Inductance of transformer coil taps question.

[anotherjim]

Something I can't seem to find an answer to with searches. I know inductors in series simply add as resistors do, but this does not seem to be the case with a tapped coil on a transformer. A primary of 4H total does not read 2H about the centre tap on my shiny new LCR meter *, instead, they might be below 1H.
I think this could be because it may be half the winding, but that half also has less core iron within it. So, around 1/4 of the total inductance might be expected.
Is there a formula for this? I have seen stuff where it's been assumed that 1/2 a winding is 1/2 the specified total inductance and I've gone along with that since we all know L1 + L2 +Ln...

*Gone 50 years without being able to measure inductance and now I can it throws up something basic I didn't know!

[FSFX]

Something I can't seem to find an answer to with searches. I know inductors in series simply add as resistors do, but this does not seem to be the case with a tapped coil on a transformer. A primary of 4H total does not read 2H about the centre tap on my shiny new LCR meter *, instead, they might be below 1H.
I think this could be because it may be half the winding, but that half also has less core iron within it. So, around 1/4 of the total inductance might be expected.
Is there a formula for this? I have seen stuff where it's been assumed that 1/2 a winding is 1/2 the specified total inductance and I've gone along with that since we all know L1 + L2 +Ln...

*Gone 50 years without being able to measure inductance and now I can it throws up something basic I didn't know!

You are not taking into account the 'mutual inductance' that any tightly coupled coils like the windings of a transformer have.

Two inductances only add together like resistors if the magnetic field from each inductor is not coupled together, which of course in a transformer, it is.

With a coil the inductance is proportional to the square of the number of turns. So, if you double the number of turns then the inductance is four times and not twice.

So with a centre tapped transformer where each half measure 1 Henry, the total across both halves will be 4 Henries (as long as there are no losses in the inductive coupling) .

[anotherjim]

Cheers, that makes sense. The mutual effect also explains why shorting out one half of the winding kills the inductance of the non-shorted half.

[Mark Hammer]

"Tapping" also implies that  there are layers under layers under layers, such that "outer" layers have a greater circumference than inner ones, altering the inductance of those layers.

[Rob Strand]

It all boils down to inductance being proportional to turns squared.  Suppose you have two cores with N turns and they have inductance L.  When you put these in series you get a total inductance Lt=2*L.   Suppose now you have two windings of N turns *on the same core* you get a total Lt = 4*L (or Lt ~ 0 if connected with the wrong phase).   The difference in the second case is the windings are coupled.

For a given core the inductance is related to the turns by  L = AL * N^2.   When you have two windings on the same core it's like having 2N turns so Lt = AL * (2N)^2 = 4 AL N^2 = 4 L.

In the above I make two windings into one with more turns.

Another view is to use mutual inductance, as FXSF mentioned.   Both views are equivalent but the mutual inductance accounts for the coupling *between* the *two* windings separately.   When you have mutual inductance the first winding increases,    Lt1 = L1 + M and the inductance of the second winding increases to Lt2 = L2 + M  then when you put those two windings in series you get Lt = Lt1 + Lt2 = L1 + L2 + 2M.    In my example L1 = L, L2 = L and M = L where L is the inductance of one of the N turns windings.  So you get  Lt = L + L + 2M = 4M.    The rabbit pulled out of the hat here is M = L, I haven't shown it to be true.  If you had two air coils M the would be less than L because the two windings aren't well coupled.  And when you have two separate coils the idea is there is no coupling, which isn't 100% true, and in this case you get M = 0 and Lt = L1 + L2 = L + L = 2L; which agree with what you see that the inductances of separated inductors just add.

Mutual inductance is harder to quantify so it's always easier to think as the two windings forming a new inductor with more turns.

If you have a transformer with with taps V1 and V2  the inductance goes up with the square of the voltages when you add them.   That's because the voltage is proportional to the turns but the inductance is proportional to the square of the turns.   If you know the inductance of a winding voltage rating V1 is L1  then you can estimate the inductance for a winding rate at V2 as L2 = (V2/V1)^2 * L1.    And if you put those windings in series you get V1 + V2 and inductance for the series connection will be L = ((V1 + V2)/V1))^2 * L1.  In the example with equal turns and hence equal voltages on V1 and V2 windings  V1 = V2  so L = ((V1 +V1)/V1)^2 * L1 = 4 L1, not 2L1.

[PRR]

> "outer" layers have a greater circumference than inner ones, altering the inductance of those layers.

Circumference has very little effect on inductance. In a closed iron-core coil, almost zero. (Inductance goes by number of passes through the window, not length and not-quite "turns".)

Circumference directly leads to resistance, DCR, but in a good iron-core coil this should be nearly insignificant to the audio.

Things is different in open-core, notably instrument pickups. But that's not the question here?

[anotherjim]

I think it was using an audio transformer winding to simulate pickup inductance where I've seen the use of a centre tap to provide a hi-lo selection. I don't remember the inductance so produced being mentioned. It may well have been understood that it doesn't halve the total but it does bring a little more versatility for the cost of a switch.

I suppose it's understandable that mainstream online information doesn't have much on the subject. If you want inductance you reach for an inductor.

There's a ton of info here that will take some time to digest - but many thanks for including it 

[Rob Strand]

Look up some of the older threads on this forum on the Zircom transformers from Mouser etc.  I may have even posted a way to ball-park the inductance from the nominal impedance rating.

The problem with using iron-core transformers as inductors is the inductance depends on the signal level.
At low levels the inductance is low, then it rises up, then falls again.  For small signal stuff you are
on the "rise up" part.  If your LCR meter tests at relatively high currents you will end-up with a larger
inductance measurement than the circuit sees (assuming the AC operating current in circuit is small). 
The falling down part is shows up in mains transformers operating at full voltage.    The thing that
saves some of those small transformers used as inductors is there are tiny air-gaps between the laminations
which tend to reduce the variation of inductance with drive level.