Microwave operation from high places requires portable operation for most of us. The most convenient power source is usually the twelve volt battery in the vehicle that gets us there, and modern solid state devices work fine at 12 volts or less. However, most surplus coax relays are designed for operation at 28 volts or higher and don't switch reliably at 12 volts. When available, 12 volt coax relays are exorbitantly priced, so it would be nice if the highervoltage ones could be converted. Since relays are ancient technology, digging through some ancient issues of QST yielded an article^{1} which detailed the calculations necessary to rewind relays for different voltages, which I will summarize here since the back issue is probably no longer available.
There is some ham folklore that says it is only necessary to take some turns off the coil until it works at 12 volts. I'm told it often works for 28 volt relays, but let's go through the numbers and see how well.
The relative force generated by the coil to close a relay is conveniently measured in ampereturns, simply the current through the coil times the number of turns. If we are rewinding a relay, rather than count thousands of turns we can simply fill the bobbin with wire and assume that the volume of wire is constant. Using this assumption and using standard US wire gauge (a.w.g.) sizes simplifies the equations. The awg wire diameters decrease geometrically with increasing awg number, so that each size is approximately 1.12 times (or 10^{0.05}) smaller than the preceding size. Using this relationship, we can calculate1 the number of turns per square inch N of bobbin cross section changing by a factor of 10^{0.1}, or 1.26, per wire size, and the resistance R per cubic inch of winding changing by a factor of 10^{0.2}, or 1.59, per wire size.
Since we are rewinding the same bobbin, area and volume are constant (k),
so
N^{2}/R = k
Multiplying by I^{2} / I^{2} , this becomes:
(NI)^{2} / I^{2}R = k
we can recognize NI as ampereturns and I^{2}R as watts, or power.
What this means is that for any wire size that fills the bobbin, the same amount of power applied provides the same number of ampereturns, so what we need to calculate is the wire size that will draw the same power at the desired voltage:
If V_{1} is the original higher voltage and V_{2} is 12 volts, then we must increase the wire diameter by:
number of wire sizes = 10log( V_{1} / V_{2})
remembering that a larger diameter wire has a smaller awg number. The original article^{1} had a graph, but this is easily solved on a calculator, which they didn't have in 1956. The most common voltages are also summarized in the following table:






The rewinding procedure is straightforward: peel the old wire off the bobbin, measure the wire size, and rewind it with larger magnet wire as calculated above. Your local Radio Shack® carries several sizes of magnet wire, which may include the one you need. Mechanical details should be pretty much like the original relay; take notes during disassembly. The most difficult part is often prying the bobbin off the metal pole. Relays in sealed cans are a larger problem, and I welcome suggestions.
The fastest way to put the winding on is to wrap masking tape around a dowel or pencil until the bobbin fits snugly over it, chuck the pencil in a variable speed drill or lathe, and run it slowly to wind the wire on. At low speeds, the wire can be guided with your fingers.
I found several excellent coax relays with Nconnectors at a hamfest, quite cheap because they required 48 volts. They were wound with #38 awg wire. From the equation above, converting from 48 to 12 volts requires wire roughly six sizes larger in diameter, so I rewound one with #32 awg wire. The original winding required 48 volts at 54 ma., pulled in at 35 volts and released at 15 volts. After rewinding, it draws 265 ma. at 12 volts, pulls in at 8.5 volts, and releases around 2 volts. The power is slightly higher now, because six wire sizes is an approximation, but I can be sure it will still operate on a low battery. My 903 MHz station now runs entirely on 12 volts.
The SMA relay in Figure 11, from Down East Microwave, was an easy one to rewind. The cover is held on with two screws, and the bobbin is easily removable. The 28 volt coil is wound with pretty fine wire  I measured the diameter, guessed the enamel thickness, and estimated the wire size as #42 awg. From the table above, the new wire should be four wire sizes larger, or #38 awg. I rewound the coil with #38, reassembled it, and tested it. The relay now switches solidly at 11 volts. A better choice might be #36 awg wire, which would give a little more voltage margin for lowbattery operation, but I don't have any in the junk box. Incidentally, this relay has an unusual construction that will not operate with the coil voltage reversed, so try it both ways to find the right polarity.
As mentioned previously, we could have just removed turns to increase the current until the relay draws the same power at the lower voltage. If we take off half the turns, the resistance drops in half. The original resistance of the 48 volt relay is 48 volts / 54 ma = 888 ohms. At 12 volts, we need 216 ma for the same power, or a new resistance of 55 ohms, so we need onesixteenth as many turns. We increased the current four times, so we end up with onequarter as many ampereturns as the original, or only one quarter as much force pulling in the relay. If we weaken the spring enough, it may work, but will it be reliable?
A few more trials will convince us that no matter how many turns of the original wire are removed from a 48 volt relay, there will be only onequarter as much force pulling it in at 12 volts. A 28 volt relay isn't as badthe force is only reduced by 12/28, to a bit less than half the original force. There is probably a combination of turns and springbending that will work pretty well, but, if you've done enough disassembly to remove some turns, why not take the rest off and rewind it for 12 volts?
I haven't tried any relays from other countries, but I wouldn't be surprised if they don't use awg wire sizes. In the U.K., they may still use s.w.g. sizes, which are different, but the relative sizes are close enough so that increasing the diameter by the number of sizes calculated above should work. So measure the wire, convert to the nearest awg or swg size, and go from there. I don't know what metric standard wire is available.
Rewinding a surplus coax relay for 12 volt operation requires only one simple calculation and perhaps an hours work; why not try it rather than paying exorbitant prices or using inefficient DCDC voltage converters?
1. L.B. Stein, Jr., W1BIY, "Some Hints on Relay Operation,"
QST, June 1956, pp. 2125.