Evolution of a method for determination of transfer functions of certain passive electrical networks

Understanding analog circuit design primarily invloves becoming familiar with passive RC and RLC networks. This is due to the fact that circuit essentially involves active elements embedded in a network of parasitics: resistors, inductors and node capacitors. Other important signal processing circuits which are made up of passive elements are attenuators, ADCs and R-2R ladder networks in DACs. Interconnects in present day VLSI can be approximated as passive RLC low pass structures from node to node. A few years ago, I was asked a question Can anyone inuitively guess the location of poles and zeros of a network transfer function? I reframed the problem as obtaining the characteristic equation of a network in a simple and straightforward manner. Once the characteristic equation has been obtained, then the roots of the polynomial will give the poles of the system. Understanding any transfer function or immittance function using the network becomes pretty simple thereafter! Evolution of a method for determination of transfer functions of certain passive electrical networks