# Calculating Inductance at DC

#### rstevens

Joined Apr 1, 2012
2
Hi there,

Hopefully this can be simply answered.

Can somebody please tell me how inductance is measured when in a DC application?

I found a datasheet on an DC choke where they measure inductance based upon a DC current through the inductor.

Im aware of the formulas below but not sure how they arrive at this inductance value...

Xl = j2∏fL

and..

Vl(t) = di/dt L

So if they rate an inductance at 3H with test conditions of a Max voltage of 600VDC and 500mA how do they get that given di/dt is 0.

What would be the equivalent at 240V 500mA 50Hz?

Last edited:

#### R!f@@

Joined Apr 2, 2009
9,734
Where did you learn that stuff ?

DC has no inductance.

An opposing current can exist if the current varies with time.

DC does not fluctuate with time.

The DC value given in that data is the Insulation resistance.

Meaning the maximum voltage a circuit should use if tht inductor is in THAT circuit

#### crutschow

Joined Mar 14, 2008
25,365
They measure the inductance by applying a small AC voltage superimposed on the DC current. The AC current due to the AC voltage is measured and used to calculate the inductance.

They measure the inductance at a DC current level since chokes normally carry DC current as power supply filters, and DC current tends to saturate the magnetic core which reduces the inductance.

#### R!f@@

Joined Apr 2, 2009
9,734
DC chokes are used to filter out AC ripple with in the DC.

Doesn't every core saturate with DC ?

#### pilko

Joined Dec 8, 2008
213
The chart in the data sheet is not showing test conditions, it is a list of different available chokes.

pilko

#### WBahn

Joined Mar 31, 2012
26,132
Inductors most definitely DO have inductance at DC; if they didn't, then they couldn't store energy:

$$E_L=\frac{1}{2}Li^2$$

No coil truly operates at DC -- after all, how can you go from 0mA to 500mA without having some di/dt in there at some point? As the coil charges or discharges, you will have a voltage across it.

Having worked with superconducting magnet coils that had 75+H of inductance and hundreds of amps DC flowing in them, I can assure you that they have inductance at DC and you better never forget it. When charging or discharging there was enough power going into (or out of) the field that we had to keep the voltage below 2V in order to avoid thermal runaway. That limited us to charge/discharge rates of about 20mA/s and, let me tell you, it takes a while to get to 100A at that rate!

The 600V max has to do with the physical limits of the coil, most notably the desire not to arc through the insulation. This means that the charge/discharge rate, under the conditions you mentioned, has to be kept below 200A/s. While that sounds like a lot, keep in mind that it is also 200mA/ms and if you have that coil charged at 500mA and open a switch on that current, then you might easily exceed that (or try to). With that much inductance, it is worth carefully looking at the protection features that are in place to deal with an unintended open.

#### crutschow

Joined Mar 14, 2008
25,365
..................
Doesn't every core saturate with DC ?
Chokes are designed to not saturate significantly until above their rated DC current. Inductors designed for switching regulators can also tolerate DC current while still providing inductance. Otherwise they wouldn't work in those applications.

#### R!f@@

Joined Apr 2, 2009
9,734
I know they operate at DC while having having inductance.. I like to know whether it is regard as DC inductance. Since when I was learning our teachers never even talked about DC circuits having inductors except as a choke. So this always led to believe me that Inductance does not effect DC at all.

Am I right ?

#### WBahn

Joined Mar 31, 2012
26,132
Again, no circuit truly operates at DC. For periods when the current isn't changing, you have no voltage across it (other than due to the resistance of the windings). But the same argument can be made for a capacitor since it will have no current flowing in it at DC. Does that mean that there is no such thing DC capacitance?

An ideal inductor has the same inductance regardless of how much current is flowing in it or how that current is or is not changing with time. But real inductors, especially ones with cores, have an inductance that is dependent on current (as well as the usual slate of other things, like temperature). So it is frequently necessary to specify the inductance at different current levels and the easiest way to do that is put a DC current through it and then put a small AC signal on top of it to get the small signal inductance at that current. Note that, in general, the inductance specified this way isn't the same as the total inductance that would need to be used to determine the total energy in the field.

#### ErnieM

Joined Apr 24, 2011
8,055
Inductors still have inductance at DC. The reactance formula 2*pi*f*L is for AC analysis, and it may be better to used the differential equation V = L di/dt to describe it's action with DC signals.

Consider a simple buck regulator:

When S is closed the inductor sees a voltage of:

VL = Vi - Vo (input voltage minus output voltage)

When S is open the inductor sees a voltage of:

VL = - (Vo + Vd) (output voltage plus diode voltage)

Note with S closed the inductor current ramps up, and ramps down with the switch open:

The rate of the ramp is due to the inductance of L, and that inductance damn well better be there even with the net DC of the load flowing thru it. In fact, it needs to support the peak current, the maximum ramp current plus the load current. This point is marked "D.T. in the figure.

(Images from Wikipedia.)

#### crutschow

Joined Mar 14, 2008
25,365
I know they operate at DC while having having inductance.. I like to know whether it is regard as DC inductance. Since when I was learning our teachers never even talked about DC circuits having inductors except as a choke. So this always led to believe me that Inductance does not effect DC at all.

Am I right ?
It's true inductance does not affect steady-state DC. But any attempt to change that DC current level, no matter how small, will be opposed by any inductance in the circuit.

#### R!f@@

Joined Apr 2, 2009
9,734
That is much better.

#### PaulEE

Joined Dec 23, 2011
423
I know they operate at DC while having having inductance.. I like to know whether it is regard as DC inductance. Since when I was learning our teachers never even talked about DC circuits having inductors except as a choke. So this always led to believe me that Inductance does not effect DC at all.

Am I right ?
Inductance is inductance; AC or DC. Whether if affects the signal, and to what extent, depends on the amplitude and frequency of the signal.

Crap...beat me to it.