(a) Design of commutating capacitor : The magnitude of the commutating capacitor is dependent on the following circuit parameters:

(i) Maximum load current to be commutated

(ii) Turn-off time of SCR, $t_{off}$

(iii) The battery voltage $E_{\mathrm{dc}}$

The turn-off time $t_{\text { off }}$ of SCR $T_{1}$ is known from the manufacturer's data sheet. The capacitor voltage changes from $-E_{d c}$ to 0 during turn-off time, $t_{\text { off }}$ Assuming load current, $I_{L},$ remains constant during turn-off time, $t_{\text { off }}$

$$C E_{\mathrm{dc}}=I_{L} t_{\mathrm{off}}$$

$$\therefore C=\frac{I_{L} t_{\mathrm{off}}}{E_{\mathrm{dc}}}$$

(b) Designing of commutating inductor : The design of the inductor L is actually dependent on two contradictory criteria as follows:

(i) The acceptable maximum capacitor current, $I_{C}$ when thyristor $T_{1}$ is fired.

(ii) The time interval $\left(t_{2}-t_{1}\right)$ during which capacitor voltage must reset to correct polarity for commutating SCR $T_{1}$ .

Since the capacitor current $\left(I_{C}\right)$ is an oscillatory current through SCR $T_{1}, L,D \ and \ C$ when SCR $T_{1}$ is triggered. Therefore the peak value of current ${I}_{C}$ is given by the expression,

$$I_{C_{(\mathrm{peak})}}=\frac{E_{\mathrm{dc}}}{W_{r} L}-----(1)$$

where $W_{r}= \frac{1}{\sqrt{L C}}$ $rad/sec.-----(2)$

Substitute Eq. (2) in Eqn (1). We get

$$I_{C_{(\mathrm{peak})}}=E_{\mathrm{dc}} \sqrt{\frac{C}{L}}-----(3)$$

Also, periodic time during oscillation $T_{r}$ is given by

$$T_{r}=\frac{2 \pi}{W_{r}}=2\left(t_{1}-t_{2}\right)$$

Now, let $I_{L(\max )}$ be the maximum current through SCR $T_{1}$ . From Eq.(3)

$$E_{\mathrm{dc}} \sqrt{\frac{C}{L}} \leq I_{L_{(\max )}}$$

OR

$$L \geq C .\left(\frac{E_{\mathrm{dc}}}{I_{L_{(\max )}}}\right)^{2}$$