**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**