Now of course if I totally understood impedances between gain stages then this wouldn't be such a time consuming task!
Well lets see if we can help.
Output Impedance- For a triode with a fully bypassed cathode resistor:
Zout (Rk bypassed) = Plate resistor||plate resistance. This expands to Ra x ra / Ra + ra.
- For a triode with an unbypassed cathode resistor:
Zout (Rk unbypassed) = Plate resisitor|| (plate resistance + Cathode resistor x (the tube amplification factor-1). This expands to Ra.[ra + Rk.(u + 1)] / Ra + ra + Rk.(u +1)
Input ImpedanceInput impedance of a triode = the grid load resistor (you can raise the input impedance by bootstrapping the grid load resistor to the stage's cathode)
Impedance bridgingis important between gain stages - Rule of thumb is to keep the input impedance of the following stage at least 5 x higher than the previous stage's output impedance, in order to preserve a good bandwidth.
Freq rolloff (or half boost point) - for cathode bypassing [where the sum of the Plate Resistor and the tube's plate resistance, is greater than the product of the Cathode Resistor multiplied by (the tube's amplification factor +1):
f(half boost) ~= 1/(2Pii x Cathode resistor x Cathode bypass cap)
- for a grid stopper is:
R = 1 / (2Pii x desired freq cutoff x Input Capacitance of the stage) where total input capacitance is the sum of the Grid to cathode cacitance and the grid to plate capacitance)
- for a coupling cap is:
C = 1 / (2Pii x desired freq cutoff x the sum of the following stage's grid load resistor and the previous stage's output impedance)
There you go