The circuit in Fig. 7.148(a) can be designed as an approximate differentiator or an integr...

The circuit in Fig. 7.148(a) can be designed as an approximate differentiator or an integratordepending on whether the output is taken acrossthe resistor or the capacitor, and also on the timeconstant τ = RC of the circuit and the width T ofthe input pulse in Fig. 7.148(b). The circuit is a differentiator if τ << T, say τ < 0.1 T, or anintegrator if τ >> T, say τ > 10T

(a) What is the minimum pulse width that will allow a differentiator output to appear across the capacitor?

(b) If the output is to be an integrated form of the input, what is the maximum value the pulse width can assume?