## Q. 7.8

A symmetric astable multivibrator with vertical edges (see in Fig. 7.20) has the following parameters,$\ V_{CC}$ = 15 V,$\ R_{C}$ = 3 kΩ,$\ R_{1} = R_{2} = R$ = 30 kΩ,$\ R_{3}$ = 2 kΩ and silicon transistors with$\ h_{FE}$ = 50 are used.$\ C_{1} = C_{2} = C$= 0.01 μF. Verify whether the ON device is in saturation or not. Find its frequency. ## Verified Solution

Assume$\ Q_{1}$ is OFF and$\ Q_{2}$ is ON and in saturation. If$\ Q_{2}$ is ON and in saturation$\ V_{C2} = V_{CE(sat)}$ = 0.2V,$\ V_{B2} = V_{σ}$ = 0.7 V then$\ D_{2}$ is ON. The collector load is$\ R_{3}||R_{C}$.

$\ R^{′}_{C} = R_{3}||RC = \frac{3 × 2}{5} = 1.2 kΩ I_{C2} = \frac{V_{CC} − V_{CE(sat)}}{R^{′}_{C}}= \frac{15 − 0.2}{1.2 kΩ} = \frac{14.8 V}{1.2 kΩ}$ = 12.3 mA

$\ I_{B2} = \frac{V_{CC} − V_{σ}}{R} = \frac{15 − 0.7}{30 kΩ} = \frac{14.3 V}{30 kΩ}$ = 0.477 mA    $\ I_{B2}(min) = \frac{I_{C2}}{h_{FE(min)}}= \frac{12.33 mA}{50}$ = 0.247 mA

$\ I_{B2} \gg I_{B2}(min)$

Hence,$\ Q_{2}$ is in saturation.
To find,$\ f$ :

For a symmetric astable multivibrator:$\ f = \frac{0.7}{RC} = \frac{0.7}{30 × 10^{3} × 0.01 × 10^{−6}}$ = 2.33 kHz