# Mutual inductance vs coupling coefficient

Question regarding this and this question about mutual inductance and coupling coefficient.

I'm trying to analyse a two coil system: It consists of two coils like in the picture with 2 cm air gap between them. I want to find out the mutual inductance and the coupling coefficient. I'm confused, because, from my understanding, to calculate the mutual inductance, we need to know the coupling coefficient: But to calculate the coupling coefficient, we need to know the mutual inductance.

Experimentaly, how should I measure coupling coefficient and mutual inductance between these two planar coils?

You can measure mutual inductance with only use of an LCR meter (or impedance analyzer). Use the following wiring while the coil position is fixed. Mutual inductance will be quarter of the difference between two readings. simulate this circuit – Schematic created using CircuitLab

Experimentaly, how should I measure coupling coefficient and mutual inductance between these two planar coils?

You start by recognizing that with no load, and perfect coupling (100%), the output voltage from coil 2 is slightly less than the input voltage to coil 1. This is because the two inductances are not the same (24uH to 20uH) and this results in a turns ratio of 1.0954:1.

In other words the square root of the inductance ratio is the voltage coupling ratio (turns ratio) when the two coils are perfectly coupled. So, with 1 volt p-p on coil 1, coil 2 produces 0.9129 volts p-p into an open circuit load.

When the two coils are not perfectly coupled (say 50% coupling), coil 2 only receives 50% of the flux generated by coil 1 hence, the output voltage will be half of 0.9129 volts i.e. 0.4564 volts p-p.

So, you can use the voltage level on coil 2 for predicting the coupling factor but, be aware of parasitic capacitance - if you are anywhere close to the natural resonant frequency of either coil you will get voltage magnification effects that ruin the ability to predict the coupling factor.

Try and use the lowest frequency you can for this experiment and stay way-below resonances.

• It seems that at different frequencies I have different output voltages. At the lowest possible 1 Khz I have nothing out, but when I increase the distance between coils, I have some voltage. How to find the 'right' point where to take the measurement? – Raitis Bērziņš Nov 22 '18 at 15:15
• That sounds odd to me but, if you already have parallel/series tuning with capacitors, then you can expect serious de-tuning effects when closely coupled. You might need to give more details about your set-up and how you are measuring the voltages. – Andy aka Nov 22 '18 at 15:18