# Reactance of pulsed DC ..#2

#### Martant

Joined Oct 30, 2023
1
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

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#### Ian0

Joined Aug 7, 2020
9,829
The reactance is not a useful thing to know, but it is still 2πfL. You might have to Fourier transform the driving waveform to get all the components of f.
If you want to calculate the current then you work it out from V/L=dI/dt
I=Vt/L
where V is the supply voltage for the period when the coil is switched on
and V = -0.7 when the coil is switched off (because of the voltage drop of the flyback diode)
In most cases the series resistance of the coil is what determines the current. The inductance only affects the rise-time.

#### BobTPH

Joined Jun 5, 2013
8,989
dI / dt = V / L

There are two segments over which you need to solve this.

The first segment is when the DC power is applied to the coil. In this segment V is the D C driving voltage.

The second segment is when the DC power is off. We have no idea what the voltage across the coil is in this segment because the TS has not told us. If the coil is driven by an ideal push pull driver, the voltage would be zero. If the driver goes to high impedance, you have a boost converter and a voltage will be induced to keep the current going.

We cannot solve or simulate this unless we know what the circuit is when it is not driven.

#### Ian0

Joined Aug 7, 2020
9,829
I assumed that being a relay coil, it would have a diode across it, meaning that the “off” voltage would be -0.7V.
But if the diode has been missed out, then it would be minus rather a lot more than that!

Assuming that the diode is in place then the current at t→∞ will be d.V/R where d is the duty cycle, V is the supply voltage and R is the coil resistance. L doesn’t feature in it.

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#### Alec_t

Joined Sep 17, 2013
14,321
Just to complicate things, the coil inductance is not constant. It will increase as the relay pulls in the armature.

#### ci139

Joined Jul 11, 2016
1,898
Just to complicate things, the coil inductance is not constant. It will increase as the relay pulls in the armature.
we might assume that if the SW is applied, the magnetic circuit remains at its high permeability state