Any circuit with a single input source and zero initial conditions and any one of its internal or output signals can be written as:
where
is a rational function of called a network function. It transforms the input into some response.
Poles
Poles of that come from are called natural poles. From , they’re called forced poles. If we take the inverse transform of , when we roughly get:
where we have exponential terms corresponding to the natural and forced response.
A circuit is stable if its natural response dies down to zero over time (in the steady state). This is important because it means it’s fundamentally controllable. If a circuit continued to oscillate forever, an unstable circuit, it wouldn’t be very useful to us.