Finding the Currents and Voltage in the Boost Regulator A boost regulator in Figure 5.18a has an input voltage of Vs = 5 V. The average output voltage Va = 15 V and the average load current Ia = 0.5 A. The switching frequency is 25 kHz. If L = 150 µH and C = 220 µF, determine (a) the duty cycle k,

Question

Finding the Currents and Voltage in the Boost Regulator

A boost regulator in Figure 5.18a has an input voltage of [latex]V_s = 5 V[/latex]. The average output voltage [latex]V_a = 15 V[/latex] and the average load current [latex]I_a = 0.5 A[/latex]. The switching frequency is 25 kHz. If [latex]L = 150 µH[/latex] and [latex]C = 220 µF[/latex], determine (a) the duty cycle k, (b) the ripple current of inductor ΔI, (c) the peak current of inductor [latex]I_2[/latex], (d) the ripple voltage of filter capacitor [latex]ΔV_c[/latex], and (e) the critical values of L and C.

Accepted Answer

[latex]V_s = 5 V, V_a = 15 V, f = 25 kHz, L = 150 H, and C = 220 µF[/latex].

a. From Eq. (5.70),

[latex]V_a=V_s\frac{T}{t_2}=\frac{V_s}{1-k}[/latex] (5.70)

[latex]15 = 5/(1 - k)[/latex] or [latex]k = 2/3 = 0.6667 = 66.67\%[/latex].

b. From Eq. (5.75),

[latex]\Delta I=\frac{V_s(V_a -V_s)}{fLV_a}[/latex] (5.75)

[latex]\Delta I=\frac{5 imes (15-5)}{25,000 imes 150 imes 10^{-6} imes 15}=0.89 A[/latex]

c. From Eq. (5.73),

[latex]I_s=\frac{I_a}{1 -k}[/latex] (5.73)

[latex]I_s = 0.5/(1 - 0.667)= 1.5 A[/latex] and peak inductor current,

[latex]I_2=I_s + \frac{\Delta I}{2}=1.5+\frac{0.89}{2} =1.945 A[/latex]

d. From Eq. (5.79),

[latex]\Delta V_c=\frac{I_ak}{fC}[/latex] (5.79)

[latex]\Delta V_c=\frac{0.5 imes 0.6667}{25,000 imes 220 imes 10^{-6}}=60 61 mV[/latex]

e. [latex]R=\frac{V_a}{I_a}=\frac{15}{0.5} =30 \Omega [/latex]

From Eq. (5.80), we get [latex]L_c=\frac{(1 -k)kR}{2f}=\frac{(1 -0.6667) imes 0.6667 imes 30}{2 imes 25 imes 10^3}=133 \mu H[/latex]

From Eq. (5.81), we get [latex]C_c=\frac{k}{2fR}=\frac{0.6667}{2 imes 25 imes 10^3 imes 30}= 0.44 \mu F[/latex]

Question 5.6: Finding the Currents and Voltage in the Boost Regulator A bo...

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