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J. Electromagn. Eng. Sci > Volume 23(4); 2023 > Article
Jang, Seong, Kang, Han, and Ahn: A New Doherty Combiner with Wide Bandwidth for Magnitude and Phase Balance Compensation

Abstract

This paper proposes a novel Doherty combiner that uses a series and parallel resonant circuit for wideband. Unlike conventional combiners, the aim of the proposed combiners is to extend bandwidth for not only the magnitude bandwidth, but also phase balance by employing series and parallel resonant circuits at the output impedance of the peaking amplifier. Considering the load impedance of the peaking amplifier, the Doherty combiners were analyzed in the theory of this study by deriving the series and parallel resonant circuit values. The output phase balances are determined for the targeted bandwidth to achieve uniform phase balance in the proposed combiner I using a series resonator. For better magnitude bandwidth, the slope of reflection coefficient (Γ) at port 3 in the combiner II using series resonator was derived using the derivative of Γ with respect to ω. Experimental results show that the proposed combiner I has 63.5% magnitude fractional bandwidth (FBW) and 118% FBW with the phase balance at ±2.5°. The proposed combiner II also has 85% magnitude FBW and 118% FBW with the phase balance at ±2.5°.

I. Introduction

RF power amplifiers used in communication base stations require high efficiency and linearity. The amplifier needs to operate at high efficiency at a back-off level [1]. However, the base station power amplifiers have low efficiency due to the back-off operation [2]. Lower efficiency causes several thermal issues and decreases the lifetime of high-power transistors [35]. Therefore, much research [612] focusing on the large back off power region has been suggested in order to improve the average efficiency of power amplifiers, one of which is commonly known as the Doherty power amplifier, first proposed by Doherty [7] in 1936, as shown in Fig. 1(a). Various applications based on improving power efficiency in Doherty power amplifiers have been researched [812]. These include the multiway [8, 9], symmetric way [10], and asymmetric methods [11, 12]. However, Doherty power amplifiers and other applications [712] require λ/4 impedance transformers in splitting and combining operations for the two signals of the carrier and peaking amplifiers. These methods operate only near the center frequency, resulting in bandwidth limitations. Another requirement for power amplifiers is the ability to operate in wide bandwidth, as well as high linearity and high efficiency in the base station. Suggestions have been offered for better bandwidth [1320], but these combiners have a phase balance limitation, despite the enhanced magnitude bandwidth.
In this paper, a new Doherty combiner is presented for improving bandwidth, not only magnitude, but also phase balance. The proposed combiners I and II were made up of series and parallel resonant circuits. The LC values in the proposed combiners were analyzed by deriving the slope of the phase differences and the reflection coefficient of the S-parameter.

II. The Proposed Doherty Combiner I with Series Resonator

The conventional Doherty combiner depicted in Fig. 1(a) consists of a carrier amplifier (CA) and a peaking amplifier (PA), as well as a phase shift and an impedance transforming network. The basic concept of the Doherty technique is that the CA is designed to saturate below the transition point (half of the maximum output voltage), and the PA commences linear operation, modulating the load of the CA from twice its optimum (2Ropt) to the optimum value (Ropt) [2]. The required load modulation method is achieved by using an impedance transforming network, which causes the limited bandwidth of the phase differences between S31 and S32. First, consider Fig. 1(b) for a wide phase balance. The series resonant circuit (L and C) at port 2 was added to the conventional Doherty combiner. Since the conventional Doherty’s phase slopes differ from S31 and S32, the phase differences vary as the frequency deviates from the central frequency [21]. The frequency deviations caused phase balance degradation. To improve the phase balance, we derived the design theory in a different way than in [22]. Instead of the derivative of phase differences, uniform phase balance was considered to set the targeted phase deviation. To analyze the proposed combiners, the output nodes of CA and PA were replaced by port 1 and port 2, respectively (i.e., input sources); however, port 3 was the output port for the combiner. Fig. 1(c) shows a modified diagram that illustrates the calculation of the phase differences S31 and S32 of the proposed combiner I in Fig. 1(b), terminating port 2 as port impedance Z0 and showing port impedance of P1 without a 90° phase shift. The input admittance looking at P1 to P2, Zins, is Fig. 1(c) is defined as (1).
(1)
Yins=1Zins=ωCZ0ωC-j(ω2LC-1)(Z0ωC)2+(ω2LC-1)2.
To simplify the calculations, a 90° phase shift was added as a phase (θp.s) at the last step, as shown in Fig. 1(c). After terminating port 2 as the port impedance Z0, the ABCD parameters from node P1 to node P3 were calculated. In addition, the ABCD parameters from node P2 to node P3 are derived after port 1 was terminated with port impedance Z0 using a modification similar to the one in Fig. 1(c). Thus, (ABCD)31 and (ABCD)32 are given in (2) and (3) below.
(2)
(ABCD)31=(cosθjZ0sinθ2Yinscosθ+j2sinθZ0jZ0sinθ2Yins+cosθ),
(3)
(ABCD)32=(1j(ω2LC-1)ωC01)=(cosθ(1+jY0AA)-2AAsinθZ0(jZ0-AA2)sinθ+jAAcosθY0cosθ+j2sinθZ0jsinθ2Y+cosθ),
where AA=ω2(LC-1)ωC.
From (2) and (3), S31′ and S32 are expressed in the Appendix. From S31′ and S32, the angular phases ∡S31′ and ∡S32 are described as (4) and (5) below.
(4)
S31=-tan-1(22(4(Z0ωC)2+3(RR)2)sin θ-Z0ωC(RR)cosθ(3(Z0ωC)2+2(RR)2cosθ+22(Z0ωC)RRsin θ),
(5)
S32=-tan-1(2Y0RRωCcosθ+22sinθ3cosθ-322Y0RRωCsinθ),
where RR = ω2LC – 1.
Consider the 90° phase shift (θps) mentioned above. The phase differences (φdiff) of S31′ and S32 are expressed as φdiff = (θps + ∡S31′ ) – ∡S32. φdiff is calculated as the center frequency (f0) and lower band-edge frequency (f1) targeted half of the bandwidth, shown as (6)–(8).
(6)
φ0=θ0+S31|θ=θ0-S32|θ=θ0,
(7)
φ1=θ1+S31|θ=θ0-S32|θ=θ1,
(8)
φdiff=φ0-φ1=(θ-θ0)+(S31|θ=θ0-S32|θ=θ0)-(S31|θ=θ1-S32|θ=θ1).
If we set the f1 and φdiff, the upper band-edge frequency ( f1) and phase differences should also be linear. θ0=π2 and θ1=ω1ω0π2 are applied to (8), and (9) is derived.
(9)
φ0-φ1-π2(1-ω1ω0)=(θ310-θ311)-(θ320-θ321),
where ∡S32|θ=θn = θ32n, n = 1, 2.
The evaluation of tangent (α) is derived in (10) using trigonometric functions; this is done after replacing the left side of (9) with α,
(10)
tan(α)=tan((θ310-θ311)-(θ320-θ321))=NumDen,
where Num=(1tan θ320+tan θ321)(1-tan θ311tan θ310)-(1tanθ311+tan θ311)(1-tanθ321tanθ320).
(11)
tan(α)=tan(θ321-θ311)=tan((φ0-φ1)-π2(1-ω1ω0)),
where θ320,θ310=π2 and ω2LC – 1 = 0.
Using (4) and (5), (11) can be derived as L and C, as in (12) and (13).
(12)
C=-BBZ0ω1tan(α)=-BBZ0ω1tan(φ0-φ1-π2(1-ω1ω0)),
(13)
L=(12πf)21C,
where BB=(ω1ω0)2-1.
Therefore, the proposed Doherty output combiner I has the values of L and C, as in (12) and (13), after setting the phase differences S31 and S32 at the center frequency f0 and target frequency f1. This could be a more practical way to set the phase balance for target frequency.

III. The Proposed Doherty Combiner II with Series and Parallel Resonant Circuits

The L and C values obtained in Section II are juxtaposed with the targeted phase differences at the center frequency f0 and the specified band frequency f1. Thus, the phase slope of phase differences had a constant value in wideband. In this section, we consider the frequency bandwidth of the magnitude balance. The proposed Doherty combiner II has a series resonator and a parallel resonator, as shown in Fig. 2(a). The added parallel resonant circuit Lp and Cp only affected the magnitude bandwidth, which had a constant phase balance. Zin as shown in Fig. 2(b), can be obtained as (14).
(14)
Zin=(Z0+jωLs-j1ωCs)(jωLp1jωCpZ0)=A+jBC+jD=AC+BC+j(BC-AD)C2+D2,
where
  • A = (Z0ω)2LpCs, B =Z 0 ωLp(ω2LsCs – 1),

  • C = 2Z0ω2CsLpZ0(ω2LsCs – 1)(ω2LpCp – 1),

  • D=Z02ωCs(ω2LpCp-1)+ωLp(ω2LsCs-1).

The input impedance Zin at port 3 can be obtained as (15) using (14). From (15), Zin can be rearranged (16).
(15)
Zin=Z02Zin+jZ0tanθ2Z02+jZintanθ=Z02AC+BCC2+D2+j(BC-ACC2+D2+Z0tanθ2)(Z02-(BC-AC)tanθC2+D2+j(AC+BD)tanθC2+D2),
(16)
Zin=Z0(Z0x2ωsec2θ+j(Z0x2ω(1-tan2θ)+(Z022-x2+y2ω2tanθ)))2(Z022-2Z0ytan θ2ω+(x2+y2)tan2θω2),
where x = AC + BC, y = BCAD, ω = C2 + D2.
The reflection coefficient (Γ) of S33 is given by (17) using (16). To determine wide magnitude bandwidth, the derivative of Γ with respect to ω is necessary, since (17) is a function of ω, Lp, and Cp.
(17)
S33=Zin-Z0Zin+Z0.
Fig. 3 shows plots of several graphs of the S33 slope versus Lp, varying from 2 to 7 nH and having a frequency range between 1.4 to 2 GHz generated using MATLAB. To obtain the Lp value for broad bandwidth, we observe that Lp = 2.35 nH is selected when the slope of S33ω=0. Cp value was also derived using the resonant frequency. Thus, the parallel resonant circuit positively affected the magnitude bandwidth, and the series resonant circuit improved phase balance.

IV. Simulation and Fabrication Results

1. Simulation Results Using Analysis Designer

To demonstrate the proposed design method, two proposed Doherty combiners (I and II) were designed using a central frequency of 2 GHz based on the algorithm below.
  1. Draw the proposed Doherty combiner I and label its essential parameters (Z0, θps, L, and C).

  2. Apply the circuit analysis on the ABCD parameter and S-parameter to obtain magnitude and phase terms, which are used to extract the required parameters when the θps = π/2 and resonant conditions are applied.

  3. Express the phase differences (φdiff) of S31′ and S32 as φdiff = (θps + ∡S31′ ) – ∡S32. φdiff is set as the center frequency (f0) and lower band-edge frequency (f1), and calculate L and C.

  4. Draw the proposed Doherty combiner II having Lp and Cp. Using the obtained value of L and C, derive the reflection coefficient of S33 at ports 1 and 2, which are terminated by a port impedance Z0.

  5. Use MATLAB to calculate the derivative of S33 with respect to ω, and plot the S33 slope according to the Lp.

  6. Perform circuit simulation and three-dimensional field analysis using ANSYS High-Frequency Structure Simulator (HFSS).

  7. If the achieved results are desirable, then fabricate the proposed circuits to check the validity of the design theory.

This section describes circuit simulations conducted on the conventional Doherty combiner and the proposed Doherty combiners I and II. The inductor value L and capacitor value C was derived as 2.37 nH and 2.67 pF, respectively at f0 of 2 GHz, f1 of 1.9 GHz, and the phase difference of S31 and S32 was 1°. The values of the series resonant circuit of the proposed Doherty combiner II were also applied using the same value of the proposed combiner I. The values of the inductor (Lp) and capacitor (Cp) in the parallel resonant circuit are 2.35 nH and 2.69 pF, respectively, at zero slope.
Fig. 4(a) and 4(b) shows the S-parameter and phase differences of comparison simulation results according to the conventional and proposed Doherty combiners (I and II). The comparison simulations were conducted using ANSYS Designer. Since the target edge frequency f1 is 1.9 GHz and the phase balance is set as 1°; the circuit simulation results are consistent with the targeted results of the designed circuit. Magnitude bandwidth also increases 110 MHz bandwidth for the Doherty combiner II having a series and parallel resonator.

2. Fabrication Results and Measurements

Fig. 4(c) shows a fabricated photograph of the conventional circuit, proposed circuits I and II, from left to right. The fabricated substrate is Rogers RT5880, and the dielectric coefficient is 2.2. The chip inductor and capacitor used in this paper have a size of 2.0 mm × 1.2 mm. The line width of port impedance Z0 is 2.38 mm and the length is 27.4 mm. Z0/2 has a width of 3.91 mm and a length 26.94 mm. For better fabrication and accurate results, the parallel resonator is replaced by the short stub [22], which has 23.23 Ω characteristic impedance and electrical length 90°. Fig. 5(a) and 5(b) show the S-parameter and phase difference of the measured results for the conventional and proposed Doherty combiners, respectively. The S31 and S32 of the conventional Doherty combiner measured at 2.77 dB and 3.45 dB, respectively, values that are similar to the simulation results. The S31 and S32 results of proposed circuit I is 3.07 and 2.93 dB, respectively. The S31 and S32 results of proposed circuit II are 3.21, and 3.38 dB, respectively. As a result of the fabrication error, the proposed circuits had a less than 0.4 dB difference compared to the simulation results. The proposed circuit I with series LC experienced a decrease of 5.9% bandwidth, but the phase slope of the proposed circuit I increases over 112%, with a variance of ±2.5°, compared to the conventional Doherty combiner. The proposed circuit II’s magnitude bandwidth with a series and parallel resonant circuit improved by about 25.9%, compared to the conventional Doherty combiner. The phase slope also increased by about 112% compared to the conventional slope. Thus, the design theory of the proposed circuits I and II are verified over a wide bandwidth by employing the proposed method.

V. Conclusion

In this paper, a novel Doherty combiner is proposed with the aim of extending bandwidth. The proposed Doherty combiners I and II consist of series or parallel resonators added to a conventional Doherty combiner. The proposed combiner I was derived by setting the targeted phase balance, and the series resonant values were obtained by setting the resonant condition as the phase balance. The proposed combiner II was calculated by obtaining the zero slope of the reflection coefficient of S33. The derived values of the proposed circuits were verified using the simulation and measured results. Both results show that the proposed combiner II has a wideband for not only magnitude bandwidth but also phase balance, with 25.9% and 112% improvement for magnitude and phase bandwidth, respectively, compared to the conventional Doherty combiner. Therefore, the proposed Doherty combiners can be applicable for wideband Doherty power amplifiers in baseband stations and various applications to balance of magnitude and phase characteristics.

Acknowledgments

This result was supported by “Regional Innovation Strategy (RIS)” through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (MOE) (No. 2021RIS-004) and the Soonchunhyang University Research Fund.

Fig. 1
(a) Conventional Doherty combiner, (b) the proposed Doherty combiner I, and (c) the modified Doherty combiner I in Fig. 1(b).
jees-2023-4-r-178f1.jpg
Fig. 2
(a) The proposed Doherty combiner II using series and parallel resonant circuit and (b) the modified Doherty combiner II.
jees-2023-4-r-178f2.jpg
Fig. 3
A simulated S33ω graph for parallel inductor value Lp.
jees-2023-4-r-178f3.jpg
Fig. 4
Comparison of the simulation results of conventional and proposed Doherty combiners: (a) S-parameter, (b) phase difference of S31 and S32, and (c) fabricated photos of the conventional, the proposed Doherty combiner I, and the proposed Doherty combiner II.
jees-2023-4-r-178f4.jpg
Fig. 5
Comparison results of (a) S-parameter and (b) phase difference.
jees-2023-4-r-178f5.jpg

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Appendices

Appendix

S-parameters S31′ and S32 can be derived from the ABCD parameter in Fig. 1(c).
S31=2S31real+jS31imag,
where
S31real=3(Z0ωC)2-2(ω2LC-1)2cosθ(Z0ωC)2+2(ω2LC-1)2+2(Z0ωC)sinθ2(Z0ωC)2+2(ω2LC-1)2,S31imag=24((Z0ωC)3-3(ω2LC-1)2)sinθ2(Z0ωC)2+2(ω2LC-1)2-(Z0ωC)(ω2LC-1)cosθ(Z0ωC)2+2(ω2LC-1)2,S32=2A+BZ0+CZ0+D=2S32real+S32imag,
where
S32real=3cosθ-32Y0(ω2LC-1)sinθ2ωC.

Biography

jees-2023-4-r-178i1.jpg
Youna Jang received her master’s degree in display engineering from Hanyang University, Seoul, Korea, in 2014. She also received her Ph.D. in electrical communication system engineering from Soonchunhyang University, Choongnam, Korea, in 2019. She designed as a designer of the RF filter in an internship program in 2015 at Qorvo, Bundang, South Korea. She was a lecturer at Soonchunhyang University from 2016 to 2020. She is currently a research professor at the Radio and Mechatronics Research Center at Soonchunhyang University. Her research areas include the design of passive components in microwave bands.

Biography

jees-2023-4-r-178i2.jpg
Cha Hye Seong received his B.E. degree in electrical engineering from Soonchunhyang University, Asan, Korea, in 2023. He received his master’s degree in ICT convergence at Soonchunhyang University. His current research interests include RF passive device theory, RF design, and RF testing. Currently, he is a member of the R&D center at SAWNICS.

Biography

jees-2023-4-r-178i3.jpg
Taehoon Kang was born in Incheon, Korea, in 1993. He received his M.S. degree from Soonchunhyang University, Asan, Korea, in 2019. Currently, he is accomplishing his Ph.D. at Soonchunhyang University. His current research interests include RF filter theory, design, and testing.

Biography

jees-2023-4-r-178i4.jpg
Sang-Min Han received his B.S., M.S., and Ph.D. degrees in radio sciences and engineering from Korea University, Seoul, Korea, in 1996, 1998, and 2003, respectively. From 1999 to 2001, he was a Lecturer with the School of Electrical Engineering, Korea University. From 2003 to 2004, he was a Post–Doctoral Research Fellow with the University of California at Los Angeles (UCLA), USA. From 2005 to 2007, he was a Senior Research Engineer with the Samsung Advanced Institute of Technology (SAIT), Korea. In 2007, he joined Soonchunhyang University, Korea where he is a professor with the Department of Information and Communication Engineering. He was a Visiting Research Faculty with the Georgia Institute of Technology (GT), Atlanta, USA from 2013 to 2014. Prof. Han is an Associate Editor of the Journal of the Korean Institute of Information Technology (JKIIT) and an Editorial Board Member of the Journal of Electromagnetic Engineering and Science (JEES). He has appeared in Marquis’ Who’s Who in Science and Engineering (2006–2007) and Marquis’ Who’s Who in Asia (2007). His research interests include RF/microwave system architectures with low-power/spectrum sensing, active integrated antennas, and reconfigurable RF systems/components.

Biography

jees-2023-4-r-178i5.jpg
Dal Ahn received his B.S., M.S., and Ph.D. degrees in electronics from Sogang University, Seoul, Korea, in 1984, 1986, and 1990, respectively. From 1990 to 1992, he worked with the Mobile Communications Division, Electronics, and Telecommunications Research Institute (ETRI), Daejeon, Korea. Since 1992, he has been affiliated with the Department of Electrical Engineering, Soonchunhyang University, Asan, Korea, where he is currently a professor. He is also currently the chief of the RF and Microwave Component Research Center (RAMREC) at Soonchunhyang University. In addition, he is a technical consultant for Tel Wave Inc., Suwon, Korea. His current research interests include the design and application of passive and active components at radio and microwave frequencies, the design of RF front-end modules for various handset systems using low-temperature co-fired ceramic (LTCC) technology, DGS circuit applications, and circuit modeling through a commercial EM analysis program. Prof. Ahn is also an editor of the Journal of Korea Electromagnetic Engineering Society and a senior member of the Korea Electromagnetic Engineering Society (KEES).
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