The boost converter of Fig. 6-8 has parameter Vs 20 V, D 0.6, R 12.5 , L 10 H, C 40 F, and the switching frequency is 200 kHz. (a) Determine the output voltage. (b) Determine the average, maximum, and minimum inductor currents. (c) Determine the output voltage ripple. (d) Determine the average current in the diode. Assume ideal components.

Answer:

a) the output voltage is 50 V

b)

- the average inductor current is 10 A

- the maximum inductor current is 13 A

- the maximum inductor current is 7 A

c) the output voltage ripple is 0.006 or 0.6%V₀

d) the average current in the diode under ideal components is 4 A

Explanation:

Given the data in the question;

a) the output voltage

V₀ = V[tex]_s[/tex]/( 1 - D )

given that; V[tex]_s[/tex] = 20 V, D = 0.6

we substitute

V₀ = 20 / ( 1 - 0.6 )

V₀ = 20 / 0.4

V₀ = 50 V

Therefore, the output voltage is 50 V

b)

- the average inductor current

[tex]I_L[/tex] = V[tex]_s[/tex] / ( 1 - D )²R

given that R = 12.5 Ω, V[tex]_s[/tex] = 20 V, D = 0.6

we substitute

[tex]I_L[/tex] = 20 / (( 1 - 0.6 )² × 12.5)

[tex]I_L[/tex] = 20 / (( 0.4)² × 12.5)

[tex]I_L[/tex] = 20 / ( 0.16 × 12.5 )

[tex]I_L[/tex] = 20 / 2

[tex]I_L[/tex] = 10 A

Therefore, the average inductor current is 10 A

- the maximum inductor current

[tex]I_{Lmax[/tex] = [V[tex]_s[/tex] / ( 1 - D )²R] + [ V

given that, R = 12.5 Ω, V[tex]_s[/tex] = 20 V, D = 0.6, L = 10 μH, T = 1/200 kHz = 5 hz

we substitute

[tex]I_{Lmax[/tex] = [20 / (( 1 - 0.6 )² × 12.5)] + [ (20 × 0.6 × 5) / (2 × 10) ]

[tex]I_{Lmax[/tex] = [20 / 2 ] + [ 60 / 20 ]    

[tex]I_{Lmax[/tex] = 10 + 3

[tex]I_{Lmax[/tex] = 13 A

Therefore, the maximum inductor current is 13 A

- The minimum inductor current

[tex]I_{Lmax[/tex] = [V[tex]_s[/tex] / ( 1 - D )²R] - [ V

given that, R = 12.5 Ω, V[tex]_s[/tex] = 20 V, D = 0.6, L = 10 μH, T = 1/200 kHz = 5 hz

we substitute

[tex]I_{Lmin[/tex] = [20 / (( 1 - 0.6 )² × 12.5)] - [ (20 × 0.6 × 5) / (2 × 10) ]

[tex]I_{Lmin[/tex] = [20 / 2 ] -[ 60 / 20 ]    

[tex]I_{Lmin[/tex] = 10 - 3

[tex]I_{Lmin[/tex]  = 7 A

Therefore, the maximum inductor current is 7 A

c)  the output voltage ripple

ΔV₀/V₀ = D/RCf

given that; R = 12.5 Ω, C = 40 μF = 40 × 10⁻⁶ F, D = 0.6, f = 200 Khz = 2 × 10⁵ Hz

we substitute

ΔV₀/V₀ = 0.6 / (12.5 × (40 × 10⁻⁶) × (2 × 10⁵) )

ΔV₀/V₀ = 0.6 / 100

ΔV₀/V₀ = 0.006 or 0.6%V₀

Therefore, the output voltage ripple is 0.006 or 0.6%V₀

d) the average current in the diode under ideal components;

under ideal components; diode current = output current

hence the diode current will be;

[tex]I_D[/tex] = V₀/R

as V₀ = 50 V and R = 12.5 Ω

we substitute

[tex]I_D[/tex] = 50 / 12.5

[tex]I_D[/tex] = 4 A

Therefore, the average current in the diode under ideal components is 4 A

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