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 g_{m} r_{a} and µ should be taken from the valve characteristics or manufacturers data ~ The default values are for an ECC81 with V_{1} Ia ≈1mA and Cathode follower V_{2} Ia ≈2.3mA ~ r_{a1}' and g_{m1}' are for information only to indicate how R_{k }affects µ and g_{m} I have also included an anode load for the cathode follower stage so the effect of such can be seen or the output A_{RL2} can be used to calculate the gain of a split load phase splitter when R_{L2} and R_{K2} are the same value so the outputs are the same level but in anti–phase 

Variables for gain stage V_{1}


Mutual conductance — g_{m1}


^{ }mA/V — See notes below 
Internal anode resistance — r_{a1}


kΩ 
Amplification factor — µ_{1}


= g_{m1} x r_{a1 } 
Anode load resistor — R_{L1} 

kΩ

Cathode resistor — R_{k1}


kΩ 
Calculated results for V_{1} gain stage


R_{k} modified r_{a1 }— r_{a1}'


kΩ = r_{a1}+ (µ+1) R_{k1} 
R_{k }modified g_{m1} — g_{m1}'


^{ }mA/V = µ_{1 }/ ( r_{a1}+ (µ_{1}+1) R_{k1}) 
Unloaded voltage gain — A_{V1}


= µ R_{L1 }/ ( R_{L1}+ r_{a1}+ (µ_{1}+1) R_{k1}) 
Unloaded voltage gain — A_{V1}


dB = 20log(A_{v1}) 
Output resistance at V_{1} anode


kΩ = r_{a1}'R_{L} 
Variables for cathode follower V_{2}


Mutual Conductance — g_{m2}


^{ }mA/V — See notes below 
Internal Anode Resistance — r_{a2}


kΩ 
Amplification Factor — µ_{2}


= g_{m2} r_{a2 } 
Anode Resistor — R_{L2}


kΩ 
Cathode Resistor — R_{k2}


kΩ 
Calculated results for Cathode Follower V_{2}


Gain at V_{2} anode — A_{RL2}


= µ_{2} R_{L2 }/ ( R_{L2} + r_{a2 }+ (µ_{2}+1) R_{k2}) 
Gain at V_{2} cathode — A_{Rk2}


= µ R_{k2 }/ (R_{L2 }+ r_{a2 }+ (µ_{2}+1) R_{k2})

Output resistance at V_{2 }Cathode — R_{out}


Ω = (r_{a2}+R_{L2}) / (µ_{2}+1)R_{k2}

Overall voltage gain at V_{2 }Cathode


dB = 20log(A_{v1}A_{Rk2})

The value entered for g_{m} is not used to calculate results but is used to calculate the value µ = g_{m }x r_{a }which should be close to the entered value of µ for the results to be valid ~ As with most calculations with triodes g_{m} and g_{m}' could be used but r_{a}' 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 g_{m} r_{a} and µ have been found and entered for both stages and that a sensible I_{a} and HT voltage have been chosen for the V_{a} used ~ Click here for other calculators 
