Causal transmission line model incorporating frequency-dependent linear resistors

An empirical transmission line (TL) model is proposed that incorporates frequency-dependent linear resistors. The use of such resistors allows experimentally observed characteristics of TLs (frequency dependence of dielectric losses, especially) to be better reproduced compared to models built only of ordinary frequency-independent RLCs. All components of the model, including frequency-dependent resistors, have well-defined time-domain responses and therefore the model is causal. The proposed model fits and reproduces the measured characteristics of TLs fabricated using a 65-nm CMOS process well in the frequency range from 0.5 to 330 GHz.