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By virtue of the negative electric parameter concept,i.e.negative lumped resistance,inductance,conductance and capacitance(N-RLGC),the lumped equivalent models of transmission line systems,including the circuit model,two-portπ-network and T-network,are given.We start from the N-segment-ladder-like equivalent networks composed distributed parameters,and achieve the input impedance in the form of a continued fraction. Utilizing the continued fraction theory,the expressions of input impedance are obtained under three kinds of extreme cases,i.e.the load impedances are equal to zero,infinity and characteristic impedance,respectively.When the number of segment N is limited to infinity,they are transformed to lumped elements.Comparison between the distributed model and lumped model of transmission lines,the expression of tanh yd,which is the key term in the transmission line equations,are obtained by RLGC,furthermore,according to input admittance,admittance matrix and ABCD matrix of transmission lines,the lumped equivalent circuit models,π-networks and T-networks have been given.The models are verified in the frequency and time domain,respectively,showing that the models are accurate and efficient.
By virtue of the negative electric parameter concept, ienegative lumped resistance, inductance, conductance and capacitance (N-RLGC), the lumped equivalent models of transmission line systems, including the circuit model, two-portπ-network and T-network, are given.We start from the N-segment-ladder-like equivalent networks composed distributed parameters, and achieve the input impedance in the form of a continued fraction. Utilizing the continued fraction theory, the expressions of input impedance are obtained under three kinds of extreme cases, iethe load impedances are equal to zero, infinity and characteristic impedance, respectively. When the number of segments N is limited to infinity, they are transformed to lumped elements. Comparison between the distributed model and lumped model of transmission lines, the expression of tanh yd, which is the key term in the transmission line equations, are obtained by RLGC, furthermore, according to input admittance, admittance matrix and ABCD matrix of transmis sion lines, the lumped equivalent circuit models, π-networks and T-networks have been given. The models are verified in the frequency and time domain, respectively, showing that the models are accurate and efficient.