Cook Your Own Distortion: math

[Noplasticrobots]

Either I'm missing the very obvious (highly possible) or there's a mistake in the CYOD article. It shows the formula for figuring what value capacitor to use for a high/low pass filter. With f being frequency, the formula states that:

f= 1 / 2*PI*R1*C1

That makes sense to me. We need to figure for R1 and C1. Well it states that to find C1 you apply the following formula:

C1= 1 / 2*PI*R1*f

Makes sense. The article continues ut doesnt explain how to get the correct R1 value. The article does mention to use at least 100k resistors for less tone loss, but there's gotta be a way to figure out what an optimum resistor value is. Without running any numbers, it seems like the following formula would work:

R1=  1 / 2*PI*C1*f

I'd like to have the correct frequencies in check because I play in an alternate tuning. Any math people out there able to help?

[Hal]

yes, thats right, but then again for any given frequency, there are infinite R/C combinations....you need to have some sort of starting point, and thats what the 100k is.  You base one off the other...

[gaussmarkov]

yeah, i asked a similar question once. i don't think i got nearly as clear an answer that time. Hal explains it perfectly. i'll just add what i read somewhere:  you go with the tried and true R/C combinations that are already out there in other circuits.  they will deliver the performance you are looking for.  the math is just an approximation that  breaks down for other values ... 

[Noplasticrobots]

Thanks for the help guys. I didn't think there could be a mistake in an article that everyone has read through!

[tweaker]

Hello all.  Since there was already a post on this subject I thought I would attach my question on to it.  This has been a great article for learning the ins and outs of distortion pedals and thanks to the author.

I understand the simple RC low and high pass circuits shown but I am a little unclear when the opamp is involved.  Previous post(s) and elsewhere I have read have stated that a resistor and cap in parallel in the feedback loop form a low pass filter but in the last section of the article in the 'My example designs' states that R4 and C3 for a high pass filter.  I had also read where the resistor and cap in series coming off the feedback loop form a high pass filter and here it states R5 and C4 form a low pass filter.  I just want to make sure I'm reading this right and not turned around on how filters are formed.  Would someone help clear up my confusion?     Thanks.

Brad

[slacker]

I've just reread the cook your own distortion article and I think you're right, C4 and R5 in the example schematic are a high pass filter, it's these components in a Tube Screamer that set the characteristic bass roll off. R4 and C3 are a low pass filter.

[Transmogrifox]

Here's a way to look at it that may clear some "high pass or low pass " problems:

Think of a capacitor as a resistor.  The only difference is that its resistance is frequency dependant (neglecting the phase aspect, but this doesn't matter for just answering the high pass or low pass question).   When the frequencies are higher, the resistance is much smaller.  When frequencies are lower, it's very large.  A capacitor is a near infinite resistor to DC, except that there is some dielectric leakage and things that are negligible for mose DC circuits, and nonexistent if you're just thinking theory so you can figure out if it's a high pass or low pass filter.

So again, a capacitor is a very high impedance at low frequencies and very low impedance at high frequencies.

In the case of no op amp, if the capacitor is in series with the output, and the resistor is parallel to ground w/ the output, it's a high pass filter.  If you have a resistor in series w/ output, and the cap parallel to ground then it's a low pass filter.

In an op amp circuit, the gain is determined by the resistor from output to neg terminal divided by the resistor from neg terminal to ground.  If the resistor to ground is small, and resistor from output to neg terminal is large, the gain is high.  If the reverse is true, then the gain is low.

So if a cap is in the neg terminal to ground path, then gain on high frequencies is higher, thus you have a high pass filter.

If the cap is in the output to neg terminal path, then it reduces the gain on high frequencies, so it's a low pass filter.

Any better?
...or did I just make it more confusing?

[gaussmarkov]

IMHO, excellent explanation.

[tweaker]

Thanks guys!  I had to re-read this a couple times to let it sink in but I understand now what you are saying about component behaviors in circuits.  Basically a cap and resistor are always going to act as a filter but by changing their positions and values we can determine their frequency response (tone?) for that portion of the circuit. 

That will help in trying to figure out how those RC combinations in effects pedals work in tailoring the response; especially the ones that hang off of the feedback loop.  It appears that they create a freq. response for that opamp and then any tone control that follows changes the response again.  Starting to make sense now.   

Figuring out tone controls is a whole other subject.   

Brad