Development Review of Highly Efficient Sequential Power Amplifier with Extended Back-Off Range for Broadband Application

Abstract

Similar to a Doherty power amplifier (DPA), a sequential power amplifier (SPA) is mainly composed of a main amplifier, an auxiliary amplifier and a combiner. However, SPA breaks the bandwidth limitation of the impedance inverter in the DPA, and also simplifies the design procedure. Since the main amplifier has no load modulation, it is easy for the SPA to realize broadband operation and improve the output back-off (OBO) power range. Therefore, SPA has great advantages and potential in expanding bandwidth, improving drain efficiency and expanding the back-off range of a power amplifier simultaneously. This paper describes the evolution and classification of the SPA. First, the basic theory of the SPA is reviewed. Then, some two-way SPAs using coupler and circulator as a power combiner are discussed. Thirdly, the latest popular sequential load modulated balanced amplifier is overviewed.

1. Introduction

The rapid progress of wireless communication technology has resulted in higher requirements for data traffic, user capacity and signal transmission speed, which leads to a continuous increase in signal peak-to-average ratio (PAPR) and bandwidth [1]. The wideband modulated signals deteriorate the average efficiency of a power amplifier (PA), which is an important part of the wireless communication system. Therefore, it promotes the improvement of the back-off efficiency of a PA. Moreover, the distribution of communication frequency band is becoming more fragmented, requiring the PA to cover a wide frequency range. Thus, to meet the requirements of the wireless communication systems, the PA should have high efficiency over a large output back-off (OBO) power range and a wide bandwidth simultaneously [2].

According to different modes of operation, there are two kinds of techniques that can be used to enhance the back-off efficiency of a PA. One is the power modulation, and the other is load modulation. Nowadays, the load modulation technique has been widely used in PA design, such as in Doherty PA (DPA) [3,4,5], Outphasing PA (OPA) [6,7,8] and the load modulation balanced power amplifier (LMBA) [9,10]. Among these load-modulated PAs, the DPA and LMBA can cover a wide frequency band by using improved design techniques [11,12,13]. However, the high-efficiency power ranges of the DPA and LMBA are mainly limited to 6 dB, which is not suitable for the current wideband signals. On the other hand, the OPA can main high efficiency over a large back-off power range by carefully selecting the reactive compensation elements in the combiner. However, it is very hard for the OPA to cover a wide bandwidth due to the frequency dispersion of the combiner. In summary, it is challenging to design a high-efficiency PA to simultaneously cover a wide bandwidth and a larger back-off power range.

As an alternative approach, Sequential PA (SPA) offers a way to achieve broadband operation through straightforward theoretical derivations and design architectures, while also enhancing efficiency at deep power back-off level [14]. Figure 1 illustrates the simplified diagram of an ideal SPA, which bears a resemblance to the well-known “Balanced Amplifier” [15]. The SPA consists of a main amplifier and an auxiliary amplifier. And the two sub-amplifiers are combined through a coupler. Since the outputs of the two sub-amplifiers are connected to the input and isolation ports of the coupler, the two sub-amplifiers work independently without load modulation. This allows for separate design of the sub-amplifiers.

In SPA, the main amplifier operates in Class-AB, while the auxiliary amplifier operates in Class-C. In the low-power region, only the main amplifier works independently, while the auxiliary amplifier remains off. In this situation, the efficiency of the SPA is determined by the main amplifier. As the input power continues to increase, the main amplifier reaches saturation, and the auxiliary amplifier starts to work. Since the main amplifier is already saturated, it maintains maximum efficiency. Consequently, the output power of the entire amplifier is mainly contributed by the auxiliary amplifier. As a result, the SPA can maintain a high average efficiency, as the main amplifier is in saturation state at the output back-off power level, when the auxiliary amplifier is in the off-state.

Firstly, to better understand the SPA, the basic principle of the SPA is introduced in this paper. Then, the design examples of the SPA based on coupler and circulator are reviewed. Thirdly, the coupler-based three-way SPA (SLMBA) is discussed, and a design example for overcoming the over-driven problem of the SLMBA is presented.

2. The Basic Theory of SPA

The theory of the SPA was well studied in [16]. The SPA consists of a power splitter, a power combiner, and two parallel sub-amplifiers. The main amplifier works in class-AB and the auxiliary amplifier works in class-C [17]. In the low-power region, only the main amplifier works and delivers power to the load. And the auxiliary amplifier is the off-state. As the input power increases, the main amplifier reaches saturation at a pre-determined OBO power level, where the auxiliary amplifier is turned on. After the the auxiliary amplifier is turned on, the gain expansion of the auxiliary amplifier will compensate for the gain compression of the main amplifier, leading to a constant gain. Because the main amplifier is close to the maximum efficiency at the pre-determined OBO power level, the overall efficiency of the SPA is improved.

Since the main and auxiliary amplifiers are turned on sequentially, the SPA has two operating regions (the low- and high-power regions). In addition, the power combiner is assumed to be ideally lossless, so the efficiency of the combiner is 100%, meaning the combiner has no effect on the efficiency of the SPA.

(1) Low-power region (main PA on, auxiliary PA off)

The ideal efficiency of SPA can be expressed as

$${\eta }_{SPA,ideal1}=\frac{P_{out,Main}}{P_{DC,Main}}\times 100\%$$

(1)

As can be seen from the above equation, the efficiency of the PA in the low-power region depends on the efficiency of the main PA.

(2) High-power area (main PA saturated, auxiliary PA on) The ideal efficiency of SPA can be expressed as

$${\eta }_{SPA,ideal2}=\frac{P_{out,Main}+P_{out,Aux.}}{P_{DC,Main}+P_{DC,Aux.}}\times 100\%$$

(2)

Since the auxiliary PA is less efficient when it is just turned on, the overall efficiency of SPA will decrease at the beginning of the high-power region. However, as the input power increases further, the efficiency of auxiliary PA will rise, and the efficiency of the SPA will rise again until the auxiliary reaches saturation. Therefore, there are two efficiency peaks in the whole power range. That is, the SPA maintains high efficiency within an OBO power range. In addition, the main amplifier sees a constant load impedance over the whole power range because the main amplifier has no load modulation. Therefore, the two sub-amplifiers of the SPA work independently. Therefore, the theoretical derivation of the class-B PA given in (3) can be adopted to analyze the SPA.

$${\eta }_{\mathrm{class}-\mathrm{B}}=\frac{\pi }{4}\frac{V_{\mathrm{out}}}{V_{DC}}=\frac{\pi }{4}\sqrt{\frac{P_{\mathrm{out}}}{P_{\mathrm{out},\max }}}.$$

(3)

In (3), $P_{\mathrm{out},\max }$ indicates the output power at maximum efficiency. Then, (1) and (2) can be rewritten as

$$\begin{array}{c}\hfill {\eta }_{\mathrm{SPA},\mathrm{ideal}1}=\frac{\pi }{4}\frac{P_{out,Main}}{\sqrt{P_{out,Main}{P}_{out,Main,max}}}\end{array}$$

(4)

$$\begin{array}{c}\hfill {\eta }_{\mathrm{SPA},\mathrm{ideal}2}=\frac{\pi }{4}\left(\frac{P_{out,Main}}{\sqrt{P_{out,Main}{P}_{out,Main,max}}}+\frac{P_{out,Aux.}}{\sqrt{P_{out,Aux.}{P}_{out,Aux.max}}}\right)\end{array}$$

(5)

Through the above analysis, it is found that, compared with the DPA, the SPA has a simpler circuit topology and is more easily implemented. In addition, the sub-amplifiers work separately, so the bandwidth of the SPA is mainly limited by the combiner.

In the above analysis, it is assumed that the power combiner is ideally lossless; that is, the output power of the main and the auxiliary PAs can be completely combined with lossless output combiner. However, in practical design, the power combiner is not lossless, and it has a greater impact on the output power. Therefore, it is very important to choose and design the power combiner when implementing the SPA. According to the previous papers, the SPA can be divided into two categories, as shown in Figure 2. The first category is circulator-based SPA, and the other category is coupler-based SPA, which includes two-way and three-way SPAs.

3. Review on Two-Way SPA

3.1. SPA Based on Coupler

Initially, the SPA is mainly designed using couplers. In [18], a SPA was realized by using a digital circuit (FPGA) and a switching coupler. The digital circuit provided the SPA with required amplitude and phase relationships. And the switching coupler worked as the power combiner, as shown in Figure 3a. In the low-power region, the FPGA delivers input signal only to the upper path (the main amplifier). In the high-power region, the main amplifier reaches saturation, and the FPGA then delivers another signal to the lower path (the auxiliary amplifier). In this situation, the auxiliary amplifier starts to work and provides output power to the load. In [18], the author found that different coupling factors have different effects on the back-off efficiency due to the loss of the combiner. A higher coupling factor will reduce the efficiency at the saturation power level, while a lower coupling factor will reduce the efficiency at deeper OBO power level. A SPA using a branch-line coupler with a 7 dB coupling coefficient and two identical Class B transistors was designed in [18]. The designed SPA in [18] achieved a 10 dB back-off efficiency of 38%. Meanwhile, the average efficiency of the whole transmitter was improved by 30% compared to conventional amplifiers. Moreover, to further improve the system efficiency, the author optimized the SPA in [18] using an adaptive coupler as the power combiner in [19].

The focus of the above studies is mainly on analyzing the influence of the coupling coefficient of the output power combiner and the power ratings of the two amplifiers. The operation bandwidth of the SPA is ignored. To realize broadband operation, continuous mode theory was introduced in the SPA in [20]. The main amplifier of the the SPA in [20] was a continuous class-F PA. And a Lange coupler with a coupling coefficient of 8.5 dB was adopted to improve the back-off efficiency, as shown in Figure 3b. A SPA working over 1.45–2.4 GHz was designed in [20]. The broadband SPA uses 10 W and 45 W transistors as main PA and auxiliary PA, respectively. Measurement results show the broadband SPA obtains an average drain efficiency of 59% in the frequency band of interest.

Notice that a digital signal processor (two RF-inputs) is required in [20] to maintain the required phase and amplitude relationship between the two sub-amplifiers over a wide bandwidth. This digital signal processor increases the complexity and cost of the system. To remove the digital signal processor, a 3 dB wideband coupler was used to realize power distribution in [21,22], leading to a single RF-input SPA, as shown in Figure 4. Furthermore, a 10 dB wideband Lange coupler was used to combine the output power from the two sub-amplifiers. To maintain optimal operation, the main amplifier is biased in class-AB, and the auxiliary PA is biased in class-C. The SPA in [21] achieves an average drain efficiency of 45–61% over the 2.1–2.9 GHz when the average output power is 35 dBm (5 dB back-off from saturation). In [22], the SPA provides a drain efficiency of 62–65% at saturation power level and a drain efficiency of 48–52% at 6 dB OBO power level.

Unlike the SPA in [21,22], a Wilkinson power divider and a 7 dB hybrid coupler were used to construct broadband SPA in [23], as shown in Figure 5. Compared with the Lange coupler, a higher coupling coefficient is more easily obtained by the hybrid coupler. The designed SPA in [23] achieves a saturation drain efficiency of 43–56% and a 6 dB back-off drain efficiency (DE) of 36–52% in the frequency band of 2.9–4.7 GHz. For comparison,

Table 1. Performance comparison of recently published SPAs based on coupler.

Ref., Year	Freq. (GHz)	BW. (GHz/%)	Pmax (dBm)	DE@Sat (%)	OBO (dB)	DE@OBO (%)
2014 [20]	1.45–2.4	0.95/49	43–45	35–44	3	54–65
2015 [21]	2.1–2.9	0.8/32	39.5	26–34	5	45–61
2015 [22]	1.1/1.5	NA	39.3/40.5	62/65	6	48/62
2022 [23]	2.9–4.7	1.8/47	40–42	43–56	8	36–52

DE@sat: DE at saturation. Pmax: Maximum output power.

lists the performances of recently published SPAs based on coupler.

3.2. SPA Based on Circulator

Recently, a circulator was utilized to design load-modulated PAs. Compared with a coupler, a circulator has a great advantage when designing SPA because of its inherent non-reciprocity. In [24,25], the authors proposed a novel PA architecture, the circulator load-modulated amplifier (CLMA), as shown in Figure 6. The CLMA includes a three-port non-reciprocal combiner, a class-B biased main amplifier, a class-C biased auxiliary amplifier, and a power divider. A phase tuning line is inserted before the auxiliary amplifier to compensate the phase difference between the two paths. In the CLMA, the load impedance of the main amplifier is modulated by the current amplitude and phase of the auxiliary amplifier. Therefore, high efficiency can be achieved over a certain OBO power level by carefully controlling the current of the auxiliary amplifier. In [25], a narrow-band CLMA working at 2.09 GHz was designed using a commercial circulator. The designed CLMA achieved a peak output power of 43.1 dBm with a drain efficiency of 73%.

Inspired by the CLMA, a SPA based on a circulator, referred to as circulator-based SPA (CSPA), was proposed in [26,27]. Figure 7 shows the block diagram of the CSPA. As shown in Figure 6 and Figure 7, the architecture of the CSPA is almost the same as the CLMA. The CSPA also consists of a three-port non-reciprocal circulator, a class-B biased main amplifier, a class-C biased auxiliary amplifier, and a power divider. Notice that the main difference between the CSPA and CLMA is that the location of the main and auxiliary amplifiers are exchanged. This is because, due to the location exchange of the main and auxiliary amplifiers, the load impedance of the main amplifier in the CSPA is constant over the whole power range. This means the main amplifier is not affected by the the auxiliary amplifier, reducing the interaction between the two sub-amplifiers. Therefore, the CSPA can maintain high efficiency over a wide bandwidth and a large output power range.

Using the S-parameter matrix of the circulator, the port current and port impedance of the main and auxiliary amplifiers can be calculated as

$$\begin{array}{c}\hfill I_M=\alpha ·\frac{I_{max}}{2}·e^{j\theta }.\end{array}$$

(6)

$$\begin{array}{c}\hfill I_A=\frac{I_{max}}{2}·\left\{\begin{array}{cc}0& \alpha <{\alpha }_B;\\ \frac{\alpha -{\alpha }_B}{1-{\alpha }_B}& {\alpha }_B<\alpha <1.\end{array}\right.\end{array}$$

(7)

$$\begin{array}{c}\hfill Z_A=Z_0·\left(1+\frac{2I_M}{I_A}\right).\end{array}$$

(8)

$$\begin{array}{c}\hfill Z_M=Z_0.\end{array}$$

(9)

where $\theta$ is the phase difference between $I_M$ and $I_A$. $I_{max}$ is the maximum drain current of the utilized transistors. $\alpha$ refers to the normalized input voltage. ${\alpha }_B$ defines the power level where the main amplifier reaches saturation. $Z_0$ is the characteristic impedance of the circulator. From (9), the load impedance of the main amplifier remains constant. That is, the impedance of the main amplifier is not modulated by the auxiliary. However, the load impedance of the auxiliary amplifier is modulated by the main amplifier. Using (8) and (9), the load modulation of the CSPA is shown in Figure 8. This figure shows the load impedance of the auxiliary amplifier is $3Z_0$ at the maximum input power level if $I_M$ = $I_A$ (same transistor) at maximum power level.

Using (6)–(9), the output power of the main amplifier, the auxiliary amplifier and the CSPA can be calculated as

$$\begin{array}{c}\hfill \left\{\begin{array}{c}{P}_M=0.5V_M{I}_M,\hfill \\ P_A=0.5V_A{I}_A,\hfill \\ P_L=P_M+P_A.\hfill \end{array}\right.\end{array}$$

(10)

Therefore, the OBO level of the CSPA can be expressed as

$$\begin{array}{c}\hfill \beta =20log\left(\frac{PM+PA}{PM}\right)\left|{}_{\alpha =1}\right.\end{array}$$

(11)

If the same transistor is adopted by the main and auxiliary amplifiers, the load impedance of the auxiliary amplifier will be $3Z_0$ at saturation power level. Therefore, the drain bias voltage of the auxiliary amplifier should be three times that of the main amplifier to maintain voltage saturation (or high drain efficiency).

In [27], a CSPA operating over 0.6–1.2 GHz was simulated and designed. The CGHV1F006S transistor was adopted by the main and auxiliary amplifiers. And a commercial circulator UIYSC25A was used as the combiner. The layout of the CSPA is shown in Figure 9 and Figure 10 shows the simulated drain efficiencies and gains of the designed CSPA versus output power in the frequency band of 0.6–1.2 GHz. Obvious efficiency enhancement at the OBO power level can be observed in Figure 10. The designed CSPA achieves a 6 dB back-off drain efficiency of 55.3–70.6%, an 8 dB back-off drain efficiency of more than 47.7%, and a saturation drain efficiency of 59.7–78.6% over 0.6–1.2 GHz.

Based on the above analysis, the load modulation of the main amplifier is eliminated by using a non-reciprocal circulator as the combiner network. In this way, the design of the main amplifier is relatively independent. Therefore, the bandwidth limitation of the traditional load-modulated PA will be avoided. For comparison,

Table 2. Performance Comparison of Recently Published PAs based on circulator.

Ref., Year	Freq. (GHz)	BW. (GHz/%)	Pmax (dBm)	DE@Sat (%)	OBO (dB)	DE@OBO (%)
2021 [24]	2.09	NA	43.1	73.2	6	73
2022 [26]	2.0–3.0	2.0/40	42–43.5	55–68	8	46–53
2022 [27]	0.6–1.2	0.6/67	39.1–40.2	59.7–78.6	8	47.7–62.5

DE@sat: DE at saturation. Pmax: Maximum output power.

lists the performances of some two-way SPAs.

4. Sequential Load Modulated Balanced Amplifier

Recently, a novel wideband PA architecture named load-modulated balanced amplifier (LMBA) has attracted the attention of the PA researchers [28]. In the original LMBA, a balanced PA (BPA) is presented with a modulated load impedance by injecting a control signal into the isolation port of the output coupler, as shown in Figure 11. Though the LMBA demonstrated wideband operation, the high efficiency is hard to maintain beyond a 6 dB dynamic power range [29,30]. Therefore, some variations were introduced to the LMBA.

In [29,30], they proposed an inverted LMBA, referred to as pseudo-Doherty LMBA (PD-LMBA) or sequential LMBA (S-LMBA). In the PD/S-LMBA, the control amplifier works as the main amplifier and the balanced power amplifier (BPA) pair works as the auxiliary amplifier, as shown in Figure 12a. In the low-power region, only the CA is on, while the BPA pair is turned off. Now, the output power of the PD/S-LMBA is provided by only the main amplifier. Once the main amplifier reaches saturation, the BPA begins to work. For this saturation, the increased output power of the PD/S-LMBA is mainly provided by the BPA pair.

Based on the simplified schematic of the PD/S-LMBA shown in Figure 12b, the load modulation of the PD/S-LMBA can be obtained as

$$\begin{array}{c}\hfill Z_{BA1}=Z_{BA2}=Z0\left(1+\frac{\sqrt{2}Ic{e}^{j\theta }}{I_b}\right)\end{array}$$

(12)

$$\begin{array}{c}\hfill Z_C=Z_0\end{array}$$

(13)

where $I_2=I_b$ and $I_4=-j{I}_b$ represent the input currents from the BPA pair and $I_3=jIc{e}^{j\theta }$ is the current from the control amplifier, as shown in Figure 12b.

Like the two-way SPA, the main amplifier of the PD/S-LMBA sees a constant load over the whole power range, as indicated in (14). This means the main amplifier reaches saturation at the pre-determined OBO power level, after which the BPA pair will be turned on. In [29], the authors implemented a 3.05–3.55 GHz SLMBA, which achieves a maximum output power of 42.3–43.7 dBm, a saturation drain efficiency of 60.8–74.8%, and a 10 dB back-off drain efficiency of 43.2–51.4%. In [30], a 1.5–2.7 GHz PD-LMBA was implemented, maintaining a drain efficiency of more than 47% over a 10 dB output power range.

Notice that the main amplifier of the PD/S-LMBA will be over-saturated in the high-power region, where the auxiliary amplifier is in the on-state. This is because the load impedance of the main amplifier is constant. The over-saturation of the main amplifier may cause stability issues for the whole PA. To avoid the over-saturation of the main amplifier, asymmetrical gate bias or an asymmetrical coupler can be adopted by the BPA pair in the PD/S-LMBA [31,32,33]. In [33], an asymmetric SLMBA (ASLMBA) with a composited impedance inverter and reciprocal operation mode is proposed, as shown in Figure 13a. The composited impedance inverter is inserted after the BPA transistor and is composed of the intrinsic elements and output matching network (BPA) of the BPA transistor. Due to the design of an OMN, optimal matching can be obtained by the BPA transistor, leading to enhanced high efficiency and output power. Moreover, by reciprocally changing the gate bias voltages of the BPA transistors, the opening sequence of the two sub-amplifiers can be changed, manufacturing the load modulation trajectory of the CA. In this way, high efficiency at deep OBO power level can be obtained by the ASLMBA over a wide bandwidth.

Using the simplified schematic of the ASLMBA shown in Figure 13b, the impedance of each sub-amplifiers at the coupler ports can be obtained as

$$\begin{array}{c}\hfill \begin{array}{c}{Z}_{C2}=j{Z}_0\left(\frac{\sqrt{2}{I}_{C1}}{I_{C2}}-\frac{I_{C3}}{I_{C2}}\right)\\ Z_{C3}=Z_0\left(2-\frac{\sqrt{2}{I}_{C1}}{I_{C3}}-\frac{j{I}_{C2}}{I_{C3}}\right)\\ Z_{C1}=Z_0\left(1+\frac{j\sqrt{2}{I}_{C2}}{I_{C1}}-\frac{\sqrt{2}{I}_{C3}}{I_{C1}}\right)\end{array}\end{array}$$

(14)

Therefore, the load impedance of each transistor at the internal plane can be expressed as

$$\begin{array}{c}\hfill \left\{\begin{array}{c}{Z}_1=\mathbf{F}\left(Z_B,Z_C,{\theta }_B,{\theta }_C,f\right),\hfill \\ Z_2=\mathbf{F}\left(Z_B,Z_C,{\theta }_B,{\theta }_C,f\right),\hfill \\ Z_3=\mathbf{F}\left(Z_B,Z_C,{\theta }_B,{\theta }_C,f\right).\hfill \end{array}\right.\end{array}$$

(15)

Equations (14) and (15) mean each sub-amplifier of the PD/S-LMBA will see a modulated load impedance versus output or input power increases. Notice that, to ensure a correct load modulation over a wide bandwidth, reciprocal bias versus frequency should be adopted by the BPA pair.

In [33], an ASLMBA working over 1.35–2.55 GHz was implemented. The measurement results show the designed ASLMBA has a saturation power of 43.2–45.1 dBm with a drain efficiency of 57.8–77.7% in the frequency band of interest, as shown in Figure 14. At the same time, the ASLMBA can maintain a 10 dB back-off drain efficiency of 47.7–68.9% over 1.35–2.55 GHz.

The above review indicates the PD/S-LMBA has great potential to maintain high efficiency over large OBO power range and wide bandwidth simultaneously. Finally, some PD/S-LMBAs with excellent results are listed in

Table 3. Performance comparison of recently published SLMBA.

Ref., Year	Freq. (GHz)	BW. (GHz/%)	Pmax (dBm)	DE@Sat (%)	OBO (dB)	DE@OBO (%)
2020 [29]	3.05–3.55	0.5/15	42.3–43.7	60.8–74.8	10	43.2–51.4
2020 [30]	1.5–2.7	1.2/57	41–43	58–72	10	47–58
2022 [32]	1.7–3.0	1.3/55	42–43	63–81	10	50–66
2023 [33]	1.35–2.55	1.2/62	43.2–45.1	57.8–77.7	10	47.7–68.9

DE@sat: DE at saturation. Pmax: Maximum output power.

.

5. Conclusions

It is clear from this paper that SPA, as an alternative, enables broadband operation through simple theoretical derivation and design architecture while achieving improved back-off efficiency. A coupler and a circulator can be used for the power combiner of the SPA. In the SPA, the main amplifier is connected to the isolation port to reduce the influence of the auxiliary amplifier, simplifying the design process. In this paper, the basic theory of SPA was briefly explained, and the coupler-based and circulator-based two-way SPA were introduced and reviewed. In addition, the development of the sequential LMBA was also presented in this paper. Finally, while SPA is improving efficiency, its linearity problem still needs to be solved, and due to the huge influence of the power synthesizer, the selection and design of the power synthesizer are also facing challenges.