Lumped Elements versus Distributed Parameters

• Masses, springs, dashpots, inductors, capacitors, and resistors are examples of so-called lumped elements

• Perhaps the simplest distributed element is the continuous ideal delay line

• Because it carries a continuum of independent amplitudes, the order (number of state variables) is infinity for a continuous delay line of any length!

• However, we typically work with sampled, bandlimited systems $\Rightarrow$ delay lines have a finite number of state variables (one for each delay element)

• Networks of lumped elements yield finite-order state-space models

• Even one distributed element jumps the order to infinity (until it is bandlimited and sampled)