A different view of the guitar tone circuit

[Tonestack]

I have been putting forth an assertion for a couple of years that goes against what guitarists are taught about the most common guitar tone circuit. Most guitarists who care to learn anything about guitar electronics are taught that the tone control is a low-pass filter. However, what the tone control actually does is lower the resonant frequency of the RLC circuit this is formed by the tone cap, tone pot, pickup coil, and volume pot. In effect, the tone cap, tone pot, and pickup coil form a crude variable band-pass filter with a resonant peak amplitude that is influenced by the volume pot (the cable capacitance and amp input impedance also affect the circuit resonant frequency and Q, but we will hold these values constant for this discussion). While the tone pot setting influences the Q of the circuit, the volume pot size and setting have a pronounced effect on the Q of the circuit. Needless to say, I have taken a beating on several guitar-oriented websites for making this assertion. However, data that is available from several guitar electronics-oriented research sites supports my claim.

Let's examine a few frequency response plots (a.k.a. transfer function graphs) from a website where the author was modeling the effect of cable length on frequency response.

The parameters for our first plot are:

Volume pot max CW (250K)
Tone pot max CW (250K)
Tone cap 0.05µF
20ft cable (50-ohm characteristic impedance)
Tele Bridge pickup




The parameters for our second plot are:

Volume pot set to be the equivalent of 100K over 150K
Tone pot max CW (250K)
Tone cap 0.05µF
20ft cable (50-ohm characteristic impedance)
Tele Bridge pickup



Now, one can clearly see that the resonant peak disappears as the volume control is rolled down. Dividing the pot introduces a series resistance and lowers the parallel resistance, which lowers the Q of the circuit.


The parameters for our third plot are:

Volume pot set to be the equivalent of 100K over 150K
Tone pot max CW (250K)
Tone cap 0.05µF
20ft cable (50-ohm characteristic impedance)
Tele Bridge pickup
0.001uF treble bypass cap on the volume control



This bypass cap restores the resonant peak by removing the series resistance and restoring the parallel load to 250K for frequencies above the corner frequency. However, the overall signal is still attenuated.


The parameters for our fourth plot are:

Volume pot max CW (250K)
Tone pot turned down slightly CCW (100K)
Tone cap 0.05µF
20ft cable (50-ohm characteristic impedance)
Tele Bridge pickup



We see that turning down the tone pot slightly also affects the amplitude of the resonant peak. This change is due to a reduction in overall resistance that is wired in parallel with the pickup coil, which in turn lowers the Q of the circuit. The resonant peak has also been shifted slightly lower in frequency.

The parameters for our fifth plot are:

Volume pot max CW (250K)
Tone pot fully CCW (0)
Tone cap 0.05µF
20ft cable (50-ohm characteristic impedance)
Tele Bridge pickup



Here's where things get interesting. Reducing the tone pot resistance from 100K down to 0 Ohms does not affect the Q of the circuit much; however, what it does is bring the full effect of the tone cap into the circuit. The tone cap adds to the self-capacitance of the coil which, in turn, reduces the resonant frequency of the circuit. The tone cap basically moves the center frequency of the passband to a lower portion of the audio spectrum.

Finally, let's see what happens when we increase the size of the volume pot to 1M.

Volume pot max CW (1M)
Tone pot fully CW (250K)
Tone cap 0.05µF
20ft cable (50-ohm characteristic impedance)
Tele Bridge pickup



The resonant frequency stays the same, but the amplitude of the peak shoots up to 6.5mV. This increase in the amplitude of the resonant peak is why most guitars get brighter when one installs higher value volume pots.

[Mike Sulzer]

Yes, you are changing the characteristics of a resonant circuit. By the way it is not a bandpass filter; it is a resonant filter, but a resonant low pass filter: the response does not continue decreasing as you go down in frequency from the peak, but levels out. At high frequencies it tends towards a 12 db per octave response, showing that it is a second order low pass filter. The pickup inductance is a series element and the cable capacitance is a shunt element. The pickup capacitance plays a small role in parallel with the cable capacitance.

The basic operation is that it lowers the Q as you turn tone down from 10, and then towards the bottom the C cuts in and lowers the resonant frequency, as you describe. I have been saying this for years, and I guess most folks are getting sick of hearing it! Not sure who agrees, though, no one says much.

However, what the tone control actually does is lower the resonant frequency of the RLC circuit this is formed by the tone cap, tone pot, pickup coil, and volume pot. In effect, the tone cap, tone pot, and pickup coil form a crude variable band-pass filter with a resonant peak amplitude that is influenced by the volume pot (the cable capacitance and amp input impedance also affect the circuit resonant frequency and Q, but we will hold these values constant for this discussion). While the tone pot setting influences the Q of the circuit, the volume pot size and setting has a pronounced effect on the Q of the circuit. Needless to say, I have taken a beating on several guitar-oriented websites for making this assertion. However, data that is available from several guitar electronics-oriented research sites supports my claim.

[Steve Conner]

I agree with Mike. This is common knowledge (or should be) amongst engineers and technicians, but just try explaining it to the average guitarist, or the average inhabitant of the average guitar forum. No, actually don't try because it's pointless

Once you've been playing guitar long enough, you get an empirical feel for what the knobs do to the sound. The theory doesn't matter unless you're designing guitars or pickups. Even then I doubt the average luthier or pickup maker understands the operation of the tone control in the way Mike puts it.

[pdf64]

See BuildYourGuitar.com :: The Secrets of Electric Guitar Pickups for a great analysis of this subject - Pete.

[Tonestack]

I agree with Mike. This is common knowledge (or should be) amongst engineers and technicians, but just try explaining it to the average guitarist, or the average inhabitant of the average guitar forum. No, actually don't try because it's pointless

I always seem to get roped into one of those mysterious “God is in the details” tone cap threads. Without fail, someone claims that the tone cap and tone pot are a simple RC low-pass filter that works by bleeding treble to ground. All heck breaks lose when the fact the tone cap is wired to an inductive element is brought into the discussion.

Guitarists who know something about electronics, but who are not formally trained tend to want to treat a pickup as an AC voltage source and not an inductive AC voltage source. RLC networks are not simple to understand like RC circuits. RLC networks were magic to me for a long time. I am not an engineer by training. My undergraduate and graduate degrees are in computer science. However, I have been into electronics since I was kid because my father was a calibration technician for a major defense contractor (my dad is no longer with us, but it was nice having access to someone who actually worked the field during the golden era of tube-type electronics while he was alive). I never fully grasped the complexities of RLC networks until I got into amateur radio a few years back. Resonant circuits became much easier to understand after I started to build and measure different antenna designs. That's when I truly began to understand what the Q of a resonant circuit was and how it affected bandwidth. It is also around that time that it dawned on me that what I had learned about the guitar tone circuit from guitar player-oriented electronics books was wrong.

[Tonestack]

Yes, you are changing the characteristics of a resonant circuit. By the way it is not a bandpass filter; it is a resonant filter, but a resonant low pass filter: the response does not continue decreasing as you go down in frequency from the peak, but levels out. At high frequencies it tends towards a 12 db per octave response, showing that it is a second order low pass filter. The pickup inductance is a series element and the cable capacitance is a shunt element. The pickup capacitance plays a small role in parallel with the cable capacitance.

Is the pickup inductance considered to be a series element due to the fact that it is also an AC voltage source? I have seen two different Thevenin equivalent circuits for a pickup. Both circuits have the pickup's inductance in series with its resistance and an AC voltage source. Where the two equivalent circuits differ is in the how the pickup's capacitance is treated. In circuit one, pickup capacitance is in parallel with the series inductance and resistance, but in series with the AC voltage source. In the second equivalent circuit, the capacitance is in parallel with the series inductance, resistance, and AC voltage source.

[Mike Sulzer]

The pickup capacitance acts like cable capacitance, just a smaller value, typically. That first figure implies that the pickup high frequency response is unlimited when operating directly into a high impedance buffer. You know that is not true.

Is the pickup inductance considered to be a series element due to the fact that it is also an AC voltage source? I have seen two different Thevenin equivalent circuits for a pickup. Both circuits have the pickup's inductance in series with its resistance and an AC voltage source. Where the two equivalent circuits differ is in the how the pickup's capacitance is treated. In circuit one, pickup capacitance is in parallel with the series inductance and resistance, but in series with the AC voltage source. In the second equivalent circuit, the capacitance is in parallel with the series inductance, resistance, and AC voltage source.

[CRU JONES]

Nice work, Tonestack!

I see your models, and don't have much to add to them or comment on. They look good to me, and I am not sure why, but: in practice turning the tone control down from 10 to 0 will initially lower the Q as the resonant circuit will have dampening added from loading. However, as the control reaches Zero, the inductive energy of the pickup is no longer buffered from the capacitive energy of the tone capacitor, therefore you will get a large rise in Q. This is in practice. It is what actual pickups do. It is the "wah sound" or the "woman tone". The Q at tone = 0 is significant to the perception of the user

My second critique might be the observation of the rise in resonant frequency Due to increasing the electrical resistance of the volume pot. A couple hundred Hz is not necessarily a small quantity. The difference between, for instance, a real PAF and the Dimarzio De-Activator (a Legitimate Death Metal Pickup), is only a couple hundred Hz.

Cheers,
Ethan

[CRU JONES]

I agree with Mike. This is common knowledge (or should be) amongst engineers and technicians, but just try explaining it to the average guitarist, or the average inhabitant of the average guitar forum. No, actually don't try because it's pointless

Once you've been playing guitar long enough, you get an empirical feel for what the knobs do to the sound. The theory doesn't matter unless you're designing guitars or pickups. Even then I doubt the average luthier or pickup maker understands the operation of the tone control in the way Mike puts it.

There are ways to explain this interaction to everyday guitarists, you just have to think like them a bit.

I would disagree with your assumption about average luthier/ pickup maker. This is a schematic with passive circuits. We draw them all the time. Most of us know how passive components work. So, in defense of my fellow winders out here without fancy degrees, this stuff isn't some amazing miracle rocket science. It certainly is not nearly as exciting as actually winding a pickup. We all know the pickup model is flawed without a clear path to fix it. Not a worthy grail to chase for IMO. So, I'm not offended Steve. I'm a big fan of your smarts. And I hope I am not offending Tonestack for his very well put together presentation. My point is: don't underestimate the winders out here to understand this really basic stuff. It's basic. It's like four chapters into the book.

Cheers,
Ethan

[Mark Hammer]

Well, I think all parties are partly correct. When the tone control is adjusted, either in conjunction with the volume control, or with volume at max, there are some things you hear less of (which is what makes it a lowpass filter), and some things you hear a little more of (which makes it a resonant lowpass).

It is that latetr aspect which makes things like the Tone Styler usable. If the tone control ONLY yielded a shallow slope of treble attenuation, then a single cap and pot would be sufficient. But the fact is that the cap and pickup inductance (among other things) interact to produce other kinds of sounds, making the variation afforded by alternate caps musically useful.

I always tinker with the tone caps/controls on my guitars. Part of that is instigated by my exasperation with the entrenched traditional approach of using the same tone cap value for the neck pickup as the bridge. Makes no sense whatsoever AFAIC. EVERY player wants something different fronm a bridge pickup than they want from neck or middle - that's why we HAVE them. Where a single master tone control is used, like on my Turser Tele, I use two different caps on the same control - tone wiper to volume pot, and different cap to ground from each outside lug. They introduce different resonances that are appropriate to different pickup settings and tunes/styles.

[Mike Sulzer]

Do you really use tone settings near zero? The cap only makes a big difference pretty close to zero. Separate tone controls are more generally useful because you can set the resistances to different values, loading the pickups differently.

I always tinker with the tone caps/controls on my guitars. Part of that is instigated by my exasperation with the entrenched traditional approach of using the same tone cap value for the neck pickup as the bridge. Makes no sense whatsoever AFAIC. EVERY player wants something different fronm a bridge pickup than they want from neck or middle - that's why we HAVE them. Where a single master tone control is used, like on my Turser Tele, I use two different caps on the same control - tone wiper to volume pot, and different cap to ground from each outside lug. They introduce different resonances that are appropriate to different pickup settings and tunes/styles.

[Tonestack]

Mike S:

I have question that you should be able to answer. With an inductor, we build a magnetic field (B) in the core using an alternating current-based magnetizing field (H) with a flux density that is determined by the strength of the H field and the permeability of the core. A magnetic field already exists in the core of a pickup. With a pickup, we induce an alternating current in the coil by vibrating ferromagnetic strings within a magnetic field. Doesn't the current that is induced in the coil create an H field that increases the size of the B field? If what I have stated is true, then we have a feedback loop that is bounded by the permeability of the core and the delta between the magnetic flux density at rest and magnetic saturation of the core.

We are always being told that one type of magnet compresses while another does not; however, if what I stated above is true, compressability based on magnet type is nothing more than a myth. Given a strong enough induced current, we should be able to push any type of magnetic material into saturation that is not already fully saturated with no induced current flowing through the coil.

Additionally, if what I stated above is true, wouldn't the delta between the flux density at rest and saturation and the rate at which the magnetic feedback loop can push the B field into saturation determine the touch sensitivity of a pickup? It should also determine the spectral purity of the signal because non-linear behavior should occur when we apply an H field to a fully saturated core.


Am I way off?

[Mark Hammer]

Sure. If one is using a cap smaller in value that .05 (and I often use 10n, 8n2 or 6n8 for the bridge), you'll turn the control down all the way. Sounds great. A small value tone cap can be just the thing to make a Tele or Strat bridge pickup sound more P90-ish.

[CRU JONES]

Mike S:

I have question that you should be able to answer. With an inductor, we build a magnetic field (B) in the core using an alternating current-based magnetizing field (H) with a flux density that is determined by the strength of the H field and the permeability of the core. A magnetic field already exists in the core of a pickup. With a pickup, we induce an alternating current in the coil by vibrating ferromagnetic strings within a magnetic field. Doesn't the current that is induced in the coil create an H field that increases the size of the B field? If what I have stated is true, then we have a feedback loop that is bounded by the permeability of the core and the delta between the magnetic flux density at rest and magnetic saturation of the core.

We are always being told that one type of magnet compresses while another does not; however, if what I stated above is true, compressability based on magnet type is nothing more than a myth. Given a strong enough induced current, we should be able to push any type of magnetic material into saturation that is not already fully saturated with no induced current flowing through the coil.

Additionally, if what I stated above is true, wouldn't the delta between the flux density at rest and saturation and the rate at which the magnetic feedback loop can push the B field into saturation determine the touch sensitivity of a pickup? It should also determine the spectral purity of the signal because non-linear behavior should occur when we apply an H field to a fully saturated core.


Am I way off?

Very interesting thoughts, Tonepad

The strings exert a coercive force on the magnetic circuit that is the pickup. I suppose you could calculate the Coercive force of the string by Amp*Turns. I have calculated this before and haven't really done anything with that tiny little number. I imagine the coercive force of the strings moving along the magnetic loadline, but I have to admit; I have not generated the B-H curves for any of my magnetic circuits to know what that loadline would look like. I have generated the B-H curves of the magnets I use and I do have a 5 Watt de-magnetizer/ calibrator that I designed and my feeling is that it takes a bit more coercivity than a string will produce to saturate or demagnetize a pickups magnetic circuit. On top of that is that in order for a pickup to work, it must have a working gap which is another name for an "air gap", making it even harder to saturate.

B-H curves DO have varying degrees of linearity to their loadlines. Selecting a magnet with low coercivity would in effect allow increased movement on the loadline, something that I think is promising.

As far as pickups being described as being "compressed", I have my own theories. I don't think for a minute that the pickup is in fact "compressing" the signal in the technical sense. It is merely an analogy guitarists use to communicate their experience of a certain pickup. Similar to how guitarists describe pickups as being "fast" etc. I will tell you this, pickups have their own unique envelope. Compressors essentially modify a signals envelope.

If anyone has generated B-H curves for their pickup, that would be interesting. I have still yet to try charging a humbuckers bar magnet post assembly

Cheers,
Ethan

[Mike Sulzer]

The fields involved, both the static permanent field but especially the much weaker fluctuating field from the vibrating strings, are not strong enough to cause saturation.

Mike S:

I have question that you should be able to answer. With an inductor, we build a magnetic field (B) in the core using an alternating current-based magnetizing field (H) with a flux density that is determined by the strength of the H field and the permeability of the core. A magnetic field already exists in the core of a pickup. With a pickup, we induce an alternating current in the coil by vibrating ferromagnetic strings within a magnetic field. Doesn't the current that is induced in the coil create an H field that increases the size of the B field? If what I have stated is true, then we have a feedback loop that is bounded by the permeability of the core and the delta between the magnetic flux density at rest and magnetic saturation of the core.

We are always being told that one type of magnet compresses while another does not; however, if what I stated above is true, compressability based on magnet type is nothing more than a myth. Given a strong enough induced current, we should be able to push any type of magnetic material into saturation that is not already fully saturated with no induced current flowing through the coil.

Additionally, if what I stated above is true, wouldn't the delta between the flux density at rest and saturation and the rate at which the magnetic feedback loop can push the B field into saturation determine the touch sensitivity of a pickup? It should also determine the spectral purity of the signal because non-linear behavior should occur when we apply an H field to a fully saturated core.


Am I way off?