# Roll Your Own RF Filters

In the November 2012 issue I wrote about combining FM antennas by way of filters. I received a question from a reader (Danny Wilson) about how to accomplish the same thing using transmission line filters. That can be done of course, and you'll save some money by rolling your own.

To do this we make use of the transformer effect of transmission lines. Over one quarter wavelength, the impedance seen at the near end is opposite of that of the far end. More specifically: if you have an exact quarter-wave length of transmission line with an open circuit on one end, you'll measure a short circuit on the opposite end. Conversely, if you short one end, you'll measure an open circuit on the opposite end. Clearly this is frequency-dependent; I'll show you the calculations shortly.

To do this we make use of the transformer effect of transmission lines. Over one quarter wavelength, the impedance seen at the near end is opposite of that of the far end. More specifically: if you have an exact quarter-wave length of transmission line with an open circuit one on end, you'll measure a short circuit on the opposite end. Conversely, if you short one end, you'll measure an open circuit on the opposite end. Clearly this is frequency-dependent; I'll show you the calculations shortly.

Figure 1.

First we determine the wavelength of the desired frequency.
c/f = λ
c = speed of light
f = frequency
λ = wavelength

Because we want to determine the 1/4λ, and we're working with megahertz and inches, we can simplify our equation to account for the multipliers and dividers and use 2952 for the constant of c. The resulting calculations for 100.3MHz:

2952/f = 2952/100.3 = 29.43"

Multiply the result by the velocity factor of the cable, which you can find online. One possible source is www.nr6ca.org/vf.html. As an example, RG-8 at 100.3MHz has a velocity factor of 0.66.

29.43 x 0.66 = 19.43"

This is the length of the inner conductor, so consider the length of the center pin of whatever connector you plan to use, and include that in the overall length.

- Next page: Notches for AM

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