A 100 m section of an air-filled rectangular waveguide operating in the TE10mode has a cross-sectional dimension of 1.071 cm x 0.5 cm. Two pulsed carriers of 21 GHz and 28 GHz are simultaneously launched at one end of the waveguide section. What is the time delay difference between the two pulses a

Question

A 100 m section of an air-filled rectangular waveguide operating in the [latex]TE _{10}[/latex] mode has a cross-sectional dimension of 1.071 cm x 0.5 cm. Two pulsed carriers of 21 GHz and 28 GHz are simultaneously launched at one end of the waveguide section. What is the time delay difference between the two pulses at the other end of the waveguide?

Accepted Answer

Time delay [latex]=T=\frac{\bar{\beta}}{\omega} z[/latex]

[latex]f_{c}=\frac{V_{0}}{2 a}=14 GHz[/latex]

[latex]\begin{aligned}&\bar{\beta}=\beta \sqrt{1-\left(\frac{f_{c}}{f} ight)^{2}}=2 \pi \sqrt{\mu E} \sqrt{f^{2}-f_{C}^{2}} \& ext { for } f=f_{1}=21 GHz \&\bar{\beta}=2 \pi \sqrt{\mu \varepsilon} \sqrt{\left[(21)^{2}-(14)^{2} ight] imes 10^{18}} \&=2 \pi \sqrt{\mu \varepsilon} 15.65 imes 10^{9} \&T_{1}=\frac{\bar{\beta}}{\omega} imes 100=2 \pi \sqrt{\mu \varepsilon} imes \frac{13.65 imes 10^{11}}{2 \pi imes 21 imes 10^{9}} \&=0.745 \sqrt{\mu \varepsilon} imes 100\end{aligned}[/latex]

for [latex]f=f_{2}=28 GHz =[/latex]

[latex]\begin{aligned}&2 \pi \sqrt{\mu E} \sqrt{\left[(28)^{2}-(14)^{2} ight] imes 10^{18}} \&\bar{\beta}_{2}=2 \pi \sqrt{\mu E} 24.2 imes 10^{9} \&\quad- \&T=-100=0.866 \sqrt{F} imes 100\end{aligned}[/latex]

Time delay difference,

[latex]\begin{aligned}T_{d}=& T_{2}-T_{1}=\sqrt{\mu E}(0.866-0.745) imes 100 \&=\frac{1}{\cdot imes 8} imes 0.121 imes 100=0.04 \mu sec\end{aligned}[/latex]

Question 4.5.3: A 100 m section of an air-filled rectangular waveguide opera...

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