A Simple, Valve Curve Plotter

[Nick]

Ra (or Rp if you want to call the anode a "plate") is a funny one as it is completely dependent on the chosen operating point (Va & Vg), i.e. its a dynamic resistance - it is defined as the change in Va (delta Va or dVa) divided by a given small change in Ia (dIa) and can be visualised as being the "slope" (first differential) of the Ia (y-axis) vs. Va (x-axis) curves for a given Vg.

If you look at these graphs it becomes obvious that Ra can change fairly dramatically depending on the chosen operating point.

The relationships between Gm (transconductance), mu (gain) and Ra are pretty straightforward:

• Ra   = dVa / dIa
  
• Gm = dIa / dVg
  
• mu = dVa / dVg
  

Gm & mu are dynamic (AC) not static (DC) values... A bit of algebra and you get:

• mu = Ra * Gm or Ra = mu / Gm
  

The effective Ra, i.e. what the circuit sees,  is the dynamic Ra from above, in parallel with the anode load resistance and the load from any following stage (e.g. the following stage's grid resistance).

Most data sheets compute Ra by simply dividing mu by Gm... i.e. its a 1st order approximation only at a stated operating point.