Hi, welcome!

In this case, simple Ohm's Law will come to the rescue.

You have to decide on an operating point for your triode - the voltage and current it will draw that will not exceed specifications. Those curves look like a 12AX7 or ilk.

Let's say you have a B+ of 250V to play with. For maximum linear class-A swing, you want the anode at B+/2, or 125V. So, go up the 125V line from the bottom and see what grid voltages it intersects for plate current on the right.

A 12AX7 works best sonically anywhere from 600uA to about 1.2mA, a 2:1 ratio - fairly forgiving in other words.

For simplicity sake, up the 125V line we see an intersection of -1.5V at 750uA. Now we use Ohm's Law for the cathode resistor:

R=E/I

E = -1.5V

I = .00075A

Therefore R = 2.0K, a standard 5% resistor value. (more on this in a moment)

Now, we know what you need in the cathode, how about the anode?

Well, we know we need a 125V drop from the 250V supply and we know there will be 750uA going through the tube. Ohm's Law again:

E = 125V

I = 0.00075

Therefor the R on the anode needs to be 166.6K. Now, this is not a 5% resistor value. The closest is 160K, but 150K is probably easier to find (this is where tube forgiveness comes in).

You will probably need to bypass that cathode resistor to get decent gain. The appropiate capacitor will depend on desired cutoff frequency. For HiFi, the bottom should go to at least 20Hz, so it's a good idea to use 10Hz for the equation.

F3 = Xc = R

Or the capacitive reactance (resistance at one particular frequency [the complex +/-

*j* stuff can be ignored at audio]) when equal to the cathode resistor will be your -3dB cutoff point. Let's figure that out:

Xc = 1/(2*pi*C*f)

And we know we habe a 2K cathode resistor so we want a capacitor with 2K reactance at 10Hz. We substitute:

C = 1/(2*pi*R*f)

We get 7.9uF. Not a standard value.

This is NOT critical, so drop in 10uF or larger.

As for voltage rating, the cathode resistor is developing 1.5V across it, so a 6.3V capacitor will do.

You want your audio linear, so use a good cap. Elna RFS (Silmic-II) or Nuchicon KZ (MUSE) are great and are only about 20% more than general purpose caps from the same companies.

Head explode yet? Well, here's some relief.

Tube projects are NOT an exact science and a tube is NOT a precision device. This is good for us, because those curves aren't in stone... they will vary quite a lot from tube lot and even more between brands. I've had some ECC83 (European 12AX7) that worked great whose curves more resembled a 12AT7.

A variation of +/- 20% in voltages and values are just fine. (a reason I think it's laughable when I see 1% or 0.5% resistors in commercial tube builds [outside of noise considerations])

I spoke of tube forgiveness... breadboard it and see! The 12AX7 is happy with anode resistors from 82K to 470K and cathode resistors from 820 to 5.6K. What chages beside operating point? Dynamic range! I have found optimum 12AX7 values to be 100K anode, 820R-1.5K cathode and as big a bypass cap as I can fit.

Some tubes do have a "sweet spot", but that's for another day.

So, why didn't I just say that in the beginning? Because you'd have learned nothing!

Cheers!