Find the impulse response of the circuit given below if vg i

Find the impulse response of the circuit given below if v_g is the input signal and v_0 is the output signal. Assume that the voltage source has the waveform shown in the following figure. Use the convolution integral to find v_0. Sketch v_0 for 0 less than or equal to t less than or equal to 2s. Does v_0 have the same waveform as v_g?

Solution

i) xc=1/(0.25s)

apply nodal analysis

(vo-vg)/5+vo*0.25s+vo/20=0

vo(1/5+0.25s+1/20)=vg/5

vo[(4+5s+1)/20]=vg/5

vo/vg=4/(5s+5)

vo=4/(5s+5)

laplace transform of impulse response=1