# Gas station without pumps

## 2013 June 25

### LC resonance

Filed under: home school — gasstationwithoutpumps @ 20:17
Tags: , , ,

Since the inductors looked ok in Fitting L and R values, I decided to check the capacitors and the LC tank circuit using the same technique. That is, I put the device under test (DUT) in series with a 100Ω resistor, fed the output of the Bitscope Pocket Analyzer function generator into pair, and measured the RMS voltages across the DUT and across the resistor with a Fluke 8060A multimeter.

This is supposed to be a 4.7µF capacitor, but seems to be a bit low.  It looks like a pretty pure capacitance, though, with no series (0Ω) or parallel (∞Ω) resistance. I only did the full set of measurements for one capacitor, but I checked a few values in the middle of the frequency range for the other, and it seems to have about the same capacitance.

I then made a tank circuit like the one in the Colpitts oscillator, with the AIUR-06-221 inductor in parallel with a pair of the (nominally) 4.7µF capacitors in series.  This should resonate at $\frac{1}{2 \pi \sqrt{LC}}$= 7kHz, with L=220µH and C=2.35µF.

The LC tank resonates at about the expected frequency (7.4kHz instead of 7kHz), but to model the data well, I had to add series resistors for both the inductor and the capacitor.  The series resistor for the inductor seems a little low and the inductance a little high, and the series resistance for the capacitor quite high, but trying to fit four parameters to the rather limited data makes errors like these probable.

It is certainly the case that the LC tank is resonating at the expected frequency, so now all I have to figure out is why the 180˚ phase changes that determine the oscillator frequency and that I measured with an external oscillator (in Colpitts LC oscillator) are not at or near the resonant frequency.