# Characteristic Impedance of a coaxial cable

• EEuser
In summary, the conversation discusses the derivation of an equation for the maximum electric field within a dielectric, as well as its application in determining the characteristic impedance of a coaxial cable for maximum power handling. The trade-off between breakdown voltage and power is also mentioned. For part b, there is a question on using equations to determine the characteristic impedance of minimum attenuation, with a suggestion to assume a fixed output load and take into account cable and reflection losses.
EEuser
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.
• For part a, I have derived an equation for the maximum electric field within the dielectric. I came up with:
with r being the radius and the electric field decreasing with increased radius r. I am not sure how this equation is to help in determining the characteristic impedance of a coaxial cable for max power handling, nor am I sure how considering the "trade-off between breakdown voltage and power" will help.
• 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:
Any assistance would be greatly appreciated.

EEuser said:
• For part a, I have derived an equation for the maximum electric field within the dielectric. I came up with: View attachment 253635with r being the radius and the electric field decreasing with increased radius r. I am not sure how this equation is to help in determining the characteristic impedance of a coaxial cable for max power handling, nor am I sure how considering the "trade-off between breakdown voltage and power" will help.
You should use only maximal field. As soon as dielectric break in maximal field (i.e. on surface of inner conductor) it turns into conductor and breakdown propagates to outer sheaf.
EEuser said:
• 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:View attachment 253636
Any assistance would be greatly appreciated.
You should assume a fixed output load. Attenuation will be product of cable loss and reflection loss.

## 1. What is characteristic impedance of a coaxial cable?

The characteristic impedance of a coaxial cable is a measure of its ability to transfer electrical signals with minimal distortion. It is a constant value that is determined by the physical dimensions and materials of the cable.

## 2. Why is characteristic impedance important in coaxial cables?

Characteristic impedance is important because it determines how effectively a coaxial cable can transmit signals without much loss or interference. If the impedance of the cable does not match the impedance of the connected devices, it can result in signal reflection and reduced signal quality.

## 3. How is characteristic impedance calculated for a coaxial cable?

The characteristic impedance of a coaxial cable can be calculated using the formula Zc = (L/ C)^0.5, where L is the inductance per unit length and C is the capacitance per unit length. These values can be determined from the physical dimensions and materials of the cable.

## 4. What is the typical characteristic impedance of a coaxial cable?

The most commonly used characteristic impedance for coaxial cables is 50 ohms, although values of 75 ohms and 93 ohms are also used in certain applications.

## 5. How does the characteristic impedance of a coaxial cable affect its performance?

The characteristic impedance of a coaxial cable affects its performance by determining how well it can transmit signals without distortion or loss. A mismatch between the cable's impedance and the devices it is connected to can result in signal reflection, reduced signal strength, and poor overall performance.

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