~ 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

kΩ

Amplification factor — µ1

= gm1 x ra1

Anode load resistor — RL1

kΩ

Cathode resistor — Rk1

kΩ

Calculated results for
V1 gain stage

Rk modified ra1 —
ra1'

kΩ  =  ra1+ (µ+1)
Rk1

Rk modified gm1 —
gm1'

mA/V  =  µ1 / (
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

kΩ

Amplification Factor — µ2

= gm2 ra2

Anode Resistor — RL2

kΩ

Cathode Resistor — Rk2

kΩ

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 = gm x ra which 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