# Inductance Measurement

1. Oct 21, 2004

### airbuzz

Inductance Measurement of a Pulsed Plasma Thruster

I´m trying to measure the total inductance of a pulsed plasma thruster. According to usual formulas found on books I calculated it should be about 200 nH (very small). The strange thing is that I measured a smaller value than this (about 130 nH). To measure inductance I put a known capacitor in the circuit (so the circuit will be one capacitor and three inductance in series, without generators) and inducted high frequency signal with a toroid, analysing then the spectrum to find the resonance frequency of the circuit and then find the inductance. Is there something wrong in this? Did anyone do something like that? Why I find a smaller inductance than the one evaluated theoretically?
Thanks

Last edited: Oct 22, 2004
2. Oct 21, 2004

### vanesch

Staff Emeritus
What comes to mind here is parasitic capacitance in the device under test, which can alter the resonance frequency you would expect without it. Just an idea.

cheers,
Patrick.

3. Oct 21, 2004

### airbuzz

I evaluated the capacitance of the circuit (about 3 pF) and used a much bigger capacitor to use the tests. Moreover I repeated the experiment with different capacitros and found always the same values. So the parasite capacitance is not the motivation of my error...

4. Oct 21, 2004

### enigma

Staff Emeritus
Might you have somehow shorted out some of the turns in the inductor?

Have you crosschecked your results with a Gaussmeter?

5. Oct 21, 2004

### airbuzz

I don´t have inductors. I have a circuit made by wires, a capacitor and two parallel electrodes. I want my inductance be as small as possible, but I need to know it exactly, because I need it for a model. And so I´d like to find similar values between measurement and calculation, but at the time I have something like 40% difference...
What is a Gaussmeter? SOmething to measure the magnetic field? And how should I use it?

6. Oct 21, 2004

### snbose

I am not familier with the exact details of this experiment. But its a good idea to calibrate your setup. The problem as it seems from the description is some component in the circuit is tending to reduce inductance. What can reduce inductance? Parasite Capacitance. To determine this, calibrate your experimental setup by using a known inductance and applying to the equation:

$$2\pi{f^'}=\sqrt{1/(L_k_n_o_w_n+C_0+C_p_a_r_a_s_i_t_e)}$$

Calculate the $$(C_0+C_p_a_r_a_s_i_t_e)}$$ and then replace this with the capacitance when measuring the unknown inductance. Are you using additional inductors in series with the unknown one. If so you could calbrate the inductors that you may be using.

7. Oct 21, 2004

### enigma

Staff Emeritus
What formulas did you use to calculate the inductance if it isn't for an inductor? (I have a feeling this may be outside of my region of knowledge...)

8. Oct 22, 2004

### airbuzz

The formula for two parallel plates in which the distance h is much more smaller than their width d is
$$L = \mu \frac {h}{d}$$
If the distance is bigger you have to add a factor k depending on h/d that comes smaller the more is h/d.
To evaluate the inductance of a wire I used this: for circular section wires of length l and diameter d
$$L = 2 \cdot 10^{-7} \cdot \ell \cdot (ln(\frac{4 \ell}{d}) - \frac{3}{4})$$
For rectangular section (b*d) wires, that is my case, I used
$$L = 2 \cdot 10^{-7} \cdot \ell \cdot (ln(\frac{2 \ell}{b+d}) + \frac{1}{2})$$
All these formulas are neglecting the copper permeability that is circa 1.
To this you must add the inductance caused by the wire loop (closed circuit), but neglecting this I have already something bigger than what I measured

Last edited: Oct 22, 2004
9. Oct 22, 2004

### airbuzz

The Parasite capacitance has already been determined doing the measurement with different capacitors and it is around 3 pF, neglectable in fornt of the capacitors I use (ca. 300 pF)

Last edited: Oct 22, 2004