## 1 Introduction  
The current wireless communication schemes employ spectrally efficient complex modulation techniques to address the high data throughput demand. The dynamic wideband envelope and high peak-to-average power ratios (PAPRs) of 4G/5G waveforms challenge the RF power amplifier (PA) linearity-efficiency trade-off. Therefore, several architectures to improve the efficiency of RF PA have been investigated, e.g., Doherty, linear amplification with nonlinear components (LINC), envelope elimination and restoration (EER), and envelope tracking (ET) [1; 2; 3; 4]. Unfortunately, architectures such as Doherty and LINC have bandwidth restrictions inherently. As for EER, the linearity of the signal is strongly dependent on the supply modulator and dependent on time-alignment between the RF phase signal and the amplitude envelope signal at the output of the PA [5]. However, these issues can be alleviated in envelope tracking (ET) architecture, which utilizes an envelope amplifier (EA) to instantly adjust the PA power supply voltage in synchronism with the envelope of the RF signal to ensure PA is always working at peak efficiencies for different output power levels. Since the EA is independent of the carrier frequency, the ET architecture has demonstrated considerable flexibility in multimode and multiband (MMMB) application scenarios. Moreover, the amplitude information is contained in the RF input under ET mode, and consequently,the envelope supply waveform can be de-troughed to prevent gain collapse and reduce the bandwidth of the envelope waveform [6], which is an advantage over EER.  
The overall efficiency of the ET architecture is given by the product of the PA efficiency and EA efficiency. The state-of-the-art wideband EA circuits in the literature demonstrate average efficiency of 70% to 85%, depending on the signal bandwidth and the load impedance [7; 8; 9; 10; 11]. Therefore, to achieve more than 50% overall efficiency by considering the statistical probability distribution function (PDF) of the modulated signal, the power added efficiency (PAE) of the RF PA at the power back-off region should necessarily surpass 70%. This is a challenging task, since the change in drain-to-source capacitance (\(C_{ds}\)) in the dynamic supply operation would result in a shift of the optimal load impedances to achieve high efficiency mode. Different modes, such as class-AB/B, class-J, and class-F Pas, have been investigated to overcome this limitation, whereas the art of ET's RF PA design is still immature as the RF PA's PAE at the power back-off region, i.e., the low drain supply voltage condition (corresponding to the average drain voltage of ET mode), is seldom above 70% at S-band [12; 13; 14; 15].  
This paper investigates, for the first time, the feasibility of utilizing hybrid continuous modes (HCM) PAs, which combine all the continuous modes between continuous Class-B/J and continuous Class-F [16], to optimize PAE trajectory for ET architecture. The design space for load impedances of the HCM PAs with nonlinear \(C_{ds}\) is deduced mathematically using the embedding transfer network. Using the optimal impedance solutions at the package plane, a GaN high electron mobility transistor (HEMT)-based PA is designed and the simulated fundamental impedances in load-pull are in good conformity with the predicted ones based on the proposed method. The ET experimental system was set up to evaluate the application of the PA circuit. Measurement results show that the proposed ET PA exhibits competitive overall efficiency and linearity.