# Exploring Inductor Design for Audio Applications

• sparks_nz
In summary, the conversation discussed the design of an inductor for audio applications using a high permeability toroid with a closed trifilar winding. The question was raised about the Q factor difference between a closed trifilar winding and a conventional single winding with the same inductance. It was suggested that the tight coupling of the three strands in the trifilar winding could add capacitance and improve the Q factor. However, there was also discussion about the difficulty of winding the 3x wire onto the toroid and the potential cost of the specialized wire. Ultimately, it was determined that the trifilar winding may not provide a significant advantage in Q factor and the decision to use it may depend on the specific design and application of the inductor.f

#### sparks_nz

TL;DR Summary
Help with understanding of Q factor difference of a toroidal closed trifilar winding verses conventional single winding of same inductance.
Hi,
I am experimenting with a design for an inductor for audio applications, and am using a high permiability toroid (12,000) having a closed trifilar winding. In this instance , it is 39T x 3 twisted wires connected in series being 117 turns in total, giving approx 180mH inductance.

In regards its Q when resonant with a small cap, I would like to know how much benefit in Q would be obtained to instead wind a single 117T coil to obtain the same inductance. I do not know how much the closed trifilar wind degrades the Q factor due to what I presume would be greater self capacitance, and hence if it is worthwhile trying to create a single wound coil.

I originally chose a trifilar wind, as it cuts down the number of turns on the (smallish) toroid, saving space. Can someone please advise me on this, and perhaps help me understand the principles involved. Thanks.

I would like to know how much benefit in Q would be obtained to instead wind a single 177T coil to obtain the same inductance.
39 * 3 = 117, not 177.

Summary: Help with understanding of Q factor difference of a toroidal closed trifilar winding verses conventional single winding of same inductance.

I am experimenting with a design for an inductor for audio applications
What is a trifilar wound inductor? I have never heard of that concept -- maybe I can learn something new.

What are the 3 separate coils? If not separate windings on a transformer, then what?

Delta2
Hi, its 3 wires twisted together and wound as a single wire would be. The 3 coils therein are connected in series to form an inductor that effectivly is 3 times the amount of turns the original winding.

39 * 3 = 117, not 177.
Thanks, I saw the error just after posting it.

Hi, its 3 wires twisted together and wound as a single wire would be. The 3 coils therein are connected in series to form an inductor that effectivly is 3 times the amount of turns the original winding.
*Sigh*

Why? Can you post the math that shows what is different from winding just 3x the turns?

The tight coupling of the three strands will add capacitance, which is negative reactance. That will reduce the reactance very slightly, which for the same resistance will increase the Q.

I am experimenting with a design for an inductor for audio applications, ...
But why is Q important over the entire audio band? 20 Hz to 20 kHz is a factor of 1000. Variation of the reactance over that range will also have a factor of 1000.

Are you building a tuned circuit or a broadband transformer?

Can you post the math that shows what is different from winding just 3x the turns?
It is easier to wind 39 turns of three wires twisted together onto a toroid, than 117 turns of thin wire.
The OP is asking what difference the twisting has on the electrical properties.

It is easier to wind 39 turns of three wires twisted together onto a toroid, than 117 turns of thin wire.
The OP is asking what difference the twisting has on the electrical properties.
Not with our toroid winding machine. But I'm still interested in the OP's response.

Delta2 and DaveE
*Sigh*

Why? Can you post the math that shows what is different from winding just 3x the turns?
Im sorry I didnt explain the matter more clearly, but the crux of it is that to wind only 39 turns of x3 is much easier than winding 117T on the toroid.

The tight coupling of the three strands will add capacitance, which is negative reactance. That will reduce the reactance very slightly, which for the same resistance will increase the Q.

But why is Q important over the entire audio band? 20 Hz to 20 kHz is a factor of 1000. Variation of the reactance over that range will also have a factor of 1000.

Are you building a tuned circuit or a broadband transformer?
Its basically a tuned circuit, but with a 2 turn primary to energise it. Are you saying the 39T trifilar wind would have higher Q than 117T?

Im sorry I didnt explain the matter more clearly, but the crux of it is that to wind only 39 turns of x3 is much easier than winding 117T on the toroid.
No it isn't, not in my experience. Who is making this trifilar 3x wire spool? What are they charging you for that? What adjustments are you making in your toriod winding machine to wind that 3x wire? What is the brand and model of your toroid winding machine?

Delta2
No it isn't, not in my experience. Who is making this trifilar 3x wire spool? What are they charging you for that? What adjustments are you making in your toriod winding machine to wind that 3x wire? What is the brand and model of your toroid winding machine?
I don't have a toroid winding machine. The trifilar wire is made manually by measuring out 3 equal lengths of wire, and then twisting them together. I use an electric drill for that. The effort is in holding the toroid and wire and doing the manual threading process. As can be imagined, 39 turns is much easier than 117T.

My gut says there's not much difference, since they are connected in series. Yes, you will have much more winding capacitance, but in a tuned circuit that will be adjusted for. Q is primarily about losses, and I don't see how the losses are any different.

Of course the best answer is to wind two each way and compare. 117T by hand is tedious but absolutely doable; I've done similar windings. A tip: start in the middle of the wire 58T one way, 59T turns with the other end.

Im sorry I didnt explain the matter more clearly, but the crux of it is that to wind only 39 turns of x3 is much easier than winding 117T on the toroid.
The effort is in holding the toroid and wire and doing the manual threading process.
We wind toroidal transformers here in the tens of millions, so obviously we use toroid winding machines for them. They are pretty specialized machines, so unless you are going into volume production, I suppose that winding them by hand is an alternative. Still, that will introduce variations in the parasitics that will alter the inductor's performance a bit, so hopefully this is not a precision application.

DaveE
In regards its Q when resonant with a small cap, ...
1. What is the value of that small cap?
2. Does it dominate the self capacitance of the coil?

In this instance , it is 39T x 3 twisted wires connected in series being 117 turns in total, giving approx 180mH inductance.
180 mH; 117 turns; AL = 180 mH / 117² = 13.15 uH / turn²

Its basically a tuned circuit, but with a 2 turn primary to energise it.
3. What is the reactance of that two turn primary winding at the unspecified centre frequency?
13.15 * 2² = 52.6 uH primary.
4. How is the primary driven?

This is a confusing question to answer because critical information is missing. Too many possible assumptions come into play. For a start, it would be helpful to know:
5. The planned resonant frequency.
6. The wire gauge and material.
7. The insulation thickness and dielectric constant.
8. The final length of each of the three wires.

DaveE
Still, that will introduce variations in the parasitics that will alter the inductor's performance a bit, so hopefully this is not a precision application.
For a start, it would be helpful to know:
5. The planned resonant frequency.
Fortunately he said it's an audio application. So, I'd guess that the high frequency stuff that we would worry about isn't applicable. Although I couldn't guess why you would want an audio tuned circuit. A filter, I guess. But that would be much better done with op-amps, IMO. No one uses inductors in op-amp filters, they're a PIA compared to R's and C's.

berkeman
Thank you all for your help. I am experimenting with PWM and using the coil / transformer driven by dc pwm switched source. To answer your questions:
The carrier freq is 32kHz. Yes the primary is approx 50uH. The added cap of 50pF does not dominate the self capacitance of the coil. The wire is 0.5mm diameter enamelled copper wire. I don't know the insulation thickness or its dielectric constant. The length of the 3 wires used is 1.77m each, being 5.32m in a total length.

Thank you all for your help. I am experimenting with PWM and using the coil / transformer driven by dc pwm switched source. To answer your questions:
The carrier freq is 32kHz. Yes the primary is approx 50uH. The added cap of 50pF does not dominate the self capacitance of the coil. The wire is 0.5mm diameter enamelled copper wire. I don't know the insulation thickness or its dielectric constant. The length of the 3 wires used is 1.77m each, being 5.32m in a total length.

At the start of this thread, I'd assumed that there was a reason that you wanted to wind this magnetic component on a toroid, but now I have doubts. We use toroids in our communication transformers to minimize the volume of those components. The other common reason is to minimize the amount of stray B-field noise that the component generates that can cause problems with other nearby mangnetic components. (But not for the B-field noise immunity of the toroid itself, unless the coil(s) on the toroid are wound a particular way -- Quiz Question: What way?)

Why are you wanting to use the most difficult magnetic component geometry to wind in your application? There are other ways to minimize B-field noise coupling while still using standard bobbin-based winding methods. And if you can use a more standard construction (pot-core, EE-core, EI-core, etc.), you can buy and use a simple hand-driven coil winding machine to give you beautifully consistent winds every time...

DaveE
The added cap of 50pF does not dominate the self capacitance of the coil.
Then why is the small parallel resonant capacitor there?
Or is it a series resonant capacitor?
Is this a sinewave narrowband communications system, or a square-wave switching power supply that is being PWM'd?
What is the Vpp primary drive voltage?

Why are you wanting to use the most difficult magnetic component geometry to wind in your application?
This. What most everyone else does is wind it on a bobbin and use an EE or EI core. Pot cores typically don't have as much winding area as you'll want, although they are great if you need lots of inductance per turn; they have a short magnetic path and a big core area compared to others.

Also 32KHz is a really low frequency for this sort of thing. The only people that make SMPS down there are using really slow devices that are required to process huge power levels. Nearly everything about these designs is easier and works better if you get up to 100-200KHz or so. This is especially true for the magnetics.

Finally, have you looked into the SMPS designs that places like TI.com or Analog.com support? They've already done a great job of most all of the design for you. They both also have great educational materials.

This. What most everyone else does is wind it on a bobbin and use an EE or EI core. Pot cores typically don't have as much winding area as you'll want, although they are great if you need lots of inductance per turn; they have a short magnetic path and a big core area compared to others.

Also 32KHz is a really low frequency for this sort of thing. The only people that make SMPS down there are using really slow devices that are required to process huge power levels. Nearly everything about these designs is easier and works better if you get up to 100-200KHz or so. This is especially true for the magnetics.

Finally, have you looked into the SMPS designs that places like TI.com or Analog.com support? They've already done a great job of most all of the design for you. They both also have great educational materials.

Thanks for the advice, Its appreciated. The use of 32kHz is due to the generator I am using. I will look up the suggested materials.

Then why is the small parallel resonant capacitor there?
Or is it a series resonant capacitor?
Is this a sinewave narrowband communications system, or a square-wave switching power supply that is being PWM'd?
What is the Vpp primary drive voltage?
The parallel cap was just to test the variation in freq to roughly ascertain what sort of Q the inductor had when already resonant with its internal capacitance. I am interested in experimenting with producing an amplitude modulated sinewave envelope using pwm. No particular dedicated project device as such. The primary Vdd supply is 9 volts.

The difference between tri-filar winding and single winding seems similar to the case of a solenoid wound either with a single layer or pile wound. Pile winding causes the turns to be more immersed in the field of other turns, so has more inductance. On the other hand, each turn will have more skin resistance as a result of the stronger field from adjacent turns.

Regarding the inter turn capacitance, this will create a self resonant frequency. If we are working below this resonance, the capacitance in parallel with the coil increases the inductive reactance. This is because the current in the capacitance leads the applied voltage by 90 degrees, whereas that in the coil lags it. As a consequence, the current taken by the coil is reduced, corresponding to increased inductance.

If we consider the measured resistance of the coil, when it has shunt capacitance the effect is to increase the resistance. This is fundamentally because there is circulating current through the coil as a result of the capacitance - we are approaching a resonant condition. The series resistance of the windings is stepped up to a higher value as resonance is approached.

The difference between tri-filar winding and single winding seems similar to the case of a solenoid wound either with a single layer or pile wound. Pile winding causes the turns to be more immersed in the field of other turns, so has more inductance. On the other hand, each turn will have more skin resistance as a result of the stronger field from adjacent turns.

Regarding the inter turn capacitance, this will create a self resonant frequency. If we are working below this resonance, the capacitance in parallel with the coil increases the inductive reactance. This is because the current in the capacitance leads the applied voltage by 90 degrees, whereas that in the coil lags it. As a consequence, the current taken by the coil is reduced, corresponding to increased inductance.

If we consider the measured resistance of the coil, when it has shunt capacitance the effect is to increase the resistance. This is fundamentally because there is circulating current through the coil as a result of the capacitance - we are approaching a resonant condition. The series resistance of the windings is stepped up to a higher value as resonance is approached.
Thanks for your reply on this. Can you elaborate please on the coil's self resonant frequency in regards the difference between the trifilar coil and single wound coil of same number of total turns? I presume the trifilar will have a much lower self resonant frequency and Q?

In principle yes, although at low frequencies I think the effects will be small.
You also mentioned you would use a thinner wire for tri-filar winding, which will reduce the Q.

Wound inductors behave in different ways dependent on their environment. If you know the length of the wire used, and the dielectric constant of the insulation, you can compute a velocity factor, then model the isolated inductor as a wire dipole. That is because the winding wire behaves like a delay line, an open-ended transmission line relative to what could be called “stray capacitance”.

You will often find the dominant self resonance at the half-dipole frequency. I expect a trifilar winding will also exhibit a resonance at three times the fundamental frequency. That is because the three close wires will form a directional coupler. Just what odd or even modes the coupling takes will be interesting. Would two or four wires change the modes?

In principle yes, although at low frequencies I think the effects will be small.
You also mentioned you would use a thinner wire for tri-filar winding, which will reduce the Q.
Thanks, It confirms what I am thinking. I wonder if this trend would just continue if the number of filar windings were increased incrementally in separately made coils (say 3 up to 10), while keeping the same number of total turns constant?

Wound inductors behave in different ways dependent on their environment. If you know the length of the wire used, and the dielectric constant of the insulation, you can compute a velocity factor, then model the isolated inductor as a wire dipole. That is because the winding wire behaves like a delay line, an open-ended transmission line relative to what could be called “stray capacitance”.

You will often find the dominant self resonance at the half-dipole frequency. I expect a trifilar winding will also exhibit a resonance at three times the fundamental frequency. That is because the three close wires will form a directional coupler. Just what odd or even modes the coupling takes will be interesting. Would two or four wires change the modes?
Thanks for this. I will sweep the trifilar winding with a freq gen to see if there are other resonances. I have only been focussed on the fundemental.