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Questions On Derivation Of Equations

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DERIVATION OF EQUATIONS The purpose of this section is to find the analytical expressions which relate the S-parameters of an SUS, S _ij and error box, S _ijE, to the whole simulation results, S _ijm. Fig. 3 describes the network flow graph of a typical and all-inclusive simulation involving an SUS, shifted (de-embedded) reference planes and wave ports. According to the wave port characteristic (Appendix), the de-embedded sections are non-reflecting transmission lines with the following known S-parameter matrix:

S_(L_dmbd )=(■(0&e^(-γL_dmb )@e^(-γL_dmb )&0@&)) (1)

In which γ is derived from the wave port 2D cross section calculation and Ldmb is the distance that reference plane is moved. In order to develop the …show more content…

For this purpose, two THRU simulations, as explained in the above method section, are performed with two different lengths (L _dmb1 and L _dmb2). Fig.3B shows the network flow graph of a THRU simulation. In this case, the equations (14) and (18) are simplified with S_11=S_22=0 and S_12=S_21=1 and the analytical expressions for the error box-related S-parameters are derived as functions of the two simulated THRU S-parameters (TT) and S-parameters of the de-embedded part as expressed in (1). The L _dmb1 and L _dmb2 are selected the shortest possible considering the minimum frequency range (more than the maximum wavelength), but their length difference must be in such a way that their

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