# Loudspeaker Inductance



## solacedagony (May 18, 2006)

I was reading the "Thoughts on TC Sounds Subs" post the other day and someone mentioned their high inductance. I decided to look into what effects inductance has on sound. My Loudspeaker Cookbook doesn't seem to have anything on it and I can't find a single thing on Google about this. I figure that since a loudspeaker is an inductor, it's a low-pass crossover of sorts on its own. This is the only idea I could come up. Any other ways inductance could effect the sound of a speaker?


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## Rbsarve (Aug 26, 2005)

It is one of the factors that determine the transient behaviour of the sub design. Low inductance is nice.
But very seldom comparative with huge excursion. Engineering is all about picking the most suitable compromise.
If you can keep BL high (and linear) and cone whight down, inductance isn't that much of a deal.


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## Guest (Mar 1, 2007)

There's _inductance_, and then there's _inductance variation_ with position.

*Inductance* creates a built-in, firt order low-pass filter. It conspires with the voicecoil resistance to determine the -3dB, or cutoff frequency. A good rule of thumb is that you want to keep the external, active xover of the sub maybe an octave below this cutoff frequency. Therefore, inductance puts a limit on the useable high-frequency extension of the sub. Voicecoil inductance impacts the rise-time of the transient response, in the same fashion that the active xover would.

*Inductance Variation* is a non-linear parameter in the sub's operation. If the inductance changes with cone position, this will give rise to harmonic and intermod distortion. How large, depends on a couple factors (including of course how large the variation is): First, frequency of operation ... since the inductive impedance must always be compared to it's series brother, voicecoil resistance, the inductive nonlinearity tends to manifest most at higher freqs where the inductive impedance is larger. Second, other nonlinear terms (like BL shape) that may swamp the inductance variation.


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## solacedagony (May 18, 2006)

werewolf said:


> There's _inductance_, and then there's _inductance variation_ with position.
> 
> *Inductance* creates a built-in, firt order low-pass filter. It conspires with the voicecoil resistance to determine the -3dB, or cutoff frequency. A good rule of thumb is that you want to keep the external, active xover of the sub maybe an octave below this cutoff frequency. Therefore, inductance puts a limit on the useable high-frequency extension of the sub. Voicecoil inductance impacts the rise-time of the transient response, in the same fashion that the active xover would.
> 
> *Inductance Variation* is a non-linear parameter in the sub's operation. If the inductance changes with cone position, this will give rise to harmonic and intermod distortion. How large, depends on a couple factors (including of course how large the variation is): First, frequency of operation ... since the inductive impedance must always be compared to it's series brother, voicecoil resistance, the inductive nonlinearity tends to manifest most at higher freqs where the inductive impedance is larger. Second, other nonlinear terms (like BL shape) that may swamp the inductance variation.


In reference to inductance, you could figure out what the low pass point was based on the inductance and the impedance of the VC, correct? Or does that only apply for crossovers?
Is it normal for inductance to change with cone position or does a good driver just minimize the amount of inductance change over travel.
When you refer to inductive impedance, you're talking about impedance based on frequency (as the freq increases, we have more impedance because of the "low pass filter"). Is that right? What is the difference between that and the VC resistance?


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## Guest (Mar 2, 2007)

solacedagony said:


> In reference to inductance, you could figure out what the low pass point was based on the inductance and the impedance of the VC, correct? Or does that only apply for crossovers?
> Is it normal for inductance to change with cone position or does a good driver just minimize the amount of inductance change over travel.
> When you refer to inductive impedance, you're talking about impedance based on frequency (as the freq increases, we have more impedance because of the "low pass filter"). Is that right? What is the difference between that and the VC resistance?


- Loudspeaker coil _inductance_ (if we ignore it's _variation_ with coil position in the gap, for a moment) is indistinguishable ... in all ways ... from a passive, first-order, low-pass filter externally applied to the driver. Why do we know this? 

- Yes, the low-pass point can be calculated based on the value of the inductance and the voicecoil resistance, just like you would for a passive x-over 

- A good driver minimizes the change of the inductance relative to coil position in the gap. Have you heard all the fancy talk of copper shorting rings? Right here is the main motivation, as far as i know.

- Yes, "inductive impedance" depends on frequency ... it's magnitude is : |Z| = (2pi*f*L). This impedance value can now be compared to voicecoil resistance (which is, to first-order, independent of frequency), since the two elements are in series. So you can see that even a large voicecoil inductance, or one with large variation, will not be very significant at very low frequencies.


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## npdang (Jul 29, 2005)

I think it's useful to take a look at some of the Klippel distortion breakdowns posted in the review section. Inductance variation tends to constitute a very small percentage of overall non-linear distortion.

You'll also notice with alot of the nearfield plots, high inductance drivers tend to have a "hump" in the 80-120hz region.


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## DS-21 (Apr 16, 2005)

npdang said:


> You'll also notice with alot of the nearfield plots, high inductance drivers tend to have a "hump" in the 80-120hz region.


Sometimes, as in the case of TC Sounds' older top-of-the-line motors (3HP and 4HP) quite a large one. I don't know if the same holds true for their newer TOTL motors, though.


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## solacedagony (May 18, 2006)

npdang said:


> I think it's useful to take a look at some of the Klippel distortion breakdowns posted in the review section. Inductance variation tends to constitute a very small percentage of overall non-linear distortion.
> 
> You'll also notice with alot of the nearfield plots, high inductance drivers tend to have a "hump" in the 80-120hz region.





DS-21 said:


> Sometimes, as in the case of TC Sounds' older top-of-the-line motors (3HP and 4HP) quite a large one. I don't know if the same holds true for their newer TOTL motors, though.



I'm guessing these would need to be EQed out or a steep crossover around 80hz or just before to minimize the hump's effects?


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## Guest (Mar 3, 2007)

npdang said:


> I think it's useful to take a look at some of the Klippel distortion breakdowns posted in the review section. Inductance variation tends to constitute a very small percentage of overall non-linear distortion.


Agreed  My only _slight_ caution would be, that inductance variation will be more significant at higher frequencies, where the *nominal* inductance yields an impedance approaching that of the coil resistance. Whereas other forms of nonlinearity *may* be more frequency-independent ... actually, i gotta ponder that some more


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## SSSnake (Mar 8, 2007)

One comment... since the inductance variation is dependant on excursion and excursion decreases with freq (assuming constant SPL), I would think that depending on the configuration - inductance variation COULD be worse at lower freqs (not IS worse but COULD be worse because an inductor acts as a low pass thus offsetting the excursion effects).

This brings me to the subject of the AA Avalanches. Has anyone noted inductance variation in the Avalanches? I have an issue with my two 18"s that seems to be a result of inductance variation but I can't swear that it is the cause (the problem is worse at lower freqs). Any input would be appreciated (sorry if this seems like a thread hijack but I think that this may be a very good point for discussion and understanding of inductance variation).


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## thechris (Jun 26, 2005)

the real issue is not low frequencies. at low frequencies, the mechanical system is more dominant.

The issue is with simultaneous play of low and high frequencies. eg, a high excursion midbass used for full range or at least vocal range sound.

this generates IMD.


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## kennyg (Jun 23, 2007)

Has anybody here read the tech paper that used to be on the Adire site when Dan Wiggins tested the effects of increasing inductance, then increasing mms, and then graphed the results? I wish I would have saved it now, but I never thought the Adire site would go down


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## Guest (Jul 6, 2007)

kennyg said:


> Has anybody here read the tech paper that used to be on the Adire site when Dan Wiggins tested the effects of increasing inductance, then increasing mms, and then graphed the results? I wish I would have saved it now, but I never thought the Adire site would go down


yes ... it was misleading. Not wrong, just misleading 

Two reasons :

1. Adire's definition of "transient response" was NOT the industry standard. Adire was referring to *only* the _leading edge_ of the time-domain response to a transient input, rather than the _complete_ time-domain response to the transient input (the industry standard definition of transient response). Yes ... inductance does limit the transient rise of the step response, because it introduces a _low-pass_ function to the sub's frequency response. And yes ... mass has no effect on the transient rise of the step response, other than a gain term related to efficiency, because the sub's output is proportional to acceleration. HOWEVER, as shown by Small (et al), mass DOES impact the _high-pass_ behavior of the sub's frequency response, by influencing Fs and Qts, and therefore it impacts transient over-shoot and ringing in the _complete_ time-domain response to a transient input. This is why you'll see a thorough analysis "transient response" by Small ... even though inductance is never even mentioned 

In short, _inductance_ impacts rise-time (or attack) in the _complete_ time-domain response, whereas _mass_ impacts over-shoot and ringing (or decay) in the _complete_ time-domain response.

2. A sub's coil inductance (in relation to coil resistance) can ... and must ... always be compared directly to the intended (typically active) low-pass crossover frequency of the sub. When you recognize that a first-order xover for the sub can be realized as a series _inductance_ (although impractical), after reading the Adire paper you may be tempted to believe that low-passing a sub is a _bad_ idea


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## Neil (Dec 9, 2005)

You can still see the document using various archive sites. Here you go:

http://web.archive.org/web/20060313114051/www.adireaudio.com/Files/TechPapers/WooferSpeed.pdf


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## Xander (Mar 20, 2007)

werewolf said:


> - Yes, the low-pass point can be calculated based on the value of the inductance and the voicecoil resistance, just like you would for a passive x-over


So how do you calculate this? I'm not experienced in crossover design...yet


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## Neil (Dec 9, 2005)

Xander said:


> So how do you calculate this? I'm not experienced in crossover design...yet


Where:
f = frequency at which rolloff begins
Re = DC resistance
Le = inductance in H (please note that you will have to convert the inductance measurement given by the manufacturer as it is usually given in mH)

f = Re / (2*Pi*Le)


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## Xander (Mar 20, 2007)

Punk0Rama said:


> Where:
> f = frequency at which rolloff begins
> Re = DC resistance
> Le = inductance in H (please note that you will have to convert the inductance measurement given by the manufacturer as it is usually given in mH)
> ...


Thanks! I wish there was a loudspeaker physics class at my university. We did a lot with LCR circuits in physics, which touched on some stuff I could use in crossovers and such, but not nearly enough.


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## Neil (Dec 9, 2005)

Xander said:


> Thanks! I wish there was a loudspeaker physics class at my university. We did a lot with LCR circuits in physics, which touched on some stuff I could use in crossovers and such, but not nearly enough.


The funny thing about loudspeaker physics: it's largely just an application of various engineering concepts. It's mass on a spring driven by an electromagnetic motor. Keep taking your classes and you'll begin to see how they relate.


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