Question 19.SP.7: A simple switching circuit for producing a sawtooth wave is ......
A simple switching circuit for producing a sawtooth wave is shown (Fig. 19-12a). The switch S is closed and then opened very quickly so that the capacitor is not fully charged but only charged to the linear portion of its charging exponential curve (Fig. 19-12b). (The linear portion is the straightest portion at the start of the charge cycle.) The switch is opened and closed at specific intervals to produce a sawtooth voltage wave across the capacitor. Find the magnitude of the v_{C} curve when the switching time interval is one-fifth the time constant of the circuit. What is the time interval?
Write the voltage formula for charging the capacitor.
v_C=V\left(1-e^{-t / R C}\right) (19-17)
If t=\frac{1}{5} R C, then
e^{-t / R C}=e^{-(1 / 5) R C / R C}=e^{-1 / 5}=e^{-0.2}=0.819Then v_C=20(1-0.819)=20(0.181)=3.62\ V
\text { Time interval } t=\frac{1}{5} R C=\frac{\left(100 \times 10^3\right)\left(1 \times 10^{-6}\right)}{5}=0.02\ s