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GATE 2016 EE – Question 54

Power Electronics · Single-phase and three-phase voltage and current source inverters, sinusoidal pulse width modulation · 2 marks · Numerical answer

The switches T1 and T2 in Figure (a) are switched in a complementary fashion with sinusoidal pulse width modulation technique. The modulating voltage $v_m(t) = 0.8 \sin(200\pi t)$ V and the triangular carrier voltage ($v_c$) are as shown in Figure (b). The carrier frequency is 5 kHz. The peak value of the 100 Hz component of the load current ($i_L$), in ampere, is ________.

(a) A half-bridge with two 250 V DC sources in series ($V_{dc}/2 = 250$ V each) and switches T1 and T2. The load is a $12\ \Omega$ resistor in series with an inductor of reactance $16\ \Omega$ at 100 Hz, connected to the midpoint. (b) A sinusoidal modulating signal of peak 0.8 against a triangular carrier of peak 1.

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Correct answer: 9.9 to 10.1

Explanation

The modulation index is $m = 0.8$. The peak of the fundamental output voltage is $m \times \frac{V_{dc}}{2} = 0.8 \times 250 = 200$ V. The load impedance at 100 Hz is $\sqrt{12^2 + 16^2} = 20\ \Omega$, so the peak current is $\frac{200}{20} = 10$ A.