Ultra-Generalized Continuous Class F Power Amplifier with Finite Third-Harmonic Load Impedance

Abstract

This paper proposes the ultra−generalized continuous class F (UCCF) mode, which combines the influences of the drain current conduction angle and overdriven transistor on the drain current waveform to achieve a broader finite third-harmonic load impedance space. The UCCF mode uses $\alpha$ to describe the magnitude of the drain current conduction angle and $pcr$ to describe the drain current peak-clipped ratio. An analysis of the effects of $pcr$ and $\alpha$ on the linearity and efficiency of the UCCF model is presented, establishing a robust theoretical foundation for achieving a balance between these two characteristics. Additionally, an examination of how $pcr$ and $\alpha$ influence the load impedance design space is conducted, demonstrating that the UCCF mode not only offers a broader finite third-harmonic load impedance space but also expands the fundamental and second-harmonic load impedance design space. For practical validation, a PA with frequency of 2.05–2.65 GHz is designed based on CGH40010F. The test results show that $S_{11}$ is less than −15 dB, the drain efficiency is 67.0–73.2%, and the output power is 40.1–41.0 dBm. The linearity is tested using a 5G NR (New Radio) signal with a bandwidth of 100 MHz and a peak-to-average power ratio of 8 dB at 2.35 GHz. The worst adjacent channel power ratio (ACPR) is −34.8 dBc without digital predistortion (DPD), and −57.8 dBc with DPD. An average output power ($P_{ave}$) of around 32.4 dBm and an average DE ($D{E}_{ave}$) of 34.39% were obtained.

1. Introduction

With the rapid development of wireless communication systems, the efficiency and linearity requirements of the power amplifier (PA) have increased. Previous work on harmonically tuned (HT) PAs [1,2,3,4,5,6,7,8,9] has achievedhigh efficiency and low loss by optimizing the output harmonic control circuit to shape the drain voltage and current waveforms. The class F PA, a typical HT PA, has garnered increased attention in the field of RF engineering [10,11,12,13,14,15,16,17,18]. This heightened interest has been driven by its unique ability to reduce the overlap between the voltage and current waveforms, substantially reducing power consumption. However, the notable limitation of the class F mode is its inherent narrowband operation.

To take advantage of the class F mode in broadband scenes, the continuous class F mode was introduced [18]. This provides a universal framework for PA design, particularly in terms of load impedance [19,20,21,22,23]. By sweeping the imaginary optimal impedance component, the continuous class F mode achieves a customized performance across a broader frequency range. However, it is worth noting that the continuous class F PA requires an accurately matched infinite third-harmonic load impedance.

Transistor parasitic effects, including capacitance and inductance, are inherent imperfections that deviate from the ideal transistor behavior, as shown in Figure 1. These imperfections can profoundly affect the impedance characteristics of the circuit and pose significant challenges to achieve an accurately matched infinite third-harmonic-load impedance [24,25], especially at higher frequencies. In order to solve this problem, the recently proposed generalized continuous class F (GCCF) [26,27,28,29] mode and peak-clipped current continuous class F (${\mathrm{PCC-CF}}_3$) mode [30] use relatively large finite third-harmonic load impedance as a substitute for infinite third-harmonic load impedance. As described in [26,27,28,29], the GCCF mode extends the drain current conduction angle of the continuous class F current waveform, thereby broadening the third-harmonic load impedance range. However, this diminishes the ratio between the current’s fundamental component and the DC component, leading to a substantial decrease in efficiency. In [30], the ${\mathrm{PCC-CF}}_3$ mode with a peak-clipped current generated by an overdriven transistor is proposed. Compared with the GCCF mode, the ${\mathrm{PCC-CF}}_3$ mode has a broader finite third-harmonic load impedance and reduced efficiency degradation. However, in the ${\mathrm{PCC-CF}}_3$ mode, the transistor works in a saturated state and therefore has nonlinear characteristics. Thus, in order to leverage the benefits of the GCCF and ${\mathrm{PCC-CF}}_3$ modes and strike a balance between linearity and efficiency, we propose the ultra-generalized continuous class F (UCCF) mode.

In the UCCF mode, two parameters, the drain current peak-clipped ratio $pcr$ and the drain current conduction angle $\alpha$ are used to reshape the drain current waveform at the same time, which can achieve a broader finite third-harmonic load impedance space. The UCCF mode comprehensively analyzes the variations in the efficiency and linearity with different combinations of $pcr$ and $\alpha$. This shows the UCCF mode can balance efficiency and linearity based on the premise of realizing finite third-harmonic load impedance. In addition, the UCCF mode provides a broader fundamental and second harmonic load impedance design space, thereby expanding the PA design freedom.

The rest of this paper is organized as follows: In Section 2, the analysis begins with the gate input voltage waveform in the UCCF mode. Then, it examines the drain current waveform and the trends in drain current components with $pcr$ and $\alpha$ in the UCCF mode. Following this, the impedance design space of the UCCF mode is presented. Finally, an analysis is conducted on of the variation in efficiency and linearity of the UCCF mode with $pcr$ and $\alpha$. In Section 3, the measurement results of the PA based on the UCCF mode are provided. Finally, in Section 4, a comprehensive summary of the entire text is presented.

2. Analysis of the Proposed UCCF Mode

2.1. Gate Input Voltage Waveform of Proposed UCCF Mode

A transistor is a voltage-controlled current source, and a change in the gate input voltage waveform can lead to a change in the drain current waveform. Therefore, it is necessary to analyze the gate input voltage waveform first. The gate input voltage waveform of the UCCF mode ($v_{GS,UF}$) in one signal period is shown in Figure 2 and can be represented as

$$\begin{array}{c}\hfill {\displaystyle v_{GS,UF}=V_{GS0}+V_{GS1}\times pcr\times \frac{\cos \left(\theta \right)-\cos \left({\displaystyle \frac{\alpha }{2}}\right)}{\left(1-\cos \left({\displaystyle \frac{\alpha }{2}}\right)\right)}}\end{array}$$

(1)

where $V_{GS0}$ is the gate threshold voltage, $V_{GS1}$ is the gate input voltage fundamental component, $pcr$ refers to the peak-clipped ratio, $\theta$ denotes the angular phase of the cosine wave, and $\alpha$ denotes the drain current conduction angle. We rearranged the terms and normalized the gate input voltage using $V_{GS1}$. The normalized gate input voltage $v_{GS,norm}$ could then be expressed as

$$\begin{array}{c}\hfill {\displaystyle v_{GS,norm}=\frac{v_{GS,UF}-V_{GS0}}{V_{GS1}}=pcr\times \frac{\cos \left(\theta \right)-\cos \left({\displaystyle \frac{\alpha }{2}}\right)}{\left(1-\cos \left({\displaystyle \frac{\alpha }{2}}\right)\right)}}\end{array}$$

(2)

where

$$\begin{array}{c}\hfill {\displaystyle pcr=\frac{v_{GS,UF}-V_{GS0}}{v_{GS,max}-V_{GS0}}}\end{array}$$

(3)

and $v_{GS,max}$ is the input voltage amplitude that just reaches the saturation point. Figure 2 depicts states of the gate input voltage waveform for various modes. As shown in Figure 2, the gate input voltage of the continuous class F (CCF) mode is an ideal cosine wave where $\alpha$ equals $\pi$ and $pcr$ equals 1. The GCCF mode achieves the finite third-harmonic load impedance by expanding $\alpha$, and in this mode, $pcr$ is equal to 1. The ${\mathrm{PCC-CF}}_3$ mode achieves the finite third-harmonic load impedance by inputting an overdriven gate voltage, and in this mode, $\alpha$ is equal to $\pi$. To leverage the advantages of both modes, the UCCF mode combines $pcr$ and $\alpha$ to reshape the drain current waveform. The GCCF and ${\mathrm{PCC-CF}}_3$ modes are special cases of the UCCF mode.

Figure 3a,b illustrate the variationin $v_{GS,norm}$ with $pcr$ and $\alpha$. When $pcr$ is the same, the peak-to-peak amplitude of $v_{GS,norm}$ decreases with an increase in $\alpha$. When $\alpha$ stays the same, the peak-to-peak amplitude of $v_{GS,norm}$ increases with an increase in $pcr$. This indicates that both $pcr$ and $\alpha$ affect the input power, as an increase in $\alpha$ decreases this parameter and an increase in $pcr$ increases it. These opposing trends lead to the different effects of $pcr$ and $\alpha$ on the PA’s performance.

2.2. Drain Current Waveform of the Proposed UCCF Mode

The drain current waveform of the proposed UCCF mode ($i_{d,UF}$) in one signal period (Figure 4) can be expressed as

$$\begin{array}{c}\hfill \begin{array}{c}{i}_{d,UF}=\hfill \\ \left\{\begin{array}{c}{\displaystyle I_{max}\times pcr\times \frac{\left(\cos \left(\theta \right)-\cos \left({\displaystyle \frac{\alpha }{2}}\right)\right)}{1-\cos \left({\displaystyle \frac{\alpha }{2}}\right)},-\frac{\alpha }{2}<\theta <-\frac{\beta }{2}}\hfill \\ {\displaystyle I_{max},\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-\frac{\beta }{2}<\theta <\frac{\beta }{2}}\hfill \\ {\displaystyle I_{max}\times pcr\times \frac{\left(\cos \left(\theta \right)-\cos \left({\displaystyle \frac{\alpha }{2}}\right)\right)}{1-\cos \left({\displaystyle \frac{\alpha }{2}}\right)},\frac{\beta }{2}<\theta <\frac{\alpha }{2}}\hfill \\ {\displaystyle 0,\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-\pi <\theta <-\frac{\alpha }{2},\frac{\alpha }{2}<\theta <\pi }\hfill \end{array}\right.\hfill \end{array}\end{array}$$

(4)

where

$$\begin{array}{c}\hfill {\displaystyle \frac{\beta }{2}=arccos\left({\displaystyle \frac{{\displaystyle 1-\cos \left(\frac{\alpha }{2}\right)+pcr\times \cos \left({\displaystyle \frac{\alpha }{2}}\right)}}{pcr}}\right)}\end{array}$$

(5)

and $I_{max}$ is the maximum drain current amplitude, and $\beta$ is the angle at which the current waveform reaches $I_{max}$. Figure 4 depicts the drain current waveform state for various modes. When $pcr$ ranges from 1 to 2 and $\alpha$ ranges from $\pi$ to $2\pi$ in (4), the GCCF mode is present, and the drain current waveform is peak−clipped with a drain current conduction angle $\alpha$ of greater than $\pi$. When $pcr$ equals 1 and $\alpha$ ranges from $\pi$ to $2\pi$ in (4), the GCCF mode is present, and the drain current waveform forms a half-sinusoidal wave with $\alpha$ greater than $\pi$. When $pcr$ ranges from 1 to 2 and $\alpha$ equals $\pi$ in (4), the ${\mathrm{PCC-CF}}_3$ mode is present, and the drain current waveform exhibits a peak-clipped drain current waveform. When $pcr$ equals 1 and $\alpha$ equals $\pi$ in (4), the continuous class F mode is present, and the drain current waveform is an ideal half-sinusoidal wave.

The Fourier-series expansion of $i_{d,UF}$ [11] can be calculated as functions of $pcr$ and $\alpha$ by (6)–(8),

$$\begin{array}{c}\hfill i_{d,UF}=I_{dc}+\sum _{n=1}^{\infty }{I}_n·\cos \left(n\theta \right)\end{array}$$

(6)

where

$$\begin{array}{c}\hfill {\displaystyle I_{dc}=\frac{1}{2\pi ·I_{max}}·{\int }_0^{2\pi }{i}_{d,UF}·\cos \left(n\theta \right)d\theta ,(n=0)}\end{array}$$

(7)

$$\begin{array}{c}\hfill {\displaystyle I_n=\frac{1}{\pi ·I_{max}}·{\int }_0^{2\pi }{i}_{d,UF}·\cos \left(n\theta \right)d\theta ,(n=1,2,3\dots )}\end{array}$$

(8)

$$\begin{array}{c}\hfill \left\{\begin{array}{c}{\displaystyle I_{dc}=\frac{{csc}^2\left[{\displaystyle \frac{\alpha }{4}}\right]\left(\beta +\left(\beta \left(-1+pcr\right)-\alpha ·pcr\right)\cos \left[{\displaystyle \frac{\alpha }{2}}\right]-2pcr·sin\left[{\displaystyle \frac{\beta }{2}}\right]+2pcr·sin\left[{\displaystyle \frac{\alpha }{2}}\right]\right)}{4\pi }}\hfill \\ {\displaystyle I_1=\frac{8sin\left[{\displaystyle \frac{\beta }{2}}\right]-pcr·{csc}^2\left[{\displaystyle \frac{\alpha }{4}}\right]\left(\beta -\alpha -4\cos \left[{\displaystyle \frac{\alpha }{2}}\right]sin\left[{\displaystyle \frac{\beta }{2}}\right]+sin\left[\beta \right]+sin\left[\alpha \right]\right)}{4\pi }}\hfill \\ {\displaystyle I_2=\frac{3sin\left[\beta \right]+pcr·{csc}^2\left[{\displaystyle \frac{\alpha }{4}}\right]·{sin}^2\left[{\displaystyle \frac{\beta -\alpha }{4}}\right]\left(-3sin\left[{\displaystyle \frac{\beta }{2}}\right]+2·sin\left[{\displaystyle \beta +\frac{\alpha }{2}}\right]+sin\left[{\displaystyle \frac{\beta }{2}+\alpha }\right]\right)}{3\pi }}\hfill \\ {\displaystyle I_3=\frac{pcr·{csc}^2\left[{\displaystyle \frac{\alpha }{4}}\right]\left(-3\left(1+\cos \left[\beta \right]\right)sin\left[\beta \right]+4\cos \left[{\displaystyle \frac{\alpha }{2}}\right]sin\left[{\displaystyle \frac{3\beta }{2}}\right]\right)+\left(8sin\left[{\displaystyle \frac{3\beta }{2}}\right]+pcr·{csc}^2\left[{\displaystyle \frac{\alpha }{4}}\right]sin\left[\alpha \right]\right)}{12\pi }}\hfill \end{array}\right.\end{array}$$

(9)

Through (9), the DC ($I_{dc}$), fundamental ($I_1$), second-harmonic ($I_2$), and third-harmonic ($I_3$) components can be computed. Figure 5 illustrates the $I_{dc}$, $I_1$, $I_2$, and $I_3$ trends in the UCCF mode with $pcr$ and $\alpha$. The origin of the coordinates represents the continuous class F mode ($\alpha =\pi$ and $pcr=1$). The horizontal axis represents the GCCF mode with $\alpha$ values varying from $\pi$ to 2$\pi$ ($pcr=1$). The vertical axis represents the ${\mathrm{PCC-CF}}_3$ mode with $pcr$ values varying from 1 to 2 ($\alpha =\pi$). The color depth in the graph represents the magnitude of the current component. As shown in Figure 5a, $I_{dc}$ increases with increases in $pcr$ and $\alpha$. Figure 5b shows that when $pcr$ is held constant, $I_1$ initially increases and then decreases with an increase in $\alpha$. Figure 5c shows that $I_2$ decreases with increases in $pcr$ and $\alpha$. Figure 5d shows that when $pcr$ is held constant, $I_3$ initially decreases and then increases with an increase in $\alpha$. The blue area in the upper left corner of Figure 5d shows that $I_3$ has reached its minimum area. The minimum value of $I_3$ in the UCCF mode is −0.179, and this occurs when $pcr$ is equal to 2 and $\alpha$ is equal to 1.184$\pi$. In this region, $I_3$ is smaller than the horizontal and vertical axes, which indicates that the UCCF mode achieves a smaller $I_3$ compared to the GCCF and ${\mathrm{PCC-CF}}_3$ modes.

2.3. Load Impedance Design Space of the Proposed UCCF Mode

The drain voltage in the UCCF mode $v_d$ [32] is the same as that in the continuous class F mode and can be calculated using

$$\begin{array}{cc}\hfill v_d=& V_k+(V_{dd}-V_k){\left({\displaystyle 1-\frac{2}{\sqrt{3}}\cos \left(\theta \right)}\right)}^2\left({\displaystyle 1+\frac{1}{\sqrt{3}}\cos \left(\theta \right)}\right)\hfill \\ \hfill & \times \left(1+\gamma sin\left(\theta \right)\right),-1<\gamma <1\hfill \end{array}$$

(10)

where $V_{dd}$ represents the drain bias voltage, $V_k$ represents the knee voltage of the transistor, and $\gamma$ is the correction factor. The load impedance design space can be obtained as follows:

$$\begin{array}{c}\hfill \left\{\begin{array}{c}{\displaystyle Z_{f0}=\frac{1}{\sqrt{3}{I}_1}·R_{opt}+j\frac{\gamma }{2·I_1}·R_{opt}}\hfill \\ {\displaystyle Z_{2f0}=-j\frac{7·\gamma }{12\sqrt{3}·I_2}·R_{opt}}\hfill \\ {\displaystyle Z_{3f0}=-\frac{1}{6\sqrt{3}{I}_3}·R_{opt}}\hfill \end{array}\right.\end{array}$$

(11)

where

$$\begin{array}{c}\hfill {\displaystyle R_{opt}=\frac{2\left(V_{dd}-V_k\right)}{I_{max}}}\end{array}$$

(12)

$R_{opt}$ is the optimal fundamental load impedance, and $Z_{f0}$, $Z_{2f0}$, and $Z_{3f0}$ are the fundamental, second-, and third-harmonic load impedances of the UCCF mode, respectively.

Equation (11) implies that the broader range of $I_3$ leads to a broader design space for the third-harmonic load impedance. The range of $I_3$ is 0 to −0.047 in the GCCF mode, 0 to −0.137 in the ${\mathrm{PCC-CF}}_3$ mode, and 0 to −0.179 in the UCCF mode. The UCCF mode can produce smaller $I_3$ values, indicating that compared to the other two modes, it offers a broader third-harmonic load impedance design space.

As shown in Figure 6, the real part of the fundamental impedance $Z_{f0}$ varies with $pcr$ and $\alpha$, and the imaginary part varies with $\gamma$. The $Z_{f0}$ and $Z_{3f0}$ of the GCCF mode are highlighted in blue, whereas the expanded $Z_{f0}$ and $Z_{3f0}$ relative to the GCCF mode in the ${\mathrm{PCC-CF}}_3$ mode are marked in green. Additionally, the expanded $Z_{f0}$ and $Z_{3f0}$ relative to the ${\mathrm{PCC-CF}}_3$ mode in the UCCF mode are denoted in red. The real part of the second harmonic load impedance is zero, and the imaginary part varies with $pcr$, $\alpha$, and $\gamma$. The $Z_{2f0}$ of the UCCF mode remains consistent with the GCCF mode, while the $Z_{2f0}$ of the GCCF mode is highlighted in blue. This shows that the UCCF mode expands not only the finite third-harmonic load impedance design space but also the fundamental and second harmonic load impedance design space.

2.4. Performance of Proposed UCCF Mode

The output power $P_{out}$ [29] and drain efficiency $DE$ can be calculated from the drain current and voltage equations, which are functions of $pcr$ and $\alpha$. They can be expressed as

$$\begin{array}{c}\hfill {\displaystyle P_{out}=\frac{1}{2}{I}_1^2·Z_{f0}}\end{array}$$

(13)

$$\begin{array}{c}\hfill {\displaystyle DE=\frac{P_{out}}{P_{DC}}}\end{array}$$

(14)

The trend of $P_{out}/P_0$ and $DE/D{E}_0$ with $pcr$ and $\alpha$ can be visualized in Figure 7a,b. $P_0$ and $D{E}_0$ represent the output power and efficiency of the continuous class F mode, respectively. In Figure 7, the coordinate origin represents the continuous class F mode, the horizontal axis represents the GCCF mode, and the vertical axis represents the ${\mathrm{PCC-CF}}_3$ mode. At the coordinate origin, $P_{out}/P_0$ and $DE/D{E}_0$ equal 1, as expected. It can be seen from Figure 7a that $P_{out}/P_0$ is greater than 1, and increasing $pcr$ and $\alpha$ can effectively enhance the output power. The range of $P_{out}/P_0$ is 1 to 1.07 for the GCCF mode, 1 to 1.218 for the ${\mathrm{PCC-CF}}_3$ mode, and 1 to 1.25 for the UCCF mode. This shows that compared with the GCCF and PCC-CF modes, the UCCF mode has a greater ability to improve the output power. In Figure 7b, it is obvious that increasing $pcr$ and $\alpha$ leads to a decrease in the efficiency, and this trend becomes more pronounced as $\alpha$ increases. The $DE/D{E}_0$ drops from 1 to 63% in the GCCF mode and from 1 to 92.6% in the ${\mathrm{PCC-CF}}_3$ mode.

The amplitude-to-amplitude modulation (AM/AM) at saturation is used as the evaluation criterion for linearity. ${\mathrm{AM}/\mathrm{AM}}_{\mathrm{U}}$ represents the AM/AM of the UCCF mode, and ${\mathrm{AM}/\mathrm{AM}}_{\mathrm{F}}$ represents the AM/AM of the continuous class F mode. ${\mathrm{AM}/\mathrm{AM}}_{\mathrm{U}}$ and ${\mathrm{AM}/\mathrm{AM}}_{\mathrm{F}}$ [29] can be expressed as

$$\begin{array}{c}\hfill {\mathrm{AM}/\mathrm{AM}}_{\mathrm{U}}=G_U-G_S\end{array}$$

(15)

$$\begin{array}{c}\hfill {\mathrm{AM}/\mathrm{AM}}_{\mathrm{F}}=G_F-G_S\end{array}$$

(16)

$$\begin{array}{c}\hfill {\displaystyle G_U=10log\frac{P_{out}}{P_{in}}}\end{array}$$

(17)

$$\begin{array}{c}\hfill {\displaystyle G_F=10log\frac{P_0}{P_{in}}}\end{array}$$

(18)

where $G_S$ is the small signal gain, $G_U$ is the power gain of the UCCF mode at saturation, and $P_{in}$ is the input power.

$$\begin{array}{c}\hfill {\displaystyle {\mathrm{AM}/\mathrm{AM}}_{\mathrm{U}}-{\mathrm{AM}/\mathrm{AM}}_{\mathrm{F}}=20{log}_{10}\frac{2I_1\left({\displaystyle 1-\cos \frac{\alpha }{2}}\right)}{pcr}}\end{array}$$

(19)

Figure 7c shows the trend of ${\mathrm{AM}/\mathrm{AM}}_{\mathrm{U}}-{\mathrm{AM}/\mathrm{AM}}_{\mathrm{F}}$ with different $pcr$ and $\alpha$ values. At the coordinate origin, ${\mathrm{AM}/\mathrm{AM}}_{\mathrm{U}}-{\mathrm{AM}/\mathrm{AM}}_{\mathrm{F}}$ equals 0, as expected. When ${\mathrm{AM}/\mathrm{AM}}_{\mathrm{U}}-{\mathrm{AM}/\mathrm{AM}}_{\mathrm{F}}$ is greater than 0, the linearity is better than that of the continuous class F PA. When ${\mathrm{AM}/\mathrm{AM}}_{\mathrm{U}}-{\mathrm{AM}/\mathrm{AM}}_{\mathrm{F}}$ is less than 0, the linearity is worse than that of the continuous class F PA. The range of ${\mathrm{AM}/\mathrm{AM}}_{\mathrm{U}}-{\mathrm{AM}/\mathrm{AM}}_{\mathrm{F}}$ is 1 to 6 in the GCCF mode and 1 to −4.3 in the ${\mathrm{PCC-CF}}_3$ mode. As shown in Figure 7c, as $\alpha$ increases, ${\mathrm{AM}/\mathrm{AM}}_{\mathrm{U}}-{\mathrm{AM}/\mathrm{AM}}_{\mathrm{F}}$ increases, but as $pcr$ increases, ${\mathrm{AM}/\mathrm{AM}}_{\mathrm{U}}-{\mathrm{AM}/\mathrm{AM}}_{\mathrm{F}}$ decreases. Therefore, the AM/AM distortion caused by an increase in $pcr$ can be offset by selecting the appropriate $\alpha$.

3. Fabrication and Measurement Result of the Proposed UCCF Mode PA

The UCCF mode enables a broader finite third-harmonic load impedance space and a better balance between efficiency and linearity. To verify this theory, the PA was designed based on CREE’s CGH40010F GaN HEMT with an output power of 10 W and an optimal impedance of 30 $\mathsf{\Omega }$.

The key issue when implementing the UCCF mode is the correct selection of $pcr$ and $\alpha$. When choosing $pcr$ and $\alpha$, it is necessary to comprehensively consider the efficiency and linearity. In this design, $pcr$ and $\alpha$ were selected according to the conditions listed in (19),

$$\left\{\begin{array}{c}{\mathrm{AM}/\mathrm{AM}}_{\mathrm{U}}-{\mathrm{AM}/\mathrm{AM}}_{\mathrm{F}}\ge 0\\ DE/D{E}_0\ge 0.9\\ P_{out}/P_0\ge 1\end{array}\right.$$

(20)

In Figure 8, the blue region indicates ${\mathrm{AM}/\mathrm{AM}}_{\mathrm{U}}-{\mathrm{AM}/\mathrm{AM}}_{\mathrm{F}}\ge 0$, while the green region indicates $DE/D{E}_0\ge 0.9$. The gray line in Figure 8 represents the contour line of $I_3$. From Figure 7a, it can be observed that $P_{out}/P_0$ is greater than 1 throughout the entire plot. When choosing $pcr$ and $\alpha$, it is necessary to ensure that they fall in the overlapping area, called the operating space in Figure 8, to achieve a balance between efficiency and linearity.

A schematic of the PA with the drain bias voltage set to $V_{DD}=28$ V and the quiescent drain current set to 265 mA is shown in Figure 9. Since the theoretical analysis is conducted in the current source plane, parasitic parameter models [33] are required to transform the packaging plane into the current source plane. In this design, $\alpha$ equals 1.17$\pi$ and $pcr$ ranges from 1 to 1.2. The corresponding impedance space is shown in Figure 10. The working state used in this design has enhanced linearity and acceptable efficiency. The impedance trajectory of this design, shown in Figure 10a, aligns with the impedance space. In Figure 10b, the simulated voltage and current waveforms of the current source plane are depicted and are consistent with the theoretical design. As shown in Figure 11, the stability factor is close to 1 and greater than 1 in 2–2.6 GHz, and the stability factor is greater than 1 in the whole frequency band, which proves that the designed PA has good stability.

As shown in Figure 12, the measurement setup includes a signal generator (SMW200A), a spectrum analyzer (FSW-43), two power supplies (E3632A, DP832A), a driver amplifier (ZHL-16W-43-S+PA), a DUT, an attenuator, and a PC. The layout design of the PA is shown in Figure 13, and the circuit size is 8.8 cm × 8.6 cm. A Rogers 4350B with a thickness of 20 mils and a dielectric constant of 3.66 was used as the substrate. As shown in Figure 14, S-parameters were measured at 2.05–2.65 GHz using an Agilent N5230C vector network analyzer.

The test results indicate that ${\mathrm{S}}_{21}$ is greater than 14 dB, ${\mathrm{S}}_{11}$ is less than −14 dB and ${\mathrm{S}}_{22}$ is less than −12 dB. Figure 15a depicts the variations in the drain efficiency and gain with theoutput power, and Figure 15b depicts the variations in the drain output power, efficiency, and gain with the frequency. The results show that the drain efficiency was 67.0–73.2%, the output power was 40.1–41.0 dBm, and the gain was 9–10.8 dB. The DPD test platform is shown in Figure 12, which includes te signal generator, spectrum analyzer, power supplies, driver amplifier, PA, attenuator, and PC. A 5G NR (New Radio) signal with a 100 MHz bandwidth (the peak average power ratio was 8 dB) was used to test the PA’s output spectrum at 2.35 GHz. The DPD in this paper adopts the GMP model and utilizes the indirect structure. $K_a=5$ and $L_a=6$ are the index arrays for the aligned signal and envelope; $K_b=5$, $L_b=6$ and $M_b=2$ are the index arrays for the signal and lagging envelope; and, $K_c=5$, $L_c=6$ and $M_c=2$ are index arrays for the signal and leading envelope. The algorithm part is processed in MATLAB, 10,000 samples are used for fitting, and another 10,000 samples are used for verification. As shown in Figure 16a, the worst ACPR was −34.8 dBc without digital predistortion (DPD) and −57.8 dBc with DPD. There was an average output power ($P_{ave}$) of around 32.4 dB and an average DE ($D{E}_{ave}$) of 34.39%. This shows that the UCCF mode performs well in terms of the adjacent channel interference. Figure 16b shows the PA’s amplitude-to-amplitude modulation (AM/AM) and amplitude-to-phase modulation (AM/PM) characteristics with and without DPD. Through testing, it can be seen that the designed PA has good linearity.

Table 1. Comparisons with previous works.

Refs.	Mode	Freq (GHz)	Pout (dBm)	DE (%)	Transistor	Substrate	Size (cm × cm)	S11 (dB)	S22 (dB)	S21 (dB)	Pave (dBm)	DEave (%)	Signal BW (MHz)	ACPR wo/w DPD (dBc) (PAPR (dB))
[23]	CCF	1.45–2.45	40.2–42.2	66–74.6	CGH40010F	Taconic RF35	N/A	N/A	N/A	N/A	35	46	40	−24.9/−49.7 (N/A)
[26]	GCCF	0.5–0.95	38–40	73–79	NXP AFT27S006N	Rogers 4003C	N/A	N/A	N/A	N/A	33	32–41	5	−35/−43 (N/A)
[30]	${\mathrm{PCC-CF}}_3$	1.6–1.8	41.6–42	72–74	CGH40010F	Rogers 4350B	5.5 × 7	N/A	N/A	N/A	35	34	20	−34/−49 (6.5)
[39]	Filtering	2.0–2.4	39–40.4	69–78.2	CG2H40010F	Rogers 4350B	8 × 6	−10	N/A	13.4–15.1	N/A	N/A	N/A	N/A
[35]	Filtering	1.85–2.1	38.6–39	58.5–73	CGH40010F	RT/Duroid 5880	N/A	−10	N/A	13	N/A	N/A	20	−34.8/−57.8 (7)
[36]	BJ	1.6–2.8	40	65–66	CGH40010F	Rogers 4350B	6.7 × 5.3	N/A	N/A	N/A	30.64	N/A	5	−36.5/−55.8 (8.2)
[40]	CF	2.25–2.51	40.8	51–67	CGH40010F	Rogers 5880	8.1 × 2.9	−10	N/A	17	N/A	N/A	N/A	N/A
[37]	${\mathrm{F}}^{-1}$	1.35–2.5	41.1–42.5	68–82	CGH40010F	Taconic RF35	N/A	N/A	N/A	N/A	34.6	37	20	−26.4/−45.2 (7)
[38]	${\mathrm{CCGF}}^{-1}$	3.05–3.85	39.9–41.4	70–78	CG2H40010F	Dupont 9K7	N/A	N/A	N/A	N/A	32	N/A	20	−26/(N/A) (10.45)
[34]	${\mathrm{iF}}^{-1}$	2.0–2.6	40.1–40.8	71.2–77.3	CG2H40010F	Taconic TLY−5	N/A	N/A	N/A	N/A	31.8	34.21	100	−22.99/−48.76 (8.5)
This work	UCCF	2.05–2.65	40.1–41	67.0–73.2	CGH40010F	Rogers 4350B	8.8 × 8.6	−14	−12	14	32.4	34.39	100	−34.8/−57.8(8)

N/A: not available, ${\mathrm{iF}}^{-1}$: a mode that utilizes input harmonics to enhance the linearity performance beyond that of the conventional ${\mathrm{Class-F}}^{-1}$ mode, ${\mathrm{CCGF}}^{-1}$: continuous class ${\mathrm{GF}}^{-1}$ mode, CCF: continuous class F mode, CF: class F mode, Filtering: Filtering PA.

presents the performance comparison with other PAs. All comparison designs are based on 10 W PA tubes. In both [34] and this work, a 100 MHz bandwidth signal was employed for spectrum testing. The ACPR presented in [34] is 11.81 dB worse than that shown in this work without DPD The ${\mathrm{P}}_{\mathrm{ave}}$ and ${\mathrm{DE}}_{\mathrm{ave}}$ of [34] are lower than that those in the UCCF mode. Although the ACPR values presented in [26,30,35,36] are comparable with those shown for the UCCF mode, the signal bandwidth was found to be relatively narrow when testing the spectrum. Moreover, in [23,37,38], the ACPR tested with a narrow bandwidth signal was worse than that measured in the UCCF mode. This shows that the proposed UCCF mode stands out due to its superior linearity. The efficiency of the UCCF mode is comparable with that shown in other works. This design effectively strikes a better balance between efficiency and linearity compared to other PAs.

4. Conclusions

In this paper, the UCCF mode, which extends the flexibility of the PA working state by considering the influence of conduction angle and overdriven transistor on the current waveform, was proposed. Following rigorous theoretical derivations, the load impedance design space tailored to the UCCF mode was deduced. Subsequently, the efficiency and linearity characteristics of this mode were comprehensively analyzed, and a balanced PA performance was achieved. The empirical test results strongly support the effectiveness of this new mode, closely aligning with our anticipated outcomes. This positions the UCCF mode as an excellent performance choice with the potential for widespread applications.