Okay so I was walking around yesterday and I found a perfectly good double air dielectric variable capacitor by the dumpster, from those vintage ones in old tube radios and took it. But there was no indication of a maximum or a minimum value so I had to measure it somehow. These are the things you need.
1. A known capacitor or inductor - I had an unknown inductor also, but had a finely specified capacitor.
2. Square Wave source - You can use a 555 timer. I used the one my oscilloscope has for tuning the probes. Any will do the trick. The frequency is important to be somewhat low because with high frequency you risk getting close to the resonance value of the tank circuit.
3. Oscilloscope - analog digital doesn't matter.
Okay so the steps I took were.
1. Firstly I had to measure the inductor value. I hooked up the circuit as shown and measured the decaying oscillations period and frequency. The period in this example is 62.5uS and the frequency 16KHz. It's very important to keep the square wave frequency much lower than the decaying oscillations. It may cause series resonance and damage your signal source. Then you can calculate the inductor value by using the resonance formula Fr=1/2пsqrtLC. I suck at math so I just used a resonance calculator. We get 4.5mH.
2. Now that we know our inductor value we can substitute the known capacitor for the unknown one and remake the same measurements. The decaying oscillation period is 14.6uS (it's easier measured on a real oscilloscope) and the new resonance frequency is 68.5KHz. We make the calculations again and find the capacitor value. Since I have a dual variable capacitor I had to make 4 measurements. Lowest and highest capacitance of one arm and lowest and highest capacitance of the other. It's a crude method but if you do your math carefully and have a digital oscilloscope you can probably get pretty close to the real value.
Some considerations. Keep in mind that measuring low capacitances will probably require either a higher frequency of the square wave oscillator or a higher inductor value. With both things there are some considerations to be taken care off. First as I mentioned a higher frequency may bring you close to the resonance frequency of the tank circuit. In our measurement it's in series and if resonance should occur it may damage your signal source. The other option is high inductor value. High value inductors have higher internal resistance. This decreases the Q factor and broadens the resonance bandwidth of the tank circuit, so once again you may end up unknowingly entering resonance. The solution is to keep the inductor value very high and keep the signal source frequency very low. My oscilloscope puts out around 400Hz square wave. Some of the measurements were at a frequency of 170KHz. You need to keep the difference between them as high as possible.
Also when using this method to measure high capacitance values make sure that the output impedance of your signal source is considerably low, and that it can sink reversre current or you can damage it at pulse moments.
I recommend adding a series resistor (100ohm - 1k) to further dampen the oscillations if you're not sure what you signal source's specifications are or have absolutely no idea what your unknown component values are.
