Cuthbert Nyack
Setting the sum of the voltages around the circuit equal to zero and after some slight rearranging, we get:-
Introducing the following substitutions
and taking the Laplace Transform gives the Laplace Transform Q(s) of q(t) as:-
The 3 parameters R, L and C are thus condensed into 2, wn and z. To determine R, L or C from these parameters at least one of R, L or C must be known.
If R is known then L = R/(2zwn)
and C = 2z/(Rwn).

If L is known then R = 2Lzwn and
C = 1/(Lwn2).
The Laplace Transform of the Capacitor, Resistor and Inductor Voltages are shown below:-
With V(t) equal to a step function of magnitude V, V(s) = V/s, we get the following expressions for the voltages across the components in the circuit.

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COPYRIGHT © 1996 Cuthbert A. Nyack.