Q1. Determine an input-output differential equation model for the circuit shown below. Hence, determine the unit Impulse response of the circuit. Solution Applying KCl: x(t) - y(t) / R1 + C1 d (x(t) - y(t)) / dt = y(t) / R2 + C2 d y(t) / dt I am using x and y instead of x(t) and y(t) x/R1 -y/R1 + C1 dx/dt - C1dy/dt = y/R2 + C2 dy/dt y/R2 + C2 dy/dt + y/R1 + C1dy/dt = x/R1 + C1 dx/dt y / (R1R2/ R1+R2) + dy/dt (C1+C2) = x/R1 + C1 dx/dt 800 y + 25 dy/dt = 1000x + 5 dx/dt 160y + 5 dy/dt = 200x + dx/dt.