Modeling Delays of Microwave Transistors and Transmission Lines by the 2nd Order Bessel Function

Abstract

At present, most of simulation programs can characterize gate delays of microwave transistors. However, the delay is mostly approximated by means of first-order differential equations. In the paper, a more accurate way is suggested which is based on an appropriate second-order differential equation. Concerning the transmission line delay, majority of the simulation programs use both Branin (for lossless lines) and LCRG (for lossy lines) models. However, the first causes extreme simulation times, and the second causes well-known spurious oscillations in the simulation results. In the paper, an unusual way for modeling the transmission line delay is defined, which is also based on the second-order Bessel function. The proposed model does not create the spurious oscillations and the simulation times are comparable with those obtained with the classical models. Properties of the implementation of the second-order Bessel function are demonstrated by analyses of both digital and analog microwave circuits.

Keywords

• Bessel function
• ordinary differential equations
• group delay
• MESFET
• gate delay
• transmission line