<math>V_{P1} = V_1(z=0) = -V_{P2} = -V_2(z=0) = V_o^+ e^{j\beta L} \left[ 1 + \Gamma_{L}^o e^{-2j\beta L} \right] </math>
The above results can clearly be observed on the voltage graphs of the previous part, which exhibit a standing wave pattern. Note that in this case, Γ<sub>L</sub><sup>e</sup> = (50-70)/(50+70) = -0.167 and Γ<sub>L</sub><sup>o</sup> = (50-30)/(50+30) = 0.25. As you already saw in Tutorial Lesson 1, the exponent βL = 2πL/λ<sub>g</sub> = 2π√(ε<sub>eff</sub>)(f.L)/c determines the frequency variation of the voltage.
For Z-parameter calculations, we open-circuit Ports 2 and 4 (Z<sub>L</sub> = ∞). In this case, Γ<sub>L</sub><sup>e</sup> = Γ<sub>L</sub><sup>o</sup> = 1, and the voltages at Ports 1 and 3 now reduce to:
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where Z<sub>S</sub> = (Z<sub>0e</sub> + Z<sub>0o</sub>)/2 and Z<sub>D</sub> = (Z<sub>0e</sub> - Z<sub>0o</sub>)/2.
== Verifying Your Simulation Results ==
The equations derived earlier for the probe voltages (VP1 and VP2) exhibit a standing wave pattern, which can clearly be observed in your node voltage graphs for both cases of even and odd mode excitations.
The above results can clearly be observed on the voltage graphs of the previous part, which exhibit a standing wave pattern. Note that in this case, Γ<sub>L</sub><sup>e</sup> = (50-70)/(50+70) = -0.167 and Γ<sub>L</sub><sup>o</sup> = (50-30)/(50+30) = 0.25. As you already saw in Tutorial Lesson 1, the exponent βL = 2πL/λ<sub>g</sub> = 2π√(ε<sub>eff</sub>)(f.L)/c determines the frequency variation of the voltage.
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