For the rectifier circuit shown in the figure, the expression for the average value of output voltage = __________, provided 'α' is the firing angle.

Single phase full wave rectifier

Case 1: From α < ωt < π + α

T1 and T2 conduct. 

So, Vo = V_s

Case 2: From π + α < ωt < 2π + α 

T₃ and T₄ conduct.

So, Vo = -Vs

\(V_{o(avg)}={1\over \pi}\int_{\alpha}^{\pi+\alpha}V_m \space sin\omega t \space d\omega t\)

\(V_{o(avg)}={V_m\over \pi}(\mathrm{cos\space \omega t})_{\pi +\alpha}^{\alpha}\)

\(V_{o(avg)}={V_m\over \pi}(\mathrm{cos \alpha-cos(\pi+\alpha)})\)

\(V_{o(avg)}=\frac{2 v_{m}}{\pi} \cos \alpha\)