Need Help: What Is Corner Frequency Of This Tone Control?

[Paul Marossy]

How do you calculate the corner frequency of this tone control? That 33K resistor is what is throwing me off, not sure how that affects its function....

[YouAre]

If you can calculate it without the 33k resistor, then you can just add the resistor back in later. It looks like a "minimum value" resistor, which restricts the potentiometer from ever fully shorting the capacitor. Someone, please correct me if I'm wrong.

Out of curiosity, what circuit is this from?

[slacker]

I think with the tone control turned all the way down it's just a low pass filter made out of R13 and C16. So the corner frequency is just the normal 1/(2*Pi*R*C) in this case 1/(2*Pi*0.01*0.01) which is about 1.6Khz. With the control all the way up I think the corner frequency is calculated for a high pass filter made out of C16 and the tone control so 1(2*Pi*0.1*0.01) which is about 160Hz, the 33k then allows some low frequencies through so you get a shelved response like a treble bleed cap on a guitar or amp.

EDIT: basically what YouAre said but with more words.

[Paul Marossy]

If you can calculate it without the 33k resistor, then you can just add the resistor back in later. It looks like a "minimum value" resistor, which restricts the potentiometer from ever fully shorting the capacitor. Someone, please correct me if I'm wrong.

Sounds reasonable to me.

Out of curiosity, what circuit is this from?

A delay pedal, on the delay output.

[Paul Marossy]

I think with the tone control turned all the way down it's just a low pass filter made out of R13 and C16. So the corner frequency is just the normal 1/(2*Pi*R*C) in this case 1/(2*Pi*0.01*0.01) which is about 1.6Khz. With the control all the way I think the corner frequency is calculated for a high pass filter made out of C16 and the tone control so 1(2*Pi*0.1*0.01) which is about 160Hz, the 33k then allows some low frequencies through so you get a shelved response like a treble bleed cap on a guitar or amp.

EDIT: basically what YouAre said but with more words.

Ah, that makes sense. I've never dealt with a "shelving tone control" before, so that's why I asked.

[GGBB]

Out of curiosity, what circuit is this from?

A delay pedal, on the delay output.

This is the SWTC2 (bottom diagram) sans volume.  According to AMZ it is both a treble cut and boost, depending on the position of the control and the resistor values.  I've wondered about the calculations for that too (thanks guys). What I'd really like to know is how to calculate values so that with the tone pot at 50% the response is basically flat (or as close as possible).

[Paul Marossy]

Out of curiosity, what circuit is this from?

A delay pedal, on the delay output.

This is the SWTC2 (bottom diagram) sans volume.  According to AMZ it is both a treble cut and boost, depending on the position of the control and the resistor values.  I've wondered about the calculations for that too (thanks guys). What I'd really like to know is how to calculate values so that with the tone pot at 50% the response is basically flat (or as close as possible).

Huh, so it is! But I still don't know how how calculate the high & low end frequency of that... 

[GGBB]

With the control all the way up I think the corner frequency is calculated for a high pass filter made out of C16 and the tone control so 1(2*Pi*0.1*0.01) which is about 160Hz, the 33k then allows some low frequencies through so you get a shelved response like a treble bleed cap on a guitar or amp.

I think the R13-C16 combination is always in effect even with the control all the way up, so the 160Hz high pass comes after the 1.6KHz filter which is partially bypassed by R14 to form a high shelf.  So there are two high pass filters - 1.6KHz high shelf then 160Hz high pass.  But I'm not sure - does that sound right?

What happens in the middle confuses me, but I think the position of the wiper and the values of the two sides of the pot form some sort of third high-pass filter to output and/or voltage divider in addition to the other two filters that combine to perform a wide sweep filter on top of the shelf, but I am just guessing.  Where are all the EEs when you need them?    

[FiveseveN]

Simulation to the rescue!
http://i.imgur.com/X2i8OzP.jpg

[GGBB]

Simulation to the rescue!
http://i.imgur.com/X2i8OzP.jpg

Interesting - thanks.  For some reason I would have expected a more obvious shelf.  Looks like it's only about 2dB down.  But what do I know.

[lvs]

How do you calculate the corner frequency of this tone control? That 33K resistor is what is throwing me off, not sure how that affects its function....

Two assumptions :
- The output resistance of the preceding stage is negligible compared to R13 (otherwise it should be added to calculations).
- Rp = Tone resistance // following resistance. Meaning, the following stage has an input resistance, which is in parallel with the tone control pot.

Somewhere between min and max exists a "home" position of the tone wiper resulting in a completely flat response, with amplitude

Vout = Vin * 1/(1+((R13+R14)/Rp)) (1).

All response curves (for any wiper position) originate (i.e. where F = 0 Hz) at this amplitude.

Turning the wiper from there towards maximum gives highpass shelving.

The maximum shelving amplitude is

Vout = Vin * 1/(1+(R13/Rp)) (2).

The -3 dB point related to this amplitude is at

F = (1/(2*PI*C16*R14)) * SQRT((((R14/(Rp+R13))+1)^2)-2) Hz (3).

Attention : formulas (2) and (3) are only valid for tone wiper maxed.

Turning the tone wiper towards ground gives first order lowpass. With the wiper at minimum, the -3dB point (relative to the amplitude given by (1)) is at

F = (1/(2*PI*C16)) * ((1/R13)+(1/(R14+Rp))) Hz (4).

Comparing formulas (1) and (2) tells more about R14. The larger R14, the stronger the shelving. But actually it's not the maximum shelving amplitude itself that becomes larger, but the amplitude at the "home" position decreases while the maximum shelving amplitude stays the same.


Um yeah, I could have posted the formulas in a more readable form. Sorry for quickness & dirtiness (and no typos, I hope).

[lvs]

http://img.photobucket.com/albums/v496/lvs/Scannen0004.gif

[Digital Larry]

Great detailed analysis.   

My unfortunate conclusion is "it doesn't take much for the math to get out of control".   

I usually try to satisfy myself with understanding behavior at f = 0 and f = infinity and going to simulation if I need more detailed understanding in between.

[GGBB]

Yes - thanks for the details.  I will attempt to process this 

[Paul Marossy]

Any more thoughts on this from anyone?

In the middle it seems to me to be relatively flat with a 100K log pot, but I don't know if it calcs out that way...