To meet the demands of modern communication systems, power amplifiers (PAs) must possess high efficiency and broadband characteristics. Therefore, to improve PA efficiency, researchers have focused on developing harmonic-controlled PAs. Accurately controlling harmonic impedance can help reduce the overlap between the drain current and voltage waveforms, thereby decreasing harmonic energy loss and improving PA efficiency.

A number of high-efficiency PAs with harmonic control have been proposed over time, including class-J, class-F, class-F⁻¹, and hybrid PAs [1–3]. Among these, class-F and class-F⁻¹ PAs have attracted increasing attention for their high efficiency, but achieving wideband is challenging. To address this, Cripps et al. [4] and Carrubba et al. [5] applied continuous mode theory to class-F and class-F⁻¹ PAs. By exploring a wide range of possible output impedance values of these PAs, impedance matching was achieved across a broad frequency band with high efficiency. Filtering structures, such as lowpass and bandpass filters, have also been employed to enhance PA performance [6–9]. For instance, Hayati and Shama [10] proposed a PA based on a quasi-elliptical lowpass matching network featuring high-frequency selectivity and wideband, with the third out-band harmonic suppression. In [11], a PA for long-term evolution is proposed, comprising a bandpass filter that acts as an impedance converter while eliminating harmonics. Furthermore, Guo et al. [12] proposed a compact wideband elliptic-function resonant cavity to suppress the n-th harmonic. In [13], a ring-resonator bandpass filter is co-designed with an impedance matching network to achieve wideband while suppressing unwanted signals. In [14], a bandpass filter based on dual composite right/left-handed transmission lines is employed to design the input/output matching networks of a PA, facilitating the design of a high-efficiency broadband PA.

In this paper, an output filtering and matching network (OFMN) composed of a three-branch line coupler with open stubs and a T-shaped matching network is proposed to achieve out-band harmonic suppression and impedance matching. The proposed PA with OFMN offers high efficiency while maintaining wideband characteristics.

PA performance is significantly degraded by out-band harmonic interferences. To suppress these interferences, a filter is usually cascaded after the PA output [15, 16], as shown in Fig. 1(a), where IMN and OMN refer to the input and output matching networks, respectively. However, this cascaded design usually causes a mismatch between the filter and OMN, which degrades overall performance. In this study, an integrated impedance matching and harmonic suppression network for PA is proposed to reduce the mismatch impact and circuit size. As illustrated in Fig. 1(b), integrating a filter into the OMN simplifies the circuit design, thus reducing both costs and complexity and making it suitable for use in practical communication systems.

In the proposed design, the OFMN serves as the PA core. First, a wideband three-branch coupler with a strong coupling degree was designed. Notably, unlike conventional three-branch couplers, the proposed coupler allows for impedance matching. Subsequently, some of the transmission lines of the proposed coupler were transformed into T-junctions with open stubs, enabling simultaneous fundamental impedance matching and second-harmonic suppression.

Since the third harmonic primarily induces high-order nonlinear distortions with little impact on class-J PA performance, its analysis could be ignored in this design. Effectively, by focusing only on second harmonic control, the design process was simplified.

To illustrate the working principle of the deformed three-branch coupler with open stubs, even- and odd-mode analysis methods was employed. The proposed coupler and its equivalent circuits for the even- and odd-mode analysis are shown in Figs. 2 and 3. Here, Z_A, Z_B, Z_C, and Z_D represent the characteristic impedances of each transmission line, and θ denotes the electrical length of each transmission line, with θ = 90°. Furthermore, Z_1b refers to the port impedance at ports 1 and 4, while Z_2b is the port impedance at ports 2 and 3.

At the center frequency, transmission matrices for the even- and odd-mode analysis can be expressed as:

where A=ZA2ZCZD-1,B=-jZA2ZC, C=-j(1ZB+1ZD-ZA2ZBZCZD),D=ZA2ZBZC-1.

Furthermore, the normalized transmission parameters can be given by:

By using the transformation relation from normalized transmission matrices to scattering parameter matrices, the scattering parameters can be calculated as follows:

where Γ_o and Γ_e are the odd- and even-mode reflection coefficients, while T_o and T_e represent the odd- and even-mode transmission coefficients, respectively. Notably, when the input port of the coupler has no reflection, the following condition should be met:

Similarly, when port 1 is isolated from port 4, the following condition should be satisfied:

Eqs. (7) and (8) can be reduced to:

Then, by substituting Eq. (9) into Eqs. (3) and (4), the following expressions were attained:

From Eqs. (10) and (11), the following expressions were deduced as:

where r=Z2bZ1b. Therefore, Eq. (12) is the first equation for Z_B and Z_D. Eqs. (5) and (6) can then be simplified into the following formulations:

Notably, the power ratio k² of output ports 2 and 3 was set as follows:

where S₂₁ and S₃₁ were calculated as follows:

Here, since c represents an imaginary number and a denotes a real number, the following relationship was derived based on Eq. (15):

Furthermore, since port 4 was considered to be an isolated port, |S₂₁|² + |S₃₁|² = 1. Therefore, based on Eq. (15), the following equation was derived:

By combining Eq. (16) with Eqs. (18)–(19), the following formulation was obtained:

Combining Eqs. (20) and (10)–(11), the second equation for Z_B and Z_D was attained as follows:

Furthermore, by combining Eqs. (21) and (12), the following expressions were obtained:

When k = 3, the output power at port 3 was nine times that of port 2, indicating the output power of the former was sufficiently high. Hence, the value of k was chosen as 3. Subsequently, by load-pull analysis, the real part of the output impedance at the drain terminal of the transistor is approximately 1 8 Ω. Therefore, the input port impedance Z_1b of the coupler was set to 1 8 Ω and the output port impedance Z_2b was set to 50 Ω, resulting in a port impedance ratio r of 2.7. Multiple simulations were conducted to ultimately find that Z_A = Z_C enabled the coupler to achieve a relatively large bandwidth. With k = 3 and r = 2.7, based on Eqs. (22)–(24), the impedances were calculated as Z_A = 2 9 Ω, Z_C = 2 9 Ω, Z_B = Z_D =10 2 Ω, Z_1b =1 8 Ω, and Z_2b = 5 0 Ω.

Port 1 was designated as the input port, port 3 served as both the coupled port and output port, and ports 2 and 4 were set as open circuits. Since port 4 was chosen as the isolated port with no output signal, it was set as an open circuit and did not affect coupler performance. As depicted in Fig. 4, within the operating bandwidth of 2.5 GHz to 3.6 GHz, |S₁₁| remained below −20 dB and |S₃₁| approached 0 dB. However, within the second harmonic frequency band of 5 GHz to 7.2 GHz, |S₁₁| was less than −10 dB while |S₃₁| exceeded −10 dB at certain frequencies, indicating ineffective second harmonic suppression. Overall, while the simulation results indicated favorable fundamental wave impedance matching, out-of-band harmonic suppression needed improvement.

Therefore, as shown in Fig. 5, the branch lines on both sides and the main transmission line of the three-branch line coupler were transformed into T-junctions using open stubs. These open stubs introduce transmission zeros in the second harmonic frequency band to provide harmonic suppression. The transmission matrix of a line depicted in Fig. 5 can be expressed as follows:

Furthermore, the transmission matrix of its transformed T-junction with an open stub can be given by:

where

To achieve similar transmission performance, the two transmission matrices were set to equal, that is M_L = M_T. As a result, the following results were obtained:

With regard to the above equations, Z_A was known, but θ₁₁ and θ₁₂ had to be determined. Notably, since θ was considered to be 90°, θ₁₁ needed to be less than 45°. Therefore, to effectively reduce the coupler size while mitigating the impact of the T-junction transformation on the original impedance matching, θ₁₁ was set to 30°. According to transmission line theory, an open-end transmission line with a quarter wavelength is equivalent to a short-circuit state. To create a short-circuit condition to suppress the second harmonic, the open stubs should be a quarter wavelength at the second harmonic frequency, requiring θ₁₂ = 45° theoretically at the center working frequency. After optimization, θ₁₂ was set to 48°. The values of θ₁₁ and θ₁₂ were then substituted into Eqs. (29) and (30) to achieve Z₁₁ = 50 Ω and Z₁₂ = 48 Ω. After transforming six branch lines into T-junctions with open stubs, their transmission zeros were located within the second harmonic frequency band. The final three-branch line coupler with open stubs is depicted in Fig. 6.

As shown in Fig. 7, within the frequency range of 2.5 GHz to 3.6 GHz, |S₁₁| remained below −15 dB and |S₃₁| approached 0 dB. Furthermore, in the second harmonic frequency range of 5 GHz to 7.2 GHz, |S₁₁| approached 0 dB while |S₃₁| remained below −20 dB. These results imply that the three-branch line coupler with open stubs effectively suppressed the second harmonic but also resulted in reduced impedance matching performance.

To better match the transistor output impedance to a port impedance of 50 Ω, a T-shaped matching network was cascaded after the coupler. The OFMN is depicted in Fig. 8, with port 1 set to 18 Ω. The entire OFMN was simulated and measured, the results of which are presented in Fig. 9. It is evident that within the frequency range of 2.5 GHz to 3.6 GHz, |S₁₁| remained below −20 dB while |S₃₁| approached 0 dB. Additionally, in the second harmonic frequency range of 5 GHz to 7.2 GHz outside the passband, |S₁₁| approached 0 dB and |S₃₁| remained below −20 dB. Therefore, the proposed OFMN achieved both fundamental impedance matching in the operating band and excellent second harmonic suppression. Notably, the proposed PA was simulated using ADS software, based on a Rogers 4350B substrate with a dielectric constant of ɛ_r = 3.66 and a height of 0.508 mm. The PA was operated at V_GS = −2.7 V and V_DS = 28 V using a Cree CGH40010F GaN HEMT transistor [17]. The structure and dimensional parameters of the proposed PA are presented in Fig. 10. In addition, to avoid transistor self-oscillation, an RC stabilizing circuit, composed of an 8 pF Murata capacitor and an 0805 packaged 5 Ω resistor, was added at the input when simulating small signal inputs.

As analyzed in [18], a PA theoretical efficiency approaches 100% when the overlap between the drain voltage and current waveforms is minimal. In this study, the transistor’s drain output fundamental impedance was obtained through load-pull simulation, with its real part found to be approximately 18 Ω. Therefore, by optimizing the dimensions of the OFMN transmission lines, the network’s input impedance was matched to the drain fundamental impedance, while the second-harmonic input impedance of the OFMN was concurrently adjusted. As depicted in Fig. 11, the fundamental impedance of the OFMN on the Smith chart is approximately 18 Ω, while the second harmonic impedance is close to 0. Furthermore, Fig. 12 shows the drain current and voltage waveforms of the transistor during large-signal simulations obtained by ADS software. It can be observed that the overlap between the drain output voltage and the current waveforms is minimal, indicating potentially high efficiency.

A photo of the fabricated PA is presented in Fig. 13, with a single-tone continuous signal input. As shown in Fig. 14, the second harmonic suppression reached 44 dBc within the frequency range of 5 GHz to 7.2 GHz, thus verifying the suppression effect of the proposed OFMN. The measured output power, drain efficiency (DE), and gain are presented in Fig. 15. Within the operating frequency range of 2.5–3.6 GHz with a relative bandwidth of 36%, the DE ranged from 63.1% to 71.6%, with a peak DE of 71.6% achieved at 3 GHz. Furthermore, the output power varied from 40.1 dBm to 41.6 dBm, while the gain fluctuated between 10.1 dB and 11.4 dB. Overall, the measured results demonstrate a DE exceeding 63% and an output power exceeding 40 dBm in the operating frequency band. The simulations and measurements exhibited similar trends, with a few small errors caused by manufacturing tolerances. A performance comparison of the proposed PA and previous designs is presented in Table 1 [12–14, 19–21], showing that the PA designed in this study achieved excellent performance, such as high efficiency and wideband, compared to the previously reported ones.

In this paper, a high-efficiency wideband PA with an OFMN is presented. The OFMN is composed of a three-branch line coupler with open stubs and a T-shaped matching network to achieve good impedance matching and sufficient second harmonic suppression. The three-branch line coupler was analyzed using the odd- and even-mode analysis method, and some lines of the coupler were transformed into T-junctions with open stubs for harmonic suppression. A T-shaped matching network was cascaded after the coupler to achieve better impedance matching. With the proposed OFMN, a PA operating at 2.5–3.6 GHz was fabricated, exhibiting an efficiency of 63.1%–71.6% and an output power of 40 dBm, thus offering a significant solution to achieving high-efficiency wideband amplifiers.