The region between a pair of parallel perfectly conducting planes of infinite extent in the y and z direction is partially filled with a dielectric as shown in figure. A 30 GHz TE 10 wave is incident on the air dielectric interface as shown. Find VSWR at the interface.

Question

The region between a pair of parallel perfectly conducting planes of infinite extent in the y and z direction is partially filled with a dielectric as shown in figure. A 30 GHz [latex]TE _{10}[/latex] wave is incident on the air dielectric interface as shown. Find VSWR at the interface.

Accepted Answer

Given, a = 5 cm

[latex]TE _{10}, f=30 GHz[/latex]

If medium – 1

[latex]\begin{aligned}&f_{c}=\frac{V_{0}}{2 a}=3 GHz \&\eta_{1}=\frac{\eta_{0}}{\left(1-\frac{f_{c}}{f} ight)^{2}}=\frac{120 \pi}{\left(1-\left(\frac{3}{30} ight)^{2} ight)^{1 / 2}}=378.89 \Omega\end{aligned}[/latex]

Medium [latex]-2, \mu=\mu_{0}, E=4 E_{0}[/latex]

[latex]\begin{aligned}&V_{P}=\frac{E}{\sqrt{E_{r}}}=\frac{3 imes 10^{8}}{\sqrt{4}}=1.5 imes 10^{8} m / sec \&f_{c}=\frac{V_{0}}{2 a}=1.5 GHz \&\eta_{0}=\sqrt{\frac{\mu}{E}}=\frac{120 \pi}{\sqrt{4}}=60 \pi \&\eta_{2}=\frac{\eta_{0}}{\sqrt{1-\left(\frac{f_{c}}{f} ight)^{2}}}=188.73 \Omega,\end{aligned}[/latex]

Reflection coeff. [latex]\Gamma=\frac{\eta_{2}-\eta_{1}}{\eta_{2}+\eta_{1}}=\frac{188.73-378.89}{188.73+378 . .89}[/latex]

|Γ| = 0.335

[latex]\operatorname{VSWR}=\frac{1+|\Gamma|}{1-|\Gamma|}=2[/latex]

Question 4.5.5: The region between a pair of parallel perfectly conducting p...

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