Calculating RC time constants...and why you should.

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VelvetGeorge
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Calculating RC time constants...and why you should.

Post by VelvetGeorge » Wed Apr 20, 2005 12:18 pm

One of the most important things to consider when tweaking amps is the interaction between resistors and capacitors. In series or parallel with each other they do particular frequency dependant things.

One thing they do depending on orientation (high pass filter, low pass filter, parallel) is create a cutoff frequency. In guitar amps, this is illustrated by the cathode cap and resistor. Their value determines at which frequency a 6db per octave rolloff happens at.

The formula to find that frequency is:

F= 1
--------------
(2 pi) R C

For your typical .68/2.7k combination the formula is this:

F= 1
------------------------------- = 87Hz
6.28 * .00000068 * 2,700

Meaning that every frequency above 88Hz is at full gain for that stage.

For the 470pf/470k mix resistor arrangement, it works out like this:

F= 1
------------------------------------ = 720 Hz
6.28 * 00000000047 * 470,000

Meaning that every frequency below 737 rolls off at a 6db per octave slope.

You can also calculate the frequency determined by coupling caps and the equivalent resistance in the circuit. In the first stage of a Marshall you have a .022 or a .0022 with a 100k plate resistor and 1M to ground via the volume pot. Your equivalent circuit resistance is 91k. Making the formula:

F= 1
-------------------------------- = 80Hz for a .022uf
6.28 * .000000022 * 91,000


F= 1
---------------------------------- = 795Hz for a .0022uf
6.28 * .0000000022 * 91,000

Doesn't that explain why a .022 sounds so much fuller?

I hope this formula will shed some light on what's happening frequency wise in amplifiers. And hopefully we can use this to achieve our desired tones.

George
Last edited by VelvetGeorge on Wed Apr 20, 2005 12:42 pm, edited 1 time in total.
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Post by VelvetGeorge » Wed Apr 20, 2005 12:21 pm

It might also be helpful for me to point out that the lowest fundamental frequency on a guitar, tuned standard, is around 80Hz.

For bass guitar, it's around 40Hz.


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Post by Flames1950 » Wed Apr 20, 2005 12:25 pm

Ummm, with the value of pi being 3.14xxxxxxxxetc. then 2(pi) would be 6.28xxxxxxxxx............right?
I may have drank my way out of the University of Iowa College of Engineering but I still have pi down cold.........
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Post by VelvetGeorge » Wed Apr 20, 2005 12:39 pm

Oops! Typing too fast.....

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Post by Flames1950 » Wed Apr 20, 2005 1:56 pm

I was figuring this stuff for the cathode RC combinations I was considering in my Dumble clone....on paper (no calculator).......and by the time you factor in all the decimal places since the formula is using farads (not microfarads) for C, the difference in pi is probably moot.
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Post by VelvetGeorge » Wed Apr 20, 2005 3:18 pm

Just a few Hertz difference. But it needs to be right. Thanks for pointing out. I promise, no more math before coffee!

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Post by Eoin » Wed Apr 20, 2005 7:09 pm

Wow, that'll come in handy. Cheers, George. :)

Eoin

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Post by flemingmras » Thu Apr 21, 2005 11:04 am

OUCH! All this math and formulas...my brain Hertz! :lol: :lol: :lol: :lol: :lol: :lol: :lol: :lol:

Actually, it did shed some light on something. The hard rock tone I've noticed centers around 700-800Hz, which I believe produces that midrange "squawk" tone you get with a lot of false harmonics(very common in the 80's, ala Warren DiMartini from Ratt). The .0022uF/1M/100K arrangement and the 470K/470pF arrangement definitely explains why it's easy to get that on Marshalls.

However, it kills me when people are like "well, since 82.41Hz is the frequency of the low E string, there's nothing below that that is essential to the guitar". But how can that be? Yeah, sure the FUNDAMENTAL frequency of the low E string is 82.41Hz, provided you're in standard tuning, however certain players(like George) are known to tune down 1/2 step, and on top of that, people forget that strings don't just produce the fundamental note, they also produce harmonics that are above and below the fundamental frequency. These harmonics are what make a guitar sound like a guitar. In order to achieve great tone one must take these factors into account.

Jon
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Post by Billy Batz » Thu Apr 21, 2005 5:09 pm

Thats like stereo manufacturers that concentrate a lot on sub-audio levels. People say "if we cant hear those frequencies anyway why waste time on them" but they do make a difference in the final tone. Too many and the bass gets out of control even if we dont percieve that much bass in the signal. Shit. Thats like saying just because the A string is 440hz cutting off all the bass below that wont effect the A string. Yeah right...

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Post by flemingmras » Fri Apr 22, 2005 4:16 pm

And that's due to the harmonics below the string's fundamental frequency. But NO...those aren't important remember? :lol: :lol: :lol: :lol: :lol: :lol: :lol: :lol:

ANd actually, 440Hz is the frequency of the high A fretted at the 5th fret high E string, the 10th fret B string(2nd), the 14th fret G string(uh...huh...huh...hhe said G string), the 19th fret D string(4th), and for those of us with 24 fret necks, the 24th fret A string(5th).WOW! So on a 24 fret neck, there's 5 places to hit the same note! However the thing most people don't realize is that in each of those positions the note has a much different tone voicing, becoming brighter closer to the top of the neck and darker closer to the body.

However, 440Hz is the standard tuning note for all instruments. This is the A note you hear large orchestras tuning to. But basically, the rule is that the frequency of a note doubles every octave. So 110Hz being the low A, the middle A on the second fret G and the 7th fret D, or the 12th fret A is 220Hz, and the next one up is 440Hz.

So on a 24 fret guitar, the highest E note would be 1318.56Hz, or 1.3KHz, so this means that boosting any frequencies above that won't make a difference right?

Jon
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Post by Billy Batz » Fri Apr 22, 2005 4:41 pm

I got ya loud and clear flem. That hit me right after I posted but I didnt bother changing it. Point still made.

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Post by Billy Batz » Thu Sep 01, 2005 6:11 pm

I know this threads long dead but can anyone explain, physicaly, why a series resistance attenuates trebles? I have an idea Im sure may be right but thats just from pure thought. I dont remember learning about this.

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Post by rjgtr » Fri Sep 02, 2005 11:29 am

Resistors resist power flowing. The smaller the power the less you get. So high frequencies, which take less power to generate are easier to block. Obviously the effect is more subtle than using caps.
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Post by VelvetGeorge » Fri Sep 02, 2005 12:53 pm

Series impedance, which like all impedances, is frequency dependant.

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Post by Billy Batz » Fri Sep 02, 2005 12:57 pm

I was 1000% correct (pleased with self). Im sure I did probably learn all about this and just forgot. I still love that quote rjgtr.

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