# How Much Power Can a Coaxial Cable Transmit Before Breakdown?

• SiberianS;pth
In summary, the conversation discusses a coaxial transmission line with an inner cylindrical conductor of radius 1mm and a cylindrical outer conductor chosen to make the characteristic impedance 75 ohms. The space between the conductors is filled with a gas that can withstand a maximum electric field of 10^5 Vm^-1 without dielectric breakdown. The task is to estimate the maximum mean radio-frequency power that can be transmitted along this line into a matching load. The equations for the impedance of a coaxial cable and the attempt at a solution are also provided. However, the calculated power is about 8 times too big, which may be due to using the peak voltage for the breakdown voltage instead of the RMS voltage.
SiberianS;pth

## Homework Statement

A coaxial transmission line consists of an inner cylindrical conductor of radius 1mm and a cylindrical outer conductor chosen to make the characteristic impedance 75 ohms. The space between the conductors is filled with a gas that can stand a maximum field of 10^5 Vm^-1 without dielectric breakdown. Estimate the maximum mean radio-frequency power that can be transmitted along this line into a matching load.

## Homework Equations

The impedance of a co axial cable is Z=Zo*ln(b/a)/n*2*pi where b is outer radius, a inner radius and n is sqrt(permittivity).

## The Attempt at a Solution

So for the empty coaxial cable I had Z=Zo*ln(b/a)/2*pi

I rearranged this to work out the value of the outer radius which I got as 3.49mm.

I used the distance between inner and outer radius and the max electric field to work out potential difference. I then tried to the use the standard P=Vi formula to work out power but my answer is about 8 times too big. I assumed all the power is transmitted due to impedance matching.

SiberianS;pth said:

## Homework Statement

A coaxial transmission line consists of an inner cylindrical conductor of radius 1mm and a cylindrical outer conductor chosen to make the characteristic impedance 75 ohms. The space between the conductors is filled with a gas that can stand a maximum field of 10^5 Vm^-1 without dielectric breakdown. Estimate the maximum mean radio-frequency power that can be transmitted along this line into a matching load.

## Homework Equations

The impedance of a co axial cable is Z=Zo*ln(b/a)/n*2*pi where b is outer radius, a inner radius and n is sqrt(permittivity).

## The Attempt at a Solution

So for the empty coaxial cable I had Z=Zo*ln(b/a)/2*pi

I rearranged this to work out the value of the outer radius which I got as 3.49mm.

I used the distance between inner and outer radius and the max electric field to work out potential difference. I then tried to the use the standard P=Vi formula to work out power but my answer is about 8 times too big. I assumed all the power is transmitted due to impedance matching.

Welcome to the PF.

The breakdown voltage is based on the peak voltage, while the power is based on the RMS voltage. Still, that should only give you a difference of √2, not 8. Can you post your work so we can check the numbers?

## What is radio frequency power?

Radio frequency power refers to the amount of energy in the form of electromagnetic waves that is transmitted through a radio frequency signal. It is measured in watts and is commonly used in communication systems, broadcasting, and other applications.

## How is radio frequency power measured?

Radio frequency power is typically measured using specialized equipment such as a power meter, which detects and measures the strength of the electromagnetic field produced by the radio frequency signal. This measurement is then converted into watts to determine the amount of power being transmitted.

## What factors affect radio frequency power?

The strength of a radio frequency signal is affected by a variety of factors, including the distance between the transmitter and receiver, the type and quality of antennas used, and any obstacles or interference in the signal's path. Additionally, the frequency at which the signal is transmitted can also impact the power level.

## What are the potential health effects of radio frequency power?

There is ongoing research on the potential health effects of exposure to radio frequency power, as it is a form of non-ionizing radiation. Some studies have suggested a possible link between long-term exposure to high levels of radio frequency radiation and certain health conditions, but more research is needed to fully understand any potential risks.

## How is radio frequency power used in everyday life?

Radio frequency power is used in a wide range of everyday devices and technologies, such as cell phones, Wi-Fi networks, and Bluetooth devices. It is also used in television and radio broadcasting, radar systems, and medical equipment. Without radio frequency power, many of these technologies would not be able to function properly.

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