Chapter 2

Q. 2.SP.28

Find v_L for the full-wave rectifier circuit of Fig. 2-43(a), treating the transformer and diodes as ideal.    Assume R_S = 0.



Verified Solution

The two voltages labeled v_2 in Fig. 2-43(a) are identical in magnitude and phase. The ideal transformer and the voltage source v_S can therefore be replaced with two identical voltage sources, as in Fig. 2-43(b), without altering the electrical performance of the balance of the network.    When v_S/n is positive, D_1 is forward-biased and conducts but D_2 is reverse-biased and blocks.    Conversely, when v_S/n is negative, D_2 conducts and D_1 blocks.    In short,
i_{D1} = \begin{cases} \frac{v_S/n}{R_L}        \frac{v_s}{n} \geq 0 \\   0\quad\quad\frac{v_s}{n} \lt 0 \end{cases} \quad   \text{and}   \quad i_{D2} = \begin{cases}   0\quad\quad\frac{v_s}{n} \gt 0 \\ -\frac{v_S/n}{R_L}   \frac{v_s}{n} \leq 0 \end{cases}

By KCL,                i_L = i_{D1} + i_{D2} = \frac{|v_s/n|}{R_L}

and so    v_L = R_L i_L = |v_s/n|.