Design of Choke Inductor in Class-E ZVS Power Amplifier Agasthya Ayachit, Dalvir K. Saini, and Alberto Reatti Marian K. Kazimierczuk Department of Information Engineering (DINFO) Department of Electrical Engineering University of Florence Wright State University Via Santa Marta 3 1-50139 Florence 3640 Colonel Glenn Hwy., Dayton, OH, 45435, USA [email protected] {ayachit.2, saini. 1 1, marian.kazimierczuk}@wright.edu Abstract-This paper presents the following for a Class-E current through the choke inductors are non-sinusoidal. The zero-voltage switching (ZVS) power amplifier: (a) design of the losses in the windings as well as in the magnetic core as choke inductor and (b) theoretical estimation of power losses in caused by the dc, fundamental, and higher order harmonics. the core and a solid round winding. The expressions required Therefore, Fourier analysis is performed and the magnitude of to design the core using the Area-Product (Ap) method are provided. The equations for the dc resistance, ac resistance the harmonic components are evaluated. at high frequencies, and dc and ac power losses are provided The objectives of this paper are as follows: for the solid round winding. A Class-E ZVS power amplifier with practical specifications is considered. A core with air gap 1) To develop a theoretical framework design the choke is selected since the choke inductor carries a dc current in inductance for a Class-E zero-voltage switching power addition to the ac component. The gapped core power loss amplifier. density and power loss are estimated using Steinmetz empirical 2) To present the design equations necessary to calculate equation. Simulation results showing the transient analysis and the dc and ac resistances and dc and ac power losses for Fourier analysis are given. It is shown that, for the given design, the winding power loss due to the fundamental component the choke inductor made up of solid round winding. is dominant and that due to higher order harmonics can be 3) To provide the necessary expressions required to design neglected. In addition, it is also proven that the power loss caused the magnetic gapped core using Area-Product method. by the dc current component is higher than that by the ac current 4) To evaluate the fundamental and higher order harmonic component, which can be neglected. components of the choke inductor current and determine I. INTRODUCTION their power losses. 5) To verify the presented analysis through circuit simula­ Magnetic components are integral parts in many electronic tions. circuits [1] - [6]. An ideal choke must reject any ac component and conduct only the dc component. However, in practical applications, the choke inductor conducts a fraction of ac II. DESIGN EQUATIONS current in addition to the dc component and the ac component can reach high-frequenies and its waveform is usually not A. Design of Class-E ZVS Power Amplifier sinusoidal. Thus, the design procedure must consider both Fig. 1 shows the circuit of the Class-E zero-voltage switch­ these components and predict the nature of losses in the ing (ZVS) power amplifier. The amplifier is supplied by a dc core and the winding. This paper presents a comprehensive input voltage source , Lf is the choke inductance, S is the procedure to design the choke inductors used in Class-E ZVS VI power MOSFET, C1 is the voltage-shaping shunt capacitance, power amplifiers. Class-E ZVS power amplifiers belong to which includes the output capacitance of the MOSFET, Land a class of highly efficient electronic circuits. Therefore, the C form the resonant circuit inductor and capacitor, while component design must be optimized to yield the maximum R is the load resistance. efficiency. The expression for the load resistance is The magnetic core for the choke inductor is designed using the Area-Product Ap method. This is a widely adopted method . =_8_Vl to magnetic components in pulse-width modulated converters R 7T2 4 (1) as well as ac resonant inductors [2]. Since a majority of the + Po' current is dc, air gap is essential to avoid core saturation. where Po is the output power. The choke inductor can be In addition, the winding power loss depends on the winding designed using geometry. In this paper, a solid round winding is used and its dc and ac winding power loss are estimated to determine the dominant power loss. Ty pically, in switching circuits, the (2) 978-1-5090-3474-1/16/$31.00 ©20l6 IEEE 5621 ILt - t 21,tm hIm ................ Iml wt ;"�Lt L C ------+ ht o wt VI R � C1 Fig. 2. Waveforms of the ac component of the choke inductor current and its fundamental harmonic component. Fig. I. Circuit of the Class-E power amplifier. and the amplitude of the third harmonic component is where is is the switching frequency of the MOSFET. The dc current flowing through the choke is equal to the input current ShJm 1ml Im 3= 97f2 = 9 . (10) and is expressed as The even harmonics (n = 2,4, 6, ... ) are zero since the PI Po 1LJ= h = -= -, (3) triangular waveform is assumed to be symmetric about its VI f/VI dc value. By expanding the series, it can be noted that the where T/ is the overall efficiency of the Class-E amplifier. The amplitudes of the harmonics for n :;0. 3, i.e., 1m3, 1m5, ... choke inductor carries an ac component in addition to the dc are much lower than the amplitude of the fundamental 1ml . current. The amplitude of the ac current through the choke is Therefore, the effect of the higher order harmonics of the given by choke inductor current on the winding and core power can VI be neglected. J = (4) h m 4isLJ' B. Design of Core Using Area-Product Method Therefore, the peak value of the choke inductor current is The area-product method relates the geometrical core pa­ Po VI rameters described by the core manufacturers with the inductor hJ(max) = hJ+ hJ m= + (5) magnetic and electric parameters The maximum energy VI 4isLJ' [3]. f/ stored in the choke inductor due to both dc and ac currents is The choke inductor must be designed to withstand the peak current hJ(max) . The winding carrying the choke inductor (11 ) current must satisfy the current density requirement as well as The window utilization factor and the saturation flux exhibit low ac power losses. Ku density are assumed a priori. The current density of the The current through the choke inductor can be approximated Bsat conductor is selected based on the peak current requirement by a symmetrical triangular wave of magnitude h m as shown J and is discussed in the following section. The core area­ in Fig. 2. The Fourier series expansion of the triangular wave product is given by is 4 ( _1 ) (n-I)/2 WLJ -'------'----,,----- (nw t) Ap= WaAc= (12) n 2 sin s . (6) KuJmBsat' where Wa is the core window area and Ac is the core The fundamental component of the triangular waveform IS cross-sectional area, both of which are mentioned in the core 1 obtained by substituting n= in (6) to get manufacturer datasheet. Further, the window area is estimated from (12) as (7) (13) where Ws is the angular switching frequency and the amplitude of the fundamental of the ac component through the choke From the selected core geometry, the number of turns N inductor is is determined using a specified window area Wa, window - h m - S J I mi 7f2 . (8) utilization factor Ku, and solid round wire current density as Jm as In (8), hJm is the peak value of the triangular waveform of WaKuJm the choke inductor current. By substituting n= 3 in (6), the N= . (14) 2 third harmonic component is hJ(max) However, for the gapped core, to achieve the desired induc­ (9) tance and strength of magnetization, the number of turns is 5622 higher than that calculated in (14). Thus, for a core with air gap with a predetermined inductance L f, the number of turns is [3] N= (15) where Ac is the cross-sectional area of the core, flo is the permeability of free-space, fLrc is the relative permeability of the core material, N is the number of turns, Ie is the mean magnetic path length, 19 is the assumed length of the air gap. Thus, the actual number of turns is WaKu max { , l:L (I (16) Fig. 3. Solid round conductor showing a reduced effective area available for N= + . 2Aw(sol) fLoAc 9 fLr�)}c current conduction at high frequencies due to skin-effect. Alternatively, low iron powder cores with a low relative permeability fLr can be utilized. However, in both of the dc current density. Assuming a copper conductor, the skin cases the core permeability is reduced, while the number of depth as a function of frequency is [3], turns required to achieve a certain inductance is increased. This affects the winding design. The dc current through the p 66.2 ' (21) choke as well as the ac current are functions of the load vITo resistance of the amplifier. In several applications, for example, where 1.7 10-8 [l·m is the resistivity of the conductor, Class-E ZVS inverter in wireless power charging systems, p= 24 x is the operating frequency, is the relative permeability the load resistance is a function of the distance between fo ILr of the conductor 1 for metals), and is the absolute the transmission coil and the receiver coil. In such operating (fLr= flo permeability of free space. Let 1 be the current density of conditions, the dc and ac current may exceed a critical value m the winding.