Tone Circuit Theory

[fuzz guy]

I just got a Power Boost clone working thanks to some help from forum members. This pedal has treble and bass tone knobs, and the bass control is very subtle while the treble has quite a big range.

I was wondering if someone could explain the theory behind what these components are doing together and why there's a big difference.



I clipped out the section of the schematic which seems to be the tone controls, but the entire build doc can be found here,

http://pedalparts.co.uk/docs/VintagePow-MkII.pdf

I'm getting better at putting these things together, but I'd like to start building an understanding of why things work the way they do.

[EBK]

Start here, perhaps:
http://makearadio.com/tech/tone.htm

Yours is arranged slightly differently, but a similar analysis would apply.

[GibsonGM]

...thus leading us to realize that things like DSC, and LT Spice etc. are invaluable tools for understanding what a tone control can/will do without having to use some very painful, and always different, equations!     Simulation can show you at a glance how these things will interact without output and input impedances, too, which is a total life-saver, as long as you know what to tell the simulation software.

IMO, as long as you 'get' how the things work mechanically...there's no shame in going to simulation and trial & error with components to get to where you need to be.  It's great to know HOW they work, absolutely.  But others have already done a bunch of hard work and math for us.

[EBK]

for understanding what a tone control can/will do without having to use some very painful, and always different, equations!     

Prediction: PRR's going to scold you and walk you through the simplifying assumptions that would allow you to analyze this or any other tone control on the back of an envelope.

Here is the same sort thing in my college Circuits textbook:

Link to larger version:
https://i.imgur.com/kcBLBQ1.jpg

[Rob Strand]

The original paper,
http://www.learnabout-electronics.org/Downloads/NegativeFeedbackTone.pdf

A more modern explanation is in this book,
https://ia803004.us.archive.org/3/items/audiohandbook/Audio%20Handbook.pdf

[tubegeek]

The original paper,
http://www.learnabout-electronics.org/Downloads/NegativeFeedbackTone.pdf

A more modern explanation is in this book,
https://ia803004.us.archive.org/3/items/audiohandbook/Audio%20Handbook.pdf

Rob: that edition of the Audio Handbook is in Italian!

I'll do some more googling for the English one, I'd like to see that book myself.

Here's the English-language edition!

http://bitsavers.trailing-edge.com/components/national/_dataBooks/1976_National_Audio_Handbook.pdf

[Rob Strand]

Rob: that edition of the Audio Handbook is in Italian!

Thanks.   Had a few pages open and copied the wrong link!

[BubbaFet]

Read the original circuit explanations from their inventors...

https://www.diystompboxes.com/smfforum/index.php?topic=88969.msg752843#msg752843

[PRR]

> I was wondering if someone could explain the theory behind what these components are doing ... I clipped out the section of the schematic which seems to be the tone controls

Nope. That snippet omits the KEY part, a high gain inverting Amplifier.

What you are trying to grok is a Baxandall.

EBK points you to an essay on the James "passive" tone control. (Since it has 20dB loss, you can't just plop it into a happy system without adding 20dB gain somehow, so "passive" is misleading.)

BubbaFet's posts link to the original papers of *both* schemes, and are great references.

And yes you can work these out with a stick in the sand. Assume caps may be zero or infinite impedance. What is the gain at center and each end of the pot?

[ElectricDruid]

PRR is right. To understand it, you just need to assume that caps are an open circuit at DC and a short circuit at some "high" frequency. In the middle (the bit we're interested in) they go from one state to the other, gently. So you can look at what happens at DC (Bass pot becomes a volume control, Treble pot totally removed) and what happens at the other end (Bass pot totally shorted out, treble pot becomes a volume control) and you've got the gist.

For drawing the interesting curves in-between and for tweaking values, use a simulation. For this tone control, someone's done it for you:

http://www.guitarscience.net/tsc/james.htm

HTH,
Tom

[fuzz guy]

Wow, first of all thanks for all the great replies. There's a lot more to this stuff than I thought and it seems I've got a bit of reading to do.

I guess what I was wondering as far as this circuit is more about the physical arrangement of the components, especially in the Bass knob circuit, and if that was related to the fact that it has a subtle affect throughout its range.

Around the PB bass pot there's just C9 and it's wired parallel to the pot. While in a more traditional Baxandall tone circuit you have two caps in a different arrangement, like in this section of a Boss FA-1 circuit,



Also, I've heard of LT Spice, but what is DSC?

[antonis]

English version (posted by tube tubegeek) of what posted by Rob expains some of those "minor" differences between traditional & americanized Baxandall EQs..

It also gives a graspable point of view about individual cut-off points, mid-band addition, interaction between them, etc..

[EBK]

Around the PB bass pot there's just C9 and it's wired parallel to the pot. While in a more traditional Baxandall tone circuit you have two caps in a different arrangement, like in this section of a Boss FA-1 circuit,

Another college homework problem that maybe sheds a wee bit of light on the different cap arrangements (or maybe it will just give you more questions).  Note that the resistors in the diagram represent a pot, with the wiper being the point in the middle.

[antonis]

Is something without Laplace transfer functions availabe, Eric..??

P.S. (ref. question b):
Aren't points x, y & inverting input parts of the very same node..??

[EBK]

Is something without Laplace transfer functions availabe, Eric..??

Just write jω instead of s, if you prefer.  You probably even have an ω key on your keyboard.   

P.S. (ref. question b):
Aren't points x, y & inverting input parts of the very same node..??

Yes, that is the result.

For completeness, here is Fig. 15.2, referenced in that problem:

[tubegeek]

Can I just say that the overall level and tone of this forum makes it one of my favorite places on the entire internet? It has been for quite some time. The amount of knowledge and curiosity interacting here just makes me happy.

[Rob Strand]

I guess what I was wondering as far as this circuit is more about the physical arrangement of the components, especially in the Bass knob circuit, and if that was related to the fact that it has a subtle affect throughout its range.

I did a lot of manual circuit analysis of tone controls about 25 years ago.  There's many finer points but I can give you a brief summary.

There's two bass variants and four treble variants, which makes for a lot of combinations.   Some of the variants are have similar performance, but they are not the *exactly* same.  We can reduce the options down to:
- Bass control with one cap two caps.
- Treble control with one cap or two caps.

All circuits have subtle differences on the finer scale.  The smaller differences are hard to capture with simple manual circuit analysis.  For a start the analysis separates the bass and treble but in the real circuit the bass and treble interact.  One reason is the circuit is an additive equalizer, instead of the cascade or  "multiplicative" equalizer we have pictured in our minds.  Through analysis it is however possible to show differences between the two bass controls.  In general these differences are best seen through circuit simulations.

The problem with the design procedures is they are concerned with the controls at maximum but the differences show-up when the controls are less than the extreme settings.  These cases are obviously more difficult and messy to analyse.

For the treble control.  The two cap variant produces less boost, or a dip, just where the frequency response starts to rise above 0dB.   That could be considered as a faster *initial* slope.   At the higher frequencies the general behaviour of the treble controls are pretty similar.   The general  behaviour at difference settings isn't too different beyond that.  The two cap treble circuits affect the bass more (in that they detune the bass frequencies).

For the bass control.  In the full boost/cut positions the two bass variants can be made to produce the same results.    The differences come in when the control is not set to the extremes.    At small boosts for example the two cap variant boosts the lower frequencies, as the control is increased the "take-off point" near 0dB moves up in frequency and the low frequency "leveling-off" point moves up in boost.    The single cap variant starts boosting around the middle of the bass frequency range, as the control is increased the "take-off" point near 0dB moves up in frequency but in this case the low frequency "leveling-off" point moves down in frequency and increases the boost.   So very roughly the two-cap variant keeps the lower frequency "leveling-off" point the same whereas the single cap variant keeps the middle of the bass frequency range the same.  The two sound quite different when swept over the full boost-cut range even if the maximum boost/cut behaviour is kept the same.   The two cap bass variant has more of a tendency to produce a dip in the middle of the response.

EDIT:  This pic might help.  The first one is more of an apple to apples comparison as the treble circuit is the same.

VT0 = one cap bass  (one cap treble), VT5 = two cap bass (one cap treble)


VT0 = one cap bass (one cap treble), VT6 = two cap bass (two cap treble)

[PRR]

The 1-cap bass plan is revealed in NSC's Audio Handbook, but may not be novel.

Douglas Self's Small Signal Audio gives more detail of the differences. Self does assume you can work out details yourself.

[Rob Strand]

Here's an exhaustive comparison of all combinations.   I didn't spend ages matching-up the bass but overall it captures the differences.  You probably won't find this info anywhere.

One feature of the single cap bass controls is the maximum treble boost dips down a bit as the bass control is advanced.   

Updated to V1.1

[PRR]

> Here's an exhaustive comparison

Thanks.

Doug Self should see/reference/borrow this for his book.