# Core saturation detector-differentiator

I am building some project that requires me to measure the saturation corrent of some homemade inductors winded on scavaged ferrite cores, so I decided to try and create a circuit that will aid me in measuring.

From what I know and read the current thru the inductor at a constant voltage rises linearly with time and when core enters saturation the current start to rise exponentially. So I've came up with something like this:

simulate this circuit – Schematic created using CircuitLab

The idea behind this is I would measure the voltage across a sense resistor R take its derivative and pass it thru a differential amplifier which will compare the current value with a previously obtained fixed value stored in S/H circuit. And if the difference is bigger than some preset value the comparator would output a high value.

Why I think this might work: The derivative of the linear function is a constant and the derivative of the exponential function is exponential function. So when the circuit would sense the that the output voltage from OA1 is not a constant it would trigger and shut off the MOSFET. I would then read on the oscilloscope the time the output was high and calculate the saturation current.

But for it to work I would need to update the S/H circuit frequently, I am planning to do this every second iteration. However I dont have this quite worked out yet, because I am stuck at the first part, the differentiator:

simulate this circuit

I've searched thru the web and found out how and why it works but never found the equations that would describe its behaviour. I would need a unity-gain differentiator with cut-off frequecies at around 100-1k Hz and 100k-1M Hz. So I decied I would go and write the equations myself. This is the furthest I've come:

Transfer function: $$H(s)=\frac{sC_1R_2}{s^2C_1C_2R_1R_2+s(C_1R_1+C_2R_2)+1}$$

Its magnitude (in hope to find cut-off frequencies): $$|H(s)|=\frac{\omega C_1R_2}{\sqrt{\omega^4 C_1^2C_2^2R_1^2R_2^2+\omega^2C_1^2R_1^2+2\omega^2C_1C_2R_1R_2+\omega^2 C_2^2R_2^2+1}}$$

I see whoule bunch of squares in the square root, but have no idea how could I simplify it.

Excuse me if this is to long of a post, but I want to make sure that this is the right approach/path that I've taken.

• Frankly, I'd do it digitally, with an MCU... – Laszlo Valko Apr 18 '15 at 18:05

I'm offering this answer as an alternative saturation detector. Pass a direct current thru the coil that can be varied from a milli amp to possibly several amps. This is easily achieved with an opamp and BJT as a constant current generator.

Next, generate a low amplitude sinwave and capacitive couple it to the inductor. Measure or view the sine amplitude on an oscilloscope and, gradually raise the dc current. At some level of current the sine amplitude will begin to drop indicating the onset of saturation. More dc will mean less sine amplitude because of more saturation.

The sinwave can be sourced from a regular bench oscillator with 50 ohm or greater output impedance.

You could even incorporate the inductor into a colpitts oscillator and watch the frequency rise as saturation increases.

Looking at your formula, it seems that the centr frequency is $\dfrac{1}{2\pi\sqrt{C1 C2 R1 R2}}$ but I'm on an android and don't have full capabilities to analyse.

Thinking about it a bit more, because of the virtual earth nature of the circuit, R1 and C1 are independent of R2 and C2 so high pass is dictated only by the input components and low pass dictated by the feedback components. This of course assumes LP and HP frequencies are significantly different and by the sound of it they are.

• I really like your solution, very simple. I'll try it out and I'll wait for Dwayne to post his schematic before accepting any anwsers. – Golaž Apr 19 '15 at 16:49

If you don't mind measuring the parameters using an oscilloscope, you could use the technique that I use.

I have a large MOSFET with a low-value current-sense resistor in the source pin to ground. The gate has a 33 Ohm resistor in series with a 10k resistor to ground. The drain goes to a terminal for one side of the inductor under test and to a clamp circuit that consists of a fast diode driving an automotive light bulb. Bulb is 1141, I think. I'll have to check.

The other side of the inductor lead goes to several large, very-low ESR all in parallel and to ground. The intent is to have a very stiff power supply when testing the inductor.

I drive the gate with my pulse generator. This is an older Continental Specialists pulse generator with separate Hi & Lo pulse adjustments.

Finally, I connect a DC power supply set to 10.0 Vdc to the reservoir capacitors.

Connect the scope across the current-sense resistor. Connect the inductor to the test jig and set the pulse repetition rate to several hundred Hz.

Now start to increase the pulse width and observe the inductor current on the scope.

You will see a nice, straight ramp as the inductor absorbs current. As you increase the pulse width, the current increases.

You can calculate the inductance from the slope of the line. That's the reason for setting the supply voltage to 10.0 Vdc - it makes things easier to calculate.

As you increase the current, you will see the current ramp bend or inflect. You can easily see how the inductor behaves as it approaches saturation.

I'll update the answer with a schematic of my test jig when I get back to work on Monday.

But the test jig works very well.