Control of DC-DC converters by PWM

1. Generate triangular waveform of period T as the carrier signal v_cr, and a DC reference signal v_r.
2. Use comparator to compare signals v_r with v_cr so that:

v _r < v_cr   where v_g = high
v _r < v_cr   where v_g = low

Apply v_g as IGBT gate pulse (gives v_ge).

k is also called the modulation index, M

Example-1

For a buck converter, R=1 ohm, V_d = 40 V, V0=5 V, f_s = 4 kHz. Find the duty ratio and “on” time of the switch.

Solution 1
k = V₀ /V_d = 5/40 = 0.125 = 12.5%
T_s = 1/f_s = 0.25 μs = 250 μs
T_on = kT_s = 31.25 μs
T_off = T_s – t_on = 218.75 μs
When the switch is “on”: V_L = V_d - V₀ = 35 V
When the switch is “off”: V_L = -V₀ = - 5 V
I₀ = I_L = V0 / R = 5 A
I_d = k I₀ = 0.625 A

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