Frequency response chart for capacitors

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Frequency response chart for capacitors

Postby supro » 22 Jan 2008, 14:17

So im studying tonestack meathods and Im trying to get my head around resistor/cap combinations for frequency response control on an effect.
In an effort to break this down in simpler forms to help me understand, I reckon a frequency response capacitor chart would help me alot.

Here is an example to make my point.....Im familiar with placing a very small value cap (10-15Pf) in a feedback loop on an opamp to cure ossilation(the cap filters out high end info). So is there a chart that could tell me at what frequency the "low pass filter" starts to work for a 10 PF cap?
My Achilees heel working on stompboxes has always been mathematics!.....I start reading some info from the top gurus and when they bring out a 6 inch long math equation to explain whats going on, well they loose me fast!.....I don't even want to start trying to understand and loose all interest.
A bit like if I have to take half an hour to put up some recording tools together, I loose all inspiration that I had a half hour ago! and forgot why I wanted so to record....
Im not saying its not the way to go, as for all of you that can handle numbers, you get the exact way of doing things, but for me, in this example, all I would want would be some kind of chart to guide me along in making tone desisions.
A bit like the chart I have printed out for cap codes and values, now I can do it in my head because I stared at that chart for so long. I would not be at this point in my head if I had to break out some funky equations to figure out cap values!
thanks for the help.
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Re: Frequency response chart for capacitors

Postby R.G. » 22 Jan 2008, 18:22

Let me try.

A capacitor has no frequency response of its own. All it has is a "resistance" to AC that decreases as frequency increases. So a cap may "resist" by the equivalent of 100 ohms at one frequency. If you double the frequency, the same cap now "resists" by 50 ohms. If you half the frequency, the same cap now "resists" by 200 ohms.

I say "resists" in quotes because it's not really resistance the same way a resistor does it. The work "impedance" was coined because the guys who messed with electricity first had used up "resistance" for what resistors do, and they needed another word for getting in electricity's way but different in some respects to a resistor.

Meanwhile, back at the capacitors. If you keep lowering the frequency you put through a cap, the "resistance" (impedance) to current flow goes up and up, until finally as the frequency goes to 0 - that is, it's DC, not AC - the impedance is infinite, and it totally blocks current flow. We use caps a lot to block DC but let AC flow through, and that's how they do it.

But if we have a resistor and a cap in series, what happens?

At DC, the capacitor blocks all current flow, so the resistor has nothing to say about it. It's blocked and the resistor doesn't matter.

If we use very low frequency AC, the "resistance" (impedance) of the capacitor is still very large, so the capacitor only lets a trickle of AC current through, and the resistor matters very little.

You can see where this is going, right? As we raise the frequency, the cap "resists" less and less. At very high frequencies, the cap's "resistance" (impedance) is so much smaller than the resistor that the current is determined entirely by the resistor, and the cap conducts so well at the high frequency that it might as well be a wire.

The frequency where the cap and resistor both matter is what the EEs take as the "rolloff frequency" of the combination.

And now we have to get to the - very little - math. You have to be able to calculate the frequency from the resistor and capacitor.

Trust me on this: the impedance of a capacitor is Xc = 1/(2*pi*F*C).

Xc is used to mean Impedance (X instead of R, cause they're a little different) subscript c (meaning, belonging to the capacitor, not something else).

"pi" is the number 3.14159; it's just a constant number that happens to make the calculations come out to the right numbers. Just memorize it. 3.14 is generally good enough for calculations.

F is the frequency in cycles per seconds, or Hertz, same thing.

C is the capacitance in Farads; a microfarad is one one-millionth of a Farad. A pico farad is a millionth of a microfarad.

Since we have to calculate the frequency where the impedance of the cap equals the resistance, we just say

R= 1/(2*pi*F*C) - I apologize, this bit of math is critical

and the frequency is then
F = 1/(2*pi*R*C) and that's how you calculate it.

You multiply the Resistance in ohms times the capacitance in farads, then multiply by 2, and finally multiply by 3.14, and divide 1 by the result. The number you get is the frequency in cycles per second or Hertz.

An example: you have 10pF cap and a 100K feedback resistor. What's the frequency where the cap starts letting more current through than the resistor?

It's the frequency where the cap's impedance is equal to the resistance. So
it's 1/(2*pi*100K*10pF).

10pF is 10 times ten to the minus twelfth power, or 1x10^-11, the "^" meaning "to the power of"

so the frequency is 1/( 2* 3.14* 100,000* 1x10^-11) and if I punched the calculator buttons right, it's 159,235 Hz, or a bit over 159kHz.

(a) did that help?
(b) OK, where did I mystify you?

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Postby supro » 23 Jan 2008, 15:43

OH my!, R.G, so far, that is the easiest explanation I ever got!
Now if I can only book a vacation somewhere nowhere with no distractions, maybe ill get all this in my thick head in a week :lol:
Seriously, Ill reread that sitting down with a beer and work at it till I get it.
Thats the least I can do to honor your generosity on the matter.
Thanks for taking the time to explain!
Cheers
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Postby R.G. » 23 Jan 2008, 17:27

supro wrote:Thanks for taking the time to explain!

You're entirely welcome. I received a lot of help when I was mystified by things, and the least I can do is return the favor. Yell if there are points that are still not clear.
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Postby ech0es » 23 Jan 2008, 18:01


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Postby analogguru » 23 Jan 2008, 18:42

here a table for the reactance of capacitors at various frequencies:

http://analogguru.an.ohost.de/techstuff/Reactance.htm

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frequency response

Postby darrenbkl@gmail.com » 11 Sep 2008, 15:08

hi,got a question here. for a distortion circuit, there are always a series resistor with a caps in the negative feedback loop of an op amp, to determine the gain. the resistor and the caps there do something about frequency response right?if not wat is the use of caps there. can anyone explain me?
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Re: frequency response

Postby modman » 11 Sep 2008, 15:26

Here is a thread about capacitor reactance:
http://www.freestompboxes.org/viewtopic.php?f=10&t=1625

Analogguru has drawn up a reactance chart is here
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Re: frequency response

Postby darrenbkl@gmail.com » 11 Sep 2008, 16:53

ok is it means that, if frequency get higher,then Xc will become smaller due to Xc=1/2πfC, then the gain of the op amp will become higher due to Rf/Ri right??
so the gain of the circuit depends on the frequency?
But what is that mean the frequency? Is it the note we play or wat?
Thx for help :applause:
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Re: frequency response

Postby TragicTravisty » 12 Sep 2008, 01:13

frequency and pitch are very similar. if you play the pitch of E open on the bottom string, and a boost at 80hz, that note will be louder than the others because it it boosted. but you still hear the other notes clearly, if that makes sense. and frequency has nothing to do with gain, resistance sets gain. the higher the value of resistance in the negative feedback loop of the op-amp, the higher the volume BUT the lower the audible distortion.
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