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**New for September 2008!** Information on this topic was a request by a Microwaves101 reader Max way back in ought-seven... about time we did something with it!

Coax power handling is a complicated subject, but it can be broken down into two phenomena. High peak power can cause failures due to arcing, while high average power can cause failure due to heat.

### Peak power handling

Power handling of air coax is a topic that is related to atmospheric breakdown.

Once breakdown occurs, a short circuit is provided across the coax, and Hell breaks loose.

Arcing is caused when the electric field E exceeds a critical value which we will denote E_{d} for electric field at discharge. In air, the critical field is about 1,000,000 volts/meter, in PTFE it is raised to about 100,000,000. These numbers are approximate, there's no sense trying to be exact in calculating breakdown, just be sure you avoid it by an order of magnitude or more and you'll have little to worry about.

The electric field of a coax varied as a function of position along the radius (denoted "" in the radial coordinate system). You'd have to use calculus to derive this, but we just looked it up in Pozar's *Microwave Engineering.*

Here, b is D/2 and a is d/2, the radii of the outer and inner conductors. The peak E-field obviously occurs right at the surface of the center conductor. If this isn't obvious to you, consider becoming a program manager!

Rearranging the equation for the maximum peak voltage,

The peak power you can put into a coax under well-matched conditions (low VSWR) is calculated from the peak voltage it can withstand:

The equation for characteristic impedance of coax can be found somewhere on this web site, we'll save you from searching for it:

Recall that 0 is the impedance of free space, or 377 ohms. Plugging it all together, we can can come up with the equation for peak power handling as a function of coax geometry.

That's the final equation for maximum peak power handling of coax, ready for us to do some analysis. Remember that this result is only true for a matched load. If you accidentally broke a connection to a high-power transmitter, you'd see a very high VSWR, in that case the peak voltage could double. If you need to consider this type of mishap, you want to further de-rate your power handling by 6 dB.

Now let's look at some coax examples... how about the air dielectric 50-ohm connectors? The breakdown strength of air 3,300,000 volts/meter according to Wikipedia, but that is at "dry air" at standard temperature and pressure, between spherical electrodes. Let's use 1,000,000 volts/meter.

Connector species (outer diameter) | Inner diameter | Voltage at breakdown | Max power (low VSWR load) | Maximum power (high VSWR load) |

3.5 mm | 1.52 mm | 634 V | 4023 W | 1005 W |

2.92 mm | 1.27 mm | 529 V | 2098 W | 524 W |

2.4 mm | 1.04 mm | 435 V | 1886 W | 471 W |

1.85 mm | 0.80 mm | 335 V | 1118 W | 279 W |

1 mm | 0.43 mm | 181 V | 325 W | 81 W |

How about PTFE-filled coax? The breakdown field strength of PTFE is about 10,000,000 volts per meter! So an "049" cable (0.049 inches "D", 0.015 inches "d") can withstand 2260 volts and pass almost 50,000 watts peak. This seems to good to be true, doesn't it? It is. The problem is that with voltage breakdown, the limitation of the weakest link in the chain is what you need to focus on. Your semi-rigid cable might be able to pass thousands of watts, but as soon as that signal crosses a path where the PTFE dielectric fill is interrupted by air, it will spark. At the end of the cable, where the connector is soldered on, there is surely going to be a gap in the dielectric. You need to revise the calculation for air dielectric, in which case you'll see 256 volts is the maximum voltage, 358 watts is the maximum power into a good load, and 89 watts is the maximum into an unmatched load. Note that at this interface the coax presents 71 ohms impedance.

Before we move on to average power handling of coax, let's look at power handing as a function of line impedance for air coax, which is part of the "coax compromise" that led to the fifty ohm standard. If you allow the center diameter freedom to move away from 50 ohms, you'll see that maximum peak power handling occurs at ~30 ohms.

By the way, if anyone wants a copy the spreadsheet that generated this curve, just ask. Eventually we will add peak power handling to our coax spreadsheet that you can grab in download area.

### Average power handling

Coming soon!

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