Capacitor rolloff frequencies

[KT66]

I have seen posts in this forum that give rolloff frequencies for coupling and cathode caps and I would like to know if there is a chart or a formula or something that someone could point me to.

[bnwitt]

Here is one for the 12AX7 with a 100K plate resistor.

[KT66]

That's cool, thanks. It's a little hard to read though, can you tell me where it is from ( book, webisite etc.) so I can try to find an easier to read version ?

Thanks again.

[bnwitt]

Did you try to download it and and then open it? It is from Bruce collins of Mission amps. I don't remember where I found it but I know it is his work.

[talbany]

Interesting Exercise -3db points for cathode resistors any bypass caps
With given Rk/Ck values the frequencies will be 3db down. Notice that the frequencies are not cut off. They are only 3db down or cut by half – an audible change.

So, with a typical 1.5 cathode resistor, any bypass cap value above 10uf is a waste. Or is it? Of course, this is pure math based on RC time constants. The real frequencies are dependent upon parts tolerance, tube capacitance, etc., etc. We know that electrolytics and poly, mylar, ceramic, etc caps of the “same” value sound different. Why?

Using the Capacitive Reactance formula alone you can find the band pass or “cut” frequencies.

F = 1/2piRC (pi = 3.1412 rounded)

1/6.2824 * 1500 (Ohms) * .00001 Farads (10uf) = 1/.094236 or 10.6 Hz

All frequencies (within the amp bandwidth) above 10 Hz will be passed and 10 Hz and below will be cut

12AX7 w/100K plate
Rk/Ck .68 uF 1 uF 2.2 uF 5 uF 10 uF 22 uF 33uF 47 uF
470 643 Hz 437 Hz 199 Hz 88 Hz 43 Hz 20 Hz 14 Hz 10 Hz
510 605 Hz 411 Hz 187 Hz 82 Hz 41 Hz 18 Hz 13 Hz 9 Hz
560 564 Hz 384 Hz 174 Hz 77 Hz 38 Hz 17 Hz 12 Hz 8 Hz
680 490 Hz 333 Hz 152 Hz 67 Hz 33 Hz 15 Hz 11 Hz 7 Hz
820 431 Hz 293 Hz 133 Hz 59 Hz 29 Hz 13 Hz 10 Hz 7 Hz
1k 379 Hz 258 Hz 117 Hz 52 Hz 25 Hz 12 Hz 8 Hz 5.5 Hz
1.2k 340 Hz 232 Hz 105 Hz 46 Hz 23 Hz 10 Hz 7 Hz 5 Hz
1.5k 301 Hz 205 Hz 93 Hz 40 Hz 20 Hz 9 Hz 6 Hz 4 Hz
1.8k 275 Hz 187 Hz 85 Hz 37 Hz 18 Hz 8 Hz 5 Hz 4 Hz
2.2k 252 Hz 171 Hz 78 Hz 34 Hz 17 Hz 7 Hz 5 Hz 3 Hz
2.7k 232 Hz 157 Hz 72 Hz 31 Hz 15 Hz 7 Hz 4 Hz 3 Hz
3k 223 Hz 152 Hz 69 Hz 30 Hz 15 Hz 6 Hz 4 Hz 3 Hz
3.3k 216 Hz 147 Hz Hz 67 29 Hz 14 Hz 6 Hz 4 Hz 3 Hz
3.9k 205 Hz 139 Hz 63 Hz 28 Hz 14 HZ 6 Hz 4 Hz 3 Hz
5k 192 Hz 131 Hz 59 Hz 26 Hz 13 Hz 4 Hz 4 Hz 2 Hz



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.

Please keep in mind this is a generalization...
and remember impedance is frequency Dependant.. Change the frequency.... impedance shifts whole new equation..Want to nail it down plot a graph throughout various points of the guitars frequency spectrum..
and that's just for that tube.. Put in a different tube and start a new graph... And On and ON!!!

Tony VVT Amps

[talbany]

Sorry Double Post Debug server error



T

[talbany]

This might be easier to read!!





T

[KT66]

Thanks to the both of you for posting this info, this is the kind of discussion I was hoping to start. I read this board religously, not because Dumbles are the holy grail for me, but because I believe the most knowledgable builders around contribute to this forum. One of these days I hope to have something to contribute here, but I sort of feel like a high school science teacher in the prescence of a bunch of Einsteins.

Thanks again bnwitt and Tony

[martin manning]

Something seems to be missing here...

The charts specify a 100K plate resistor, but the equation given is not a function of the plate load. Also, the tables show 20Hz for 1K5 Rk and 10uf Ck, but I get half of that value using the equation given, 1/(2Pi Rk Ck), just like Tony did above.

A concise summary of the frequency response of a triode stage can be found at this site (under Triode Gain Stage):

http://www.valvewizard.co.uk/

It shows that the response is at two levels, corresponding to the un-bypassed and bypassed gains, connected by a ramp whose mid-point frequency (the half-boost frequency) can be approximated by 1/(2Pi Rk Ck).

It seems to me that the important things are the difference between the un-bypassed and bypassed gains, or the "apparent" treble boost, and the frequency at which it is located. Curious about the reasoning behind choosing larger than typical values for Ra and Rk, I constructed the attached plot using the more detailed equations, and make the following observations:

Reference case:
Ra = 100K, Ck = 10 uf, Rk = 1K5
Half-Boost Frequency = 12.5 Hz, Treble Boost = 5.7 dB

Then:

Doubling Ra
Un-bypassed gain increased by 3.6 dB, bypassed gain increased by 1.9 dB
Apparent treble boost is reduced by 1.8 dB

Doubling Ck
Half-boost frequency is reduced by half (shifts transition ramp down one octave)
Un-bypassed and bypassed gain levels unchanged

Doubling Rk
Half-boost frequency is reduced by half (shifts transition ramp down one octave)
Un-bypassed gain reduced 3.4 dB, bypassed gain unchanged
Apparent treble boost increased by decrease in un-bypassed gain, 3.4 dB

If Ra and Rk are increased together, as is typical to keep quiescent point centered, stage gain and treble boost are nearly constant (with typical Ra and Rk, treble boost is about 6 dB)
Both move the quiescent operating point down into the more non-linear portion of the plate characteristic curves, enabling larger anode voltage swing
Ck can be adjusted to position the half-boost frequency as desired, typically 10-20 Hz


MPM

Edit: Attachment replaced. The equation as written was in error. Now 0.5Rk(mu+1) instead of 0.5(Rk+1) in the numerator of f Half-Boost. The calculation was/is correct.

[dogears]

Thanks Martin....

Tony's chart is wrong because it doesn't take the plate load into consideration. In addition to a small effect from the prior stages output impedence. Rkout (Cathode output impedence) is Rk//Rk'
Rk= Cathode resistor
Rk' = (Ra+ra)/(mu+1)

The effective cathode resistor size needs to be adjusted for the parallel loads. The effect is about an octave of response that moves the knee upwards. So, the truth is you can really notice upping a 10uf to a 22uf cap on a 100K stage because the correct knee for a 22uf is about where Tony says the 10uf knee is.

There is more going on than the simple equation. We have been down this road before.

Here is Gil's spreadsheet with the correct knee frequencies. It corresponds with the above table from Bruce at Mission Amps.

https://tubeamparchive.com/download/file.php?id=2838

[martin manning]

Dogears, thanks for passing along the link to the spreadsheet.

I'm still trying to connect all the dots here with respect to the treble boost frequency associated with the Rk and Ck though.

The result of using the equation from Blencowe (the Valve Wizard) agrees very well with the numbers given and the trace shown on Aiken's site. I get, for the 100K plate load R, 1K5 Rk, and 0.1 uf Ck in Aiken's example a half-boost frequency of 1.25 KHz, un-bypassed gain of 30.1 dB, and bypassed gain of 35.8. The half-boost gain is the average of those, or 32.9... about 3 dB down. Aiken's numbers are 30 and 35.7 dB for un-bypassed and bypassed gains, and 33 dB and 1.2 KHz for the mid point.

I had checked this previously, and concluded that Blencowe's equation is another way to get to the same place (and he even references Aiken). Note that Aiken does not give the equations to calculate the treble boost frequency, only the results in the form of the (simulator?) trace. The note at the bottom of the page explains that the calculation has been removed due to an error.

Gil's spreadsheet gives for the same R's and C a value for frequency fk of 2.22 KHz. There's that factor of ~2 again. Is this even supposed to be the same thing? The transition ramp occupies two decades, so we could be talking about different points along the same response.

MPM

Edit: Looks like maybe we are talking about different points on the response...

Blencowe's equation claims to locate the mid-boost point, where the total boost (or attenuation) might be as much as 10 dB. The method used on Gil's spreadsheet looks like it determines the frequency for 3 dB attenuation, so there could be a dB or two difference between this and the mid-boost. The maximum slope of the curve can be 1.4 to 3 dB per octave (RDH4, p. 485), so a difference of the better part of an octave in frequency might be explained by this.

[martin manning]

PS Is there a thread that goes along with Gil's spreadsheet?

MPM