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Novel telegrapher equations with radiation parameters for a double step microstrip discontinuity

In this paper, a new analysis for a double step microstrip discontinuity is presented by using a novel kind of telegrapher equations with radiation parameters. The new telegrapher equations are derived from circuit theory while equation coefficients are determined from full-wave numerical Solutions. In comparison with the conventional telegrapher equations, the new equations have two additional terms - dependent series voltage and shunt current sources - which represent local radiation effect from discontinuities of the non-uniform transmission line itself. For a double step discontinuity, it can be regarded as a finite-length non-uniform transmission line and the novel telegrapher equations could be directly implemented. Since the novel telegrapher equations coefficients are determined by dynamic numerical methods and the coefficients are invariant with the line excitation and load, the novel equations are dynamic rather than TEM only. The interested discoveries are that the novel telegrapher equations with radiation parameters for the whole double step structure or a partial double step structure can give us the same results and the novel telegrapher equations have broadband frequency characteristics. For the double step structure used in this paper for the analysis, the S-parameters for a frequency band from 0.5GHz to 10GHz can be well calculated by using only two groups of novel telegrapher equations separately at frequency of 3GHz and 8GHz.