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Question 3.3: HIGHER ORDER MODE OF A COAXIAL LINE Consider a RG-401U semir...

HIGHER ORDER MODE OF A COAXIAL LINE

Consider a RG-401U semirigid coaxial cable, with inner and outer conductor diameters of 0.0645 in. and 0.215 in., and a Teflon dielectric with \ \epsilon_{r}= 2.2. What is the highest usable frequency before the \ TE_{11}waveguide mode starts to propagate?

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We have

\ \frac{b}{a}=\frac{2b}{2a}=\frac{0.215}{0.0645}=3.33.

From Figure 3.16 this value of b/a gives \ k_{c}a= 0.45[the approximate result is\ k_{c}a=2/ \left(1+b/a \right)=0.462]. Thus,\ k_{c}=549.4m^{-1},and the cutoff frequency of the \ TE_{11} mode is

\ f_{c}=\frac{ck_{c}}{2\pi \sqrt{\epsilon _{r}} } =17.7GHz.

In practice, a 5% safety margin is usually recommended, so

\ f_{\max }=\left(0.95\right) \left(17.7GHz\right) =16.8GHz.

 

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