Part 11

The s-domain, transfer functions and plots

FD returns answers in s, which is where transfer functions come from. The t2s and s2t shortcuts, and all four plot types.

Last updated 2026-09-11

FD

Choose FD and the answers come back as functions of s, initial conditions included.

Circuit Description

e,1,0,vs
r,1,2,1'k
c,2,0,1'u

voltage drop across c

\[v_{c} = \dfrac{1000\,vs}{s + 1000}\]

Leave the source symbolic and the answer is the transfer function: divide by vs and you have H(s) = 1000/(s + 1000), a first-order low pass with its pole at −1000. Nothing is labelled "transfer function" because nothing needs to be — it is the answer with the input left as a symbol.

Poles and zeros are then yours to take: factor the denominator, or hand the expression to SymPy, which is what the answer already is.

t2s and s2t

Two shortcuts convert an expression between the domains:

t2s(10*exp(-1000*t))
s2t(1000/(s + 1000))

Curly brackets are shorthand for the same thing inside a value, so a source may be written in t and used in an FD run.

The four plots

The Plot card offers four, and which ones are available depends on the analysis:

Plot	Analysis	What it wants
Plot a function of time	TR	an answer name, and a time range
Bode plot of a variable	FD	an answer name, and a frequency range
Bode plot of transfer function H(s)	—	H(s) typed directly
Plot a variable against another	DC	two answer names, and a sweep range

The third needs no circuit at all: type 1000/(s+1000) and get its magnitude and phase. Useful when the transfer function came from somewhere else, or when you are checking a hand derivation.

The fourth is a DC sweep — one answer plotted against another as a value varies, which is how a load line or a maximum-power curve is drawn. Give it the two names and a range.

Resonance

There is no resonance tool. Resonance is the frequency that clears the reactance, so it is a Solve problem: take the impedance answer, set its imaginary part to zero, and solve for ω. The same works for half-power points, which makes bandwidth and Q two more lines of algebra rather than a feature.