Transfer function analysis for model topology determination of on-chip transmission lines

A novel method to determine the topology of the equivalent circuit model of on-chip transmission line by transfer function analysis is presented. The fitting capacities of the equivalent circuits with different number of 1-π segments are clearly evaluated through the calculation of their transfer functions. A broadband macromodel is proposed by rational approximation of measured network parameters. By comparing the poles and zeros of the transfer functions of the equivalent circuit model and macromodel, a reliable and efficient criteria for choosing model topology for transmission lines at various frequencies is developed. It is found that the number of poles and zeros provided by certain topology is a constant, while complex poles are responsible for the broadband fitting capacity of the model. Measured S-parameters of a coplanar waveguide (CPW) transmission line up to 50 GHz have verified that the proposed method is quite helpful in finding the simplest topology with sufficient accuracy. This transfer function analysis based method for model topology determination is also applicable to other passive devices, such as inductors and transformers.