Ebow Exposé - Part III

[Rob Strand]

I thought what the hell, how's the new coil lock to the string compared to the previous sim.

Just to be clear the receive coil on the previous sim was only an estimate (50mH 200 ohm).   Paul's later experiments let us get a better estimate for the actual receive coil (145mH 565 ohm).

As far as comparing the old simulation to the new, the new coil has more turns so it has three times the sensitivity of the old coil.  That alone means we needs to increase the string coupling kf by a factor of 3 to match reality.

Previously with strong string coupling (kf = 7.5e-3) the self-oscillation transitions to the string oscillation in 0.7 sec - but that was with Rf=130k. 

With the new coil I had to increase the string coupling to kf=1.6*3*7.3e-3 = 36e-3  to get the oscillations to transition in 0.7sec but now it just locks with Rf=13k.   Rf=13k makes it "10 times" harder to lock.   The 3 times increase sensitivity helps and we only need to bump the coupling another 1.6 times to get it over the line.   As I mentioned before no idea if the kf values line-up with the physics (that's a much harder estimate).

Here's the schematic,  (the 4.7m resistor is 4.7m milliohms, that's just to remove that resistor)



And here's the oscillation transition,  you can see it staggering a bit,


(For some reason I can't fixed the filename, it should be 13k in the filename.)

EDIT: I had to fixed this post:

I jumped in a bit too quick in my previous post.   Somewhere along the way I forgot I changed the feedback resistor to the likely value of 13k (as per Paul's best guess).     I couldn't understand why kf had to be increased, it was bugging me, then I realized I set Rf=13k - so not apples to apples with previous simulation (Rf=130k).  In the previous simulation where Rf=13k didn't lock to the string, so now the increased sensitivity of the new coil is evident!

My apologies.

[johngreene]

This thread sparked my curiosity so I did a quick search to see if anyone was selling one. There are a -lot- for sale! But everyone wants at least $79. Too much to feed my curiosity. I'll just have to wait for someone to break one I guess and put it for sale as "non-working".
🤔

[anotherjim]

I thought it was just a coating on a steel ring... but perhaps could be MuMetal underneath. I wouldn't know how to make that determination.

Neither would I. A common first test to determine a metal is to see if it sticks to a magnet. I asked the search engine "is mu metal magnetic?"
I get...

MuMetal® is the most widely used alloy for magnetic shielding purposes. Its composition of 80% nickel, 4.5% molybdenum and balance iron gives it highly permeable properties. This tells us that the material has high magnetic susceptibility to an applied magnetic field; it readily accepts the flow of magnetic field.

Ok, but is it magnetic? I was hoping for a yes/no answer!
Not that that would prove entirely what it is but the only other ideas I found is that it doesn't like being bent too much without cracking and will produce sharp burrs if cut with shears - and you aren't going to able to try either of those.

[Rob Strand]

Ok, but is it magnetic? I was hoping for a yes/no answer!

I'm pretty sure mu-metal is magnetic.  However I suspect the ring is just electrical steel and not mu-metal for a few reasons:
- mu-metal is used to shield low level fields.  As far as I'm aware it's never part of the main magnetic path of a magnet, and I seem to remember they warn against putting it in strong fields.
- mu-metal is normally soft as it is annealed.  The non-annealed form doesn't shield well due to the low mu.
- expensive

It's normally supplied in thin sheets.

[johngreene]

Ok, but is it magnetic? I was hoping for a yes/no answer!

I'm pretty sure mu-metal is magnetic.  However I suspect the ring is just electrical steel and not mu-metal for a few reasons:
- mu-metal is used to shield low level fields.  As far as I'm aware it's never part of the main magnetic path of a magnet, and I seem to remember they warn against putting it in strong fields.
- mu-metal is normally soft as it is annealed.  The non-annealed form doesn't shield well due to the low mu.
- expensive

It's normally supplied in thin sheets.

I happen to have a half dozen or so wah inductors that have a mu-metal shield "cap" covering them. 🤷‍♂️

[Paul Marossy]

Ok, but is it magnetic? I was hoping for a yes/no answer!

I'm pretty sure mu-metal is magnetic.  However I suspect the ring is just electrical steel and not mu-metal for a few reasons:
- mu-metal is used to shield low level fields.  As far as I'm aware it's never part of the main magnetic path of a magnet, and I seem to remember they warn against putting it in strong fields.
- mu-metal is normally soft as it is annealed.  The non-annealed form doesn't shield well due to the low mu.
- expensive

It's normally supplied in thin sheets.

I happen to have a half dozen or so wah inductors that have a mu-metal shield "cap" covering them. 🤷‍♂️

Makes some sense in that application... those wah pedal inductors are susceptible to picking up EMI noise. Been there done that!

[Rob Strand]

I happen to have a half dozen or so wah inductors that have a mu-metal shield "cap" covering them. 🤷‍♂️

I'm aware of those caps. They are usually made from pressed sheet mu-metal.   That type of part is common for mu-metal.
The difference to the ebow rings are:
- You are placing the cap, which has a closed top, over a material which is magnetically permeable.
   The whole idea is to prevent an external AC field from passing through the center leg of the inductor.
- In a wha the material is not in a strong (DC) magnetic field.   The mu-metal is fending off external low-level AC fields.

Magnetics comes down to a lot of specifics.   You might look at the coils on those buzzers and the Ebow and see similar construction: outer rings, pole-pieces, back plate and coil.   But from a DC magnetic field they are quite different, from an AC magnetic field perspective they have differences as well.

For the Ebow, the outer rings will:
- Stop some of the AC field between the coils.  (The magnet at the back does not form a "shielding cap" with the outer ring.)
- *not* increase the inductance a great deal (That's because the ferrite magnet on the back
   has *low* permeability - ferrite magnets in that position do not act like the ferrite on the back of a pot core -
   completely different!)
- Makes the DC magnetic field at the front wider, to some degree like a larger pole piece.
  The front of the pole piece and the edge of the ring have the *same* magnetic polarity.
  The field pattern is like a normal guitar pickup.
  (In the buzzer design the magnetic field is concentrated *across* the gap between the pole-face and front
   of the ring.   The pole-face and front of the ring have different magnetic polarities.)

FWIW, in the ebow it's not important at all that the (DC) magnetic field from the magnets of the receive and output coils interfere or mix.

[Paul Marossy]

Here's another update:

I replaced the output cap last night. It didn't really do anything to change the operation of the circuit but at least now I can check that off the list as suspect. It still doesn't want to do anything to get the string vibrating.

I was simulating stuff in LTSpice and it appeared that 1M feedback resistor might be better, but in real world the circuit would not oscillate at all. So then I soldered a 1M pot in place of that feedback resistor and determined that it will oscillate with it being 250 ohms to about 190K. However, if not the correct value the harmonic mode won't work. After monkeying around with it some more it seems that with my modified circuit (the input & output coils) it seems to like 56K.

Next, I looked at the waveforms with small handheld digital o'scope. Here is where things get interesting. In both modes it's oscillating at about 6.6-6.7kHz. The waveform at the input (Pin 3) is a sine wave at about 34mV RMS. Waveform looks roughly the same on both modes. The output is square wave-ish, looks basically like a massively clipped sine wave with very tiny rounding on the corners. Regular mode was 1.74 VRMS and harmonic mode was 2.10V RMS. In harmonic mode there was a little bit of a slant on the top of the waveform and not as much on the bottom. It appears that it basically amplifies the heck out of the input until it's kinda square waves.

These findings kind of go along with what I initially thought might be happening. I am a little stumped why it's not a functioning Ebow at this point... I would think I'd be able to get at least a little something out of it. My current theory is that the input coil is basically numb, just not sensitive enough. I can get the circuit to respond when I put a guitar string across the coils, drops the frequency about 0.2kHz and the waveform moves a little bit horizontally on the screen, so it appears that it's sensing the string.

This leaves me with a few questions:
1 -- Does there need to be an air gap in between the windings and those coated steel rings?
2 -- If I rewind the input coil, what is the DC resistance I should be aiming for? 400-500 ohms?
3 -- Could it be that I have input and output coil out of phase? Does phase even matter?
4 -- Why oscillating so fast?
5 -- What exactly determines the oscillation frequency?

In LTSpice, when I simulate it with no input, it happily oscillates at 1kHz. The actual circuit is oscillating at nearly seven times that. I can't get it to be anything else than 1kHz in LTSpice. Where is that coming from?! Is that the frequency that it operates on? I don't recall seeing anything about that on the datasheet and couldn't really find anything on the 'net about that. IN the app notes of the datasheet it does have a square wave oscillator, and it's running at 1kHz.

I guess I'll try swapping the wires on one of the coils and if still not working then I'll try rewinding the input coil.

[Rob Strand]

Here's another update:

I replaced the output cap last night. It didn't really do anything to change the operation of the circuit but at least now I can check that off the list as suspect. It still doesn't want to do anything to get the string vibrating.

Something that occurred to me is when you wound the new coil did you get the same direction?  If the magnet or the coil has been flipped the phasing of the feedback via the string will be around the wrong way.   Maybe you could try flipping the coil.

The orientation of the coil is not important for *self* oscillations but it is important for oscillations via the string.

I was simulating stuff in LTSpice and it appeared that 1M feedback resistor might be better, but in real world the circuit would not oscillate at all. So then I soldered a 1M pot in place of that feedback resistor and determined that it will oscillate with it being 250 ohms to about 190K. However, if not the correct value the harmonic mode won't work. After monkeying around with it some more it seems that with my modified circuit (the input & output coils) it seems to like 56K.

Interesting results.  I guess they are in the same ball-park as the simulation.

Next, I looked at the waveforms with small handheld digital o'scope. Here is where things get interesting. In both modes it's oscillating at about 6.6-6.7kHz. The waveform at the input (Pin 3) is a sine wave at about 34mV RMS. Waveform looks roughly the same on both modes. The output is square wave-ish, looks basically like a massively clipped sine wave with very tiny rounding on the corners. Regular mode was 1.74 VRMS and harmonic mode was 2.10V RMS. In harmonic mode there was a little bit of a slant on the top of the waveform and not as much on the bottom. It appears that it basically amplifies the heck out of the input until it's kinda square waves.

The 6.6kHz to 6.7kHz oscillation is set by the receive coil inductance and the 33nF cap.  It's a parallel LC oscillator.   The amount of feedback required for *self* oscillation is determined largely by the losses in the receive coil.   More losses means a lower valued feedback resistor is required.

The losses in the inductor are caused by the winding resistance and losses in the steel pole-piece.  You can modelled the inductor losses with an effective parallel resistance, Rp.   At the resonant frequency, the feedback resistor forms voltage divider with the feedback resistor Rf (the parallel L and C look open circuit at resonance).   The LM386 has a voltage gain of 200 so in order to maintain self oscillations the voltage divider  Rp / (Rf + Rp) must be larger than 1/200.
If the largest Rf that still oscillates is 1M then that implies Rp is about 5k ohm; the Rp calc only works when the largest Rf is chosen.

The oscillation frequency is,

                  f = 1/(2*pi sqrt(LC))

If you are seeing 6.65kHz, we know C = 33nF so  L = 17mH.   

I estimated about 23mH (15mH to 28mH) for your rebuilt receive coil.     So L=17mH is in the ball-park.

Without an amplitude control circuit or some form of soft non-linearity, oscillators will tend to oscillate with a clipped output.  Clipping is a way to reduce the effective gain of an amplifier.

These findings kind of go along with what I initially thought might be happening. I am a little stumped why it's not a functioning Ebow at this point... I would think I'd be able to get at least a little something out of it. My current theory is that the input coil is basically numb, just not sensitive enough. I can get the circuit to respond when I put a guitar string across the coils, drops the frequency about 0.2kHz and the waveform moves a little bit horizontally on the screen, so it appears that it's sensing the string.

Try flipping the wires to one of the coils.

This leaves me with a few questions:
1 -- Does there need to be an air gap in between the windings and those coated steel rings?

That gap isn't doing much at all.  You only need a large enough gap to get the coil in without damaging it,
(I'm guessing you want to add more turns?)

2 -- If I rewind the input coil, what is the DC resistance I should be aiming for? 400-500 ohms?

Based on your previous tests on the real ebow, it's looking like the receive coil is approx 3000 turns
of 44AWG which will end-up with about 565 ohm.    The turns is what determines the sensitivity of the coil
but you need to fit those turns in the available winding space and that determines the wire diameter
and then the resistance.

3 -- Could it be that I have input and output coil out of phase? Does phase even matter?

Definitely, and it is very import to get it right to drive the strings in a way which gives positive feedback.

4 -- Why oscillating so fast?

For your rebuilt coil it has less turns and hence less inductance than ebow coil.

5 -- What exactly determines the oscillation frequency?

f = 1 / (2*pi * sqrt(LC)) ; where C = 33nF input cap.

You can try playing with the value of C in order to lower the oscillation frequency.
It certainly won't hurt to play with it.   Lowering Raising the cap might give you a small
increase in sensitivity as well.   Over all though it's hard to increase the sensitivity without
increasing the turns - or putting the coils closer to the string.

As a DIY experiment, if you placed a non-inverting gain of 3 amp before the LM386 it would
compensate for the loss in sensitivity of the rebuilt input coil.   The sensitivity to electrical
noise will be worse than the higher number of turns so you might need to be more careful
about shielding such an amplifier.

In LTSpice, when I simulate it with no input, it happily oscillates at 1kHz. The actual circuit is oscillating at nearly seven times that. I can't get it to be anything else than 1kHz in LTSpice. Where is that coming from?! Is that the frequency that it operates on? I don't recall seeing anything about that on the datasheet and couldn't really find anything on the 'net about that. IN the app notes of the datasheet it does have a square wave oscillator, and it's running at 1kHz.

If 1kHz doesn't match up with 1/(2*pi*sqrt(LC)) where L = input coil inductance and C = 33n then there's something wrong with the simulation.

I guess I'll try swapping the wires on one of the coils and if still not working then I'll try rewinding the input coil.

Definitely.

[Rob Strand]

FYI,

I took these estimates for the rebuilt receive coil,

Receive coil:    L = 23mH, R = 108 ohms

Then did a simulation for the self-oscillation case,  I got,

fosc = 5.68kHz

Which needed a feedback resistor Rf <= 1MEG for self oscillation.

If we calculate f = 1/(2*pi*sqrt(LC)) = 5.78kHz.

The reason it's not exactly 5.68kHz is due to the fact the oscillation is based on L, C, R in parallel but the actual circuit has a resistance in series with the inductor.  This is a known effect but I don't want to get into explaining conversions between parallel and series resistances in resonant circuits.   What I can say is the 108 ohm inductor series resistance translates to (approx)  an equivalent parallel resistance of,

Rp = (2*pi*f*L)^2 / Rs = (2*pi*5.68k*23mH)^2/108 = 6.2k ohms.

If we now form the divider between the 1MEG feedback resistor and the equivalent parallel resistance, division factor = Rp /(Rp + Rf) = 6.2k/(6.2k + 1M) = 6.16e-3 = 1/162.   The gain of the LM386 is 200 so 200/162 = 1.2 is just over unity, which allows self oscillation to occur.   (prev post I got a nominal 5k)

Without getting into fine details it all makes sense.

Just for the record: the LM386 adds another 50k in parallel with the inductor loss.  6.2k//50k = 5.5k, then 5.5k/(5.5k+1M) = 1/183, and 200/183 = 1.1.  That shows oscillation but the main point is it shows how close these the calculations can be to what we see in the simulation.

[anotherjim]

Thanks, Rob, you got the self-oscillation over 5Khz. Past the roll-off of guitar cabs. If you had to pick an excitation frequency, isn't this the lowest you would aim for?

[Rob Strand]

Thanks, Rob, you got the self-oscillation over 5Khz. Past the roll-off of guitar cabs. If you had to pick an excitation frequency, isn't this the lowest you would aim for?

I'm not 100% sure because when I do fiddly stuff like thus I tend to play with the parameters so the performance is as good as you can get it.

I have a strong instinct that a low oscillation frequency would be better for locking  (much better in fact) and for improving sensitivity.   If the parallel cap is made large it will lower the self-oscillation frequency.  That will help locking to the string frequency.   However the cap causes some peaking in the high frequencies.  In fact if the feedback resistor is low enough for self oscillations the peaking is infinite at the self oscillation frequency and that will start to screw-up the phase response for the string.   Putting all that together you make the self-oscillation frequency low as possible but above the highest string frequency.   The fundamental on the high E would be upto 1.32kHz (24th fret).   We may also need to allow for the phase-shift due to the output and receive coils being at different places of the string.  If you throw in harmonic mode we have to deal with higher frequencies.   Perhaps the 2.2kHz Paul measured for the original ebow has been engineered for success.

I guess for Paul's rebuilt coil we might be inspired from all that to increase the 33n cap to around 220nF to 330nF.  Even 100nF could help the cause!.

Something I noticed looking at Paul's video of his ebow rebuild test jig - when he turns on the switch you can hear a high frequency whistle getting into the audio! (page 3 reply #47)   That could be 6kHz.
[I just checked, the whistle is 6.2kHz.  So ebow magnetic field is getting into the camera audio path.   That's the case against self oscillation!  A few posts back Paul measured 6.6kHz to 6.7kHz.]

[anotherjim]

I did a search to look for complaints of whining, or even heterodyne problems with other gear and found nothing in particular. Only thing I found was some reports of new users getting some kind of modem FSK noise which was solved by replacement units.

[johngreene]

FYI,

I took these estimates for the rebuilt receive coil,

Receive coil:    L = 23mH, R = 108 ohms

Then did a simulation for the self-oscillation case,  I got,

fosc = 5.68kHz

Which needed a feedback resistor Rf <= 1MEG for self oscillation.

If we calculate f = 1/(2*pi*sqrt(LC)) = 5.78kHz.

The reason it's not exactly 5.68kHz is due to the fact the oscillation is based on L, C, R in parallel but the actual circuit has a resistance in series with the inductor.  This is a known effect but I don't want to get into explaining conversions between parallel and series resistances in resonant circuits.   What I can say is the 108 ohm inductor series resistance translates to (approx)  an equivalent parallel resistance of,

Rp = (2*pi*f*L)^2 / Rs = (2*pi*5.68k*23mH)^2/108 = 6.2k ohms.

If we now form the divider between the 1MEG feedback resistor and the equivalent parallel resistance, division factor = Rp /(Rp + Rf) = 6.2k/(6.2k + 1M) = 6.16e-3 = 1/162.   The gain of the LM386 is 200 so 200/162 = 1.2 is just over unity, which allows self oscillation to occur.   (prev post I got a nominal 5k)

Without getting into fine details it all makes sense.

Just for the record: the LM386 adds another 50k in parallel with the inductor loss.  6.2k//50k = 5.5k, then 5.5k/(5.5k+1M) = 1/183, and 200/183 = 1.1.  That shows oscillation but the main point is it shows how close these the calculations can be to what we see in the simulation.

But isn't the Rp you calculated just what you use in order to get the Q of the inductor? Xl/Rp?

[Rob Strand]

We have to be careful how far we take the conclusions from Paul rebuilt unit since there is still some uncertainty about value of the feedback resistor.

The metal rings will help divert a lot of whining magnetic field from sides but they can't do much about field directly in front of  or behind the unit.

[Rob Strand]

But isn't the Rp you calculated just what you use in order to get the Q of the inductor? Xl/Rp?

Yes, exactly that.    You can calculate the Q from the series or parallel resistance but when you have series inductor resistance in a parallel resonant circuit you need to do a transformation.  There's a simple formula for high Q's and a more complicated one for low Q's (which also changes the inductance).   Most radio people know the trick.

My formula comes from the high Q case,

Q = XL/Rs = Rp / XL

So Rp = XL^2 / Rs

[johngreene]

Right, I just didn't see where you included the reactance of the inductor in your calculations. I went back through and see it now, so my bad.

[johngreene]

Right, I just didn't see where you included the reactance of the inductor in your calculations. I went back through and see it now, so my bad.

Wait, I still think you are only using Rp in your gain calculations (the equivalent parallel resistance) and are ignoring the reactance. Shouldn't you be using Xl // Rp to get the actual impedance value at a particular frequency? mainly when you are calculating gains because it this case the DC resistance is actually a significant percentage of the total reactance it makes more sense to use the series model to compute the AC impedance which is Rs+jXL. So if you are going to use the impedance you need to simply add the reactance to the series resistance. So you get an equivalent impedance of 820(XL) + 108 (Rs) = 928 ohms. Actually, since XL is 90 degrees out of phase you need to do a vector sum to get real impedance of the two combined which would be |ZL| = sqr(XL^2 + Rs^2) = 827 ohms.
Rp comes in handy when calculating the loading effect on tank circuits when you attach them to a load but for using AC impedance in a gain calculation you should really be using the series equivalent to get the AC impedance at the frequency of analysis.
It's been a long time since I've had to calculate RLC impedances and such but I think I am correct? It is also why people get fooled by pSpice simulators when they use ideal inductors.

[Rob Strand]

Wait, I still think you are only using Rp in your gain calculations (the equivalent parallel resistance) and are ignoring the reactance. Shouldn't you be using Xl // Rp to get the actual impedance value at a particular frequency?

I've got some level of confidence the calculations and simulation agree and are correct.  However, because the simple calculations assume high Q you can get small errors (like the oscillation freq isn't quite 1/ (2*pi*sqrt(LC)) since you need to change L as well.

The idea is when you transform Rs to Rp it transforms the inductor from Rs in series with L to Rp in parallel with L.   When you resonate the L with the C,  XL and XC cancel out and that leaves only Rp.   That's the reasoning why you don't need to include XL or XC.    Whatever resonant frequency you *really* get the oscillator with find it, and within the approximation the loss, Rp, will still end-up at Rp.  So that's why the divider calculation with Rp works.   

If you plug in frequencies which don't quite cancel XL and XC you could get errors.   If you start with a calculated frequency f=1/(2*pi*sqrt(LC)) = 5.777kHz then XL = 834.9 ohm and XC = 834.8 ohm.  XL and XC essentially cancel leaving only the parallel Rp.  If you use the measured f = 5.68kHz then XL won't quite cancel XC.

However, if you do the the full low Q transformation on L and Rs the calculated frequencies will be closer to reality and then all the number will be self consistent.

It's been a long time since I've had to calculate RLC impedances and such but I think I am correct? It is also why people get fooled by pSpice simulators when they use ideal inductors.

Like wah pedal simulations!

[johngreene]

Wait, I still think you are only using Rp in your gain calculations (the equivalent parallel resistance) and are ignoring the reactance. Shouldn't you be using Xl // Rp to get the actual impedance value at a particular frequency?

I've got some level of confidence the calculations and simulation agree and are correct.  However, because the simple calculations assume high Q you can get small errors (like the oscillation freq isn't quite 1/ (2*pi*sqrt(LC)) since you need to change L as well.

The idea is when you transform Rs to Rp it transforms the inductor from Rs in series with L to Rp in parallel with L.   When you resonate the L with the C,  XL and XC cancel out and that leaves only Rp.   That's the reasoning why you don't need to include XL or XC.    Whatever resonant frequency you *really* get the oscillator with find it, and within the approximation the loss, Rp, will still end-up at Rp.  So that's why the divider calculation with Rp works.   

If you plug in frequencies which don't quite cancel XL and XC you could get errors.   If you start with a calculated frequency f=1/(2*pi*sqrt(LC)) = 5.777kHz then XL = 834.9 ohm and XC = 834.8 ohm.  XL and XC essentially cancel leaving only the parallel Rp.  If you use the measured f = 5.68kHz then XL won't quite cancel XC.

However, if you do the the full low Q transformation on L and Rs the calculated frequencies will be closer to reality and then all the number will be self consistent.

Doh, I completely forgot about the cap. No wonder I was confused.
"freq isn't quite 1/ (2*pi*sqrt(LC)) since you need to change L as well."
It's obviously right there!