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On another thread, I said that I suspected that real Part 15 AM installations perform much worse than their owners think they do, for several reasons. One of the reasons I mentioned is that the losses in the loading coils are much higher than several published sources (such as The Low Power AM Broadcasters Handbook) say they are. The thread also mentions an online coil calculation utility program that also gives overly optimistic values of coil loss. I also mentioned my measurements on the B&W type 3062 Air Inductor which showed that the coil loss was much higher than expected for that type of coil.
I am posting here because I may have found a way to calculate the actual coil loss of the B&W coil I mentioned. My calculated coil loss was almost the same as my measured coil loss. That these two numbers match each other is almost certainly a coincidence, because I have usually had poor results when comparing coil calculations with measurements. I am, nevertheless, encouraged. I think that coil calculations that are consistently between one half and twice the measuremnts are useful, and this result causes me to think that such accuracy may be possible.
The B&W 3062 coil is two inches in diameter and ten inches long. It has 160 turns of #16 wire. The measured inductance at 1 MHz is 326 uH, and the equivalent series resistance was measured to be 10 ohms. 326 uH is a useful Part 15 AM loading coil inductance, but the low-frequency inductance was only 235 uH. This indicates that the coil capacitance is quite high, about 30 pF. I measured the DC resistance of the coil to be .4 ohms. Using the length of the wire in the coil, and the resistance of #16 wire per 1000 feet, I calculated the DC resistance to be .346 ohms. Using Equation 94 in Section 2 of Terman’s Radio Engineers’ Handbook (1943), this coil operated at 1MHz has a series resistance that is 15.1 times the DC resistance. This calculates to be 5.2 ohms. which is less than the 10 ohms of series resistance actually measured. The 30 pF of coil capacitance reduces the Q of the coil and increases the equivalent series resistance. It happens that this series resistance is close to 10 ohms, which is the measured series resistance.
Equation 94 gives the coil loss due to the skin effect and the proximity effect. In most coils, the proximity effect is appreciably higher than the skin effect. By increasing the spacing between turns, the proximity effect is reduced, but this causes other coil losses to increase because the wire must then be longer and/or thinner.
Adding the reduction of Q due to the coil capacitance gives the total series resistance. The combination of skin effect, proximity effect, and coil capacitance cause the loss resistance of the coil to be high.
So, what can be done to reduce coil losses? It seems that reducing one kind of loss increases another kind of loss. For example, copper losses can be reduced by winding the coil on a ferrite core. However, this produces core losses. Litz wire is good for reducing skin effect at the lower frequencies, but its effectiveness is not very good at the upper end of the AM BCB. Twisting a bundle of insulated wires eliminates the proximity effect between adjacent turns of the bundle, but there is still a proximity effect between the wires inside the bundle. (A twisted bundle of wires is not the same as Litz wire.) Making a coil with a Q above several hundred is still an open problem in electrical engineering. High Q has been obtained with mechanical resonators, such as tuning forks and piezoelectric crystals, and with resonant cavities, but not with coils. Some improvements in coils may be possible with further research.