# Relay coil has inductive reactance proportional to sqrt(f)

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I assume this is because of eddy current losses. Does anybody know how to model sqrt(f) as an impedance in Pspice? I'm guessing a series combination of parallel LR's, but I don't know how to calculate the values.

Red trace is measured impedance vs frequency. Black dotted trace is 10*sqrt(f), a nearly perfect match.

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10*sqrt(f), a nearly perfect match.

Why does this even matter?

Jeroen Belleman

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I saw a clever circuit one time that used the back-emf kick from a relay disengaging to generate a low-current HT for some other function of the circuit. Like an incidental mechanical boost converter...

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So, instead of impedance being proportional to frequency (like a perfect inductor), it's only half that, over some range. But, it's not really a range of INTEREST, the 50Hz -60 Hz range shows nice constant-impedance (coil resistance, maybe the inductor is saturating).

Instead of an inductor, you have an inductor with series resistance; get that low-F corner first, then worry about the high-F asymptotic behavior.

If there iS saturation going on, the drive level matters. A LOT. Spice is intended to be pretty good at small-signal analysis, you might just have to use pencil and paper for the hard-drive cases.

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Because the relay is being connected across a circuit that is sensitive to impedance.

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to model sqrt(f) as an impedance in Pspice? I'm guessing a series combina tion of parallel LR's, but I don't know how to calculate the values.

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*sqrt(f), a nearly perfect match.

inductor), it's only

he 50Hz -60 Hz

is saturating).

that low-F

is intended

ncil and paper

The data was taken at very low drive level. The small-signal impedance is increasing as the square root of frequency. I don't care about 50-60Hz. T here are switchmode frequencies in my application that I need to worry abou t. Is there some way to model sqrt(f) without defining a frequency-depende nt component?

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Assumptions are not so good. Can you provide a connection diagram and data to support your "assumption"?

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The circuit:

The math:

The data:

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A ladder of series L and shunt R, as many as you need to get the right characteristic. Dunno what progression of values you'd need, though.

```--
Tim Wescott
Wescott Design Services ```
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There has to be an analytical approach to this, but I haven't found it. I do analog consulting in the Portland/Hillsboro area. Sounds like you are close by. Check your spelling on "therapeutic" on your website.

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Was there, by any chance, an instrument scale change at 1kHz? I find the instantaneous amplitude change at that point hard to reconcile.

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Excellent information. It appears that your relay inductance is changing with frequency. At frequencies below about 1kHz, it appears to be about .05Hy. Above that it diminishes to about .037Hy at 10kHz.

I cannot tell you what would cause it, but I suspect it is a DC relay and loses inductance (as you already suspect) due to some other factor. I find it puzzling that this precision of knowledge is required just to PWM a relay. But, that's your business.

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Haven't tried exactly that, but I have generated a family of RC circuits which have a tunable slope - i.e. f^alpha, where alpha= -1..0. This would seem to the the dual of that.

The method is simple. You develop a ladder network, in this case with each stage having a single L and R. Each inner stage has an impedance some constant factor higher than the preceding stage. The factor will determine how many sections you need to cover the desired bandwidth. The ratio of the L vs R impedances will control the slope.

It's easy to write a script to automate generation of different ladders with different slopes and impedances that can be read by various analysis programs.

This is all from memory, but I'm pretty sure it should work. The impedance of a ladder network of this type can be expressed as a continuing fraction - and there's a lot of theorems that can be used on such structures.

Hope that helps...

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** The relay mechanism responds to the average DC value of the PWM signal. Long as there is a diode across the relay - inductive effects create ripple superimposed on the average current value created.

If there is no diode - then god help him.

.... Phil

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If you look at the data, you will see that I switched resistor values at the discontinuities.

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The PWM signal will add quite a bit of dissipation in the coil and core. I need a rough idea of the PWM ripple current through the coil.

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No diode. If I tell you any more, I will have to.....you know the rest.

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Thanks. Good to know that it's doable.

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The relay has a laminated stator, so for increasing frequency the iron losses increases (eddy current)

Chees

Klaus

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Interesting. Looks like eddy currents are opposing the flux, preventing it from entering the core at high frequency. Flux has to diffuse into conducto rs. Thermal diffusion into an infinite heat sink shows a sqrt(f) dependence at the top surface, complete with a constant 45-degree phase shift.

The good news about this is that the flux has to diffuse out again as well, which will help limit the amplitude of the inductive kick at turn-off.

Cheers

Phil Hobbs

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