operating points

here are two simple formulas for determining operation points for power triodes. they work around the assumption that either you are prepared and able (driver stage…) to go into class A₂ when needed. or that you are using only one out of ten available watts, stay within A₁ and the rest is glorious headroom.

the formulas are: V = √(P_d × Z_load) and I = √(P_d ⁄ Z_load)

where V and I are the voltage and current of the operating point, P_d is the plate dissipation and Z_load the load on the tube, in volts, ampères, watts and ohms.

usually the first thing to choose is the plate dissipation of the tube. this is a matter of how far you want to go, compared to the published value. 50%, 90%, 100% or 125%? what the formulas then do is shown below:

plotted here are a 15 watt plate dissipation hyperbole and ‘ideal 50% efficiency class A₂’ load lines for 2k5, 5k and 10k loads. the operating points happen to be where the load line touches, and has the slope of, the hyperbole. the two formulas above calculate these points.

at these operating points, we stay away in equal measures from zero current—where the tube is very unlinear for the first ten milliamps or so—and from zero plate volts—where grid current gets more and more severe until you hit the V_grid = V_plate. the result: very clean ‘first watt’(s).

‘so can we now design tube amps using spreadsheets?’

no. you still need to work with the plate curves to get anywhere. and the ‘right’ Z_load depends very much on the tube used, for both linearity and damping factor. both the 10Y and the 2A3 are 15 watt P_d tubes, but a 5k load means something completely different for either.

you can also turn the two formulas around. stuck with a certain plate voltage (reusing some power supply, or a maximum voltage given for a tube)?

P_d = V² ⁄ Z_load, alternatively Z_load = V² ⁄ P_d

stuck with a certain plate current (reusing some power supply, or a maximum current given for a OPT)?

P_d = I² × Z_load, alternatively Z_load = P_d ⁄ I²

no need to take all this as the law, just have fun exploring possibilities with it…