969 First-Order Circuit Step Response In Chapter 7, we found that the step response of a first-order circuit can be written as where f 0

9–69 First-Order Circuit Step Response In Chapter 7, we found that the step response of a first-order circuit can be written as

where f ð0Þ is the initial value, f ð∞Þ is the final value and TC is the time constant. Show that the corresponding transform has the form

and relate the time-domain parameters f ð0Þ, f ð4Þ, and TC to the s-domain parameters K, γ, and α.

f(t) = f(00) + [f(0) -f(00)] e-1/Tc