A power amplifier (PA) is always an important component in a transmitting chain of a wireless system, since its performance strongly influences the overall system features, including bandwidth, output power, efficiency, and linearity. In a modern PA design, wide bandwidth and high efficiency are two major requirements that increase the number of frequency bands and reduce thermal problems in the power devices and their sizes and auxiliary costs. A switch-mode class-E PA with shunt capacitance is attractive for these purposes, due to its high efficiency and simple topology [1, 2]. However, [1] and [2] only concentrate on simplifying the analysis of the class-E PA while neglecting the actual characteristic of the shunt capacitance. In fact, the operation of the linear shunt capacitance class-E PA in theory is completely different from its practical operation. Because the parasitic drain-to-source capacitance of the switching device, which significantly contributes to the overall shunt capacitance in the operation, is nonlinear, it is necessary to take into account the nonlinear characteristics of this capacitance.

The theory of the class-E PA with a nonlinear capacitance was first published in Chudobiak’s work [3] in a case of the grading coefficient m = 0.5. Then several numerical analyses were performed with the grading coefficient m ≠ 0.5 [4, 5]. In these articles, only a nonlinear shunt capacitance of the power transistor is considered. Suetsugu and Kazimierczuk [6] has proposed an analysis and a design procedure for the class-E PA with a shunt capacitance composed of both transistor nonlinear output capacitance and linear external capacitance. This theory has been verified in a design of a high-efficiency class-E PA for 13.56 MHz wireless power transmission application [7]. The study of frequency limitation based on the nonlinear shunt capacitance theory has been presented in article [8], which showed the nonlinear dependence of frequency upon supply voltage, output power, and transistor characteristic. The performance as well as the topology of the class-E PA depends on the maximum frequency. An optimum performance is only addressed when the operating frequency does not exceed the maximum frequency. In the event that the operating frequency is lower than the maximum frequency, an added external shunt capacitor is necessary to obtain an optimal value of the shunt capacitor, as in the topology used in Suetsugu’s work, whereas the topology used by Chudobiak [3] is optimum if the operation and maximum frequencies are equal.

The mentioned studies concentrated on designing a class-E PA at a single frequency using an output resonant circuit with a high unloaded quality factor to tune the operating frequency. In the present work, a practical approach to designing a broadband high-efficiency class-E PA based on the nonlinear shunt capacitance theory is proposed. Applying nonlinear design equations from previous works [6, 8], the dependence of class-E PA operation on the frequency is focused on extracting the optimal values of the circuit parameters, including external shunt capacitance and output impedance. The topology of a low-pass matching network is utilized to overcome the restriction of the output resonant circuit for the broadband design. A prototype of a broadband class-E PA is implemented to validate the theoretical analysis.

A conventional circuit of the MOSFET class-E PA with shunt capacitance is illustrated in Fig. 1(a). Without an input driving signal, a DC-voltage V_GS is applied to the gate of the transistor to turn the transistor off. A DC-supply voltage V_DD connects to the drain of the transistor through the choke coil L_RFC with the only purpose of supplying DC power to the transistor. A shunt capacitor C_p, in parallel with the transistor, keeps a sinusoidal current waveform to alternate flow between the transistor and the shunt capacitor C_p. In common, C_p, consisting of a nonlinear shunt capacitance of a transistor C_ds and a linear external capacitance C_e, is described as follows:

where C_j0 is the shunt capacitance at the drain-to-source voltage v_s = 0 V, and V_bi is the built-in potential of the MOSFET body diode. A series-resonant C₀L₀ circuit tunes to the fundamental frequency with a high unloaded quality factor Q to shape the output current to be sinusoidal at the fundamental frequency. At the fundamental frequency f₀, a load Z_E is inductive, as shown in Fig. 1(a). An optimal value of Z_E guarantees that there is no overlap between the transient drain current and the voltage.

In previous works [6, 8], the design equations expressed the relationship among the operating frequency f₀, the supply voltage V_DD, the output power P_o, the external linear capacitance C_e, and the characteristic parameters of MOSFET, C_j0, V_bi. The numerical solutions, a set of tables and figures, illustrate that relationship. For the purpose of broadband design, this work gives a practical scenario in which a specification of class-E PA is defined as containing the operating frequencies, the output power, and the model of the MOFET transistor. Based on this specification, the analysis concentrates on the dependence of the circuit parameters on the operating frequency and the DC-supply voltage. For selected values of output power P_o and MOSFET transistor parameters C_j0, V_bi, and for swept values of operating frequency f₀ and DC-supply voltage V_DD, this work re-solves the nonlinear design equation to extract the values of external linear capacitance C_e and fundamental load Z_E. Then the optimal values of these parameters are chosen to obtain the highest efficiency of class-E PA.

To verify the above analysis, a prototype of class-E PA circuit was designed for public and homelands security application with P_o of 34 dBm over a bandwidth of 140–170 MHz. The MOSFET used in this design was MRF282SR1, with C_j0 described by the following:

where C_oss and C_rss, respectively, are the output and reverse transfer capacitances of the transistor, (often provided in catalogs by power MOSFET manufacturers), and V_spec is a special value of supply voltage used to measure the values of C_oss and C_rss. Using MATLAB, the C_e as a function of f₀ for selected values of V_DD was plotted in Fig. 2. From Fig. 2, the actual V_DD and C_e were 8 V and 1.2 pF, respectively. Eqs. (5)–(6) were solved using MATLAB to determine the output impedance at various frequencies. Fig. 3 plots the output impedance versus the operating frequency. By setting the output impedances at corresponding frequencies, the ADS Impedance Matching Tool synthesized the matching network. A three-stage LMN with a bandwidth of 20% was extracted, illustrated in Fig. 4. The simulated drain minimized power dissipation on the transistor. A voltage and current waveforms depicted in Fig. 5 under the optimum operation slightly overlap, resulting in a prototype of class-E PA circuit was realized on a Taconic TLC PCB material with a thickness of 0.787 mm and a dielectric constant of 3.2. A photograph of the prototype is shown in Fig. 6. The output power was measured using an Agilent 85665EC spectrum analyzer with a maximum measurement output of 30 dBm. An attenuator of − 39.67 dB was added at the end of the circuit. The PAE and output power versus the frequency and input power were plotted in Fig. 7. The lumped components are available only in discrete values provided by the manufacturers, which is the main reason for the differences between the simulated and measured results. A summary of the experimental results compared with other articles on high efficiency proving this method’s advantages is shown in Table 1.

This work presented a practical method to implement a high-efficiency broadband class-E PA using a MOSFET transistor with nonlinear output capacitance. The extraction of the shunt capacitance and the fundamental output impedance via numerical analysis was the principal step in this article. The peak PAE of 82% and the average PAE of 80% with the output power level of 34 dBm at frequencies from 140 MHz to 170 MHz were experimental results that validated the accuracy of this method. Two of the most outstanding advantages of the class-E power amplifier with shunt capacitance as high efficiency and simple topology were shown in this work.