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2021-09-14

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Author：Frank

This article introduces a method to increase the bandwidth of a power amplifier (PA), which is designed in the form of resistance-reactance continuous class F mode series (SCFM). By introducing the third harmonic load into the resistance-reactance SCFM PA, the overlap between the fundamental wave and the harmonic impedance is solved, and the bandwidth is improved. Using this method, the author designed a high-efficiency PA with an operating frequency of 0.5 to 2.3GHz. The experimental results show that the PA achieves an output power of 10W, and the drain efficiency from 0.5 to 2.3GHz can reach 59% to 79%.

With the rapid development of wireless communication technology, next-**generation wireless systems **require wider bandwidths to achieve higher data transmission rates. As a key transmission device, PA needs to have higher efficiency in a wider bandwidth and be able to meet a variety of standards.

In recent years, many studies have explored ways to improve PA bandwidth and efficiency. In 2009, S. C. Cripps1 proposed continuous mode PA, which solved the bandwidth limitation of traditional switch mode PA by appropriately introducing reactance-like second and third harmonics. Subsequently, continuous B/J type, continuous F type and inverse F type PA were successively proposed 2-6. Theoretically, due to the harmonic impedance at the edge of the Smith chart, the maximum bandwidth of continuous B/J, continuous F, and inverse F PA modes is limited to one octave. Therefore, this strict limitation of harmonic load makes it difficult for PAs to achieve multi-octave performance. In 2013, Lu and Chen7 proposed a resistance-reactance continuous mode series method, introducing resistance-like harmonic impedance into the continuous mode to ease the strict restrictions on harmonic loads8-9. Using this method, the bandwidth can be more than one octave by introducing resistance, and the second harmonic load also has a wider fundamental impedance space, which further improves the bandwidth of the broadband PA. The inverse continuous mode resistance-reactance series PA was proposed by Li et al. 9 and revealed a similar method for designing a **broadband PA**.

In this article, the extended mathematical formula is used for resistance-reactance SCFM analysis. The introduction of the third harmonic impedance further expands the design space and provides greater freedom when designing high-efficiency, multi-octave PAs.

Extended resistance-reactance SCFM

The traditional resistance-reactance SCFM has a half-wave rectified sinusoidal current waveform in the inherent current generator plane of the device, that is, ids(θ) in the following form:

The voltage waveform vds(θ) is no longer strictly limited to a square wave, and includes a set of variables that depend on the parameters α and γ:

By multiplying the current waveform of the resistance-reactance SCFM by the parameter (1+βcosθ), the third harmonic impedance of the resistance is introduced while keeping the voltage waveform unchanged. New current wave

In this way, an alternative impedance solution with resistive second and third harmonic impedance can be obtained. By dividing the voltage by the current, the load impedance present at each harmonic can be calculated. Here, Zn is designated as the nth harmonic impedance.

The values of Z1, Z2, and Z3 depend on whether the conditions 0≤α≤1 and -8/3π≤β≤0 can be realized. Figure 1 shows the fundamental and harmonic impedance changes relative to α and β. The second harmonic region moves toward the fundamental wave region with the changes of α and β, and the third harmonic region tends to the fundamental wave region as β decreases. This feature allows us to resolve the overlap between the fundamental and harmonic impedances in a multi-octave design.

Drain efficiency is a function of α and β. The changes in drain efficiency and output power relative to α and β are shown in Figure 2. The changes of α and β should be limited to the effective area, so that acceptable drain efficiency can be achieved even with a slight drop in output power. In the design of this paper, the condition ranges of 0≤α≤0.4 and -0.4≤β≤0 are selected to achieve a drain efficiency greater than 65%.

Simulation and measurement

In order to verify the effectiveness of this method, the author uses Wolfspeed CGH40010F GaN transistors to design a resistance-reactance SCFM PA with an operating frequency of 0.5 to 2.3 GHz. It works at 28V and 68mA static drain bias. The substrate medium is Rogers. 4350B (εr=3.66), thickness 30mil, metal layer thickness 35μm.

Through the iterative process from high frequency to low frequency, harmonic load pulling simulation can be realized, and then the best load impedance can be obtained. Among them, the impedance obtained at **high frequency** is used to terminate low frequency harmonics. Repeat this process until the best load impedance is obtained. The output matching network is designed with real-frequency direct calculation technology10. Figure 3 shows the broadband output matching network of this design. Since the input harmonic impedance has a very small impact on the PA performance11, when designing the input matching network, more attention should be paid to the fundamental wave matching.

The accurate model of the parasitic network of the widely used CGH40010F transistor was derived by Tasker and Benedikt12. Based on this parasitic network model, on the packaging plane of the I-gen and output matching network, the impedance trajectory in the Smith chart is shown in Figure 4. In the working frequency band of 0.5 to 2.3 GHz, the calculated fundamental wave impedance of the current plane remains within or near the theoretical area.

The final design of the resistance-reactance SCFM PA is shown in Figure 5. In the case of a continuous input power of 29dBm, the simulation and experimental results are shown in Figure 6. In the frequency range of 0.5 to 2.3GHz, the drain efficiency is 59% to 79%, and the saturated output power is 39.4 to 41.6 dBm. The experimental results are consistent with the simulation results.

To characterize the linearity of the PA, we use a 20MHz LTE signal with a peak-to-average power ratio of about 7.5dB to drive the PA at 0.8, 1, 1.6, and 2 GHz. As shown in Figure 7, the broadband PA shows good linearity at about 5dB of saturation margin power, where the adjacent channel leakage power ratio (ACLR) is lower than -30dBc, and the average efficiency is 34.1 to 49.1%. Table 1 compares the performance of this PA with other similar advanced broadband PAs.

in conclusion

The **pcb design** space of resistance-reactance SCFM is expanded by introducing the third harmonic impedance. Using this method, the overlap between the fundamental and harmonic impedance is effectively resolved. This article uses this method to design, build and test a broadband high-efficiency PA. The agreement between the experimental and simulation results verifies the effectiveness of this method for the design of multi-octave, high-efficiency PA. Driven by a 20MHz LTE signal, the ACLR of the proposed PA is lower than 30dBc when the output power is about 35dBm, and the average drain efficiency is higher than 34%.