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~ un bypassed Cathode Calculator ~

This Calculator is to support my Amplifier–Buffer project and can be used to calculate the gain of a triode amplifier using a common cathode gain stage with a cathode follower output buffer so the overall gain is not significantly affected by the output load

The results update as new input values are entered ~ Values for gm ra and µ should be taken from the valve characteristics or manufacturers data ~ The default values are for an ECC81 with V1 Ia ≈1mA and Cathode follower V2 Ia ≈2.3mA ~ ra1' and gm1' are for information only to indicate how Rk affects µ and gm

I have also included an anode load for the cathode follower stage so the effect of such can be seen or the output ARL2 can be used to calculate the gain of a split load phase splitter when RL2 and RK2 are the same value so the outputs are the same level but in anti–phase

Variables for gain stage V1
Mutual conductance — gm1
 mA/V  —  See notes below
Internal anode resistance — ra1
Amplification factor — µ1
= gm1 x ra1 

Anode load resistor — RL1

Cathode resistor — Rk1
Calculated results for V1 gain stage
Rk modified ra1 — ra1'
kΩ  =  ra1+ (µ+1) Rk1
Rk modified gm1 — gm1'
 mA/V  =  µ/ ( ra1+ (µ1+1) Rk1)
Unloaded voltage gain — AV1
=  µ RL1 / ( RL1+ ra1+ (µ1+1) Rk1)
Unloaded voltage gain — AV1
dB  =  20log(Av1)
Output resistance at V1 anode
kΩ  =  ra1'||RL
Variables for cathode follower V2
Mutual Conductance — gm2
 mA/V  —  See notes below
Internal Anode Resistance — ra2
Amplification Factor — µ2
= gm2 ra2 
Anode Resistor — RL2
Cathode Resistor — Rk2
Calculated results for Cathode Follower V2
Gain at V2 anode — ARL2
=  µ2 RL2 / ( RL2 + ra2 + (µ2+1) Rk2)
Gain at V2 cathode — ARk2
=  µ Rk2 / (RL2 + ra2 + (µ2+1) Rk2)
Output resistance at V2 Cathode — Rout
Ω  =  (ra2+RL2)  / (µ2+1)||Rk2
Overall voltage gain at V2 Cathode
  dB = 20log(Av1ARk2)
The value entered for gm is not used to calculate results but is used to calculate the value µ = gx rwhich should be close to the entered value of µ for the results to be valid ~ As with most calculations with triodes gm and gm' could be used but ra' would also be needed ~ the factor (µ+1) helps simplify things ~ a little bit

It is assumed the bias is optimised for both the gain stage and follower and that separate values for gm ra and µ have been found and entered for both stages and that a sensible Ia and HT voltage have been chosen for the Va used ~ Click here for other calculators

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