Some Hams are familiar with the Q-line as it is seen as the shorter pair of pipes on the ever popular J-Pole ("J") antenna. Some recognize it as an 'impedance inverter' for a handy and 'high Q' method of impedance transformation, and some folks realize that it does all these things and more! So how does this simple device do all of these things?
First lets look at a quarter wavelength long wire or other conductor from a perspective of 'voltage distribution'. We can use the venerable dipole antenna as our model for this purpose. A dipole has two poles. In the typical half wavelength dipole these are two quarter wavelength wires. At the center of this dipole we have maximum current, and virtually no voltage. At the tip ends of these poles, one quarter wavelength away, we have maximum voltage and minimal current. Another way of saying the same thing is that we have a maximum impedance at the tips, and a minimum impedance at the center (or the opposite end of this quarter-wavelength pole).
In a "J" antenna, we use this to match the very high impedance encountered at the bottom end of the antennas half-wavelength radiating element {Hint: the impedance is the same - one halfwavelength away}. In a quarter waavelength coaxial cavity filter, this becomes a handy 'notch filter' to assist with radio duplexing etc. There are in fact so many useful ways in which we can utilize thus very handy Q-line impedance inverter, it becomes pretty difficult to list them all! Lets look at that notch filter though. If you get the wisdom and method of how to build and use one of these widgets, you will I'm sure go on to build and use this construct for all kinds of Ham Radio projects.
Often coaxial filters are built using sheet metal formed into the shape of a can or tube. Sometimes copper pipe is used to form the outside coaxial sleeve of the cavity. I have even seen a 55 gallon oil drum used in this way so as to fabricate a 6 Meter wavelength band cavity filter. For our purposes, we will use a common piece of coax cable!
Lets try this for the 2 Meter wavelength band; and we will use nice common cheap coax! I recommend for this first coaxial cavity notch filter that you build; use Belden RG58A/U cable. This is nice Mil Spec cable of known specifications. If you try to use some other weird cable you found laying around - its not my fault when you realize you have been chasing your tail with this project!
RG58A/U cable has a 'velocity factor' of signal propagation of 66%. This means that 34% of one quarter wavelength (of a signal as propagated through space) gets removed. With other kinds of cable this velocity factor, and consequential length, would be different. Hence, the chasing your tail effect!
To calculate the length for a quarter wavelength of such cable we start thusly. Divide 300 by the desired frequency; lets use 147.210 MHz. So, 300/147.210 = 2.037905 Meters. Multiply this number by 39.37 so as to convert to inches. 2.037905 X 39.37 = 80.232319 inches. So one wavelength at this frequency is a bit over 80 inches! Divide this by 4 to find one quarter-wavelength. 80.232319/4 = 20.058079 inches. Lastly, and very importantly, multiply this by the velocity factor of the cable. 20.058079 X .66 = 13.238332 inches. Put an appropriate connector on one end of this cable, screw that into a coaxial 'T-fitting', at the antenna input to your receiver and you have a quarter wavelength notch filter. If we did this same calculation at 147.810 MHz, we would have a handy filter to reduce 'desensitization' of our duplex receiver for this pair of repeater frequencies.
You can build such a filter in less than 30 minutes, and you will be amazed at the results. Try it!