Hi HG,
the large ampltude of the impulse response is correct. (has the original question been edited?) This has to be the case since the step response is the time integral of the impulse response. The step response = 1 for large t, Since the width of the impulse response is tiny, its amplitude must be large. Just eyeballing the impulse response 3x10^9 * .4x10^(-9) = 1.2, which works.
impulse response:
let a = 2.274e-10 let impulse response = (1/a) e^(-t/a) % very large amplitude
Laplace transform to check:
Int{0,inf} (1/a) e^(-t/a)*e^(-st) dt = (1/a) * 1/(s+1/a) = 1/(a*s +1) % ok
For the step response, integration in time gives an extra factor of 1/s in the s domain.
let step response = Int{0,t} (1/a) e^(-tau/a) dtau = 1 - e^(-t/a)
Laplace transform to check:
Int{0,inf} (1-e^(-t/a))*e^(-st) dt = 1/s - 1/(s+1/a) = (1/a)/(s*(s+1/a))
= 1/(s*(a*s +1)) % ok
