# L/R time constant and core saturation?

#### electronice123

Joined Oct 10, 2008
315
Hi all,

I have a series LR circuit, I apply a DC voltage to it for a time period equal to 5 time constants.
At the end of the 5th tc the inductance is near zero and the only thing limiting current is R.
If the inductor has a ferrite core does the core saturate after 5t if R is low enough?

Seems to me that if current is 99% after 5t then inductance is near zero, which means the core is saturated?

#### Ian0

Joined Aug 7, 2020
3,517
Hi all,

I have a series LR circuit, I apply a DC voltage to it for a time period equal to 5 time constants.
At the end of the 5th tc the inductance is near zero and the only thing limiting current is R.
If the inductor has a ferrite core does the core saturate after 5t if R is low enough?

Seems to me that if current is 99% after 5t then inductance is near zero, which means the core is saturated?
Maybe, but the current will be 99% of V/R after 5τ even for a perfect inductor.
V = L. dI/dt, so when the current is no longer changing there will be no voltage across the inductor.
How do you know that the inductance is near zero?

#### electronice123

Joined Oct 10, 2008
315
Maybe, but the current will be 99% of V/R after 5τ even for a perfect inductor.
V = L. dI/dt, so when the current is no longer changing there will be no voltage across the inductor.
How do you know that the inductance is near zero?
I only read that the inductance is near zero on another site while searching for answers, I think it was on Stackexchange.

#### Ian0

Joined Aug 7, 2020
3,517
Do you know the saturation current of your inductor?
True - the inductance would have dropped to near zero IF it had saturated;
but it doesn't follow that it must be saturated, nor that the inductance is zero simply because I=0.99V/R

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#### electronice123

Joined Oct 10, 2008
315
Do you know the saturation current of your inductor?
True - the inductance would have dropped to near zero IF it had saturated;
but it doesn't follow that it must be saturated, nor that the inductance is zero simply because I=0.99V/R
This is more like what I am thinking, yes current is at a maximum after 5tc but saturation depends on other factors like core cross sectional area and current?

#### Ian0

Joined Aug 7, 2020
3,517
Saturation will occur at a flux density of about B=0.3T for ferrite.
B=Φ/cross sectional area
Φ=F/R (Hopkinson's law)
where F= magnetomotive force (current x number of turns) and R = reluctance = 1/aL

#### crutschow

Joined Mar 14, 2008
27,949
Core saturation occurs at some current level as determined by the core material flux density characteristics, the core size, and the number of wiring turns.
It has nothing to do with the L/R time-constant.

#### ronsimpson

Joined Oct 7, 2019
1,549
I have a series LR circuit,
Please post a schematic. Inductor part number or picture. We should all have the same circuit in our head(s).

Some inductors will not saturate. (air coil)
If you put voltage across the inductor for a long period of time the inductor will saturate if it has core material. I think your circuit (if I understand it) the voltage starts out across the inductor and shifts to all across the resistor. One way to think about saturation is the inductor can handle only say 10 volts for 1mS. The area of 10V X 1mS is for square wave. You might start out at 10V but the voltage drops at "RL" and approaches 0V in time. (you can think in Voltage Time or in Current Time)

#### Papabravo

Joined Feb 24, 2006
17,028
For all practical purposes, the inductance of an inductor is constant. If it is an air coil inductor there is no "core" to saturate.

#### crutschow

Joined Mar 14, 2008
27,949
One way to think about saturation is the inductor can handle only say 10 volts for 1mS.
That's not a good way.
Core saturation is determined solely by current.
It is not directly determined by voltage, only by the current that voltage generates over time due the inductance.

#### BobTPH

Joined Jun 5, 2013
3,821
The inductance does not change until saturation is approached, it is the voltage across the inductor, and hence the change in current that decreases in an RL circuit. The change in voltage is due to the voltage drop across the resistor as the current increases and has nothing to do with saturation.

Bob

#### ronsimpson

Joined Oct 7, 2019
1,549
Core saturation is determined solely by current.
It is not directly determined by voltage, only by the current that voltage generates over time due the inductance.
You say it is not voltage then turn around and say if it voltage.
When I design transformers I can use Voltage Time or Inductance Current to get to flux. V × T = L × I

I think this is like arguing about Time vs frequency. There are more than one way to think bout it.

#### crutschow

Joined Mar 14, 2008
27,949
You say it is not voltage then turn around and say if it voltage.
No, that's not what I said.
Voltage is, of course, needed to generate the current, but it's the current that determines when the core saturates.
The value of voltage only determines how long it takes to reach the saturation current.

#### Ian0

Joined Aug 7, 2020
3,517
When I'm designing a transformer, I use the voltage-time product. When I'm designing an output inductor, I use the current.

#### electronice123

Joined Oct 10, 2008
315
Thanks for the replies everyone. I just needed clarification. I didn't think the core would saturate since it depends on other factors, I just needed to understand it in a different way.

#### MrAl

Joined Jun 17, 2014
8,504
Please post a schematic. Inductor part number or picture. We should all have the same circuit in our head(s).
Some inductors will not saturate. (air coil)
If you put voltage across the inductor for a long period of time the inductor will saturate if it has core material. I think your circuit (if I understand it) the voltage starts out across the inductor and shifts to all across the resistor. One way to think about saturation is the inductor can handle only say 10 volts for 1mS. The area of 10V X 1mS is for square wave. You might start out at 10V but the voltage drops at "RL" and approaches 0V in time. (you can think in Voltage Time or in Current Time)
That's not a good way.
Core saturation is determined solely by current.
It is not directly determined by voltage, only by the current that voltage generates over time due the inductance.
v=L*di/dt
v*dt=L*di
v*dt/L=di
di=v*dt/L

It is very handy to understand the point of view of volt seconds for an inductance. That's because it allows a lot of flexibility that relates directly to the dimensions we are working with. For the example given by @ronsimpson of 10v and 1ms, we know that it can also take 1v for 10ms, 5v for 2ms, 20v for 0.5ms, 100v for 0.1ms, etc., etc. Those dimensions are often seen in calculations involving switching regulators.
Now if we were to go by the current we could also figure the saturation level out, but then we'd have to calculate or measure the current rather than the voltage and time, and note that when we choose to use voltage and time we dont have to concentrate on the inductance itself because in order to know the saturation level we would have had to do that beforehand and we would not have to do it again we would only have to know the volt seconds because then the inductance is implied. This would be handy when calculating the maximum pulse time before saturation with a given (relatively) constant DC buss voltage.
So i think it really depends on what you are doing at the time when working with an inductance.
As i am sure you know, when purchasing an inductor we do have to know the saturation current because they usually use that dimension as one of the specifications for saturation.