# Waveguides and Plumbing

Quote of the Day

History is a trick we play on the dead.

- Voltaire

Figure 1: Examples of Copper Pipe.

I never thought much about what he said until I read this article about the history of 50 coaxial cables being used in Radio Frequency (RF) applications. Here is the quote that got me thinking about copper pipes and waveguides.

The most common story is that 50-ohm high power coaxial lines were first made using standard sizes of copper pipe, such as 3/4 inch for the inner conductor and 2 inch for the outer conductor. While this may explain why certain transmission lines are 52 or 53 ohms versus 50 ohms, I don't think this is the entire story of how 50 ohms became the most common standard.

I thought I would do a quick calculation here and check this statement out. I grabbed the formula for the characteristic impedance of a coaxial structure from the Wikipedia and performed the calculation shown in Figure 2.

Figure 2: Characteristic Impedance of a 3/4 inch Copper Pipe inside of a 2 in Copper Pipe.

It does look like the computed characteristic impedance of this coaxial configuration of common plumbing pipe is about 50 ?.

For another reference that discusses using common copper plumbing pipe for a waveguide, see this article. Figure 3 shows the inner and outer diameters of common copper pipe sizes (source). Type M pipe is the most commonly seen.

Figure 3: Inside and Outside Diameters of Common Copper Pipes.

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