Modeling And Analysis Of Cascading Transmission Lines Based On Resonant Cavity Theory

With the continuous innovation of the semiconductor industry,high-speed systems are gradually developing in the direction of low power consumption,miniaturization,and high density.At the same time,the clock frequency in high-speed circuits is getting higher and higher,causing the interconnection in the system to become no longer transparent,which will cause a series of signal integrity problems such as reflection,loss,crosstalk,ground bounce and so on.These problems can cause signal distortion and may even cause the system to not work properly.To improve product design efficiency and reduce design costs,engineers need to anticipate and resolve potential signal integrity problems.This requires engineers to use various simulation tools to simulate the system,then find the interconnection network that violates the integrity of the system and redesign before completing the product design.The key of simulation is to build the circuit model of the system,and the quality of the model will directly affect the accuracy of the simulation results.Transmission line is the most common interconnect structure in various electronic systems,and its resonant cavity model is one of the high effective modeling methods.Based on the transmission line resonant cavity theory,this paper studies the resonant cavity modeling method of the transmission line cascade structure with different characteristics.The work content is summarized as follows:First,because the current fast algorithm of the transmission line resonator model cannot be applied to the cascaded transmission line structure,the author proposes a new fast algorithm:the inductance approximation method.The resonant cavity model of the transmission line has infinitely many resonant modes.This method divides all the modes into two parts,one part is the low-order resonant mode that determines the impedance within the bandwidth of the transmission line,and the other part is the higher-order resonant mode with less influence.The low-order mode is retained,and the high-order resonant mode is approximately regarded as linear.By using two sections of inductance correction circuits to de-equivalent higherorder modes,a transmission line resonant cavity model combined with inductance approximation is derived.Compared with other fast algorithms,the inductance approximation method has a simpler solution process for correcting circuit parameters,and can be used to improve the computational efficiency of the resonant cavity model of the cascaded transmission line.The effectiveness of the method is verified by error analysis and simulation in frequency domain.Then,aiming at the cascading problem of transmission lines,in this paper,by deriving the impedance matrix of the overall structure of the two cascading transmission lines,the resonance modes of the cascading structure of transmission lines with different characteristics are solved,and the resonant cavity circuit model of the cascading structure of two transmission lines is established.And by deriving the transfer parameter matrix of the cascade structure of multiple transmission lines,the situation of two transmission lines being cascaded is extended to the case of multiple transmission lines being cascaded.The derivation results of cascading transmission lines show that when transmission lines with unequal characteristic impedance are cascading,the original modes will be coupled with each other to form new resonance modes,and the cascading resonant cavity model contains infinitely many resonance modes.The accuracy of the model is proved by simulations in the frequency and time domains.Finally,the loss problem in the cascading transmission line is analyzed.In the resonant cavity model,the loss terms of the resistance and conductance are combined,and the conductance is used to represent the total loss per unit length.A lossy cascading transmission line resonant cavity model containing only LCG is derived by equating the series resistance,which characterizes conductor losses,into the parallel conductance.