Resonance, Tank Circuits

published 2025-11-14

By Christopher Howard

I had this epiphany moment last night, as I was dropping off to sleep — after working through some AC circuit problems — where a lot of the fog about parallel RCL circuits and resonance cleared up in my mind. The next morning I found myself working through related questions in my head, as I was getting ready for work. Then later I found myself surrounded by pages of scribbled resonance calculations, and also building and measuring a little RCL network with some spare micro-henry inductors and pico-farad caps.

In the last post, I mentioned my Pickett N-16-ES slide rule includes specialized scales for calculating capacitive or inductive reactance. Another nifty set of scales, the C'r and L'r scales, along with the frequency, wavelength, or angular velocity scales — whichever you prefer — can be used to solve resonance problems. I familiarized myself with that, and was getting the same results as when I did it with the generic scales. Basically how it works is that, when an arrow mark is pointed at a certain frequency, then the C'r and L'r scales are lined up such that, where ever you move the cursor, the capacitance and inductance combination shown is resonant. So, you just need to know two of those three values, and the other one will show on the appropriate arrow or scale. There are another set of scales to help you with calculating the exponents.

I set up a small LC network, calculated for about 7.3 Mhz resonance, with resistor attached for dip measurements. The circuit turned out to dip at about 5.2 Mhz — and also 14.4 Mhz — so it looks like there is additional factors at work that I didn't account for. The probe I was using for the measurements is 15 pF, whereas my network capacitor was 47 pF, so maybe that is something I need to work into the math.

On a related subject, I read through the Wikipedia page on spark gap transmitters, which I hadn't studied before. Previously, I had the nebulous notion that the spark somehow transmitted the radio waves. But actually, the spark gap is there to generate a pulse when the capacitor reaches full charge, and that pulse is fed into a tank circuit, to start an oscillation. The pulse repeats rapidly to sustain a steady tone. Actually, when the transmitter was first invented, they just dumped the pulse straight into the antenna. But that generated a lot of noise, so the tank circuit was added to make the output cleaner. The spark rate was at audio frequencies, so various designs and constructions of spark gap transmitters had different tonal or musical qualities.

modern amateur who built his own spark gap transmitter

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