# Gas station without pumps

## 2013 June 24

### Fitting L and R values

Filed under: home school — gasstationwithoutpumps @ 23:54
Tags: , ,

I decided to measure the two inductors that were confusing me in Colpitts LC oscillator, using the same method I’ve used before to model loudspeakers, that is, applying a known frequency sine wave to the unknown inductor in series with a known resistor, and measuring the RMS voltage across the inductor and across the resistor.

I decided to use the Bitscope Pocket Analyzer’s built-in function generator, rather than the external one I used before, because it is easier to set the frequency precisely, so I did not have to keep switching my Fluke 8060A multimeter between voltage and frequency measurement.  For the big inductor, I used a 100Ω resistor (measured at 100.64Ω), while for the AIUR-06-221 inductor I used a 1Ω resistor (measured at 0.98Ω).  To prevent overloading the function generator, I added another 100Ω resistance in series with the AIUR inductor+1Ω load, so the voltages measured for the AIUR inductor were pretty small.

My son helped me take some of the measurements, which was pretty boring, in part because it often took the Fluke multimeter 30–60 seconds to stabilize after changing what was being measured.

I computed the magnitude of the impedance of the unknown device as $\frac{V_L}{V_R} R$, and fit the function $| R+ 2 \pi f L j |$ to the resulting impedance values.

The AIUR-06-221 inductor data sheet claims that it is 220µH and 0.252Ω, with ±10% tolerance. My measurements come pretty close to those specs—certainly within tolerance.  The standard error of the fit is about 2.3% for the resistance and 1.5% for the inductance.
The top 4 frequencies were not included in the fit, because the voltages across the 1Ω resistor were getting too small for reliable measurement. Increasing the resistor size to 22Ω could help a little, but the multimeter starts having trouble at high frequencies even with large enough voltages.

The top 4 frequencies for the large inductors were not used, again because the voltages across the resistor were too small to measure reliably.
This curve could be pushed to higher frequencies by using a larger series resistor (say 10kΩ instead of 100Ω).  I added some extra points at the lowest frequencies to try to get a better estimate of the series resistance, since the corner frequency is around 32Hz.  The asymptotic standard error of the fit is 1.2% for inductance and 2.3% for the resistance.

These measurements are consistent with the data sheet for the AIUR-06-221 inductor, and consistent with the L/R time constant measurement for the big inductor.

I still don’t understand why the Colpitts oscillator and the phase-shift measurements were indicating a different inductance.  Maybe I need to check the capacitor values (I did check the markings on the capacitors, tiny as they were).