Finding the Values of L’s and C’s for a Class E Rectifier

The class E rectifier of Figure 7.23a supplies a load power of $P_L = 400 mW$ at $V_o = 4 V$ . The peak supply voltage is $V_m = 10 V$ . The supply frequency is f = 250 kHz. The peak-to-peak ripple on the dc output voltage is $ΔV_o = 40 mV$ . (a) Determine the values of L, C, and $C_f$ ; and (b) the rms and dc currents of L and C. (c) Use PSpice to plot the output voltage $v_o$ and the inductor current $i_L$ .

Question

Finding the Values of L’s and C’s for a Class E Rectifier

The class E rectifier of Figure 7.23a supplies a load power of [latex]P_L = 400 mW[/latex] at [latex]V_o = 4 V[/latex]. The peak supply voltage is [latex]V_m = 10 V[/latex]. The supply frequency is f = 250 kHz. The peak-to-peak ripple on the dc output voltage is [latex]ΔV_o = 40 mV[/latex]. (a) Determine the values of L, C, and [latex]C_f[/latex]; and (b) the rms and dc currents of L and C. (c) Use PSpice to plot the output voltage [latex]v_o[/latex] and the inductor current [latex]i_L[/latex].

Accepted Answer

[latex]V_m = 10 V, V_o = 4 V, ΔV_o = 40 mV[/latex] and [latex]f = 250 kHz[/latex].

a. Choose a suitable value of C. Let [latex]C = 10 nF[/latex]. Let the resonant frequency be [latex]f_o = f = 250 kHz. 250 kHz = f_o =1/[2\pi \sqrt{L imes 10 nF} ][/latex], which gives [latex]L = 40.5 µH[/latex]. [latex]P_L = V_o^ 2 /R[/latex] or [latex]400 mW = 4^2/R[/latex], which gives [latex]R = 40 Ω. I_o = V_o/R = 4/40 = 100 mA[/latex]. The value of capacitance [latex]C_f[/latex] is given by

[latex]C_f=\frac{I_0}{2f \Delta V_0}=\frac{100 mA}{2 imes 250 kHz imes 40 mV}=5 \mu F[/latex]

b. [latex]I_m = V_m/R = 10/40 = 250 mA[/latex]. The rms inductor current [latex]I_L[/latex] is

[latex]I_L(rms)=\sqrt{100^2+\frac{250^2}{2} }=203.1 mA[/latex]

[latex]I_{L(dc)} = 100 mA[/latex]

The rms current of the capacitor C is

[latex]I_{c(rms)}=\frac{250}{\sqrt{2} }=176.78 mA[/latex]

[latex]I_{C(dc)} = 0[/latex]

c. [latex]T = 1/f = 1/250 kHz = 4 µs[/latex]. The circuit for PSpice simulation is shown in Figure 7.24. The list of the circuit file is as follows:

Question 7.10: Finding the Values of L’s and C’s for a Class E Rectifier Th...

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