# Reactance of pulsed DC

#### eromlignod1

Joined Sep 26, 2017
47
Hi guys,

I'm a mechanical engineer, so my knowledge of electrical physics is limited.

I have a situation where I'm basically driving a relay coil with pulsed DC at a frequency of about 60 Hz. I'd like to calculate the inductive reactance. I know about X = 2*pi*f*L, but I don't think I can apply that here. Not only is my wave square, not sinusoidal, it is also DC and the current never reverses direction.

How do I calculate the inductive reactance?

Don

Joined Jul 18, 2013
28,695
Is there a particular reason for the pulsed DC?
You are basically dealing with resistance, the inductive reactance will only be of significance if AC is used.

#### crutschow

Joined Mar 14, 2008
34,456
If it's to determine the current through the relay coil from the pulsed DC, then you want its inductance, not the reactance.

This can be calculate by measuring how fast the current increases when a DC step is applied to the coil.

#### eromlignod1

Joined Sep 26, 2017
47
I was wondering about that...whether there would be reactance at all.

Basically, I'm using ferrite-core inductors as electromagnets. I pulse them anywhere from 60 Hz to a few kHz. Ideally I'd like to drive them somewhere around their saturation current to get the maximum pull and I'd like to select an inductance that gives me the proper impedance at 5V to get that current.

Can I just use the DC resistance rating of the coil?

Don

#### crutschow

Joined Mar 14, 2008
34,456
Can I just use the DC resistance rating of the coil?
That tells nothing about the inductance/reactance.

#### eromlignod1

Joined Sep 26, 2017
47
Well, that's my question: how do I calculate the impedance of an inductor driven with pulsed DC?

Don

#### Ian0

Joined Aug 7, 2020
9,831
The average current will be the voltage divided by the resistance multiplied by the mark:space ratio of the waveform - with no need to know the inductance.
Knowing the inductance will let you calculate the ripple current. Knowing x=2πfL isn't much use. What you need to know is dI/dt=V/L. So ΔI=Vt/L

#### crutschow

Joined Mar 14, 2008
34,456
You can determine the inductance by measuring the time it takes to the current to increase after a DC voltage step is applied.
You put a small resistance in series (e.g. 1 ohm) with the coil and measure the voltage across the resistor to show the rise in current.
The time to 0.632 of the final current is one time-constant (L/R) where R is the total coil circuit resistance.
From that you can calculate the inductance.

#### crutschow

Joined Mar 14, 2008
34,456
What you need to know is dI/dt=V/L. So ΔI=Vt/L
That's if there is no significant resistance in the circuit.

#### eromlignod1

Joined Sep 26, 2017
47
Well, I realize I can set up an experiment and find out empirically. But I was hoping to calculate on paper and figure what coils I need for various frequencies. Surely there's a way to calculate the impedance of a buzzer.

Don

Joined Jul 18, 2013
28,695
DC At 60pps all you have to do is just measure the current.

#### eromlignod1

Joined Sep 26, 2017
47
I want to be able to select coils that run near their saturation current based on what frequency I drive them at. Some will be 60 Hz; some may be 5000 Hz or more. I don't want to have to buy one of every inductance and test them all. I want to calculate it like an engineer, using spec sheets.

Don

#### nsaspook

Joined Aug 27, 2009
13,300
I want to be able to select coils that run near their saturation current based on what frequency I drive them at. Some will be 60 Hz; some may be 5000 Hz or more. I don't want to have to buy one of every inductance and test them all. I want to calculate it like an engineer, using spec sheets.

Don
There are really too many unknowns because there are many types of relays with many types of relay coils. Most spec sheets have relay switching information, some have internal coil electromagnetic details, some don't.
https://www.mouser.com/datasheet/2/316/s-catalog-25939.pdf
https://www.mouser.com/datasheet/2/315/sp-catalog-1299295.pdf

https://www.te.com/usa-en/products/...ning-relay-coil-inductance.html?tab=pgp-story

#### Ian0

Joined Aug 7, 2020
9,831
That's if there is no significant resistance in the circuit.
If you assume that the inductor consists of R+L in series, then for a rough approximation of the ripple current assume that the average current gives a fixed voltage across R, equal to IR.
Then the peak current will exceed the average current by (V-IR).t/L , where t is the time for which the voltage is applied. This approximation gets better the as the inductance increases.
If you think of the R+L as a filter, then it will have a -3dB point at f=R/(2πL). That would probably be a minimum frequency at which you would wish to operate it, to avoid having too much ripple current.

#### crutschow

Joined Mar 14, 2008
34,456
I want to calculate it like an engineer, using spec sheets.
Then use the spec-sheet inductance to determine the rise-time (time to 0.632 of the final value) of the current using L/R where R is the total circuit resistance, or V = L di/dt if there is no significant resistance.
From that you can determine how long a pulse-width will generate the inductor saturation current.

The value of coil reactance only works for sinusoidal excitation.

A Spice simulator, such as the free LTspice from Analog Devices, will allow you to rapidly see many variations of pulse and inductance values, and save you a lot of calculations (example below):

#### BobTPH

Joined Jun 5, 2013
8,994
dI / dt = V / L

If you know how much current you want, choose an inductance such that it that will rise to that value in a time small compared to the pulse width.

For example, if you want 1 A in the coil at 10V with a pulse width of 1ms. Calculate the rise in current needed to get to the max in 100 usec:

dI / dt = 1 / 0.0001 = 10000 A / sec

10000 = 10 / L

L = 10 / 10000 = 0.001 H or 1mH

#### Ian0

Joined Aug 7, 2020
9,831
Is it the intention that the inductance should average out the current (and thus the magnetic field)? Or that the 60Hz signal should produce 60Hz pulses of maginetic field?
A usual sort of 24V relay has an inductance of about 1H, so it will average the current, and the contacts will stay closed.

#### eromlignod1

Joined Sep 26, 2017
47
I'd just like to maximize the saturation of the coil at a given frequency without oversaturating and unnecessarily heating it up and wasting power. I need to select coils over the whole gamut from 60 Hz to over 5000 Hz that perform like this. Hopefully there will be enough overlap that I'll only need a few different coils to cover the range.

I was hoping that someone, somewhere had integrated the current curve for a DC square wave across an inductance and determined a simple formula.

I'm thinking the current wave would be an exponential decay curve upward, then another downward (looking like shark fins) with the rate determined by a time constant L/R. If this curve could be integrated, a formula for reactance could be determined.

Don

#### Ian0

Joined Aug 7, 2020
9,831
I was hoping that someone, somewhere had integrated the current curve for a DC square wave across an inductance and determined a simple formula.
The average current will be the voltage divided by the resistance multiplied by the mark:space ratio of the waveform - with no need to know the inductance.

#### Ian0

Joined Aug 7, 2020
9,831
a formula for reactance could be determined.
The reactance is still 2πfL, but reactance isn't that useful when dealing with a non-sinusoidal waveform, unless you want to decompose the squarewave into all its fourier components.