Adding inductance?

[zebra50]

Hi!
What is the maths for adding inductance together? I know there is a squared relationship between windings and inductance

L = (number of turns)^2 x constant

So I know that if I'm winding on a single core then 200 turns will give me 4 times the inductance of 100 turns. So, for example if I wound 2 x 100 mH I could either have them separate for 2 x 100 mH or in series I would get 400 mH.

But what happens if I have two separate inductors on separate cores and add them together in series.

Do I still get the square rule? So do 2 x 100 mH give me 400 mH or 200mH?

And is there a general rule for unequal inductors? I'm thinking about the Gyraf pultec filter in particular - 100 + 100 + 47 + 22 mH.

Many thanks - my brain is staring to smoke over this onw. I've had a look in AofE but found nothing that helped me.

Stewart

 

[mcs]

Inductors are just like resistors. Two inductors in series = L1+L2. Two in parallel = (L1^-1 + L2^-1)^-1 (I hope I got that one right...).

Best regards,

Mikkel C. Simonsen

 

[Guest]

[quote author="zebra50"]Hi!
What is the maths for adding inductance together? I know there is a squared relationship between windings and inductance
L = (number of turns)^2 x constant
[/quote]
There is strange maths to compute mutual inductance,
gamma matrices etc., you can read Guillemin s "Basic circuit
theory", but somewhat simply:
L=L1+L2+M12+M21;
where M is mutual inductancy.
If you adds two coils at different cores, mutual inductancy is near 0
and you gets simple:
L=L1+L2.
If you have two coils at the some core and they have the some
turns number, then mutual inductancy is M=+-L. You can connect
it in series and give
L=L1+L2+2*L1 = 4*L1 (where L2=L1, the some turns)
or in antiseries (opposite wounding dirrection in series)
L=L1+L2-2*L1 = 0.
(It is method, how to do variable coil...
simply do two concentric coils and rotate second in the first)
For coil at good core there is true
L = (number of turns)^2 x constant
For paralel coils at different cores is true:
Two in parallel = (L1^-1 + L2^-1)^-1
Paralel coils at the some core changes nothing if
numbers of turns are the some. Only some reduction in
series resistancy and leak inductancy.
xvlk

 

[zebra50]

Many thanks - that sorts it out for me.
:thumb:

 

[PRR]

> if I'm winding on a single core then 200 turns will give me 4 times the inductance of 100 turns.

> But what happens if I have two separate inductors on separate cores and add them together in series.

All the windings on one core are turns-squared.

Windings on two separated cores just add, like resistors.

With iron-core chokes, two adjacent cores will have very little coupling (like 1/1,000). Iron carries magnetism at least 1,000 times better than air. Given a choice between flowing around the core or jumping through air to the adjacent iron, 99.9% of the flux stays in the core it started in. So you can usually treat them as independent. 2H+3H= 5H. Maybe really 4.995H or 5.005H, but who cares? Audio chokes are rarely accurate to 10%, and iron-core chokes vary a lot with current.

With air-core chokes, adjacent windings will couple to some degree, so you can not treat them independently. This is an important issue in AM radio design, where two semi-coupled tuned windings can give a better response shape than two independent tuned windings. Try Radiotron for simplified analysis of this problem. I don't think you ever "want" this at audio frequencies. The coupled-winding analysis might be useful to guide how far apart two air-core chokes must be to have negligible coupling. But in practice you either put them at right angles (which ideally cancels all coupling) or very far apart (several diameters), and then pretend they are independent.