# Power Handling in Waveguide

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Waveguide power handling is subject to both heat (average power) and voltage breakdown (peak power) limitations.

Voltage breakdown in rectangular waveguide at sea-level air pressure can be predicted by the following approximate equation:

Pbr=600,000*a*b*(Lambda/Lambdaguide) (watts) Equation 1

where a and b and in centimeters.

Lambdaguide is explained here. To take a step back further in equation land, Pbr may be written as a function of the breakdown field strength (although we don't have an exact reference for where this came from, except some PowerPoint found on the web by Roy...)

Pbr=6.63E-4*a*b*(Lambda/Lambdaguide)*(Ebr)^2 (watts) Equation 2

where Ebr is in volts/cm, a and b are in centimeters.

In this case you will notice that the Ebr value that corresponds to 600,000 value in Equation 1 is 30,000 volts/cm which represents a 7mm gap at one atmosphere.

If you plug in the dimensions for WR-90, the power handling is in excess of 1 megawatt at band center where lambda/lambdaguide is 0.75. Yikes!

For circular waveguide, the approximate power handling equation becomes:

Pbr=450,000d^2(Lambda/Lambdaguide) (watts)

where d is diameter in centimeters.

These two equations came from page 70 of Gershon Wheeler's excellent book, *Introduction to Microwaves,* circa 1963. Look for Wheeler's book on our book page! Note that his information on the critical field for breakdown probably dated to WWII and more accurate numbers are now available. If knowing the exact power handling of a particular waveguide is important to you, you need to dive into this topic a little more than we have. Be sure to consider altitude effects on Ebr!

Waveguide power handling can be increased by pressurizing, or using certain inert gases which can withstand higher much electric fields, such as freons.