# Spice modeling solenoid flyback voltage

#### hormel09

Joined Aug 14, 2018
2
I want to model the flyback voltage of a real solenoid in LTspice. The solenoid is powered by rectified, unfiltered 230Vrms. The power is controlled by switching the AC to the rectifier. I measured a DC resistance of 2.5kohm, and ‘scoped a flyback voltage of ~400V when AC is turned off. I have modeled the magnetic circuit of the solenoid in QuickField and have come up with a value of 3.4mH for the winding. I want to model the fly back voltage that the solenoid will produce when the AC is switched off. I modeled this using a 3.4mH inductor with 2.5kohm series resistance as the solenoid and using a voltage controlled switch to turn it on and off. Below is a spice screenshot of the switch on the AC side of the rectifier which is the way the real solenoid is controlled. When this is the case, there is no fly back voltage at all. This doesn’t line up with the measured flyback voltage.

Below are screenshots of the model with the switch on the DC side of the rectifier. They're the same except with different y-axis scales. This time it does generate a flyback voltage, but it is ~100MV which is far from reasonable. Less importantly, it’s negative and I measured a positive flyback voltage with the real solenoid.

Does anyone know what is wrong with my model? Why is there no flyback when the switch is on the AC side? Why is the flyback so big when the switch is on the DC side?

#### Danko

Joined Nov 22, 2017
990
Does anyone know what is wrong with my model? Why is there no flyback when the switch is on the AC side? Why is the flyback so big when the switch is on the DC side?
Polarity of flyback (self-induction) voltage always is opposite to polarity of operating voltage, as in your case.
Flyback voltage is I_L * (R_outer_circuit + R_switch +R_L). Therefore, if resistance of switch is infinity, flyback voltage will be infinite too.
When the switch is on the AC side, then flyback current goes through diodes of bridge and flyback voltage is limited at level about 1.5V only.
Inductance L has its own capacitance C, connected in parallel with L. This LC is resonant tank, and after negative half cycle (-1.5V) you can see at oscilloscope screen positive half cycle (+400V in your case) of damped oscillations.

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#### crutschow

Joined Mar 14, 2008
25,432
As Danko stated, the flyback voltage will be negative for a positive applied voltage to the solenoid.
If you measured a positive voltage then your measurement is wrong.

And to model the real solenoid you will need to include its capacitance in parallel with the inductance.
That can be determined by determining the ringing frequency in the real solenoid when the switch is opened, and calculate the capacitance from the known inductance value.

#### ebp

Joined Feb 8, 2018
2,332
3.4 mH seems rather low to me for 2.5k DC resistance. That will yield very little reactance at AC main frequency. The inductance of a solenoid with a movable "plunger" or even a relay with a moving armature changes depending on where the plunger or armature is. Since turn off, except in unusual circumstances, would be expected when the plunger is all the way in or the armature down, that is where condition where the inductance should be measured - unless it is a push type solenoid.

I would expect a 2.5k winding to have quite substantial distributed capacitance - certainly enough to get megavolts down a few orders of magnitude. With 2.5k resistance, peak value of stored energy is quite small (32 µJ if I didn't botch my calculation).

When you are doing a simulation like the first one with switched AC, it is always instructive to look not only at the voltage but also the current.

#### hormel09

Joined Aug 14, 2018
2
3.4 mH seems rather low to me for 2.5k DC resistance. That will yield very little reactance at AC main frequency. The inductance of a solenoid with a movable "plunger" or even a relay with a moving armature changes depending on where the plunger or armature is. Since turn off, except in unusual circumstances, would be expected when the plunger is all the way in or the armature down, that is where condition where the inductance should be measured - unless it is a push type solenoid.

I would expect a 2.5k winding to have quite substantial distributed capacitance - certainly enough to get megavolts down a few orders of magnitude. With 2.5k resistance, peak value of stored energy is quite small (32 µJ if I didn't botch my calculation).

When you are doing a simulation like the first one with switched AC, it is always instructive to look not only at the voltage but also the current.
Should have added this info in the first post. It is 400Hz and the plunger is pushed.
Also like your idea of measuring the current in my simulation. For some reason it is in phase with the voltage. I expect it to be lagging by 90 degrees.

#### ebp

Joined Feb 8, 2018
2,332
If you change the parameters for your simulation so that you only have a little off time before and after the first on time, you'll be able to see what is going on with current and voltage in better detail. Crutschow and Danko are both very expert in this sort of thing if you have difficulty getting it set up. I mostly emulate Statler and Waldorf.

If the inductance of the solenoid really is only 3.4 mH and the resistance 2.5k, the time constant is only 1.4 µs, so you will see almost no phase difference between the voltage and current. I was forgetting this little (in magnitude, but rather large in implication) detail when I suggested you look at the current. I was thinking (or so I claim) that you would see the exponential decay of inductor current after turn-off, but of course it vanishes into obscurity with the time scale. I also would have clued in to the AC frequency, had I looked at the X axis.

#### Danko

Joined Nov 22, 2017
990
If you measured a positive voltage then your measurement is wrong.
In fact, positive half cycle exist, but with very small amplitude.
...the plunger is pushed
If measurement is not wrong, maybe positive spike appears from plunger releasing? Keep it pushed when AC switched off and see on scope what happens.
EDIT: Is it permanent magnet solenoid?

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