Question 20.6: Determine the maximum output voltage for the RL integrator i...
Determine the maximum output voltage for the RL integrator in Figure 20–35 when a single pulse is applied as shown. The rheostat is set so that the total resistance is 50 Ω. Assume the inductor is ideal.
Calculate the time constant.
\tau=\frac{L}{R}=\frac{100 mH }{50 \Omega}=2 msBecause the pulse width is 5 ms, the inductor charges for 2.5\tau. Use the exponential formula derived from Equation 14–8 with V_{i} = 0 and \tau = L/R to calculate the voltage.
v=V_{F}+\left(V_{i}-V_{F}\right) e^{-R t / L} Equation 14–8
v_{o u t(\max )}=V_{F}\left(1-e^{-t / \tau}\right)=25\left(1-e^{-5 ms / 2 ms }\right)= 25\left(1-e^{-2.5}\right)=25(1-0.082)=25(0.918)= 2 3 . 0 V
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