Inductors in series - What happens to Q value?

[lassoharp]

I was looking at connecting two inductors of 465mH and 562mH in series to get a single value of 1.027H for use in the low freq boost section of the MEQ and wanted to know what if anything happens to the net Q value.

Assuming the coils are high-Q type and their max Q values are at similar freq locations, what happens to the Q value when connected in series?  Stays the same?  Less?

Stringing together some transformer windings of larger unequal Q(say 10 and 3) in series I'm getting the resultant Q as roughly the difference(or avg) - or slightly less than.  When connecting two of very close Q I'm getting essentially an average of the two.  So for both call it the average?

 

[JohnRoberts]

You need to lump the sundry terms. Resistance in series simply sums, capacitance and inductance in series follows the relationship total = 1/(1/x+1/y+1/z).

JR

 

[dmp]

capacitance and inductance in series follows the relationship total = 1/(1/x+1/y+1/z)

Wrong - inductance in series are summed, like resistances
Because in series, impedances are summed: Ztot=Z1+Z2...
where inductance impedance = jwL

The Q factor of an inductor reflects how close it is to ideal, i.e. zero resistance, I think. The lower the Q, the more resistance due to windings, these non-ideal resistances will add in series.

 

[JohnRoberts]

Thanx for the correction... you can tell how many multiple inductor designs I have ever done. I find them more useful in switching power supplies and filters in the output of class D stuff and never in series or parallel...

I still have a bag of inductors I bought to make a 5 band EQ back about 40 years ago...  Never finished that puppy.

JR

 

[lassoharp]

I understand the Q as a ratio of winding resistance to reactance - so Q of 50 would mean  50 times more reactance compared to winding resistance at a given frequency.


@JR - When you say lump terms do you mean combine the entire resonant circuit? - as in include the cap(s) paired with the 2 series inductors and compute from there?

That equation is one I haven't worked yet and I'm unsure of how to use the x, y and z variables - have any text examples handy?

 

[PRR]

What's limiting the Q?

Could be series or shunt resistance.

At audio frequencies we always have nagging series resistance. The shunt resistance may be negligible or significant.

Plot impedance magnitude from zero to infinite frequency. It will be flat from DC to maybe 100Hz, rise like an inductor (or maybe not quite as fast; eddy losses), finally decline (there's capacitance in everything), with maybe a flat plateau before it falls.

Where are you working? Closer to the low frequency flat or the high frequency flat?

In most low-audio applications, the low-freq DCR dominates. Add the Ls. Multiply by your F and two pies. Add the Rs. Find the ratio. Unless the two coils are very different, the result will be esssentially an "average".

(If shunt resistance were dominant, you would use the one-over formula John gave.)

In most audio apps, you don't want a specific Q but a maximum R. Lowest production cost comes with an R just barely under the max. Stray-parts DIY, you either find coils that won't work or coils that are "too good"; add resistance to slug the Q down to desired value.

 

[owel]

Wrong - inductance in series are summed, like resistances

Partially correct. Unfortunately, that's not the total picture.

If the 2 inductors are spaced apart such that their magnetic fields do not interact with one another, yes...  you just simply add them up, like resistances.
LT = L1 + L2  ; where L = inductance

But if the 2 inductors are spaced close together that their magnetic fields interact, their magnetic fields could be opposing or aiding each other.  The mututal inductance (M) then will have an effect on LT.

If the Mutual inductance (M) is aiding each other, then Total Inductance is:
LT = (L1 + M) + (L2 + M)  <---- as you can see, it's not just a simple L1 + L2.

If the Mutual inductance is opposing each other, then
LT = (L1 - M) + (L2 - M)  <---- again, not a simple L1 + L2 equation.

You can easily verify this effect using an Inductance meter (on your tester).

Get two inductors and measure the total inductance in series... then switch the 2nd inductor around (in polarity) and measure again in series. You'll measure (2) different values! ... and yet both inductors are still connected in series.

Now, get a metal rod and place it nearby both inductors, you'll get another LT reading. The metal rod would be affecting the M value and thus changing the overall LT value again.

Now, to compute the value of M is more involved. See here http://farside.ph.utexas.edu/~rfitzp/teaching/em/lectures/node83.html

 

[PRR]

> if the 2 inductors are spaced close together that their magnetic fields interact

Yes. But many useful audio inductors are semi closed core.

If core is closed, the stray and possibly mutual inductance is like 1/1000th of the total.

If gapped cores have gaps aligned it may be several percent; but this won't happen casually.

Yes at the higher frequencies we DO use rod-cores which throw stray flux all over. These interact so much that in speaker crossovers they must be mounted right-angles. We prefer semi-closed cores for low-level work because they don't absorb external (hum/buzz/audio) fields so well; but in DIY we sometimes use what we can find, and in some ranges (not 465mH) rod-cores are commodity items.

And people ask why we don't use inductors in audio.......