electrical engineering

Question

A dc-dc buck converter has the following design parameters: 𝑉𝑖𝑛 = 120 V, 𝑅 = 25 Ω, 𝑃𝑜𝑢𝑡 = 150 W, 𝑓𝑠𝑤 = 200 kHz, and L = 0.4 mH. What should the load value be changed to in order for the converter to operate at the boundary of continuous conduction mode (CCM) and discontinuous conduction mode (DCM)?

Answer 1

Given Parameters:

1. Input voltage: Vin=120 V
2. Output power: Pout=150 W
3. Load resistance (initial): R=25 Ω
4. Switching frequency: fsw=200 kHz=2×105 Hz
5. Inductance: L=0.4 mH=0.4×10−3 H

Find output voltage:

1. Use the power and resistance:

P_out​ = V_out²​​ / R ⇒ V_out​ = sqrt{Pout​⋅R} ​ = sqrt{150×25} ​= sqrt{3750} ​≈ 61.24V

1. Calculate duty cycle D: 

V_out​ = D⋅V_in​ ⇒D = V_out​​ / V_in = 61.24 / 120 ​≈ 0.51

1. L_crit​ = ​(1−D)⋅R​ / 2fsw

To find the boundary resistance R_crit for the given L:

R_crit ​= 2L*fsw / (1−D) ​​= 2*0.4×10⁻³*2×10⁵ / (1−0.51) ​= 160​ / 0.49 ≈ 326.53Ω

Therefore, to operate at the boundary of CCM and DCM, the load resistance should be changed to approximately   326.53Ω.