# A High-Relative-Bandwidth Doherty Power Amplifier with Modified Load Modulation Network for Wireless Communications

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## Abstract

**:**

## 1. Introduction

## 2. Analysis of DPA Theories

_{L}/2 at the combiner. In addition, a quarter-wavelength transmission line is used in the main PA branch in order to achieve impedance conversion [5]. According to the DPA theory [5], several impedance relationships are given as

_{M1}and Z

_{A1}are the load impedances of the main and auxiliary PA branches, respectively. Z

_{M}and Z

_{A}represent the load impedances of devices for main and auxiliary PAs, respectively. The subscripts SAT and OBO refer to impedance conditions at the saturation and OBO levels, respectively. In the traditional DPA topology, the λ/4 line is responsible for converting the impedance well only at the center frequency, thus restricting the bandwidth of the resulting DPAs.

_{L}(1 + jX). The auxiliary PA branch also includes a generalized transmission line to represent the output network that is employed to obtain finite impedance Z

_{A1,OBO}(unlike that of infinity in traditional DPAs). The modified coupler structure shown in Figure 2b consists of a traditional branch line coupler and a reactance connected to port 2. Port 4 and port 1 are input and output terminals, respectively, while port 3 is open-circuited. The relationship between the four ports for this coupler arrangement is expressed as

_{0}is the system impedance. Based on the condition of terminals shown in Figure 2b, the following relationships are obtained:

_{3}= 0

_{2}represents the impedance of port 2.

_{4}and the impedance of port 1 Z

_{1}is derived as

_{4}/Z

_{1}has a constant resistance, as required for DPA synthesis [23]. Moreover, the resistance is independent of the normalized frequency f, which provides the possibility to realize operation in a lower normalized frequency band than the previous works [29,30]. Next, an analysis of this LMN and corresponding parameter solutions are given.

#### 2.1. Power Back-Off Level

_{M1,OBO}(Z

_{1}) is as follows:

_{A}refers to the normalized reactance of the auxiliary PA branch at the OBO level.

_{M,OBO}(Z

_{4}) can be obtained as

_{L}= 0.5R

_{OPT}.

_{4}$Re({Z}_{4}/{R}_{\mathrm{OPT}})$ should be set equal to 2. Then, we can deduce the following two expressions about X

_{A}:

_{A}and X to realize the desired OBO, in this case, 6 dB, for different values of f. Indeed, we can let $Re({Z}_{4}/{R}_{\mathrm{OPT}})$ be equal to a different value for obtaining different OBO values if desired. For example, an OBO of 9 dB can be obtained by setting $Re({Z}_{4}/{R}_{\mathrm{OPT}})$ = 4.

_{A}in the normalized frequency band of 0.4–1.6. This provides more freedom to satisfy the impedance requirements of DPAs at the specified saturation level. Moreover, the value of X

_{A}changes sharply around f = 1. This variation hinders the realization of ultra-wideband DPAs in the normalized frequency range of 0.4–1.6. Therefore, the proposed topology can theoretically only achieve wideband DPA in the 0.4–1.0 or 1.0–1.6 frequency range. In order to obtain the maximum relative bandwidth, this paper chooses the frequency range of 0.4–1.0 for the following analysis and design.

#### 2.2. Saturation Level

_{L}(1 + jX). According to the DPA theory, the load impedance of the main PA transistor Z

_{M,SAT}(Z

_{4}) can be expressed as

_{4}$Re({Z}_{4}/{R}_{\mathrm{OPT}})$ should be equal to 1. Hence, the parameter X can be determined as

_{A}at these frequencies f can be further obtained as shown in Table 1. We note here that X

_{A}has two solutions caused by (11) and (12), while X only has one solution.

_{M, OBO}| ≤ 2R

_{OPT}, the main PA does not reach the saturation level; thus, the current I

_{M, OBO}is I

_{max}/4, and the voltage V

_{M, OBO}is equal to I

_{M, OBO}Z

_{M, OBO}. The output power of the DPA at the OBO level can be calculated as follows:

_{M, OBO}| is larger than 2R

_{OPT}, the main PA is overdriven. The output power of the DPA at the OBO level should be calculated as

_{A}listed in Table 1 and (18) and (19), the drain efficiency at the OBO level can be calculated, as shown in Figure 6a. In addition, for comparison, the drain efficiency for a traditional DPA is added in Figure 6a. It is obvious that the proposed DPA can maintain a higher drain efficiency over a wide bandwidth. In order to ensure a stable power output, we define the real part of the impedance Z

_{M,OBO}as 2R

_{OPT}without specifying the imaginary part. Therefore, the drain efficiency of the proposed DPA reduces with frequency, caused by the undesired imaginary part of Z

_{M,OBO}. Figure 6b displays the frequency characteristic of Z

_{M,OBO}, which indicates an imaginary part that varies with normalized frequency. Moreover, the higher X

_{A}, the higher the undesired imaginary part that is obtained based on (10). It is seen from Table 1 that the first solution of X

_{A}(X

_{A1}) has a smaller value than the second solution X

_{A2}. Therefore, the solution for X

_{A1}in Table 1 is taken in the following analysis.

#### 2.3. Improved Main PA Branch

_{M}and Z

_{M2}can be expressed as

_{M,OBO}as shown in Figure 8a. Comparing Figure 8a with Figure 6b, it can be seen that the imaginary part of Z

_{M,OBO}in Figure 8a lies closer to zero. In addition, the corresponding drain efficiency at the OBO level is calculated in Figure 8b by using (18) and (19). As shown in Figure 8b, the drain efficiency of the improved main PA roughly maintains a constant profile across the normalized frequency band of 0.4–1. In addition, Figure 8c shows the drain efficiency of DPAs in [29,30], where the normalized frequency bands are 0.8–1.2, and 0.7–1.3 for [29,30], respectively. As shown in Figure 8b,c, the presented DPA has the ability to work in a lower normalized frequency band so as to have a larger relative bandwidth.

_{load}, and their values are complex. At the same time, the load impedances of the two PAs’ transistors are both R

_{OPT}. The impedance conversion situation is the same as that of a conventional DPA, except that the load impedance Z

_{load}of DPA is a complex impedance. At the OBO level, regarding the auxiliary PA branch, the impedance of this branch is finite and is defined as jX

_{A,}while the load impedance of the device is infinite. This impedance conversion is realized by employing the generalized transmission line. At the OBO level, regarding the main PA branch, the impedance of this branch is Z

_{load}in parallel with jX

_{A}, which is different from that of the traditional DPA due to the introduction of the finite impedance of the auxiliary PA branch, while the load impedance of the transistor is 2R

_{OPT}. This impedance conversion as required by the main PA is achieved by employing the modified coupler and the injected transmission line. The utilization of this modified coupler and the injected transmission line allows DPA operation with an acceptable efficiency into a lower normalized frequency band so as to achieve a larger relative bandwidth as compared to previous DPAs in the literature. Furthermore, the introduction of the finite load impedance of the auxiliary PA branch and the complex load impedance of the DPA effectively assists in meeting the impedance requirements required for the modified coupler deployment.

_{A1}is equal to jX

_{A}and 2Z

_{load}at the OBO level and saturation level, respectively. Then, the calculated Z

_{A2}and θ

_{A}are expressed as

## 3. Design of The Proposed DPA

_{OPT}is 32 Ω when considering V

_{knee}.

#### 3.1. Output Networks

_{M}varies from 46.7° to 0° in the frequency range of 1.0–2.5 GHz. In practical design, the package parameters of the transistor are considered [31] as part of the whole output network. Therefore, the injected transmission line and the modified coupler must adjust a little to meet the impedance requirements. The synthesized output circuit of the main PA is shown in Figure 10a. Figure 10b displays the simulated s11 of the designed output network under the condition of Z

_{M1,OBO}and Z

_{M1,SAT}. It can be seen that the simulated S

_{11}is smaller than −10 dB across the frequency range of 1–2.5 GHz at both saturation and OBO levels, which validates that the designed output network is effective at realizing the impedance conversion well at different power levels within the target frequency band.

_{OPT}to R

_{OPT}over the target frequency range of 1–2.5 GHz, with the phase θ

_{A}being between 85.4° and 90°. Similarly, the package parameters of the transistor are also included in the practical design. The complete output circuit including the package parameters is shown in Figure 11a. The simulated impedance Z

_{A}is displayed in Figure 11b. It can be seen that the simulated Z

_{A}is close to the open circuit at the OBO level and R

_{OPT}at the saturation level is matched, in 1.0–2.5 GHz. These realized impedance trajectories indicate the effectiveness of the output circuit of the auxiliary PA branch.

#### 3.2. Post-Matching Network

_{load}is a complex impedance that is equal to 0.5R

_{OPT}(1 + jX). The value of X changes from 1.37 to 0 in the frequency range of 1.0–2.5 GHz. Therefore, a post-matching network is needed to transform this load impedance to 50 ohms. The complete matching network is synthesized as shown in Figure 12a,b; the simulated Z

_{load}is acceptable compared with the theoretical value of Z

_{load}.

#### 3.3. Input Networks and Complete DPA

_{M}and Z

_{A}varying with power levels are plotted in Figure 15a,b at several representative frequencies. The load trajectories of Z

_{M}and Z

_{A}reveal that the designed DPA realizes the load modulation desired requirements across 1.0–2.5 GHz by using the proposed LMN structure.

## 4. Experiment and Results Analysis

_{r}= 3.66, H = 20 mils) substrate based on the schematic shown in Figure 13. Figure 16 shows a photograph of the fabricated DPA. The overall size of the circuit is 11.2 cm × 5.3 cm.

#### 4.1. Continuous Wave Testing

#### 4.2. LTE Testing at 40 MHz and 6.5 dB

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Nghiem, X.A.; Guan, J.; Hone, T.; Negra, R. Design of concurrent multiband Doherty power amplifiers for wireless applications. IEEE Trans. Microw. Theory Techn.
**2013**, 61, 4559–4568. [Google Scholar] [CrossRef] - Huang, H.; Zhang, B.; Yu, C.; Gao, J.; Wu, Y.; Liu, Y. Design of Multioctave Bandwidth Power Amplifier Based on Resistive Second-Harmonic Impedance Continuous Class-F. IEEE Microw. Wirel. Compon. Lett.
**2017**, 27, 830–832. [Google Scholar] [CrossRef] - Safari Mugisho, M.; Makarov, D.G.; Rassokhina, Y.V.; Grebennikov, A.; Thian, M. Generalized Class-E Power Amplifier with Shunt Capacitance and Shunt Filter. IEEE Trans. Microw. Theory Techn.
**2019**, 67, 3464–3474. [Google Scholar] [CrossRef] [Green Version] - Li, Q.; He, S.; Shi, W.; Dai, Z.; Qi, T. Extend the class-B to class-J continuum mode by adding arbitrary harmonic voltage elements. IEEE Microw. Wireless Compon. Lett.
**2016**, 26, 522–524. [Google Scholar] [CrossRef] - Zhou, X.Y.; Zheng, S.Y.; Chan, W.S.; Chen, S.; Ho, D. Broadband efficiency-enhanced mutually coupled harmonic post-matching Doherty power amplifier. IEEE Trans. Circuits Syst. I Reg. Pap.
**2017**, 64, 1758–1771. [Google Scholar] [CrossRef] - Chang, H.C.; Hahn, Y.; Roblin, P.; Barton, T.W. New mixed mode design methodology for high-efficiency out-phasing chireix amplifiers. IEEE Trans. Circuits Syst. I Reg. Pap.
**2019**, 66, 1594–1607. [Google Scholar] [CrossRef] - Collins, D.J.; Quaglia, R.; Powell, J.R.; Cripps, S.C. The Orthogonal LMBA: A Novel RFPA Architecture with Broadband Reconfigurability. IEEE Microw. Wirel. Compon. Lett.
**2020**, 30, 888–891. [Google Scholar] [CrossRef] - Zhang, Z.; Cheng, Z.; Li, H. A Power Amplifier with Large High-Efficiency Range for 5G Communication. Sensors
**2020**, 20, 5581. [Google Scholar] [CrossRef] - Bathich, K.; Markos, A.Z.; Boeck, G. Frequency response analysis and bandwidth extension of the Doherty amplifier. IEEE Trans. Microw. Theory Techn.
**2011**, 59, 934–944. [Google Scholar] [CrossRef] - Giofre, R.; Piazzon, L.; Colantonio, P.; Giannini, F. A Doherty architecture with high feasibility and defined bandwidth behavior. IEEE Trans. Microw. Theory Techn.
**2013**, 61, 3308–3317. [Google Scholar] [CrossRef] - Kang, D.; Kim, D.; Cho, Y.; Park, B.; Kim, J.; Kim, B. Design of bandwidth-enhanced Doherty power amplifiers for handset applications. IEEE Trans. Microw. Theory Techn.
**2011**, 59, 3474–3483. [Google Scholar] [CrossRef] - Xia, J.; Yang, M.; Zhu, A. Improved Doherty amplifier design with minimum phase delay in output matching network for wideband application. IEEE Microw. Wirel. Compon. Lett.
**2016**, 26, 52–54. [Google Scholar] [CrossRef] [Green Version] - Rubio, J.M.; Fang, J.; Camarchia, V.; Quaglia, R.; Pirola, M.; Ghione, G. 6-GHz wideband GaN Doherty power amplifier exploiting output compensation stages. IEEE Trans. Microw. Theory Techn.
**2012**, 60, 2543–2548. [Google Scholar] [CrossRef] [Green Version] - Xia, J.; Yang, M.; Guo, Y.; Zhu, A. A broadband high-efficiency Doherty power amplifier with integrated compensating reactance. IEEE Trans. Microw. Theory Techn.
**2016**, 64, 2014–2024. [Google Scholar] [CrossRef] [Green Version] - Xia, J.; Chen, W.; Meng, F.; Yu, C.; Zhu, X. Improved three stage Doherty amplifier design with impedance compensation in load combiner for broadband applications. IEEE Trans. Microw. Theory Techn.
**2019**, 67, 778–786. [Google Scholar] [CrossRef] - Fang, X.-H.; Liu, H.-Y.; Cheng, K.-K.-M.; Boumaiza, S. Modified Doherty amplifier with extended bandwidth and back-off power range using optimized auxiliary combining current ratio. IEEE Trans. Microw. Theory Techn.
**2018**, 66, 5347–5357. [Google Scholar] [CrossRef] - Yang, Z.; Yao, Y.; Li, M.; Jin, Y.; Li, T.; Dai, Z.; Tang, F.; Li, Z. Bandwidth extension of Doherty power amplifier using complex combining load with noninfinity auxiliarying impedance. IEEE Trans. Microw. Theory Techn.
**2019**, 67, 765–777. [Google Scholar] [CrossRef] - Pang, J.; He, S.; Huang, C.; Dai, Z.; Peng, J.; You, F. A post matching Doherty power amplifier employing low-order impedance inverters for broadband applications. IEEE Trans. Microw. Theory Techn.
**2015**, 63, 4061–4071. [Google Scholar] [CrossRef] - Zhou, X.Y.; Zheng, S.Y.; Chan, W.S.; Fang, X.; Ho, D. Postmatching Doherty power amplifier with extended back-off range based on selfgenerated harmonic injection. IEEE Trans. Microw. Theory Techn.
**2018**, 66, 1951–1963. [Google Scholar] [CrossRef] - Pang, J.; He, S.; Dai, Z.; Huang, C.; Peng, J.; You, F. Design of a post matching asymmetric Doherty power amplifier for broadband applications. IEEE Microw. Wireless Compon. Lett.
**2016**, 26, 52–54. [Google Scholar] [CrossRef] - Kang, H.; Lee, H.; Lee, W.; Oh, H.; Lim, W.; Koo, H.; Park, C.; Hwang, K.C.; Lee, K.-Y.; Yang, Y. Octave bandwidth Doherty power amplifier using multiple resonance circuit for the auxiliarying amplifier. IEEE Trans. Circuits Syst. I Reg. Pap.
**2019**, 66, 583–593. [Google Scholar] [CrossRef] - Shi, W.; He, S.; Zhu, X.; Song, B.; Zhu, Z.; Naah, G.; Zhang, M. Broadband continuous-mode Doherty power amplifiers with noninfinity auxiliarying impedance. IEEE Trans. Microw. Theory Techn.
**2018**, 66, 1034–1046. [Google Scholar] [CrossRef] - Huang, C.; He, S.; You, F. Design of broadband modified class-J Doherty power amplifier with specific second harmonic terminations. IEEE Access
**2018**, 6, 2531–2540. [Google Scholar] [CrossRef] - Zhang, Z.; Cheng, Z.; Li, H.; Ke, H.; Guo, Y.J. A Broadband Doherty Power Amplifier with Hybrid Class-EFJ Mode. IEEE Trans. Circuits Syst. I Reg. Papers.
**2020**, 67, 4270–4280. [Google Scholar] [CrossRef] - Wu, D.Y.-T.; Boumaiza, S. A modified Doherty configuration for broadband amplification using symmetrical devices. IEEE Trans. Microw. Theory Techn.
**2012**, 60, 3201–3213. [Google Scholar] [CrossRef] - Gustafsson, D.; Andersson, C.M.; Fager, C. A modified Doherty power amplifier with extended bandwidth and reconfigurable efficiency. IEEE Trans. Microw. Theory Techn.
**2013**, 61, 533–542. [Google Scholar] [CrossRef] - Giofre, R.; Piazzon, L.; Colantonio, P.; Giannini, F. An ultrabroadband GaN Doherty amplifier with 83% of fractional bandwidth. IEEE Microw. Wirel. Compon. Lett.
**2014**, 24, 775–777. [Google Scholar] [CrossRef] - Jundi, A.; Boumaiza, S. A series-connected-load Doherty power amplifier with push–pull main and auxiliary amplifiers for base station applications. IEEE Trans. Microw. Theory Techn.
**2020**, 68, 796–807. [Google Scholar] [CrossRef] - Li, M.; Pang, J.; Li, Y.; Zhu, A. Bandwidth Enhancement of Doherty Power Amplifier Using Modified Load Modulation Network. IEEE Trans. Circuits Syst. I Reg. Papers.
**2020**, 67, 1824–1834. [Google Scholar] [CrossRef] - Xu, Y.; Pang, J.; Wang, X.; Zhu, A. Enhancing Bandwidth and Back-Off Range of Doherty Power Amplifier with Modified Load Modulation Network. IEEE Trans. Microw. Theory Techn.
**2021**, 69, 2291–2303. [Google Scholar] [CrossRef] - Zhang, Z.; Cheng, Z.; Ke, H.; Liu, G. A Broadband High-Efficiency Power Amplifier by Using Branch Line Coupler. IEEE Microw. Wirel. Compon. Lett.
**2020**, 30, 880–883. [Google Scholar] [CrossRef] - Moreno Rubio, J.J.; Camarchia, V.; Pirola, M.; Quaglia, R. Design of an 87% fractional bandwidth Doherty power amplifier supported by a simplified bandwidth estimation method. IEEE Trans. Microw. Theory Techn.
**2018**, 66, 1319–1327. [Google Scholar] [CrossRef] [Green Version] - Naah, G.; Giofrè, R. Empowering the Bandwidth of Continuous mode Symmetrical Doherty Amplifiers by Leveraging on Fuzzy Logic Techniques. IEEE Trans. Microw. Theory Techn. Techn.
**2019**, 68, 3134–3147. [Google Scholar] [CrossRef] [Green Version] - Liu, H.-Y.; Fang, X.-H.; Cheng, K.-K.-M. Bandwidth enhancement of frequency dispersive Doherty power amplifier. IEEE Microw. Wirel. Compon. Lett.
**2020**, 30, 185–188. [Google Scholar] [CrossRef]

**Figure 4.**Relationships between X

_{A}, X, and f: (

**a**) relationship expressed by (11); (

**b**) relationship expressed by (12).

**Figure 6.**Drain efficiency and impedance versus the normalized frequency: (

**a**) drain efficiency versus the normalized frequency; (

**b**) impedance Z

_{M}versus the normalized frequency.

**Figure 15.**Trajectories of impedance Z

_{M}and Z

_{A}at several representative frequencies: (

**a**) impedance Z

_{M}; (

**b**) impedance Z

_{A}.

Value | X | X_{A1} | X_{A2} |
---|---|---|---|

f = 0.4 | 1.37 | −0.50 | −3.37 |

f = 0.5 | 1 | −0.40 | −2.62 |

f = 0.6 | 0.72 | −0.34 | −2.15 |

f = 0.7 | 0.51 | −0.30 | −1.93 |

f = 0.8 | 0.32 | −0.25 | −2.09 |

f = 0.9 | 0.16 | −0.15 | −3.40 |

f = 1.0 | 0 | 0 | ∞ |

_{A1}refers to the first solution of X

_{A}; X

_{A2}refers to the second solution of X

_{A}.

Parameter | f = 0.4 | f = 0.5 | f = 0.6 | f = 0.7 | f = 0.8 | f = 0.9 | f = 1.0 |
---|---|---|---|---|---|---|---|

X | 1.37 | 1 | 0.72 | 0.51 | 0.32 | 0.15 | 0 |

θ_{M} (°) | 46.7 | 37.4 | 30.1 | 23.7 | 17.0 | 8.9 | 0 |

X_{A} | −0.42 | −0.38 | −0.35 | −0.33 | −0.26 | −0.15 | 0 |

Z_{A2} | 1.52 | 1.27 | 1.12 | 1.04 | 1.00 | 1.00 | 1.00 |

θ_{A} (°) | 85.9 | 85.7 | 85.4 | 85.5 | 86.2 | 87.6 | 90 |

Ref. | Freq (B.W.) (GHz) | Pout@SAT (dBm) | DE@SAT (%) | DE@ 6 dB OBO (%) | Device |
---|---|---|---|---|---|

[17] | 1.1–2.4 (74%) | 43.3–45.4 | 55–68 | 43.8–54.9 | 2 × 13 W GaN |

[22] | 1.6–2.7 (51%) | 43.8–45.2 | 56–75.3 | 46.5–63.5 | 2 × 13 W GaN |

[23] | 3.3–3.75 (13%) | 48–48.5 | 58–71 | 47–59 | 2 × 16 W GaN |

[24] | 1.2–2.8 (78%) | 43.7–44.1 | 60.5–74.2 | 48.1–57.6 | 2 × 13 W GaN |

[27] | 1.0–2.5 (83%) | 40–42 | 45–83 | 35–58 | 2 × 8 W GaN |

[29] | 2.8–3.55 (24%) | 43–45 | 66–78 | 42–53 | 2 × 13 W GaN |

[32] | 1.5–3.8 (87%) | 42.3–43.4 | 42–63 | 33–55 | 2 × 13 W GaN |

[33] | 1.2–2.4 (67%) | 42–45 | 41.6–81 | 35–63 | 2 × 13 W GaN |

[34] | 1.4–2.55 (58%) | 41.9–42.2 | 62–74 | 48–58 | 2 × 8 W GaN |

This work | 1.0–2.5 (85.6%) | 43.9–44.5 | 63.7–71.6 | 45.2–53.7 | 2 × 13 W GaN |

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## Share and Cite

**MDPI and ACS Style**

Zhu, H.; Zhang, Z.; Gu, C.; Xuan, X.
A High-Relative-Bandwidth Doherty Power Amplifier with Modified Load Modulation Network for Wireless Communications. *Sensors* **2023**, *23*, 2767.
https://doi.org/10.3390/s23052767

**AMA Style**

Zhu H, Zhang Z, Gu C, Xuan X.
A High-Relative-Bandwidth Doherty Power Amplifier with Modified Load Modulation Network for Wireless Communications. *Sensors*. 2023; 23(5):2767.
https://doi.org/10.3390/s23052767

**Chicago/Turabian Style**

Zhu, Haipeng, Zhiwei Zhang, Chao Gu, and Xuefei Xuan.
2023. "A High-Relative-Bandwidth Doherty Power Amplifier with Modified Load Modulation Network for Wireless Communications" *Sensors* 23, no. 5: 2767.
https://doi.org/10.3390/s23052767