Finding the Values of L and C for a Zero-Current-Switching Inverter

The ZCS resonant converter of Figure 7.27a delivers a maximum power of $P_L = 400 mW$ at $V_o = 4 V$ . The supply voltage is $V_s = 12 V$ . The maximum operating frequency is $f_{max }= 50 kHz$ . Determine the values of L and C. Assume that the intervals $t_1$ and $t_3$ are very small, and $x = 1.5$ .

Question

Finding the Values of L and C for a Zero-Current-Switching Inverter

The ZCS resonant converter of Figure 7.27a delivers a maximum power of [latex]P_L = 400 mW[/latex] at [latex]V_o = 4 V[/latex]. The supply voltage is [latex]V_s = 12 V[/latex]. The maximum operating frequency is [latex]f_{max }= 50 kHz[/latex]. Determine the values of L and C. Assume that the intervals [latex]t_1[/latex] and [latex]t_3[/latex] are very small, and [latex]x = 1.5[/latex].

Accepted Answer

[latex]V_s = 12 V, f = f_{max} = 50 kHz[/latex], and [latex]T = 1/50 kHz = 20 µs. P_L = V_oI_o[/latex] or [latex]400 mW = 4I_o[/latex], which gives [latex]I_o = 100 mA[/latex]. The maximum frequency occurs when [latex]t_5 = 0[/latex]. Because [latex]t_1 = t_3 = t_5 = 0, t_2 + t_4 = T[/latex]. Substituting [latex]t_4 = 2V_sC/I_m[/latex] and using [latex]x = (V_s/I_o)\sqrt{C/L}[/latex] gives

[latex]\pi \sqrt{LC}+\frac{2V_sC}{I_o}=T[/latex] or [latex]\frac{\pi V_s}{xI_o}C+\frac{2V_s}{I_o}C=T[/latex]

which gives [latex]C = 0.0407 µF[/latex]. Thus, [latex]L = (V_s/xI_o)^2C = 260.52 H[/latex].

Question 7.11: Finding the Values of L and C for a Zero-Current-Switching I...

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