 70, NO. 3, MARCH 2023
919
A Compact and Broadband Doherty Power
Amplifier Without Post-Matching Network
Li-Heng Zhou , Xin Yu Zhou , Senior Member, IEEE, and Wing Shing Chan , Member, IEEE
Abstract—Post-matching network (PMN) dominates broadband Doherty power amplifier (DPA) design, but at the cost
of large footprint. This brief presents a PMN-free, compact and
broadband DPA based on dual-mode impedance transformer (IT)
which can simultaneously realize a complex-to-real conversion at
two frequencies. The conversion ratio of the IT is significantly
increased while its fluctuation is reduced after collaborating
a short drain bias. The dual-mode ITs are used as the output
matching networks in the carrier and peaking paths. An out-ofphase 2nd harmonic injection path is constructed based on the
inherent structure of the IT without additional bridge, resulting
in enhanced saturated efficiency and output power at the upper
band edge. A prototype circuit operating from 2.1 to 3.1 GHz
is fabricated, and measured results show a 7-8.2 dB gain and
42.2-43.3 dBm output power at saturation. The 6-dB OBO and
saturated efficiency is 42.3-52% and 60.4-67.7%, respectively. The
area of the whole OMNs is only 19×37 mm2 , indicating a significant size reduction, while the DPA’s performance is comparable
with the PMN types.
Index Terms—Broadband Doherty power amplifier, compact,
dual-mode impedance transformer, harmonic injection.
I. I NTRODUCTION
IGH-ORDER modulation format signals with multiple
sub channels have demonstrated its practicality in modern
wireless communications but still have challenges due to its high
peak-to-average power ratio (PAPR). These practical challenges
lie mainly in the power amplifiers, to not only maximize output
power and efficiency at saturation, but also to maximize high efficiency at output power back-off (OBO). A variety of techniques
have been developed to mitigate degradation in performance
with high PAPR, for example Chireix outphasing [1], Doherty
power amplifier (DPA) [2], envelope tracking [3], envelope
elimination and restoration [4], and sequential PA [5]. Among
them, Doherty power amplifiers (DPAs) have been widely
adopted in modern base-stations due to its simplicity and ruggedness. Although ever-evolving mobile communication standards
H
Manuscript received 30 September 2022; accepted 24 October 2022. Date of
publication 31 October 2022; date of current version 6 March 2023. This work
was supported by the Research Grants Council of Hong Kong under Project
11206820. This brief was recommended by Associate Editor L. B. Oliveira.
(Corresponding author: Wing Shing Chan.)
Li-Heng Zhou is with the School of Information Science and Technology,
Nantong University, Nantong 226019, China (e-mail: marldini@hotmail.com).
Xin Yu Zhou is with the Department of Electrical and Computer
Engineering, Princeton University, Princeton, NJ 08544 USA.
Wing Shing Chan is with the Department of Electrical Engineering, City
University of Hong Kong, Hong Kong (e-mail: eeej2710@cityu.edu.hk).
This article has supplementary material provided by the
authors and color versions of one or more figures available at
https://doi.org/10.1109/TCSII.2022.3218006.
Digital Object Identifier 10.1109/TCSII.2022.3218006
require a broadband design, but DPA’s bandwidth is limited
by its drain-source capacitance Cds , offset line and impedance
transformer (IT) [6]. An output matching network (OMN) with
high conversion is desirable in the classic DPA but conversion ratio is inversely proportional to bandwidth. Post-matching
networks (PMNs) are commonly used to broaden the bandwidth
of DPAs, where the impedance conversion is moved to the rear
of summing node [7], [8], [9], [10], [11], [12], [13]. PMNs
based on lowpass impedance matching network, are usually
comprised of multi-section stepped-impedance lines or shunt
stubs. This inevitably occupies a large area and subsequent
higher loss, which are especially noticeable at high frequency
or in on-chip designs.
Modern wireless transmitters are evolving into ever dense,
distributed small-cell base stations, requiring for more compact
DPAs. Some techniques have tried to broaden DPA’s bandwidths
without the use of PMNs. In [14], Cds was absorbed into the
IT to increase the MMIC DPA bandwidth. In [15], the OMNs
were elaborately designed with no need of an IT and offset
line thus eliminating its bandwidth limitation. In [16], an LC
tank was placed in parallel at the summing node to form
a new combiner that extends the bandwidth. However, their
bandwidths are significantly smaller than for the PMN scheme.
In this brief, a dual-mode IT is proposed, where its equivalent LC circuit and a microstrip implementation are analyzed, verifying the capability of impedance conversion at
two frequencies simultaneously. An elaborately designed short
drain bias can increase the conversion ratio of the IT with
small fluctuation. Therefore, the required conversion ratio can
be fulfilled before the summing node and a PMN is no longer
needed. A 2nd harmonic injection is introduced to improve the
performance of the DPA. The circuit is designed and fabricated
using Rogers RO4003C with a thickness of 0.813 mm.
The rest of this brief is organized as follows. In Section II,
the characteristic of the dual-mode IT will be analyzed and the
mechanism of the harmonic injection based on the IT is illustrated. In Section III, the complete topology of the proposed
DPA and the simulation results are presented. Section IV
presents the measured results and a performance comparison
with other broadband DPAs is discussed. This will be followed
with a conclusion in Section V.
II. D UAL -M ODE IT
A. LC Circuit Analysis
Fig. 1 (a) shows a simplified configuration of a broadband
DPA where Zlp refers to the load-pull impedance. An OMN
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920
Fig. 1.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS, VOL. 70, NO. 3, MARCH 2023
(a) Configuration of DPA. (b) LC circuit of the dual-mode IT.
Fig. 3.
(a) Real part. (b) Imaginary part. Zc1 =32, Zc2 =70, Zc3 =24,
θ c1 =20◦ , θ c2 =70◦ , θ c3 =13◦ , θ b =30◦ , RL =50.
Fig. 2.
(a) Normalized real part. (b) Normalized imaginary part (L1 =0).
converts Zlp to RL (2RL ) at OBO (saturation) and a PMN is
therefore not needed anymore if RL =50.
Fig. 1 (b) shows the LC circuit of the dual-mode IT and its
input impedance is also given by Zlp
Zlp = jwL1 +
1
jwC2 + 1/jwL2 + 1/(RL + jwL3 )
(1)
B. Transmission Line Implementation
L3 is negligible in this design, and thus the real and imaginary
parts of Zlp can be simplified to
Rlp =
RL w2 L22
R2L (1 − w2 C2 L2 )2 + w2 L22
Xlp = wL1 +
wL2 R2L (1 − w2 C2 L2 )
R2L (1 − w2 C2 L2 )2 + w2 L22
(2)
(3)
L1 can tune X lp independently, while Rlp is simultaneously
converted to RL and 2RL at OBO and saturation.
RL w2 L12
=
2
R2L (1 − w2 C1 L1 )2 + w2 L1
2RL w2 L12
4R2L (1 − w2 C1 L1 )2 + w2 L12
(4)
There are two positive solutions for (4) which can be given as
w1 =
L12 + 8R2L L1 C1
−L1 + L12 + 8R2L L1 C1
w2 =
√
√
2 2RL L1 C1
2 2RL L1 C1
L1 +
(5)
For the dual-mode IT, Rlp can realize the expected conversion at two frequencies. Substituting (5) into (2), results
in a conversion ratio of 1.5 (1.5Rlp =RL ). The relationship
between normalized L2 and C2 can be obtained after normalizing RL to 1 and normalizing the frequency w1 +w2 =2.
2
2 2
L2 + 8L2 C2 = 8L2 C2
inductive LC tank, they approach each other to form a broadband design with a bandwidth of ∼w. However, a limitation
can be observed where there is a crest at w ≈ 1, here Rlp ≈ 1.
This gives rise to a low conversion ratio that prevents the drain
voltage from reaching its maximum value, thus degrading
efficiency and output power.
X lp monotonically decreases within the range of ∼w, as
shown in Fig. 2 (b). This matches the feature of a PA design
because there are numerous parasitic capacitances in a transistor which becomes more pronounced as frequency increases.
Meanwhile, the fluctuation of X lp is smaller for an inductive
tank, which can cater to the needs of a broadband PA.
(6)
Two groups of L2 and C2 are selected based on (6) and
the normalized Zlp can be plotted as a function of normalized frequency, as shown in Fig. 2. It can be seen that the
solid and dashed lines have two intersection points, verifying (5). In other words, the dual-mode IT can work as an
OMN at the frequency bands near these two points. For an
Fig. 3 (a) inset shows the microstrip dual-mode IT of the LC
circuit shown in Fig. 1 (b), where the bias stub first appears
invisible. The ABCD matrix of the microstrip IT is given by
1
0
A B
cos θ1 jZ1 sin θ1
=
jY1 sin θ1 cos θ1
1/(jZ2 tan θ2 ) 1
C D
1 RL
cos θ3 jZ3 sin θ3
(7)
jY3 sin θ3 cos θ3
0 1
S21 of the OMN can be solved based on (7). The expression for input impedance Zlpt can also be easily obtained. The
performance of the microstrip IT can be better presented by an
intuitive example rather than by cumbersome algebraic calculations. Since L3 is negligible, both Zc3 and θ c3 are small. The
inductive LC tank is realized by a shunt short-ended stub θ c2
with a large Zc2 . Zc1 and θ c1 can be tuned for impedance
matching and subsequent harmonic injection. The example
exhibits a bandstop response, as shown in Fig. 3 (a). Besides
being part of the dual-mode IT, the shunt stub can create
a notch located at 2fn . Therefore, if a PA based on this dualmode IT works at fn , its second harmonic generated by the
nonlinearity of the transistor will be suppressed.
Fig. 3 (b) shows the characteristics of Zlpt , which are very
similar to zlp in Fig. 2. The dotted lines represent the conversion ratio of 1.5 (2MaxRlpt /3). Like the analysis in Fig. 2 (a),
the proposed DPA is expected to work in the range of f,
where Rlpt exhibits a parabolic type shape with Xlpt dropping
continuously. For the solid line, the peak with Rlpt ≈ RL implying a degradation at center frequency f 0 , while, losses are large
within the range of f, as shown in Fig. 3 (a), thus deceasing
the PA’s efficiency.
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ZHOU et al.: COMPACT AND BROADBAND DPA WITHOUT PMN
Fig. 4.
(a) Simplified OMN. (b) Phase change.
Secondly, a drain bias stub is visible, which is usually set
to be λ/4 at f 0 to eliminate its impact on the OMN, but its
length θ b is shortened to improve Zlpt in this design, as shown
in the dashed line. Obviously, f 0 is shifted up to f 0 while
Rlpt and Xlpt have smaller fluctuations which are beneficial to
a broadband PA design. More importantly, the whole conversion ratio is significantly increased after reducing θ b . At peak,
Rlpt decreases from ∼50 to 24 after adding the short bias,
therefore doubling the conversion ratio. The inherent limitation
of the dual-mode IT is improved.
The short bias has negligible impact on S21 except at the
low edge frequencies while f 0 aligns roughly with the point
of minimal loss. The dual-mode IT together with the short
drain bias is therefore a good candidate for broadband DPA.
921
Fig. 5.
Schematic of the proposed DPA.
Fig. 6.
Simulated ZL at OBO and saturated states in the carrier path.
C. Out-of-Phase 2nd Harmonic Injection
The PA’s fundamental waveform can be reshaped for
performance enhancement by injecting an external signal at
its harmonics, at the cost of a more complex circuit with
an additional signal source. DPA topology has innately two
paths, which facilitates self-generated harmonic injection [17].
This requires an OMN which can reject harmonics and also as
a bridge to guide harmonics between the two paths. Similarly,
this bridge also needs to block the fundamental frequency.
The proposed DPA is able to exploit the existing structure to
realize such an injection bridge without any additional paths.
The second harmonic will be rejected due to the shunt stub
θ 2 if the DPA based on the dual-mode IT operates at fn . At
the same time, the two stubs that respectively belonging to the
carrier and peaking paths can construct a couple-line bandpass filter, as shown in Fig. 4, which allows 2fn pass and
suppresses fn (S21 <−13 dB). A wideband coupler is used to
split the input signal for this design, and thus the phase difference of drains between the two paths is about 90◦ at fn
(180◦ at 2fn ). The phase of the injection path marked by the
double arrow line is designed to be ∼0◦ at 2fn by adjusting θ c1 and θ p1, resulting in an out-of-phase injection. It is
worth noting that the injection must be narrow band due to
the strict phase requirement, and is optimal at saturation as
this is where the because peaking transistor produces a large
amount of harmonics.
The normalized synthesized impedance at the intersection
plane can be expressed as Zsy = (1 + r)/(1 − r), where r is
the ratio between peaking and carrier current [18]. Derivation
process of Zsy can be found in the Appendix. The proposed
DPA is symmetrical and thus the peaking current at 2fn is
Fig. 7. Simulated intrinsic voltage and current at saturation. (a) 2.6 GHz.
(b) 3 GHz.
slightly smaller than in the carrier path. Due to the out-ofphase injection, −1<r<−0.5 which engenders a small Zsy .
III. C IRCUIT I MPLEMENT
After carrying out load-pull simulations based on Cree
CGH40010F GaN HEMT, the load-pull impedance is determined to be 20 + 3j. The configuration of the proposed
DPA is shown in Fig. 5, where a commercial wideband coupler 11306-3S from Anaren is used and followed by steppedimpedance lines that are used as IMNs. The dual-mode IT
together with a short drain bias functions as the OMN for the
two paths, while a two-order cascaded structure extends the
bandwidth of the notch. Fig. 6 shows the simulated ZL , where
XL is small and RL approaches 50 at OBO (100 at saturation), resulting in a PMN-free broadband DPA, although
the conversion ratio slightly decreases at f 0 . In this design,
2fn is selected at around 6 GHz, and simulated Zsy are all
small: 8.3-17j, 1.5-13j and 3-6j at 5.8, 6 and 6.2 GHz, respectively, thus verifying previous analysis. These 2nd harmonics
are short-circuited by the out-of-phase injection. Fig. 7 shows
the intrinsic voltage and current in the carrier path after
de-embedding the parasitics of the active device. Current bifurcation in Fig. 7 (a) is caused by harmonics which reshape the
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922
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS, VOL. 70, NO. 3, MARCH 2023
Fig. 8.
Simulated performance comparison for whether using harmonic
injection in OMNs.
Fig. 10. (a) Measured performance versus frequency. (b) Measured lower of
ACPR.
respectively. Saturated output powers change from 42.2 dBm
to 43.3 dBm. Measured small-signal gain varies slightly from
10-11.1 dB with frequency, and the gain compressions at saturation are less than 3.8 dB. Fig. 10 (a) shows the drain
efficiency η at 6-dB OBO and saturation varies from 44.3%
to 52% and 60.4% to 67.7%, respectively.
B. Modulated Signal Measurement
Fig. 9.
DPA’s performance. (a) Small signal. (b) Large signal.
waveforms. After introducing the out-of-phase injection, the
bifurcation disappears and the voltage rises, as shown in Fig. 7
(b), implying a higher output power. The current and voltage
waveforms show the standard half-sine waveform similar to
what you get for Class-B. The overlapping area is smaller,
indicating enhanced efficiency. Fig. 8 shows a performance
comparison between with and without using the out-of-phase
harmonic injection. The OBO efficiency is similar while the
saturated efficiency and output power at high frequency show
significant improvements. The performance at low frequency
is degraded slightly due to the phase mismatch.
IV. M EASURED R ESULTS
A photograph of the complete fabricated circuit is shown in
inset of Fig. 9 which occupies a small area of 68 × 48 mm2 .
The proposed DPA is biased with carrier quiescent current of 54 mA and peaking gate DC bias of −6.2 V. The
drain supply voltages of both the carrier and peaking devices
are 28 V.
A. Continuous-Wave Signal Measurement
Small-signal performance is measured using Agilent
ENA series network analyzer E5071C. Fig. 9 (a) shows
both simulated and measured S parameters for the proposed
DPA. Good agreement can be observed with a slight deviation at high frequency due to parasitic effects of the surface
mount components and fabrication tolerance. The measured
return losses are better than 7 dB from 2 to 3.2 GHz, while
the maximum measured small-signal gain is about 11.7 dB.
Fig. 9 (b) shows the measured large-signal results of the
proposed DPA. From 2.1 to 3.1 GHz, the PAEs at 6-dB
OBO and saturation span from 39.5%-46% and 51.4%-59.3%,
To verify the linearity of the proposed DPA, measurements
are done using a Keysight signal generator E4433B and an
R&S FSV signal analyzer. A single carrier test signal with
PAPR of 6.5 dB at 0.1% probability of complementary cumulative distribution function is generated. Adjacent channel
power ratio (ACPR) was measured with a 3.84 MHz channel bandwidth. The measured results are shown in Fig. 10 (b)
with only one shown due to symmetry of the ACPR for
both lower and upper bands. The lower ACPR performance
of the proposed DPA is better than −24 dBc from 2.1 to
3.1 GHz.
C. Comparison and Discussion
A performance comparison between the proposed DPA
and published state-of-the-art broadband DPAs is summarized in Table I, where most of them adopt PMNs to expand
the bandwidths. F-η is an important power amplifier figure of merit because efficiency and frequency can be jointly
evaluated. The performance of the proposed design is comparable to the traditional post-matching DPAs [7], [8], [9].
In [10], the OMN before the summing node is omitted and
the impedance conversion relies entirely on the PMN, obtaining the broadest bandwidth, but efficiency inevitably degrades.
Efficiency in [11] and [12] is higher than others, but their
bandwidths are only about 0.7 GHz. The BW and efficiency
of the proposed DPA are obviously better than the other
two PMN-free DPAs [15] and [16]. The proposed DPA occupies a smallest area, especially for the OMN which is only
0.26 × 0.51 λ2g .
Furthermore, the proposed dual-mode IT can be replaced
by an equivalent LC circuit, which is convenient when transferring to on-chip designs, where the fabrication cost is also
reduced due to the size reduction. These features make it an
idea candidate for potential small-cell and femto-cell applications where size and cost are important factors that contribute
to it success.
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ZHOU et al.: COMPACT AND BROADBAND DPA WITHOUT PMN
923
TABLE I
C OMPARISON W ITH P UBLISHED PCB DPA S
V. C ONCLUSION
This brief proposes a novel broadband OMN that can
realize high impedance conversion and harmonic injection.
A broadband DPA is developed, which possess comparable
performance to traditional DPAs. Benefitting from the dualmode IT, the proposed DPA occupies a very small area due
to the removal of the PMN. The proposed DPA is suitable
for the realization of broadband and multi-standard smallcell base stations and is easy to incorporate into on-chip
designs.
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