Answer to Question #199850 in Electrical Engineering for LUCKY

Question #199850

Design an op-amp based integrator with a time constant of 

1 second, if the capacitor is 1µF. If a constant voltage 

of -1V is applied at t=0 seconds, how long will it take to an output of +10V (assume initial capacitor voltage 

= -10V). Sketch the input and output waveforms.


1
Expert's answer
2021-06-01T03:45:47-0400

Av=V0Vin(jw)=1jwCR=1wCR=VVA_v=\frac{V_0}{V_{in}}(jw)=\frac{-1}{|jwCR|}=\frac{-1}{wCR}=\frac{-V}{V}

Confirming the capacitance ability

1104C100103=1    C=1nF\frac{-1}{10^4*C*100*10^3}=-1 \implies C=1nF



For Vin(t)= 2*sin 10000t

V0(t)=1RC0tVin(τ)dτ=100000tsin(1000τ)dτ=2[cos1000t1]V_0(t)=\frac{-1}{RC}\int_0^t V_{in}(\tau) d\tau=-10000\int_0^t sin(1000\tau) d\tau=2[cos 1000t-1]


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