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GATE 2015 EE – Question 43

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

The single-phase full-bridge voltage source inverter (VSI), shown in figure, has an output frequency of 50 Hz. It uses unipolar pulse width modulation with switching frequency of 50 kHz and modulation index of 0.7. For $V_{in} = 100$ V DC, $L = 9.55$ mH, $C = 63.66\ \mu$F, and $R = 5\ \Omega$, the amplitude of the fundamental component in the output voltage $V_o$ (in Volt) under steady-state is ________.

A DC source $V_{in}$ feeds a full-bridge VSI, whose output $V_R$ drives an inductor L, then a capacitor C in parallel with the load R, across which $V_o$ is measured.

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Correct answer: 60 to 64

Explanation

The fundamental of the inverter output has an amplitude of $0.7 \times 100 = 70$ V. At 50 Hz, $X_L = 2\pi \times 50 \times 9.55 \times 10^{-3} = 3\ \Omega$ and the capacitor admittance is $\omega C = 0.02$ S. The parallel $R$ and $C$ have the admittance $0.2 + j0.02$, so their impedance is $4.96 - j0.5\ \Omega$ with magnitude 4.985. The total impedance is $4.96 + j2.5$, with magnitude 5.55. The output is $70 \times \frac{4.985}{5.55} = 62.9$ V.