# Measuring time-varying inductances

I am using a circuit based on an LC tank and Arduino that is used to measure inductances. The amplitude for the current pulse is of 40 mA, approximately the current that an Arduino pin gives at 5V. The values ​​for the pulse rise and fall times are also fixed according to the Arduino ones, from what I read, about 10 ns. The diode would be to protect the output pin of the Arduino from high voltages that could occur at the output of the RLC circuit. The resistor connected to the comparator output is a pull-up resistor, so it is not " floating", since the output is open collector. I have tried it to measure fixed inductances and it works, since the pulse signal from the LM339 comparator is of the same frequency as the resonant frequency of the RLC circuit. We measure the width of the pulse with the "pulseIn()" function of Arduino and from there, performing the appropriate operations, we could obtain the value of the inductance.

But my idea is to use the circuit to measure a time-varying inductance. To simulate this, I assume that the coil flux varies in time as the function f(x)=x. Since LTSpice derives with respect to the variables of the functions we input, we have to use their integral, that is, x^2/2. We replace the variable "x" with the variable "time", since we want the inductance to vary with the simulation time: time^2/2. Finally, in order for its value to vary slowly and give the RLC circuit time to resonate somewhat for each value of inductance, it occurs to me to multiply the function by a very small slope. So the function "0.0001*(time**2)/2" is the expression you finally input as a stream. However, when simulating the output of the RLC circuit, no oscillation is seen and it appears that only the inductance is seen varying with time. Is there a flaw in the approach or just couldn't this circuit be used for this?

Here are the results of the simulation:

• If it's time varying then you can't use a pulse to measure the oscillations, since these will also vary. Try using a ramp of known di/dt. The voltage across your inductor will be directly proportional to its derivative. Also, your expression will give a variation from zero(!) to 100u. If you want from 100u to something, then you need x+x**2/2 (as in 1+x). Mar 26, 2022 at 21:17
• If the inductance varies in time due to flux variation, after the current pulse and for the duration of the RLC circuit oscillation, I thought that the oscillation would not have a constant resonant frequency, but would vary with the value of the inductance. Since f=1/(2*pi*sqrt(LC)). Then the frequency of the pulse signal (output of the comparator) would do the same and we could measure the different values ​​of inductance by measuring the pulse signal. I have tried to excite with a current ramp and the same result continues for VLC. Mar 26, 2022 at 22:59