A mathematical technique that simplifies the study of the transient behaviour of circuits by using the Laplace transform, which results in a transformation into the s-domain. This technique avoids the formulation of differential equations in the time domain in favour of much simpler algebraic manipulations in the s-domain. The function F(s) given by the Laplace transform can be expressed as the ratio of two factored polynomials given by:

where s = σ + jω, the complex frequency or complex operator.

The roots of the denominator polynomial, –b₁, –b₂,…, –b_n, are called the poles of F(s) and at these values of s, F(s) tends to infinity. The roots of the numerator polynomial, –a₁, –a₂,…, –a_n, are called the zeros of F(s) and at these values of s, F(s) becomes zero. It is often convenient to visualize the poles and zeros of F(s) as points on the complex plane called the s-plane.