A modified Branin model of lossless transmission lines

Nowadays, absolute majority of circuit simulation programs contains classic Branin model of lossless transmission lines. However, characterizing the four delays (t - T_D) incorporated in the model still causes difficulties due to incompatibility with most algorithms for solving algebraic-differential equations. In the paper, a mathematical substitution of the delay is suggested which smoothly cooperates with the circuit algorithms. Moreover, results of the simulation do not contain spurious oscillations that are practically irremovable when an LC model of the line is used. As the model is suitable for RF circuits, its properties are demonstrated by means of an analysis of a microwave oscillator.