Helical Resonator Design for Filters
One of the most prominent ISM bands (900 MHz) falls squarely in the middle of the region. Thanks to the wireless revolution, there are a plethora of SAW and dielectric filters available for the 840 – 980 MHz band, but that is about it, and they are only rated for relatively low powers (maybe 20 dBm). Helical filters fill that gap nicely, and are a combination of all three formats.
Like cavity filters, the Q of the helical resonators is very high if constructed properly. That is because at the frequencies of operation, the skin thickness is getting very small and most of the current is flowing on the surfaces. Plating the cavity walls and helix with a high conductivity material increases the Q even more that bare of tinned copper.
Sorry, but I do not have equations for the tuning slug’s diameter or how it affects the resonant frequency as it is advanced into the helix. A wag would be that if the outside diameter of the tuning slug is very close to the inside diameter of the helix, then the resonant frequency is modified as if the total height of the helix and shield are shorter than when the tuning slug is fully retracted.
The graphs illustrate how the equations are affected when the diameter of the helix, d, is varied. Notice that the wire diameter, g, increases with frequency so that an adjustment of the helix diameter, d, is needed to keep the wire size and space between the turns reasonable.
Check this out - someone reference this page on Wikipedia!