Since I started entering M/M contests I have been using Coax Stubs for filters to help separate stations. They have worked just fine and have provided around 30 to 40 db of attenuation of harmonics. I have been curious about a few points of using them though, like:

1. How much attenuation should a stub provide?
2. What kind of bandwidth should a stub cover?
3. How does the cable loss affect attenuation?
4. How much power gets dissapated in the cable? (I didn’t consider this until a stub made out of RG-59 melted down in one contest.)

This ‘document’ was created by using “MathCAD”. “MathCAD” is a program for IBM PC’s and compatibles(and also Unix workstations) that provide the capability to write formulas and then plug in numbers to calculate results, solve equations, and plot results. The original equations for this calculation were from the “MathCAD” electical engineering applications pack.

In this initial example I will attempt to answer the first two questions using a 1/4 wave shorted stub of RG-8 for attenuating the second harmonic of 20 meters that would interfere on 10 meters.

To get the calculations started I have provided the following characteristics of the cable itself:
Impedance
Z.0 = 50W
VelocityFactor
V = .66
Loss
a = 1 db/100′
Length
d = 11.5′
TerminationImpedance
Z.L = 0W

The frequency range I want to plot will cover the lower end of the 10 meter band that could be covered by a 20 meter harmonic.

Now the calculations begin, this is where “Math CAD” really does its job:
Define complex wave number.
b(f)=a+2ipf/Vc

Define impedance as a function of frequency and distance to termination:

Z.trans(freq,len) =

((Z.L + Z.0 tanh(b(freq) len )
Z.line (———————-)
((Z.0 + Z.L tanh(b(freq) len )

loss(f) = 20 log(1 + ((Z(f,d) – Z.0)/(Z(f,d) + Z.0))

This is a plot of the attenuation provided by the stub. You can see that it provides about 32db of attenuation at 28.25Mhz. The bandwidth seems much narrower than I had expected, but I don’t really have anything to measure it that accurately. I have seen about 30db of attenuation in some rather crude tests here so the overall result seems reasonable.
From these results I am considering making 2 sets of stubs, or providing a way to add or remove a few inches between CW and SSB contests since there could beover 10db attenuation difference across the band. Using a better cable would make the attenuation better, but would also make the bandwidth even narrower.

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David Robbins, K1TTT K1TTT@arrl.net