## 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 $R_S = 0$.

## Step-by-Step

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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    $v_L = R_L i_L = |v_s/n|$.

Question: 2.2

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