# Electric field near dynamic loudspeaker at resonant frequency

Background

I am driving a cheapo 8 Ohm speaker with an LM386. The LM386 circuit is nearly identical to the one in the datasheet shown below, except Vin is AC coupled through a 10uF capacitor and the 250uF capacitor is only 100uF. The speaker looks similar to the one in the digikey link below, but I am not sure about the exact model.

I am connecting the input of the LM386 to a function generator and driving it with a sine wave. Then, I am using a near field E-field probe to measure the electric field next to the speaker. My E-field probe is the broadband one in the kit linked below.

https://www.com-power.com/ps-400_near_field_probes.html

At the resonant frequency of the speaker (~510Hz), I am able to measure about 10mV pk-pk sine with the E-field probe right in front of the speaker diaphragm. The amplitude decreases when the probe moves away from the center of the diaphragm. The signal becomes very small or unmeasurable at other frequencies.

When the E-field probe is in front of the center of the diaphragm, the measured E-field is 180 degrees out of phase with the LM386 output. If I move the E-field probe to center of the back of the speaker, the measured E-field is smaller and it is also in phase with the LM386 output. Swapping the speaker leads maintains the 180 degree phase difference between the field measured in front of the diaphragm and behind the speaker, but the phase relative to the LM386 output is reversed.

Opening up the speaker and looking at the voice coil, the wire wraps down and then wraps back up on the outside. The result is that both ends of the wire are at the same end of the coil and there are 2 concentric cylinders of wire.

As a side note, I am not able to measure anything with the H-field probe. Neither at the center of the diaphragm nor along the wires connecting to the speaker. I realize the bandwidth of the probe is much higher frequency and it may not be sensitive enough.

Question

How is the speaker radiating E-field? Why is it only happening at the resonant frequency? Why is the phase different between the front and back of the speaker?

Thank you!

EDIT: After opening up the speaker I found that the voice coil is wound in a way that the two ends of the wire end up on the same side. This may disprove the hypothesis that there are opposite charges on opposite sides of the coil.

The speaker is radiating E-field because it has charges on opposite ends of the voice coil that are moving.

The field is at a maximum at the resonant frequency because the peak velocity of the voice coil is at a maximum. Though the amount of peak charge is proportional to the peak voltage and is constant, the higher the peak velocity of the voice coil the greater the rate of change of the current density and the greater the electric field.

The field has opposite phase on opposite sides of the speaker because it is dominated by the field from the nearest charge, and the opposite sides of the coil have opposite charges.

The analysis for these answers is shown below.

The voice coil has a sinusoidal motion at resonance with position $$\x\$$, velocity $$\x'\$$, and acceleration $$\x''\$$. The force on the coil is proportional to both the current and the acceleration, so the current and acceleration are in phase. The voltage is equal to the current multiplied by the coil inductance, because at resonance the reactive part of the mechanical system is zero. The voltage has a 90 degree phase lead relative to the current and the acceleration, so it is in phase with the velocity of the voice coil. The charge on the voice coil is also proportional to the voltage and is in phase with the velocity.

The curl of the magnetic field is equal to the current density which is proportional to the charge multiplied by the velocity. Since the charge and the velocity are in phase, the current density is proportional to $$\cos^2(t)\$$. The curl of the electric field is proportional to the negative of the time derivative of the magnetic field and is proportional to $$\-cos(t)\$$

The greater the time derivative of the current density the greater the electric field. Since the amplifier has low output impedance, the voltage across the coil is constant and the charge is constant. Only the velocity of the coil can be increased to increase the time derivative of the current density. The velocity of the coil is maximum at the resonant frequency.

• Is this a plastic speaker? Or is it oldschool black paper? Unless your humidity is very high, all plastic surfaces are usually left with electrostatic charge from touching other objects. (Letting the speaker-cone hammer against any non-metal surface would definitely charge up the speaker!) Apr 27 '19 at 2:17
• @wbeaty The speaker is plastic. I connected the ground plane of the board to earth ground through my scope and touched another scope ground lead to the diaphragm to discharge any static charges. I was still able to measure a similar amplitude with my E-field probe. Apr 29 '19 at 17:18
• a metal surface connected to a vibrating plate is called a "WOBBULATOR," and was used as the modulator in early history of FM radio. google.com/search?q=wobbulator+capacitor Also, I'm in Seattle too, over on the UW campus. I'll try the spkr-with-foil trick on a scope input, and drive it with a sig generator. Instant electrostatic field-sensor, a detector with several meters range, for sensing hair-rubbed balloons or recently-used scotch tape dispensers. Apr 30 '19 at 0:51

The metal case should give you lots of shielding. And the e-field should all be coming from the solder terminals and the coil-wires on the cone.

Since this doesn't appear to be the case, then probably your speaker has a plastic cone. If the plastic has been touched by fingers, or worse, rubbed against a plastic bag, or against clothing, then the plastic may still have a significant surface-charge of several hundred volts wrt earth. (How low is the humidity at your workbench?!)

Plastic typically charges negative when touched by human skin, so the moving speaker would produce a negative peak when it physically moves towards the e-field sensor. Also, as the charged speaker-cone moves in and out, it would produce a strong opposite charge on the metal frame, caused by electrostatic induction (as if the speaker cone is a vibrating capacitor plate, and the metal frame a second capacitor plate.)

Try holding the vibrating cone with fingers, to see if the large signal disappears when AC is applied yet the speaker cone doesn't move. If an electrostatically-charged plastic plate is vibrating, it will produce a strong AC e-field easily detected by nearby electrode-antennas.

To get rid of any surface-charging, perhaps use a slightly-damp bit of toweling to wipe down the entire plastic speaker surface. If after discharging the plastic, your strong signal is smaller (or even missing,) then the cause was a charged-up speaker cone, rather than the AC drive voltage. Or instead, before wetting it, try rubbing the speaker cone with a plastic sheet, a rubber balloon, or arm-hair. If this makes your e-field signal enormous, then you've found the most probable cause. (And in that case, also try rubbing it with plumber's teflon tape, or with a plastic bag, with rubber, paper, etc. Check for different polarity of sensed pulses!)

Also, using a vibrating or rotating surface is a classic way to create a "Field Mill" for detecting any e-fields which have no AC component. Your near-field probes can only detect the changes in fields, not the fields themselves. Attach a small disk of foil to your vibrating speaker, connect it to an AC dvm or scope-input using thin foil strip, then vibrate the speaker. See if you can use this Field Mill to detect a distant hunk of styrofoam which you've rubbed on your hair.

Also, you can sense a charged plastic speaker-cone by waving the gate-lead of a JFET/LED circuit near it, as with http://amasci.com/emotor/chargdet.html

• I am in Seattle WA so my bench is fairly humid. I tried touching an oscilloscope ground lead to the speaker diaphragm but the measurement with the E-field probe did not change. Also, the metal back is floating. When it is grounded there is no measurable field behind the speaker but there still is in front of the diaphragm. Apr 29 '19 at 17:35
• @DavidG25 what happened when you rubbed it on arm-hair or a plastic bag? What happened when you wetted the plastic surface? Touching plastic to metal does nothing, cannot ground an insulator, only a metal. Apr 29 '19 at 21:42
• wow wetting it with a wet q tip completely made the measured field disappear! Apr 29 '19 at 21:52
• Yep, it was charged up all along. Even in humidity, an extremely clean plastic can stay charged for days. Apr 29 '19 at 21:55
• I am able to make the measurement increase by rubbing my arm hair on it and decrease by wetting it. Thanks a lot for your help! Apr 29 '19 at 22:17

How is the speaker radiating E-field?

The voice coil has a voltage imposed across it, plus it is physically moving back and forth. Together, these produce a measurable field.

Why is it only happening at the resonant frequency?

At the mechanical resonance frequency, the physical movement of the coil is greatest.

Why is the phase different between the front and back of the speaker?

You're seeing the opposite ends of the motion, along with the voltage on the opposite end of the coil.

• Do the fields from the opposite ends of the coil not cancel each other like in a parallel plate capacitor? Apr 25 '19 at 21:15
• Only at a distance. That's why you need to be close to measure anything at all. Apr 25 '19 at 21:25
• A parallel plate capacitor doesn't have canceled fields. Instead, it just has much stronger fields down between the plates. If there's a voltage on the capacitor plates, then there's an e-field outside the capacitor, in the space near those plates Apr 25 '19 at 21:55
• Can you go into more detail on the origin of the E field? I understand there is charge on opposite ends of the coil due to the voltage across it. Does the motion of this charge create a circulating H field in the same plane as the speaker diaphragm which in turn creates a circulating E field perpendicular to the diaphragm? The circulating E field adds constructively in the center of the coil, is this correct? Apr 26 '19 at 14:51
• I have no idea where you're going with this. There is a potential difference between the ends of the voice coil, and this creates an E field. This is true regardless of whether the voice coil moves or not. The physical motion simply enhances the ability of your "E-field probe" (which you haven't described) to pick it up. Charge and H field has nothing to do with it. Apr 26 '19 at 14:59