Introduction
The essential function of the radio frequency power amplifier (PA) is to amplify the input signal, but the signal will inevitably produce high-order harmonic interference after being amplified by the transistor. Several PA topologies have been proposed to improve the efficiency and harmonic suppression ability of PA at the same time.
In [Reference Haider, You, Shi, Ahmad and Qi1], hairpin bandpass filter (BPF) is used in the output matching network (OMN), and the filter input port is directly connected to the transistor drain, which leads to the compact overall structure. A new combination of PA and an integrated hybrid cavity–microstrip BPF is proposed in [Reference Guo, Zhang, Xu, Li and Xue2]. The metal cavity resonator has high Q-value and low passband loss, but manufacturing costs are expensive. In [Reference Su, Yu, Tang and Liu3], a design method of integrating a BPF structure in the input matching network and OMN of the PA is proposed. It reduces the structure of the PA, but the operating frequency band is too narrow. In [Reference Estrada, Montejo-Garai, de Paco, Psychogiou and Popović4], an approach for co-designing of filtering matching network and PA is proposed. The theory is general and applies to both input and output complex-impedance filter matching networks. In [Reference Qi and Xiao5], a bandpass power divider is proposed for both frequency selection and power allocation. It can suppress up to fourth harmonics; however, suppressing higher harmonics inevitably leads to a reduction in operating bandwidth and efficiency.
In this paper, a new type of BPF is integrated in the output matching circuit to expand the bandwidth while maintaining high drain efficiency (DE). The filter uses a new type of terminated coupled line structure (TCLS), which allows the return loss to be in an ideal range over a wide operating bandwidth. Moreover, through the tuning of the T-shaped matching network, the second harmonic impedance value is kept in an efficient range. In order to verify the feasibility of the proposed scheme, a wideband filtering PA based on TCLS is fabricated.
Design and theoretical analysis
Design of OMN
The new OMN structure with integrated BPF proposed in this paper is shown in Fig. 1(a). The BPF is based on TCLS, where three ports are loaded with a stepped impedance resonator (TL1 and TL2) and two short-circuit stubs (TL3 and TL4) and the fourth port remains open. The topology of TCLS is shown in Fig. 1(b), where Z T1, Z T2, Z T3, and Z T4 represent the loads loaded to the four ports of the coupled line, respectively. Define R = Z 1/Z 2 and θ = 90°. The input impedance of the TCLS is defined as Z BPF and can be calculated as [Reference Zhang, Wu and Liu6]
\begin{equation}{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad Z_{{\text{BPF}}}} = \frac{{{Z_{{\text{T1}}}}({Z_1}B + {Z_2}C + {Z_3}D + {Z_4}E)}}{{{Z_{{\text{T1}}}}B + {Z_1}B + {Z_2}C + {Z_3}D + {Z_4}E}}\end{equation}Schematics of (a) proposed filter OMN and (b) proposed TCLS in [Reference Qi and Xiao5].
where
\begin{equation}\begin{gathered}
{Z_1} = - j\frac{{{Z_{0e}} + {Z_{0o}}}}{{2\tan \theta }},{Z_2} = - j\frac{{{Z_{0e}} - {Z_{0o}}}}{{2\tan \theta }} \hfill \\
{Z_3} = - j\frac{{{Z_{0e}} - {Z_{0o}}}}{{2{\text{sin}}\theta }},{Z_4} = - j\frac{{{Z_{0e}} + {Z_{0o}}}}{{2{\text{sin}}\theta }} \hfill \\
\end{gathered} \end{equation}
\begin{equation}\begin{gathered}
B = ({Z_2}({Z_1} + {Z_{{\text{T2}}}}) - {Z_3}{Z_4})({Z_2}{Z_3} - {Z_4}({Z_1} + {Z_{{\text{T4}}}})) + \hfill \\
\begin{array}{*{20}{c}}
{}&{}
\end{array}({Z_3}({Z_1} + {Z_{{\text{T3}}}}) - {Z_2}{Z_4})(Z_3^2 - ({Z_1} + {Z_{{\text{T2}}}})({Z_1} + {Z_{{\text{T4}}}})) \hfill \\
\end{gathered} \end{equation}
\begin{equation}\begin{gathered}
C = ({Z_2}{Z_4} - {Z_3}({Z_1} + {Z_{{\text{T3}}}}))({Z_3}{Z_4} - {Z_2}({Z_1} + {Z_{{\text{T4}}}})) \hfill \\
\begin{array}{*{20}{c}}
{}&{}
\end{array} + (Z_3^2 - Z_2^2)({Z_2}{Z_4} - {Z_4}({Z_1} + {Z_{{\text{T4}}}})) \hfill \\
\end{gathered} \end{equation}
\begin{equation}\begin{gathered}
D = {Z_3}(({Z_1}{Z_3} - {Z_2}{Z_4})({Z_1} + {Z_{{\text{T2}}}} + {Z_{{\text{T4}}}}) + {Z_3}(Z_2^2 - Z_3^2 \hfill \\
\begin{array}{*{20}{c}}
{}&{}
\end{array} + Z_4^2 + {Z_{{\text{T2}}}}{Z_{{\text{T4}}}}) - ({Z_1}{Z_2}{Z_4}) \hfill \\
\end{gathered} \end{equation}
\begin{equation}\begin{gathered}
E = {Z_3}(({Z_1}{Z_4} - {Z_2}{Z_3})({Z_1} + {Z_{{\text{T2}}}} + {Z_{{\text{T3}}}}) + {Z_4}(Z_2^2 + Z_3^2 \hfill \\
\begin{array}{*{20}{c}}
{}&{}
\end{array} - Z_4^2 + {Z_{{\text{T2}}}}{Z_{{\text{T3}}}}) - ({Z_1}{Z_2}{Z_3}) \hfill \\
\end{gathered} \end{equation}In addition, when the impedance values of the four ports of the TCLS are set as shown in Fig. 1(a), Z BPF can be expressed as follows:
\begin{equation}{Z_{{\text{BPF}}}} = {Z_{{\text{BPF}}}}\left| {_{{Z_{{\text{T1}}}} = j{Z_2}\frac{{\tan \theta - R\cot \theta }}{{1 + R}},{Z_{{\text{T2}}}} = j{Z_3}\tan \theta ,{Z_{{\text{T3}}}} = \frac{{j50{Z_4}\tan \theta }}{{50 + j{Z_4}\tan \theta }},{Z_{{\text{T4}}}} = \infty }} \right.\end{equation}According to the co-design theory, the proposed TCLS needs to be integrated into the OMN of PA and provide the function of impedance conversion. Therefore, the input port value of the TCLS is no longer 50 Ω but is changed to the real part of the optimal fundamental load impedance Z op(f_0) of the transistor obtained by load pulling. When f 0 = 3.3 GHz is selected as the center frequency, Z op(f_0) = (14.2 + j*2.7) Ω can be determined by load pulling. Through the above analysis and combining Equations (1) and (4), the designed parameters of the proposed TCLS can be determined as follows: Z 1 = 54 Ω, Z 2 = 36 Ω, Z 3 = 35 Ω, Z 4 = 20 Ω, Z 0e = 99.8 Ω, and Z 0o = 46.5 Ω. In order to complete the match between the TCLS and the transistor, a T-shaped match network composed of TL5, TL6, and TL7 is selected. So as to reduce the number of design parameters and simplify the design process, define Z 5 = Z 6 = Z T. The input impedance of the OMN can be calculated as follows:
\begin{equation}{Z_{{\text{in}}}} = {Z_{\text{T}}}\frac{{{Z_{\text{N}}} + j{Z_{\text{T}}}\tan {\theta _5}}}{{{Z_{\text{T}}} + j{Z_{\text{N}}}\tan {\theta _5}}}\end{equation}where
\begin{equation}{Z_{\text{N}}} = \frac{{ - j{Z_{\text{T}}}{Z_{{\text{BPF}}}}{Z_{\text{7}}}\cot {\theta _7} + Z_{\text{T}}^2{Z_{\text{7}}}\tan {\theta _6}\cot {\theta _7}}}{{{Z_{\text{T}}}{Z_{{\text{BPF}}}} + jZ_{\text{T}}^2\tan {\theta _6} - j{Z_{\text{T}}}{Z_{{\text{BPF}}}}{Z_{\text{7}}}\cot {\theta _7} + Z_{\text{T}}^2{Z_{\text{7}}}\tan {\theta _6}\cot {\theta _7}}}\end{equation}Under the premise of Zin(f_0) = Z load(f_0), it is necessary to take into account that the second harmonic impedance of the frequency point in the passband is located in the high-efficiency region. When it is determined that θ 5 = 13°, θ 6 = 5°, Z T = 32 Ω, Z 7 = 42 Ω, and θ 7 = 45°, the fundamental impedance traces of BPF and OMN are also shown in Fig. 2(a). The second harmonic impedance traces of several key frequency points in the passband are all in the high-efficiency region as shown in Fig. 2(b). It can be seen that the T-shaped matching circuit provides five free design parameters. Hence, there is a larger design space when designing the matching circuit.
(a) Fundamental impedance traces of BPF and OMN. (b) Second harmonic impedance traces of OMN and second harmonic load-pull results of several key frequency points.
Analysis of proposed OMN
Figure 3 exhibits the difference of the S-parameter of OMN when TCLS is loaded with different terminal impedances. It can be observed that after adding the condition of Z T2 = jZ 3tanθ, the stop-band suppression of OMN is optimized by about 10 dB, but the in-band loss hardly changes. Finally, when the structure proposed in this article is adopted, the stop-band suppression is limited to below −31 dB and the in-band loss reaches below −22 dB by generating two additional transmission poles (TPs). Figure 4(a) shows the structure of π-shaped resonator in TCLS, where CLin’ is one of the two microstrip lines that make up the coupled microstrip line. Also define Z c = √(Z 0e × Z 0o). TPs can be calculated by the following condition as in [Reference Huang, Zhang and Li7]
Comparison of S-parameters of OMN with different structures.
\begin{equation}Z_{{\text{in}}}^{{'}} = \infty \end{equation}Z ′in can be calculated as
\begin{equation}Z_{{\text{in}}}^{{'}} = \frac{{j{Z_3}{Z_{\text{c}}}\left( {{Z_4} + {Z_{\text{c}}}} \right){\text{tan}}\theta }}{{{Z_{\text{c}}}\left( {{Z_3} + {Z_4} + {Z_{\text{c}}}} \right) - {Z_3}{Z_4}{\text{ta}}{{\text{n}}^2}\theta }}\end{equation}Based on Equations (7) and (8), frequencies of three TPs (f TP1, f TP2, and f TP3) can be calculated as
\begin{equation}{f_{{\text{TP1}}}} = \frac{{2{f_0}}}{{{\pi }}}{\text{arctan}}\sqrt {\frac{{{Z_{\text{c}}}\left( {{Z_3} + {Z_4} + {Z_{\text{c}}}} \right)}}{{{Z_3}{Z_4}}}} \end{equation}
\begin{equation}{f_{TP2}} = {f_o}\end{equation}
\begin{equation}{f_{{\text{TP}}3}} = 2{f_0} - \frac{{2{f_0}}}{{{\pi }}}{\text{arctan}}\sqrt {\frac{{{Z_{\text{c}}}\left( {{Z_3} + {Z_4} + {Z_{\text{c}}}} \right)}}{{{Z_3}{Z_4}}}} \end{equation}The frequencies of TPs in the proposed OMN are close to the frequencies obtained by analyzing the π-shaped resonator. Figure 4(b) shows how f TP1, f TP2, and f TP3 change with Z 3 and Z 4. It can be seen that by adjusting the values of Z 3 and Z 4, a better return loss in the passband can be obtained, but it is accompanied by a reduction in bandwidth. Hence, after comprehensive consideration, the proposal adopted in this design is Z 3 = 35 Ω and Z 4 = 20 Ω. This proposal has a wide bandwidth and good in-band loss at the same time.
(a) Structure of π-shaped resonator in TCLS. (b) |S11| of OMN with varied Z 3 and Z 4. (c) Frequencies of f tz2 and f tz3 with varied R.
The frequencies of the transmission zeros (TZs) can be calculated by the following condition as in [Reference Zhang, Wu and Liu6]
\begin{equation}{Z_{{\text{BPF}}}} = \infty \end{equation}Based on Equations (1), (4), and (10), the values of f TZ1, f TZ2, f TZ3, and f TZ4 can be calculated as
\begin{equation}{f_{{\text{TZ1}}}} = 0\end{equation}
\begin{equation}{f_{{\text{TZ2}}}} = \frac{{2{f_0}}}{{{\pi }}}{\text{arctan}}\sqrt R \end{equation}
\begin{equation}{f_{{\text{TZ3}}}} = 2{f_0} - \frac{{2{f_0}}}{{{\pi }}}{\text{arctan}}\sqrt R \end{equation}
\begin{equation}{f_{{\text{TZ4}}}} = 2{f_0}\end{equation} It can be seen from the calculation results that the values of f TZ1 and f TZ4 are fixed, but the values of f TZ2 and f TZ3 are affected by the free design parameter R. Figure 4(c) shows the position shift of 
${f_{{\text{TZ}}2}}$ and 
${f_{{\text{TZ}}3}}$ when R changes in the range of 0–5. In order to meet the target operating frequency band of this design, select 
$R = 1.5$ as the design index. Because if the interval between two TZs is too close, it will affect the performance in the passband, and if it is too far, it will affect the suppression of harmonics.
Simulation and measurement results
In order to verify the correctness of the above theory, a 2.9–3.7 GHz filter PA is designed and fabricated using CGH40010F transistor, based on the Rogers 4350B substrate (ε r = 3.66, H = 20 mil). The bias voltages of the drain and gate are 28 V and −2.7 V, respectively. The final complete circuit structure and the photograph of the fabricated filter PA are shown in Fig. 6(a). The size of the entire circuit is 50.9 mm × 40.2 mm (1.1λg × 0.85λg), which accomplishes the small size design goal well.
Figure 5 shows the S-parameters of the proposed PA, and it can be found that the simulation and test results are roughly consistent. The differences may be caused by machining errors and testing instrument errors, which is acceptable. By observing the S 21 of PA, it can be found that PA has good suppression ability at the second harmonic, which can effectively improve the efficiency of PA and is in line with theory. By using a continuous signal to measure the proposed PA, the simulation and measurement results are shown in Fig. 6(b). In addition, the DE and gain changing with the input power are shown in Fig. 6(c). It can be seen that the output power measured in the range of 2.9–3.7 GHz is between 40.1 dBm and 41.2 dBm. The maximum gain is 11.2 dB. In addition, the DE varies between 60.3% and 67.6%. Since the coupling structure requires high precision in the manufacturing process, there is a deviation between the simulation results and the final physical measurement results, but the degree of deviation is within an acceptable range. In order to show the linearity of the designed PA, the PA is driven by a 10 MHz Wideband Code Division Multiple Access（W-CDMA) signal with peak-to-average ratio of 6.5 dB. The obtained adjacent channel leakage ratio (ACLR) is displayed in Fig. 6(d). The PA achieves an ACLR greater than −27.5 dBc when the average output power is 34.5 dBm. Figure 6(e) shows the third-order intercept point (TOI) of PA when the input power is 15 dBm and the frequency interval of the dual tone signal is 5 MHz. Due to the potential for additional nonlinearity caused by equipment such as power splitters and attenuators used in actual measurements, it is normal for the actual measured TOI to be lower than the simulated value. Therefore, it is believed that the proposed PA has qualified linearity.
S-parameters of the proposed PA. (a) S11. (b) S21.
(a) Complete circuit of proposed filtering power amplifier and photograph of fabricated PA. (b) Measured and simulated output power, drain efficiency, and gain. (c) Measured drain efficiency and gain versus output power. (d) ACLR. (e) TOI when the input power is 15 dBm and the frequency interval of the dual tone signal is 5 MHz.
Several performance indicators of this PA are compared with those of some related PA in recent years in Table 1. By comparison, it can be easily found that the designed PA has a significantly wider bandwidth. Although the expansion of the bandwidth has caused the decline of DE to a certain extent, the decline of DE is not large and is still at a high level. In addition, the performance of the designed PA in terms of gain and output power also reached the expected target.
Performance comparison of filter power amplifiers
a MI-SISL: metal-integrated and substrate-integrated suspended line.
Conclusion
In this work, a wideband filter PA based on TCLS is designed and manufactured. Through the designed OMN, the fundamental frequency impedances are perfectly matched with the optimal fundamental load impedances and the second harmonic impedances are also in the high-efficiency region. This design increases the working bandwidth of the PA by optimizing the in-band return loss and stopband suppression. Compared with some recently proposed filter PA, the designed filter PA has better overall performance and smaller size. Making it work in the 5G commercial frequency band is in line with current design trends and has greater commercial prospects.
Acknowledgements
This work was partly supported by Zhejiang Provincial Public Technology Research Project (LGG21F010006).
Competing interests
All authors disclosed no relevant relationships.
Guohua Liu received the M.S. degree from East China Normal University, Shanghai, China, in 2004, and the Ph.D. degree in electronic science and technology from Hangzhou Dianzi University (HDU), Hangzhou, China, in 2020. He is currently a Professor with HDU. His research interests include microwave circuits, sensors, antennas, and wireless systems design.
Jianyuan Yu received the B.E. degree from Shaoxing University, Shaoxing, China, in 2021. He is currently pursuing the M.S. degree with Hangzhou Dianzi University, Hangzhou, China. His research interest is focused on the design of microwave sensors and RF communication circuits.
Yijun Lin received the B.S. and M.S. degrees in electronic information engineering from Hangzhou Dianzi University, Hangzhou, China, in 2020 and 2023, respectively. His research interests include broadband and high efficiency power amplifier design.
