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EEuser

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- Homework Statement
- Why are coaxial cables designed for a 50 ohms characteristic impedance?

(a) Find the characteristic impedance of a coaxial cable for maximum power handling. Hint:

consider the trade-off between breakdown voltage and power. For the breakdown voltage

write an expression for the maximum electric field within the dielectric in terms of V and a,

b where a and b are the radii of the inner conductor and outer conductor, respectively.

(b) Next, determine the characteristic impedance of minimum attenuation. The attenuation constant simplifies to: attenuation constant= R/(2*Z0) (see image 1 below) in the low-loss case with zero dielectric loss. Due to the skin effect the current in the conductor will be confined to flow in a thin cylinder at the periphery of the inner conductor. The width of this thin cylinder is given as (see image 2 below)

- Relevant Equations
- see below for images of equations

Image 1:
Image 2:

I am attempting to learn about transmission lines and am having problems with this homework problem.

I am attempting to learn about transmission lines and am having problems with this homework problem.

- For part a, I have derived an equation for the maximum electric field within the dielectric. I came up with:
- For part b, I understand all equations and their origins, but I am not sure how to use this information to determine the characteristic impedance of minimum attenuation. I know that the typical equation for characteristic impedance is as follows: