A 440Mhz UHF Cavity Design and Simulation

I was inspired over the past couple of days to investigate the design and cost of building a Shawyer cavity that resonates in the low end of the UHF band, which ranges from 300Mhz to 3GHz [Wikipedia].  At first, I chose a resonate frequency where the cone could be cut from the remains of a 3’x8′ sheet of copper I have and the cavity, shown below resonates at 600Mhz.

Shawyer_UWH_truncated_cone_rolled_out_on_3by8_foot_sheet
A render of a 600Mhz cavity unrolled onto a 3 foot by 8 foot sheet of copper.
Shawyer_UHF_600Mhz_60cmH_83cmDL_50cmDS_Q_of_104000_eigenmode_solver_1MK_tetrahedral_JDM
A simulation of the cavity in CST Microwave Studio showing the TE0,1,1 mode at 600Mhz with a Q of 104,000!
  • The cavity size is 91.4cm high, 83.4cm for the large diameter end and 50cm for the small diameter end.
  • The cone rolled out just fits inside of a 3′ by 8′ sheet of standard mill dimension sheet of copper.
  • As expected, the larger cavity produced a theoretical maximum Q of 104,000!!

The reason for using a lower frequency is that it means less expensive, tunable HAM radio sources and a higher Q.  In other words, a cavity with a fixed resonate frequency and without a troublesome tuning mechanism means the source needs to be tunable.  (And with an ultra-high Q comes an ultra-narrow bandwidth)

However, 600Mhz is outside the HAM radio spectrum and because I want cheap and easy, modding a UHF rig to transmit at that frequency is too difficult, not to mention the amplifier.

So I flipped the problem around, and simulated a cavity that resonated at 440Mhz right in the middle of the UHF HAM radio spectrum allowable in Canada.  My actual process was to take the 600Mhz cavity size and increase it by 1.3636 which is decreased the frequency to 440Mhz (because frequency has an inverse relationship with size).  The simulation came out dead on the first run:

Eigenmode JDM 1.2M tretrahedral simulation showing the resonate frequency at 440Mhz
Eigenmode JDM 1.2M tetrahedral simulation showing the resonate frequency at 440Mhz
  • A Q of 121,000! (A nice 20% bump from a 600Mhz cavity)
  • The size is 81.8cm in height, 113.7 cm for the large diameter and 68.2 cm for the small diameter
  • The simulation was done with a eigenmode JDM solver with 1.2M (million) tetrahedrals using adaptive meshing.  (My AMD eight core 8350 just tore through the simulation which still took hours!)

Then I took the measurements from the simulation and figured out how much copper I would need, shown below:

A 440Mhz cavity rolled out on a 3 by 10 foot sheet of copper and half of a 3 by 8 foot sheet.
A 440Mhz cavity rolled out on a 3 by 10 foot sheet of copper and half of a 3 by 8 foot sheet.

Copper (from ThyssenKrupp) comes in standard sizes, 3’by8′ and 3’by10′ in 12oz or 16oz gauges.  What is shown is *half* of the cone rolled out on top of one 3’by10′ sheet with half of a 3’by8′ sheet next to it.  With a few extra pieces soldered from the unused edges, the entire shape could be cut with tin snips.  To build the entire cone, two of the shown pieces would need to be cut and then soldered together, then formed into the cone.

A 3′ by 10′ copper sheet at 12oz gauge, at today’s prices costs $290 and with the 3′ by 8′ 12oz sheet I already have, I would need two 10′ ones, bringing the cost up to $600.  This would not include the top or bottom sections which I would either make from a 3′ by 8′ sheet of 32oz copper I have or from aluminum sheeting (not ideal only because it cannot be soldered to the copper – the conductivity difference shouldn’t matter because it carries hardly any current).

Of course, with 12oz copper, the cavity will likely need an external support structure which I haven’t figured out yet.

Building the cavity would be the first step and with my SignalHound spectrum analyzer good to 4Ghz, I could figure out if the Q is in the right place and high enough.

Then I would need to purchase the Ham radio equipment, two pieces of it pretty exotic, a 1Kw linear amplifier and a isolator that can handle 1kW returned load.

I found a commercial linear amplifier that can be had for $5KUS (pretty good!) from Lunar-Link International. You can also buy a kit and make one yourself starting at $1275US from W6PQL, however, all the connectors, housing and everything else could easily add another grand and I run the risk of messing something up.  However, I could modify it by adding a 1KW isolator on the output which would be nice.

I found some good information on isolators here and even a commercial one that can handle 400Watts here for $1700US.

The next step is to add a power and measurement probe to the simulation and then do a high-count tetrahedral transient solver simulation.  With that result in hand, the next step would be to build the cavity and test it.  If the Q was high enough and stable enough (didn’t move because of a flexing cavity), it would then be time to source the HAM equipment and test it for movement – hoohah!