With the continuous progress of semiconductor technology,integrated circuits are gradually developing in the direction of high integration,high performance,and low power consumption.Signal integrity problems caused by interconnect structures in high-speed systems have become increasingly prominent,and serious signal integrity problems will bring hidden dangers to the normal operation of the system.In order to shorten the product design cycle and reduce design costs,engineers usually verify whether the interconnection network meets the system requirements through electromagnetic simulation or circuit simulation.When the system structure is large and complex,circuit simulation is more efficient than electromagnetic simulation.The key to circuit simulation is to model the structure in the system,and the modeling method will directly affect the accuracy of the simulation results.As a common interconnection structure in high-speed systems,transmission lines currently have a variety of modeling methods.This paper mainly studies the resonant cavity model of the transmission line and the coupling of resonant modes between different transmission lines based on the transmission line telegraph equation.The main research contents and results are as follows:Based on the single-ended transmission line telegraph equation,the impedance matrix of the single-ended transmission line is derived according to the general solution of the telegraph equation and the definition of impedance,and the elements in the impedance matrix are expanded and summed by Laurent series to obtain the sum of the infinite series expressed in the resonance mode The impedance expression is completely consistent with the expression of the one-dimensional resonator transmission line model obtained by simplifying the two-dimensional rectangular plane resonator model,which provides a theoretical basis for the one-dimensional resonator transmission line model based on the telegraph equation.For the parallel coupled transmission line resonant cavity model,based on the coupled transmission line telegraph equation,the impedance matrix expression of the multi-signal parallel coupled transmission line is derived through impedance matrix and matrix function methods.This expression is completely consistent with the expression of the parallel coupled resonant cavity transmission line model,which confirms the correctness of the assumption of the electric and magnetic field coupling in the parallel coupled resonant cavity transmission line model based on the telegraph equation.In addition,in the hypothesis of the parallel coupled resonant cavity transmission line model,only the coupling amount of the electric field and the magnetic field of the corresponding modes between different transmission lines is given,and it is not given whether there is coupling between the different modes of different transmission lines.The derivation of the telegraph equation of the parallel coupled transmission line shows that the coupling of the resonance mode only exists between the corresponding modes of different transmission lines,that is,the nth mode of the transmission line is only coupled with the nth mode of other transmission lines,and there is no correspondence.There is no coupling between the modes.The amount of capacitive coupling between modes does not change with the number of modes,and is always the total mutual capacitance between the transmission lines.The amount of inductive coupling varies with the number of modes,but the inductive coupling coefficient does not vary with the number of modes,and is always the inductive coupling coefficient between transmission lines.Aiming at the problem of transmission line loss,through the expression of transmission line unit length attenuation α_n,it is proved that parallel conductance can be used to replace the series resistance that characterizes conductor loss.The resonant cavity model of the lossy transmission line is derived based on the multi-conductor transmission line model in parallel with capacitance,inductance,and conductance combined with the telegraph equation.The conductor loss and dielectric loss of the transmission line are represented by the parallel conductance in the resonance mode,and it is compared with the multi-conductor transmission line model.The comparison of the simulation results verifies the accuracy of the model from the perspective of impedance parameters. |