# Inductive kick-back voltage calculation

I am controlling a stepper motor (M42SP-5P) with BUZ11 MOSFETs. The winding resistances are $22\Omega$ and each winding is 18 mH as I measured. I am driving it with 24V, so let's say the drive voltage is about 1A. I know that the datasheet doesn't agree with me, however, this motor is M42SP-5P, not x-5K or x-5.

According to the MOSFET datasheet, turn off time is about 150 nS.

I want to pick a kick-back diode, however I am confused with the kick-back voltage calculation. The equation is:

$v(t)=L*\frac{di(t)}{d(t)}$

$v(t)=18*10^{-3}*\frac{1}{150*10^{-9}}$

That gives us 120 KV. This is insane and cannot be true, right? Where is my mistake in this scenario?

Also, which one of the following should one look for in the datasheet of a kick-back diode for this specific purpose?

$I_{FSM}$ : Non-repetitive peak forward current?

$t_{rr}$ : Maximum reverse recovery time ?

$V_{RRM}$: Maximum repetitive peak reverse voltage ?

Will 1N4148, BA157 be suitable for this application?

However, that assumes a perfect inductor. A real inductor has interwinding capacitance and parasitic capacitance will will cause the peak voltage to be a lot lower (try it in SPICE with/without e.g a 100pF capacitor in parallel with the inductor)
Also things like air ionising will stop the voltage reaching huge levels under normal circumstances.

Basically, the voltage will rise towards the peak until (usually) something gives, which is hopefully not your transistor/IC or whatever else you want to remain operational.
So something in parallel to allow the voltage to find an easy route of discharge is necessary, like a diode or a resistor/capacitor.
Any diode capable of turning on quickly enough and handling the brief 1A current would do, the BA157 should be okay (I'd say the 1N4148 is borderline with that current)

Note the the discharge time will be proportional to the voltage across the inductor, so if you need faster discharge then you can either put a resistor in series with the diode, or just use a resistor in parallel instead an calculate for the maximum allowed voltage rise. Another good option for fast discharge is a zener to clamp to the maximum allowed voltage.
Since all these methods raise the voltage drop across the inductor, it will discharge faster.

• Nope, 100pF didn't change it. 200nF changes it to 450V from 900V. – abdullah kahraman Feb 5 '12 at 10:24
• @abdullahkahraman - Where did the 900V come from? I meant it would reduce it from the "ideal" 120kV scenario. In SPICE, if you put a 1A current source in parallel with an 18mH inductor and a e.g. 1Meg resistor and step it over 150ns from 1A to 0A, you should see the 120kV predicted. Now add a 100pF in parallel and it should drop a fair bit. – Oli Glaser Feb 5 '12 at 20:45
• Where did that 1Meg come from? – abdullah kahraman Feb 6 '12 at 7:23
• Just to put some limit on the upper voltage "generated" by the current source (1MV) so SPICE doesn't get confused. Think of it like a very small series resistance in a voltage source. – Oli Glaser Feb 6 '12 at 11:49
• Ok. I will try that out and notify ASAP. – abdullah kahraman Feb 10 '12 at 6:43

I had a solenoid in a mechanical counter that had a large kickback. I added a diode as suggested which helped a lot but didn't eliminate the noise that was being coupled into some input circuits. Adding a Boucherot cell (a 100 nF axial ceramic cap in parallel with a 4.7 ohm resistor - anything from 2 to 5 ohms is recommended) across the solenoid solved the problem.

The improvement was obvious with a scope. With the diode alone where was still 20v of very fast oscillation, which the cell knocked down.

I now make up circuits with the diode, cap and resistor soldered together and covered with black shrink tubing and a ring of red shrink tubing to mark the polarity. These are added across solenoids and relay coils.

• Interesting, I never heard of a snubber as a Boucherot cell before. Looks like it's got its roots in audio, although general snubbers have been around for quite a while. – akohlsmith Dec 20 '12 at 19:41