How to measure an unknown inductance
Required equipment:
-
Oscilloscope
-
Function Generator: (Sine wave 5v 0-p, 100 – 1 M hertz, higher frequency is better, lower can be used with some additional thought for capacitance value used)
-
1 K ohm resistor
-
Capacitor: Any value; 1 pf - 1000 uf may be used. However, choose an appropriate value (if you have one available).
-
Inductor to test
Construct the following circuit:
Simple operation: (assumes well chosen value of C1 and a function generator capable of high frequencies)
- Set up function generator to produce a 5 volt 0-p sine wave (any voltage may be chosen)
- start the function generator on its lowest frequency.
- watch the output voltage on the oscilloscope
- begin to sweep the function generator up through its capable frequencies
- When the amplitude of the output sine wave peaks, that is the resonant frequency of the RLC circuit.
- Plug the resonant frequency into this equation to find the approximate value of the inductor.
Where C is the known capacitance in Farads, f0 is the
resonant frequency in Hertz, and L (the result) is the inductance in Henries.
A little bit more information for the curious.
The resonant
frequency (in hertz) of a RLC network is given as:
If the capacitor
value is chosen poorly (for example: 100 pf with an educated guess for the
inductance of 1 microhenry; giving a resonant frequency of 15.9 Megahertz) then
the resonant frequency might be well outside of the range of your function
generator and / or your oscilloscope.
You may use this
equation to choose an appropriate value of C with an educated guess for L.
Choose f0 to be ½ the frequency of your function generator or oscilloscope, which ever is lower.
How it works:
Consider the
circuit at DC. The inductor is
basically a shorted wire, and therefore pulls the output to ground regardless of
the input. The 1k resistor drops all
the voltage of the input and limits the current, protecting your function
generator. At low frequencies, the
inductor will allow current to flow, and therefore the 1k resistor will drop
considerable voltage, causing the output sine wave to be smaller than the input.
At extremely high
frequencies, the capacitor will act like a short, once again causing a voltage
drop across the resistor, and making the output waveform small.
At the point of
resonance, the inductor and the capacitor will trade energy back and forth,
requiring very little current, and therefore creating very little voltage drop
across the resistor. At this point,
the amplitude of the output waveform should almost match the input waveform.
This is the peak you should be looking for.
In case this is still not clear, here is an example:
In this case, the
inductor was 1 millihenry and the capacitor was 1 microfarad.
The resonant frequency was calculated at 5.0329 Kilohertz, and as you can
see, the peak occurred at 5.0257 Kilohertz (obviously the method is prone to
small interpretation errors)
p.s. it says
502.572m (which stands for milliseconds btw).
This circuit was controlled by a time dependent frequency source, so the
value is multiplied by 10,000 to get the frequency at that particular time.
