Voice Coil Position: Impact of Fringing Field on Dynamic Microphones

[jamesadrian]

If you have a cylindrical permanent magnet with a voice coil around it, sound moving the voice coil a small distance back and forth along the length of the bar magnet will produce an RMS voltage across the voice coil; but not very much RMS voltage if the voice coil is in the center of the magnet's legth. I believe that the lines of the field are too constant there. It is when the voice coil is closer to one end of the magnet than the other end that the field density changes around the voice coil as the voice coil changes location.

Can anybody confirm this? Is this what is called a fringing field? Do dynamic microphones depend upon their voice coils moving in a fringing field?

Thank you for your help.

James Adrian

 

[Bob S]

Two things:

1) A loudspeaker works by using the Lorentz force on current in the voice coil
$$\overrightarrow{F}=\int \overrightarrow{I}\times \overrightarrow{B} d\ell$$
2) while using the voice coil as a sound pickup uses the Faraday induction law.
$$V=-\frac{d}{dt}\int N \space B\cdot n \space dA$$
where N is the number of turns of the voice coil. So the voice coil will not work as a pickup in a uniform magnetic field, while the loudspeaker will. Voice pickup coils must move in a fringe field.

 

[jamesadrian]

Two things:

1) A loudspeaker works by using the Lorentz force on current in the voice coil
$$\overrightarrow{F}=\int \overrightarrow{I}\times \overrightarrow{B} d\ell$$
2) while using the voice coil as a sound pickup uses the Faraday induction law.
$$V=-\frac{d}{dt}\int N \space B\cdot n \space dA$$
where N is the number of turns of the voice coil. So the voice coil will not work as a pickup in a uniform magnetic field, while the loudspeaker will. Voice pickup coils must move in a fringe field.

This makes sense. Thank you Bob.

Jim Adrian

 

[Philip Wood]

JA. The magnetic field in which the voice coil moves in a real loudspeaker is a radial field, quite different from that of a bar magnet. A real loudspeaker (with a step-up transformer) serves as quite a sensitive microphone (though its frequency response can be very poor). It works because emfs are induced in the coil as it moves, cutting the radial field lines.

I expect you know this. In which case please regard this contribution as gratuitous rather than insulting.

 

[Bob S]

JA. The magnetic field in which the voice coil moves in a real loudspeaker is a radial field, quite different from that of a bar magnet. A real loudspeaker (with a step-up transformer) serves as quite a sensitive microphone (though its frequency response can be very poor). It works because emfs are induced in the coil as it moves, cutting the radial field lines.

There are two basic types of loudspeaker voice coils; overhung and underhung. The reasons for this is to maximize linearity (displacement per amp) and minimize distortion. See attachment and also http://en.wikipedia.org/wiki/Voice_coil#Design_considerations.

In both designs the net number of field lines that the voice coil cuts as it moves does not change, so no voltage is induced in the coil (see Faraday's Law in post #2) when the coil moves in response to sound. So the speaker will not be a good microphone.

 

[Philip Wood]

Bob: I beg to differ...
(a) Cutting is cutting. Please see thumbnail. The argument applies to the underslung case as well as to the overslung.
(b) As a boy I used a loudspeaker (with its output transformer) as a microphone on several occasions. It gave a larger output than a piezo-electric crystal microphone (a cheap but quite sensitive microphone of the era). Admittedly the step-up transformer stops this from being a proper like-with-like comparison, but clearly the emf from the voice coil (only 20 turns or so) was not negligible. [If I now had access to an oscilloscope I'd measure the output from a loudspeaker voice coil when I whistled into the cone. Not a pretty sound.]

 

[Philip Wood]

So obsessed am I with this emf in a loudspeaker voice-coil, that I've drawn a diagram to show that there is a change in the flux linking the voice coil when it moves in the gap between the magnet's poles, even when the coil is nowhere near the edges of the gap.

 

[Bob S]

So obsessed am I with this emf in a loudspeaker voice-coil, that I've drawn a diagram to show that there is a change in the flux linking the voice coil when it moves in the gap between the magnet's poles, even when the coil is nowhere near the edges of the gap.

Suppose we had an overhung voice coil with M turns, and N turns in the radial magnetic field, specifically from the nth turn to the (n+N)th turn (n+N < M). Now the voice coil moves 1 turn, so that the (n+1)th turn to the (n+N+1)th turns are in the field. So the voice coil cut field lines on one end, and simultaneously uncut the same number of field lines on the other, and still has N turns in the field. I do not believe a voltage was developed in the voice coil.

 

[Philip Wood]

Bob. Thanks for reply. In what follows, I'm dealing just with the overhung case. There are two ways of describing the origins of the (alleged) emf, are there not?: in terms of flux cutting, and in terms of flux linkage changing.

(a) Flux cutting. As long as turns are cutting flux lines and the direction of motion and direction of flux lines doesn't change, there will be an emf. It doesn't matter which turns are doing the cutting. When you talk about uncutting of lines of flux as turns emerge from the radial field, I think you're possibly being misled by the analogy of the magnet moving inside the long solenoid, where the cutting due to each pole of the magnet is equal and opposite, because of the opposite radial field components. In this case, at the end of the coil which is emerging from the field, there is no longer cutting, but turns near the other end are entering the field and cutting instead.

(b) Flux linkage changing. For me, this is the preferred viewpoint. If you draw in some field lines for the overhung case, in the way I've done for the single turn, I think you might come round to my conclusion that as the coil goes upwards in the field there will be less linkage of the coil by field lines. Basically none of the turns that are emerging from the field at the top will have flux linked with them any more. Those turns entering the field at the bottom – and this is the key point – won't get any more flux linked with them as they enter the radial field, as they had the maximum flux linked with them when they were overhung at the bottom, because the magnet's flux is going through the central cylinder of the magnet and therefore through these turns!

 

[jamesadrian]

Thank you all for your help on the fringing field issue as it applies to dynamic microphones. I have a very related question about fringing fields in electret microphones:

A conductor, like a metal string, is moving in an electric field.

The metal string is under mechanical tension and is electrically connected to a resistor. The other end of the resistor is connected to the remaining end of the string.

The electrical field is the static field of an electret material that is not part of the above circuit. The electret is near the string. The string moves sometimes toward the electret and sometimes away from the electret. The surface of the electret is non-conducting and it is not touching the string or the resistor. The field that the electret produces in not uniform. The intensity of its electric field diminishes with distance away from the electret. The string is therefore in a static but fringing field.

Will there be a time varying current in the string that corresponds to the movement of the string in the field?

Thank you for your help.

James Adrian

 

[Philip Wood]

Sorry - trying to answer a question you hadn't asked.

 

[jamesadrian]

I'd have thought not, but this is little more than an intuitive response. What makes you think there should be?

if you put a conductor in a static electric field then the free charge in the conductor rearranges itself to cancel out the field inside the conductor. So if the conductor is moving about in a changing E field there will be a time varying current. I don't see the difference between the E field intensity changing because the E field changes, or on the other hand, the E field around the conductor changing because the conductor is in a different part of a static but fringing E field. Maybe there is a difference, but I don't yet see it.

Thank you for thinking about it.

Jim Adrian

 

[Philip Wood]

I can see the sense in this. Earlier, I was trying to investigate whether there would be an electromagnetically induced emf, but failed to convince myself one way or the other. On the face of it, and working in the frame of reference in which the electret is stationary, and producing a non-uniform but static electric field, there won't be.

 

[jamesadrian]

I can see the sense in this. Earlier, I was trying to investigate whether there would be an electromagnetically induced emf, but failed to convince myself one way or the other. On the face of it, and working in the frame of reference in which the electret is stationary, and producing a non-uniform but static electric field, there won't be.

Under what conditions would current be induced in a conductor by a purely electric field?

Jim Adrian

 

[Philip Wood]

Well, I think you've got it: if you move a conductor about in a non-uniform electric field, free charges will move inside it, re-distributing the charge.

 

[sophiecentaur]

Movement in a uniform field can involve energy transfer. What counts is change in Potential (integral of field dot displacement).

 

[jamesadrian]

Philip Wood and sophiecentaur,

I don't understand. Is it possible to generate a current in a conductor with a purely electric field? How?

I have been trying to understand the theory of operation of electret microphones. The theory is not exactly the same in every device. I know that some have a stationary electret in the device that does not get electrically connected to the diaphragm (which is a conductor from which a signal is amplified).

Will a fringing field work? Is there a way without a fringing field?

Thank you for your help.

James Adrian
jim@futurebeacon.com

 

[Philip Wood]

I'm no authority on electret microphones, but I think they can be modeled like this...

The electret is in the form of a parallel-sided film, effectively occupying part of the gap between the plates of a capacitor (perhaps attached to one of the plates). The electret induces equal and opposite charges, ±Q, on the capacitor plates. When the plates change their separation, s, in response to air pressure changes, the capacitance changes, and so the voltage between the plates varies. Insofar as the geometry is that of a parallel plate capacitor with a small gap, Q will not change when s changes.

Thus $V=\frac{Q}{C}=\frac{Qs}{\epsilon_0 \epsilon_r A}$. So $\Delta V=\frac{Q}{\epsilon_0 \epsilon_r A}\Delta s$.

Here, $\epsilon_r$ is a numerical factor, the effective relative permittivity of the air together with the electret, in the gap.

 

[sophiecentaur]

Philip Wood and sophiecentaur,

I don't understand. Is it possible to generate a current in a conductor with a purely electric field? How?

I have been trying to understand the theory of operation of electret microphones. The theory is not exactly the same in every device. I know that some have a stationary electret in the device that does not get electrically connected to the diaphragm (which is a conductor from which a signal is amplified).

Will a fringing field work? Is there a way without a fringing field?

Thank you for your help.

James Adrian
jim@futurebeacon.com

As I said before, it's Potential, not Field that counts. If you move an intermediate plate from one potential to another by changing its position between two charged plates, for instance, then its potential (wrt one of the plates) will change and charge will flow into an amplifier. The work done in moving the plate is transferred to electrical energy, Needless to say, this is, essentially, AC coupled but that's what microphones are for (sound IS AC).

 

[truesearch]

In post2 it was stated that a voice coil in a uniform field would not act as a pickup coil and would not act as a microphone. This is not correct.
It is akin to saying that a wire moving at constant velocity at right angles to a uniform field will not produce an emf. Effectively the wires of the coil are exactly this and an emf will be induced.
I, like Philip Wood, am fairly obsessed with these principles. Like Philip I have used loudspeakers as loudspeakers and microphones. Old telephone handset earpieces work well as both. It would be difficult to describe them either as speakers or microphones.

 

[truesearch]

In post2 what is the quantity ndA in the integral? what is n?
Post5 states that the speaker will not work as a GOOD microphone...does that mean it will be a microphone of some sort and physics principles can be ued to explain this.