Value of cathode bypass capacitor

In a common cathode tube stage with a bypassed cathode resistor, we choose the value of the cap after the resistor. 1/(2πRf)


however, doesnt the cap sees booth the resistor to ground and the impedance of the cathode,  so shouldnt we use the parallel resistance of the cathode resistor and the cathode impedance (1/gm)

if we have a 330R cathode resistor and a tube that has an  gm of 3mA/V at its workingpoint

1/0.003 = 333R

then the paralell resistance would be about half the cathode resistor. so we should choose a cap that is double the size that we had in mind from the start.

> doesnt the cap sees booth the resistor to ground and the impedance of the cathode

Yes.

In actual fact, for general audio, you pick the cap much-much greater than "required". It does not add much cost. Over-size cap has lower THD. Oversize cap can degrade longer before bass is lost. Oversize cap can help reduce heater hum.

5v333 said:

however, doesnt the cap sees booth the resistor to ground and the impedance of the cathode,  so shouldnt we use the parallel resistance of the cathode resistor and the cathode impedance (1/gm)

Click to expand...

Our elders did not care much about it; they established a rule of thumb using 10x the value calculated with the cath resistor alone. As PRR mentions, it took care of capacitance drift.
Today, if you want to be finicky, you can use calculations or Spice to determine a precise value. Anyway, when you buy the capacitor, its tolerance probably says something like +20/-30%, and since electrolytics come in E6 values, you'll end up using a significant higher value than strictly needed.

The calculation may prove most useful if trying to get some equalization, but then, frequently I find physical substitutions with measurements more appropriate. 

PRR said:

> doesnt the cap sees booth the resistor to ground and the impedance of the cathode

Yes.

In actual fact, for general audio, you pick the cap much-much greater than "required". It does not add much cost. Over-size cap has lower THD. Oversize cap can degrade longer before bass is lost. Oversize cap can help reduce heater hum.

Click to expand...

thanks!
degrade, as in drying out of age?

or we talking temprature drift.

yes ive found a couple schematics that dont seem to use very big caps when calculating the freq point...

im thinking that a good value to settle with is around the output response of that stage, atleast when talking transformer coupled tube stage. R/(2πL)
and if theres a NF loop around the circuit, the cap should be choosed for the closed loop response.
so if the plate Z is 10k and transformer is 200H = 7.9Hz
and there is NF with a a factor of 10, the cap should be set to about 0,79Hz

and prob same for interstage caps inside a loop.

5v333 said:

In a common cathode tube stage with a bypassed cathode resistor, we choose the value of the cap after the resistor. 1/(2πRf)

however, doesnt the cap sees booth the resistor to ground and the impedance of the cathode,  so shouldnt we use the parallel resistance of the cathode resistor and the cathode impedance (1/gm)

Click to expand...

The bypass cap creates a shelved response (pole-zero pair), so there are two formulas:

1/(2πf [Rk||Zk]) applies to the pole;
1/(2πf Rk) applies to the zero.

But since these are nearly always very close together it doesn't really matter which you use. The zero formula is simpler so most people use that, and simply place the zero at some arbitrarily sub-audio frequency where you can forget about both the zero and pole.

PRR said:

> doesnt the cap sees booth the resistor to ground and the impedance of the cathode

Yes.

In actual fact, for general audio, you pick the cap much-much greater than "required". It does not add much cost. Over-size cap has lower THD. Oversize cap can degrade longer before bass is lost. Oversize cap can help reduce heater hum.

Click to expand...

Wisdom. Thanks PRR

I liked this quick vid about bypass caps
https://www.youtube.com/watch?v=HrkYUPmEUhk