A single phase full converter delivers power to a resistive load R. For an AC source voltage of V_s, the average output voltage V_o is given by (where α is firing angle):

1ϕ full converter with resistive load

Case 1: During +ve half cycle (α to π) 

T₁ and T₂ are forward-biased.

Vo = Vs

Case 2: During -ve half cycle (π+α to 2π) 

T₃ and T₄ are forward-biased.

Vo = -V_s

The waveform is given below:

The average output voltage is given by:

\(V_{o(avg)}={1\over 2π}({\int_{α}^{π}V_s\space sin\omega t\space d\omega t}+{\int_{π +α}^{2π}-V_s\space sin\omega t\space d\omega t})\)

\(V_{o(avg)}={V_s\over 2\pi}(cos\alpha-cos\pi+cos2\pi+cos(\pi+\alpha))\)

\(V_{o(avg)}={V_s\times 2\over 2\pi}(1+cos\alpha)\)

\(V_{o(avg)}={V_s\over \pi}(1+cos\alpha)\)

Here, V_s is the RMS value.

The average output voltage in terms of the maximum value is:

\(V_{o(avg)}={\sqrt{2}V_s\over \pi}(1+cos\alpha)\)