Calculate the cut off wavelength for a TE2,1 wave propagating through a coaxial cable that have the following parametric values: permitivity of copper 1.2 , outer conductor inside radius of 2.2 MM and inner conductor diameter of 1.4 mm
The cut off wavelength for a TE2,1 wave in a coaxial cable is given by:
$$\lambda_c = \frac{2\pi}{\sqrt{\epsilon_r}} \frac{a}{\sqrt{1-(b/a)^2}}$$
where $\epsilon_r$ is the relative permittivity of the medium between the conductors, $a$ is the radius of the outer conductor, and $b$ is the radius of the inner conductor.
In this case, we have:
- $\epsilon_r$ = 1.2 (permittivity of copper)
- $a$ = 2.2 mm (outer conductor inside radius)
- $b$ = 0.7 mm (inner conductor radius = diameter/2)
Plugging in these values, we get:
$$\lambda_c = \frac{2\pi}{\sqrt{1.2}} \frac{2.2}{\sqrt{1-(0.7/2.2)^2}} \approx \boxed{11.8\text{ mm}}$$