Calculate i) RMS output voltage at the fundamental frequency ii) Output power P0. iii) The average and peak current of each thyristor. iv) The peak reverse blocking voltage of each thyristor.

Single Phase Half-Bridge Inverter Problem

The given data -

Resistive Load = R = 3 Ω

DC Input Voltage = E_dc = 50 V

To find -

i] RMS output voltage at the fundamental frequency = $E_{1 \ rms}$ = ?

ii] The output power = $ P_o$ = ?

iii] The average current of each thyristor = $ I_{T\ (av)}$ = ?

The peak current of each thyristor = $ I_{T\ (peak)} $ = ?

iv] The peak reverse blocking voltage of each thyristor = $ E_{BR} $ = ?

Formulae -

i] RMS output voltage at the fundamental frequency - $$E_{1 \ rms} = \frac{2E_{dc}}{\sqrt 2 π}$$

ii] The output power - $$ P_o = \frac{E_o^2}{R}$$

Where,

$E_o = RMS\ output\ voltage = \frac {E_{dc}}{2}$

iii] The average and peak current of each thyristor -

$$The\ Average\ Current = I_{T\ (av)} = \frac {E_{dc}}{4R}$$

$$The\ Peak\ Current = I_{T\ (peak)} = \frac{E_{dc}\over 2}{R}$$

iv] The peak reverse blocking voltage of each thyristor - $$ E_{BR} = 2 \times \frac {E_{dc}}{2} = E_{dc}$$

Solution -

i] RMS output voltage at the fundamental frequency:

$$E_{1 \ rms} = \frac{2E_{dc}}{\sqrt 2 π} = \frac{2 \times 50}{\sqrt 2 \times π} = 22.5\ V$$

ii] The output power:

First, calculate

$$E_o = RMS\ output\ voltage = \frac {E_{dc}}{2} = \frac{50}{2} = 25\ V$$

Therefore,

$$ P_o = \frac{E_o^2}{R} = \frac{25^2}{3} = 208.34\ W$$

iii] The average and peak current of each thyristor:

$$The\ Average\ Current = I_{T\ (av)} = \frac {E_{dc}}{4R} = \frac{50}{4 \times 3} = 4.167\ Amp$$

$$The\ Peak\ Current = I_{T\ (peak)} = \frac{E_{dc}\over 2}{R} = \frac{50\over 2}{3} = 8.34\ Amp $$

iv] The peak reverse blocking voltage of each thyristor:

$$ E_{BR} = 2 \times \frac {E_{dc}}{2} = E_{dc} = 50\ V$$

Final Summarization of the above Findings -

i] RMS output voltage at the fundamental frequency = $E_{1 \ rms}$ = 22.5 V

ii] The output power = $ P_o$ = 208.34 W

iii] The average current of each thyristor = $ I_{T\ (av)}$ = 4.167 Amp

The peak current of each thyristor = $ I_{T\ (peak)} $ = 8.34 Amp

iv] The peak reverse blocking voltage of each thyristor = $ E_{BR} $ = 50 V