Question about tone control frequencies...

[Projectile]

The thing is, this tone circuit is not your basic RC-filter, so your basic formulas won't apply unless you formulate your own. I've never seen an op-amp with the inverting and non-inverting inputs connected together like that, either. I'd really like to hear you view on how these components interact with electrons. Maybe it would clear some things up.

Well, I'm not going to get into the gory details at the moment, but as far as the negative and positive terminals of the opamp being connected together is concerned it's pretty straightforward. Ignoring the 220ohm resistor at the moment, which just complicates things, when the wiper is all the way toward the negative terminal the 20K impedance of the pot + the 1K resistor after the output of the first opamp equals 21K in an RC combination with the .22uf cap on the wiper. This passes nearly the entire frequency range for the positive input side of the tone control to ground, so you can essentially ignore it. In fact, if you dissconect the lug from the positive terminal while the pot is turned all the way up you can barely detect an audible difference. You can't really see a difference on the frequency plot either. The same thing happens when you turn the pot all the way in the other direction: you get 20K +1K in the feedback network and .22uf on the wiper, essentially taking it out of the equation.

Furthermore, when the pot is rotated to it's midpoint you basically have 11K with .22uf RC filter from one lug, and 11K with with .22uf RC on the other lug. Now, I know the interactions of these filters is far more complicated than i am describing because the cap is seeing current from the output of both opamp stages, but for all practical purposes we can say that the rolloff is still really low, likely below 100hz, so we can basically take the entire tone control pot out of the picture at it's midpoint. If you remove both lugs while the pot is at it's midpoint there is only barely a discernible difference in the frequency response by ear, and you can also barely see any change on the frequency plot. What we have is essentially a tone control that only does anything at it's extremes. This is probably why it uses that fancy "W taper" or "eq taper" pot, which is gradual at either end and very steep in the center. Though even with such a steep change at the center, the biggest eq changes only happen at the top quarter and bottom quarter rotation of the pot. It's pretty dead in the middle.

There have been many times that I've been sure I understand something perfectly only to be proven completely wrong with an even more logical explanation. I don't claim that I understand this circuit perfectly and I'm not claiming that you're wrong, I just hope someone like R.G. himself could swoop in here and explain his article.

That's why I posted here in the first place. I fully expected to get a more logical explanation.

[MohiZ]

I simulated the opamp with the tone control with Aplac, a circuit analysis software and here are the results. I ignored the 1k/.22u low-pass filter right before the op-amp for the sake of simplicity. When looking at these results you have to remember it cuts off some treble, and the clipping stage freq response also affects the total freq response at this point.

Here is the response at the output of the opamp, with 5 different tone control settings. We can clearly see that all it does is boost treble. The bass frequencies have an amplification of 0 dB, that is gain of 1. The point of 3 decibel boost seems to be a little less than 600 Hz.


Jumpering the 220 ohm resistor only seems to steepen the treble boost curves:


The 1k resistor affects gain. Of course, the 3dB roll-off point changes, but it seems it's only because the amount of total boost changes - the curves stay the same shape. Note the different vertical scale:

[MohiZ]

These might be slightly more informative. Here's the response of the whole tone stage, with the RC lowpass filter at the beginning. I've arranged the scales so that you can directly see the 3dB cutoff frequency at the bottom of the graph.

http://www.aronnelson.com/gallery/main.php/v/diyuser/ts3.JPG.html?g2_imageViewsIndex=1

It's interesting to note that the op-amp does not affect the frequency response AT ALL when the tone is rolled full down. It's also interesting to see that you were totally right, the frequency response is flat with the 220ohm resistor shorted. But, only when the tone control is on full. There's still a mid hump when the tone control is somewhere in the middle.

The highs-boosting op-amp seems to create the mid hump in conjunction with the low-pass filter right before it. The peak is, however, only about one decibel, so I'm not sure if it's even audible. It does seem that the Geofex article is wrong.

[aziltz]

That's why I posted here in the first place. I fully expected to get a more logical explanation.

While I think you'd get a lot opinions that you can trust, a lot of people on here are simply enthusiasts, but I don't think people overstep when giving advice.  Let's face it, you don't need an EE degree to build stomp boxes, not to say there aren't some fabulously brilliant people on here.  Of course there are.

I've been responding because I was interested in this topic, and I wasn't seeing many members contribute.  I tried to offer a few educated guesses, but I made sure to indicate what was a hunch.  There are no "gaping hole's in my understanding of how RC filter's affect electrical currents", and I take offense to that remark.  No, I don't know everything about this circuit. I haven't yet studied it, but as I said before, this is not a basic application of op-amps and RC Filters.  I said I was an experimentalist, not a theorist, and there's definitely a difference.  My occupation should make no difference here, and your sarcastic and snide remarks are uncalled for.  I was never preaching to you, or anyone, about this.  I just haven' had the time to breadboard this, and so for the sake of discussion, I offered a few suggestions, based on the basics of RC Filters and Op-Amps.

I feel like I've been set up to be shut down.  You solicited explanations, then ran your own tests.  No need to call bullshit on us here. Your posts have included more and more examples of things you've discovered on the breadboard, and I applaud you for testing things out.  I would be really excited to read all your findings once you complete what you are testing.


Discussion and suggestion really are the cornerstone of experimentation and ultimately, research and education.  If I've offended your or wasted your time by offering up what were my first instincts as to how the circuit works, then I apologize.  Perhaps it would have been better for my occupation to remain unmentioned.  I think I am done sharing on this topic for now.  I don't wish to create enemies in this community, especially over a misunderstanding such as this.  Good Luck in your endeavors, and I hope you find the answer and share it for others to hear.




MohiZ,
Thank you for your simulations.  I think these kinds of calculations are a great tool here dealing with these kinds of questions.  I hope I can learn to use these programs as effectively in the next few weeks so I can begin my own explorations.

[Projectile]

Sorry Aziltz, but I came here as a novice looking for advice from people who I assumed were clearly more knowledgeable than I am. The issue seemed fairly straight forward to me and I just got frustrated to no end when after hundreds of people had read my post I was still getting back responses from obviously educated people that appeared very clearly to be wrong, and no one was willing to back me up or give me a correction in any way that makes sense. I apologize for being abrasive.

Thank you MohiZ for your analysis. Your findings are pretty close to what I am seeing since I isolated the tone control and refined my simple measurement system. At this point I still don't quite understand exactly how the 220 resistor effects the filter, but it is very clear that it works in conjunction with the 1K resistor to set the roll off point (in this case the boost point) to a value slightly below 720Hz, but it seems to only effect the roll off point very slightly. Most of its effects seems to be more in softening the curve of the filter. It doesn't contribute to the mid hump as much as I had thought, but the fact remains that the 220ohm resistor and the .22 cap alone do not set the roll off point of the filter. I don't know where so many people got the notion that you can calculate RC filters that way, because the AMZ article makes the same mistake in its analysis of the clipping section of the tube screamer. It seems very obvious to me with only my elementary knowledge of how these components work that you cannot calculate a filter that way. I'm just baffled that so many people have read this post and those articles are so well circulated, yet nobody has caught these errors when it seems so apparent to just a novice like me. I find it very odd, and the whole thing has left me rather frustrated and confused. Thank you for posting some data to help to clear up the confusion. Now at least I know I'm not completely crazy. 

[MohiZ]

Most of its effects seems to be more in softening the curve of the filter. It doesn't contribute to the mid hump as much as I had thought, but the fact remains that the 220ohm resistor and the .22 cap alone do not set the roll off point of the filter. I don't know where so many people got the notion that you can calculate RC filters that way, because the AMZ article makes the same mistake in its analysis of the clipping section of the tube screamer.

I agree with you there. The 220ohm resistor and .22 cap don't even LOOK like an RC filter. I'm pretty sure the 1K resistor only sets the gain of the op-amp. But of course that affects the roll-off point of the stage, because the op-amp only boosts highs. Could you post a link to the AMZ article?

Sorry for not being able to answer your question, but you see, I'm relatively new to this stuff, too. I've done tons of research and studying, though. It seems strange that there's not many members answering to this thread. I'm sure there are people on the forum who could answer this. Maybe they got bored reading the long posts 

[Projectile]

Here's the AMZ article:

http://www.muzique.com/lab/fatt.htm

I'm in the middle of doing frequency plots of this filter right now, but I'm having trouble because when I remove the diodes it's very easy to send the opamp into clipping when I mess with resistor values. Regardless, it is pretty clear at this point that the AMZ article is also wrong.  The 4.7K resistor once again does not by itself set the rolloff of the filter. The 51K resistor is what actually interacts most with the .047 cap to set the rolloff point. As you turn up the gain pot and add more resistance to the feedback loop, the rolloff point drops and more bass comes through. What makes it more complicated though is when you add the diodes in. When the voltage gets high enough the diodes open and the cap sees more current, so the filter starts cutting more highs into the negative input. If the diodes were to stay completely open then the cap would block all frequencies, but since the diodes are usually in some state part way between fully open and fully closed, they just seem to put a kink in the whole interaction and soften the effect of the gain pot on the roll off point. What is clear is that the gain pot still effects the roll off point. It is definitely NOT set alone by the 4.7K resistor, like it says in the AMZ article, and it is not 720Hz. It depends greatly on the amount of current in the feedback loop, which is controlled by the pot and the 51K resistor.

This is what I would expect from my elementary understanding, and it is in line with what I am seeing on the frequency plots. I just can't figure out how these "experts" keep getting these things wrong when it seems so obvious to me as a novice that they wouldn't work like that. I also don't understand why there is a complete lack of interest in the fact that there are all of these errors and misunderstandings circulating about. I don't get it. 

   

[slacker]

I'll try and add something to the discussion but bear in mind that I'm not an expert, and what I'm saying is based on what little knowledge I have and from playing with LTSpice for half an hour.

First read this http://en.wikipedia.org/wiki/Cutoff_frequency especially the bit about the -3dB point. With a standard RC filter with no active parts involved the cutoff frequency, which is the point where the output is 3dB less than the input is set by the equation F = (2*Pi*R*C). Depending on whether it's a high pass or a low pass filter the volume then drops off on a slope above or below these frequencies.
I'm saying this so that hopefully we're on the same page for the next bit, or at least in the same book

To look at the first stage what I did was remove the diodes and run it at 30volts so there's no clipping messing things up.
With the gain set at minimum so you've just got the 51k resistor and 51p cap in the feedback loop, you get a maximum boost of about 21 dB, if you follow the line down to the point 3dBs lower, ie:18 dB you should see that it's at about 720Hz. Which is where the RC filter equation for the 4k7 resistor and 47n cap says it should be.
If you then make the total resistance in the feedback loop 551k (maximum gain) you get a maximum gain of about 40dB and the -3dB point appears to be at about 550Hz. I think this is because like R.G. says in the TS article the lowpass cutoff frequency of the 51p and the resistance in the feedback loop lowers as the resistance increases. This then starts to interact with everything else so you don't get the answer you were expecting. To verify this if you remove the 51p the maximum gain increases slightly and the -3dB point moves back to 720Hz.

So basically I don't think there's anything incorrect in R.G.s or Jack's articles. The RC filter cutoff for the 4k7 and 47n resistor is 720Hz, it's just that the other things in the circuit change the overall frequency response. They aren't changing what those 2 components do.
They're maybe not giving you the full picture or giving a simplified explanation, but they're not wrong in what they're saying. 

I'm guessing its a similar story for the tone control but I haven't had chance to look at it in much detail. I think the portion of the tone control between the 200n and the negative input added to the 220R resistor set the rolloff frequency.

Don't know if any of that helps, it might make someone who knows what they're talking about jump in and tear what I've said to pieces if nothing else 

[aziltz]

To look at the first stage what I did was remove the diodes and run it at 30volts so there's no clipping messing things up.
With the gain set at minimum so you've just got the 51k resistor and 51p cap in the feedback loop, you get a maximum boost of about 21 dB, if you follow the line down to the point 3dBs lower, ie:18 dB you should see that it's at about 720Hz. Which is where the RC filter equation for the 4k7 resistor and 47n cap says it should be.
If you then make the total resistance in the feedback loop 551k (maximum gain) you get a maximum gain of about 40dB and the -3dB point appears to be at about 550Hz. I think this is because like R.G. says in the TS article the lowpass cutoff frequency of the 51p and the resistance in the feedback loop lowers as the resistance increases. This then starts to interact with everything else so you don't get the answer you were expecting. To verify this if you remove the 51p the maximum gain increases slightly and the -3dB point moves back to 720Hz.

THAT, makes a lot of sense to me.

One thing we all need to keep in mind here is, the easiest way to describe the way something works its to break it down and simplify it.  Take RG's explanation of the Tone Curve of the TS Clipping Stage as an example.  Yes, the full frequency response depends on everything attached to the op-amp, but the easiest way to describe it (in words) is to separate the 4k7/4n7 720Hz Low Pass from the 51pF/1M Gain control.  While I can't speak for them directly, I think this is what the Author's intended to do with their articles.

Thank god for these simulation tools though!

[Projectile]

I'll try and add something to the discussion but bear in mind that I'm not an expert, and what I'm saying is based on what little knowledge I have and from playing with LTSpice for half an hour.

First read this http://en.wikipedia.org/wiki/Cutoff_frequency especially the bit about the -3dB point. With a standard RC filter with no active parts involved the cutoff frequency, which is the point where the output is 3dB less than the input is set by the equation F = (2*Pi*R*C). Depending on whether it's a high pass or a low pass filter the volume then drops off on a slope above or below these frequencies.
I'm saying this so that hopefully we're on the same page for the next bit, or at least in the same book

To look at the first stage what I did was remove the diodes and run it at 30volts so there's no clipping messing things up.
With the gain set at minimum so you've just got the 51k resistor and 51p cap in the feedback loop, you get a maximum boost of about 21 dB, if you follow the line down to the point 3dBs lower, ie:18 dB you should see that it's at about 720Hz. Which is where the RC filter equation for the 4k7 resistor and 47n cap says it should be.
If you then make the total resistance in the feedback loop 551k (maximum gain) you get a maximum gain of about 40dB and the -3dB point appears to be at about 550Hz. I think this is because like R.G. says in the TS article the lowpass cutoff frequency of the 51p and the resistance in the feedback loop lowers as the resistance increases. This then starts to interact with everything else so you don't get the answer you were expecting. To verify this if you remove the 51p the maximum gain increases slightly and the -3dB point moves back to 720Hz.

So basically I don't think there's anything incorrect in R.G.s or Jack's articles. The RC filter cutoff for the 4k7 and 47n resistor is 720Hz, it's just that the other things in the circuit change the overall frequency response. They aren't changing what those 2 components do.
They're maybe not giving you the full picture or giving a simplified explanation, but they're not wrong in what they're saying. 

I'm guessing its a similar story for the tone control but I haven't had chance to look at it in much detail. I think the portion of the tone control between the 200n and the negative input added to the 220R resistor set the rolloff frequency.

Don't know if any of that helps, it might make someone who knows what they're talking about jump in and tear what I've said to pieces if nothing else 

Once again, that doesn't make any sense.  You people are driving me freaking crazy!

If you roll off highs in a negative feedback loop, you BOOST highs in the output, which looks like a bass cut, but what you are actually doing is boosting highs. The point at which the highs are down 3db because of the filter isn't going to be where the bass rolls off 3db at the output, it's going to be where the BOOST STARTS, which is AT THE BOTTOM OF THE CURVE. 

I'm trying to help, but I seriously can't put up with this nonsense any longer unless someone is going to back me up. I feel like I'm wasting my time and just going around in circles. The GeoFX article is clearly wrong. We have already seen that with Mohiz's Aplac analysis. I feel like we are moving backwards instead of making progress and it is very frustrating. I am fairly confident that the AMZ article is also wrong. I'm kind of shocked that nobody else can see these clear errors.  Everyone just seems intent on kludging the data to fit the GeoFX and AMZ articles rather than stopping for a moment and actually thinking for themselves.


Look, you can't build an RC filter like this:



I'm a newb at this stuff, and even that is very clear to me. I don't see why you people can't understand that. If you still can't see why that can't be an RC filter by itself, then may god help you because you obviously don't understand the very basics of how electrical circuits work.

In order have a filter of any kind, you have to create some sort of voltage divider. Like this:



R1 is not necessary for creating a filter, but R2 is essential! You cannot calculate the rolloff of this filter without taking in account R2, period. You also have to account for R1 in the calculation, but just  using R1 and C1 to calculate the filter is ridiculous. It doesn't make one bit of sense. Why is that so hard to understand?

Now look at the tubescreamer circuit. The output of the opamp is the source of the voltage potential. The filter in the gain stage is on the other side of the 51K resistor and the tone pot. The 51K resistor + the tone pot, in combination the .047 cap is what calculates the rolloff. The 4k7 resistor is involved in that calculation too, but I don't understand exactly how it works into the calculation, just that is softens the curve and appears to also effect the rolloff by some small amount. This is, of course, with the diodes TAKEN OUT of the feedback loop. If you JUMPER the diodes, then the negative input of the opamp sees the output without any interference by the filter. The filter is essentially out of the equation. Get it?

Same thing with the filter section. We can disconnect the lug of the pot that goes to the positive input of the opamp, because it doesn't really effect the signal when the tone control wiper is all the way on the negative input side of the pot. That has been established. Okay, now the output of the opamp is the source of the voltage potential that the negaive input "sees". The 1K resistor is your R2 from the graphic above, the .22cap is C1, and the 220 ohm resistor is R1. See how that works? You NEED that 1k resistor for the calculation. It is not something you can ignore out of convenience. It is essential to the calculation of the RC rolloff. To just use the 220 resistor and .22cap in the RC calculation is FLAT OUT WRONG. The actual filter is rolling off nowhere near 3.2Khz, period.

I'm getting really frustrated over this and I'm thinking I'm going to abandon this forum altogether. No offense, but I feel like I'm talking to a bunch of dunces here that don't understand simple concepts. I'm a newb for christ's sake!  I know you people are not retards. You all seem very intelligent and educated. If anything I am the dunce in the room, which is why I am so incredibly confused? Am I the butt of some elaborate joke? Hello??!!!!!

   



 

[Projectile]

To look at the first stage what I did was remove the diodes and run it at 30volts so there's no clipping messing things up.
With the gain set at minimum so you've just got the 51k resistor and 51p cap in the feedback loop, you get a maximum boost of about 21 dB, if you follow the line down to the point 3dBs lower, ie:18 dB you should see that it's at about 720Hz. Which is where the RC filter equation for the 4k7 resistor and 47n cap says it should be.
If you then make the total resistance in the feedback loop 551k (maximum gain) you get a maximum gain of about 40dB and the -3dB point appears to be at about 550Hz. I think this is because like R.G. says in the TS article the lowpass cutoff frequency of the 51p and the resistance in the feedback loop lowers as the resistance increases. This then starts to interact with everything else so you don't get the answer you were expecting. To verify this if you remove the 51p the maximum gain increases slightly and the -3dB point moves back to 720Hz.

THAT, makes a lot of sense to me.

One thing we all need to keep in mind here is, the easiest way to describe the way something works its to break it down and simplify it.  Take RG's explanation of the Tone Curve of the TS Clipping Stage as an example.  Yes, the full frequency response depends on everything attached to the op-amp, but the easiest way to describe it (in words) is to separate the 4k7/4n7 720Hz Low Pass from the 51pF/1M Gain control.  While I can't speak for them directly, I think this is what the Author's intended to do with their articles.

Thank god for these simulation tools though!

No, you cannot separate the 4k7/4n7 720Hz Low Pass from the 51pF/1M Gain control. That doesn't make any sense. It's not merely a convenience. It drastically changes the calculations. This is not an explanation. It is a complete fallacy. You simply cannot do that. There is a world of difference between a cap seeing the low impedance output of an opamp, versus the same cap seeing the high impedance of a 51K pot and a 500K gain control. That impedance is ESSENTIAL in setting the rolloff of the filter. If you take those parts out of the equation, then the filter doesn't work anymore, at all.

AAAAARRRRRGGGGGGHHHHHH!!!!!!!!!

[aziltz]

LOOK... you really should be more polite if you want help, even if you disagree.  referring to members as dunces and insulting their understanding of electronics will get you no where.  you seem like a smart guy.  get an reference book and figure it out if you don't like the answers provided, no reason to rip everyone a new one.

good luck.

btw, the 4k7/4n7 isn't a simple RC filter.  It sets the gain bandwidth of the clipping stage because, below the RC cut-off, its a essentially an open circuit, above it, its essentially a 4k7 resistor.  I say essentially because I'm simplifying things.  If you don't want to simplify, play with the differential equations.

[biggy boy]

[MohiZ]

Now I agree with Projectile. If you think about it, considering the tone knob resistance as "large", we can replace it with an open circuit when it's either full on or full off. With this simplification, the tone stage looks like this:



Now it's starting to look easier to calculate. If we short the 220 ohm resistor, it's even easier. When the tone is full off, after the input there's just a low pass filter with two caps to ground in parallel. And since parallel caps add up, we get its roll-off: f = 1/(2*pi*0.44u*1k) ~ 360 Hz. The op-amp after that is just a unity gain buffer. And take a look back at my analysis here, the middle graph, the first blue line (tone control fully off position): http://www.aronnelson.com/gallery/main.php/v/diyuser/ts3.JPG.html?g2_imageViewsIndex=1

Its 3dB roll-off pretty much exactly 360 Hz in the graph so the approximation was correct!

When the tone is fully on, and the 220 ohm resistor shorted, it's like a LPF with a highs boosting op-amp configuration after it. First of all, the Low Pass Filter roll-off before the op-amp is f = 1/(2*pi*0.22u*1k) ~ 720 Hz. Calculating the op-amp's bandwidth roll-off frequency is easy, too. The 1k resistor from the output and the .22u cap from inverting to ground, form a LPF, so f = 1/(2*pi*0.22u*1k) ~ 720 Hz. Note that everything below this frequency is fed to the inverting input of the op-amp, thus REDUCING those frequencies. Thus, the op-amp boosts frequencies above 720 Hz.

With the LPF and the highs-boosting op-amp the sum of their frequency response should be flat, since both their roll-off is 720 Hz.... and it is! The tone control sort of smoothly morphs between those response curves.

All the 220ohm resistor does in my mind is "prevent" the frequency response from becoming completely flat. As you can see in the graphs, with the 220ohm resistor shorted the graphs look the same at first, but it's as if the range of the tone control is extended in the high frequency range.

So, in light of this realization and my graphic analysis I'd say Projectile is correct and the Geofex article is wrong. Good job pointing that out!

EDIT: Some mild spell checking after proofreading.

[aziltz]

Now I agree with Projectile. If you think about it, considering the tone knob resistance as "large", we can replace it with an open circuit when it's either full on or full off. With this simplification, the tone stage looks like this:



Now it's starting to look easier to calculate. If we short the 220 ohm resistor, it's even easier. When the tone is full off, after the input there's just a low pass filter with two caps to ground in parallel. And since parallel caps add up, we get its roll-off: f = 1/(2*pi*0.44u*1k) ~ 360 Hz. The op-amp after that is just a unity gain buffer. And take a look back at my analysis here, the middle graph, the first blue line (tone control fully off position): http://www.aronnelson.com/gallery/main.php/v/diyuser/ts3.JPG.html?g2_imageViewsIndex=1

Its 3dB roll-off pretty much exactly 360 Hz in the graph so the approximation was correct!

When the tone is fully on, and the 220 ohm resistor shorted, it's like a LPF with a highs boosting op-amp configuration after it. First of all, the Low Pass Filter roll-off before the op-amp is f = 1/(2*pi*0.22u*1k) ~ 720 Hz. Calculating the op-amp's bandwidth roll-off frequency is easy, too. The 1k resistor from the output and the .22u cap from inverting to ground, form a LPF, so f = 1/(2*pi*0.22u*1k) ~ 720 Hz. Note that everything below this frequency is fed to the inverting input of the op-amp, thus REDUCING those frequencies. Thus, the op-amp boosts frequencies above 720 Hz.

With the LPF and the highs-boosting op-amp the sum of their frequency response should be flat, since both their roll-off is 720 Hz.... and it is! The tone control sort of smoothly morphs between those response curves.

All the 220ohm resistor does in my mind is "prevent" the frequency response from becoming completely flat. As you can see in the graphs, with the 220ohm resistor shorted the graphs look the same at first, but it's as if the range of the tone control is extended in the high frequency range.

So, in light of this realization and my graphic analysis I'd say Projectile is correct and the Geofex article is wrong. Good job pointing that out!

EDIT: Some mild spell checking after proofreading.

Now I agree with Projectile. If you think about it, considering the tone knob resistance as "large", we can replace it with an open circuit when it's either full on or full off. With this simplification, the tone stage looks like this:



Now it's starting to look easier to calculate. If we short the 220 ohm resistor, it's even easier. When the tone is full off, after the input there's just a low pass filter with two caps to ground in parallel. And since parallel caps add up, we get its roll-off: f = 1/(2*pi*0.44u*1k) ~ 360 Hz. The op-amp after that is just a unity gain buffer. And take a look back at my analysis here, the middle graph, the first blue line (tone control fully off position): http://www.aronnelson.com/gallery/main.php/v/diyuser/ts3.JPG.html?g2_imageViewsIndex=1

Its 3dB roll-off pretty much exactly 360 Hz in the graph so the approximation was correct!

When the tone is fully on, and the 220 ohm resistor shorted, it's like a LPF with a highs boosting op-amp configuration after it. First of all, the Low Pass Filter roll-off before the op-amp is f = 1/(2*pi*0.22u*1k) ~ 720 Hz. Calculating the op-amp's bandwidth roll-off frequency is easy, too. The 1k resistor from the output and the .22u cap from inverting to ground, form a LPF, so f = 1/(2*pi*0.22u*1k) ~ 720 Hz. Note that everything below this frequency is fed to the inverting input of the op-amp, thus REDUCING those frequencies. Thus, the op-amp boosts frequencies above 720 Hz.

With the LPF and the highs-boosting op-amp the sum of their frequency response should be flat, since both their roll-off is 720 Hz.... and it is! The tone control sort of smoothly morphs between those response curves.

All the 220ohm resistor does in my mind is "prevent" the frequency response from becoming completely flat. As you can see in the graphs, with the 220ohm resistor shorted the graphs look the same at first, but it's as if the range of the tone control is extended in the high frequency range.

So, in light of this realization and my graphic analysis I'd say Projectile is correct and the Geofex article is wrong. Good job pointing that out!

EDIT: Some mild spell checking after proofreading.

interesting.

separating full and off was the same method used by RG and AMZ to explain this.  Rereading RG's article though, I don't believe it to be wrong in anyway, just over-simplified for our man Projectile's purpose.  I can see how his descriptions fit into your plots of the tone curve, (great job btw).

I'm going to do some calculations today.  I believe I can add some more justification to your 220 resistor argument.  I have a feeling that the 220 resistor prevents the 1k + .22uF filter from having any effect until you are over the 3.2kHz cut-off (of 220/.22uF).  In a nutshell, you get the roll-off curve/slope of the 1k/.22uF, but only in frequencies above 3.2kHz.  This is because below 3.2kHz, that leg looks like an open circuit.  I will flesh this out as much as possible so please don't bash me before I can determine if I'm wrong or not.  This would explain a lot about how series Caps/Resistors to ground act differently from regular RC filters, and hopefully clear up a lot of confusion in this thread.

[MohiZ]

Yes, it may be that RG's article just looks at this from a different viewpoint. The two filters interact a lot. I'm interested to see what you'll come up, with, aziltz!

[aziltz]

Yes, it may be that RG's article just looks at this from a different viewpoint. The two filters interact a lot. I'm interested to see what you'll come up, with, aziltz!

instead of paying attention in stat-mech, i did a quick calculation of the gain as a function of frequency of a Low Pass Filter that includes a 2nd resistor in series with the Capacitor to ground.  The results are interesting.  If ya'll can give me til Thursday after my E&M test I'd be happy to post my math and hopefully a plot of the gain curve. 

EDIT:  I don't want to jump the gun until I'm sure I did it right and get some plots going.

ya'll don't mind hand-written math in a pdf?

[slacker]

Once again, that doesn't make any sense.  You people are driving me freaking crazy!

Fair enough I'm fully prepared to accept that I'm wrong.
It could just be coincidence, or a quirk of the simulator, that where the signal is 3dB down compared to the max gain corresponds to 720Hz.
The above is a genuine statement by the way, not some sort of snide remark. just in case anyone reads it as one

In all seriousness if you've got issues with R.G.'s article why not PM him and put your points to him?

[aziltz]

In order have a filter of any kind, you have to create some sort of voltage divider. Like this:

ok thats just wrong.

read up on RC filters and you'll find all kinds of variations, parallel arrangements, etc.  The thing is, R1/C1 has a certain property at its cut-off frequency, no it doesn't act like a filter on its own, but place it in the feedback loop of an op-amp and it controls the bandwidth of the gain. 

[Projectile]

In order have a filter of any kind, you have to create some sort of voltage divider. Like this:

ok thats just wrong.

read up on RC filters and you'll find all kinds of variations, parallel arrangements, etc.  The thing is, R1/C1 has a certain property at its cut-off frequency, no it doesn't act like a filter on its own, but place it in the feedback loop of an op-amp and it controls the bandwidth of the gain. 

Uh... No.

 I'd be entirely willing to back down and eat everything I've said, but at this point I haven't actually seen any information that would contradict my understanding of how these filters work. I have done a lot of reading and breadboarding since the beginning of this post, and so far everything that I have learned has done nothing but strengthen my position, and it has shown to me very clearly that you don't really know what you are talking about. Sorry if you take that personally, but I have a hard time seeing it any other way, and believe me, I've tried! You seem to be very good at math and juggling variables. That's great! I can't do that stuff nearly as well as you can, so my props to you. But you seem to have a problem with understanding how this stuff works in context and it is causing you to make obvious errors in the way you are applying your formulas. You don't seem to actually understand why they work.

I'm sure you could get very creative with resistors and capacitors in a feedback loop to create all kinds of interesting filter arrangements. The fact remains that you need some type of voltage divider or you aren't going to get a different frequency response at the output. Sure, without R2 the arrangement may still be filtering certain frequencies and have a rolloff that you could calculate, but it's like a tree falling in the woods with nobody around to hear it. So, it would be a pretty pointless exercise.

My point was not that the 2nd example is the ONLY way to make a filter. My point was that the first example isn't a filter at all. I don't care whether you put it in the feedback network of an opamp or not, it's not going to DO anything. The GeoFX and AMZ articles seem to be claiming that C1 and R1 in the feedback loop of an opamp make a filter. They don't. Can you see why the first example above is not a filter when simply placed in a feedback loop? Opamps have a very low output impedance, so in order to make a filter that works like the one in the example you MUST have R2, and R2 is what get plugged into the formula to calculate the rolloff. It is essential.

I created this thread to clear up my understanding of how RC filters work. Because my own understanding was directly conflicting with the GeoFX and AMZ articles, I initially thought that there must be something I was missing in my general analysis of these filters. The process of discussing and analyzing these filters on in this thread have now cleared up any contradictions I was having with the GeoFX and AMZ articles. I am now quite confident that those articles are in fact incorrect. It doesn't mean that I don't still have questions, but there is no misunderstanding about the GeoFX and AMZ articles any longer. They're just wrong.

Anyway, thank you to everyone who has participated in this thread. Although it was quite frustrating, this thread has been an enormous learning experience for me. What confuses me now is the total lack of interest in the fact that there are obvious errors in well circulated documents, and why nobody has caught them before. I know I'm not the only person who understands this stuff, so why is there such dead silence except for the small handful of people who have particpated in this thread? Hello? Anyone out there? ...weird.