~ Cathode Coupled Amplifier Calculator ~

This signal gain calculator is to support my QUAD II
Triode driver article but can be used to calculate the gain of any
cathode coupled amplifier provided µ and ra for V1
and V2 are known for their operating condition ~ For the phase
splitter it is assumed that V2 grid is at signal ground and
using a negative Rk supply this means simply connected to
ground

The calculation takes into account additional
anode loads for each output due the input impedance of following stages or
any bias components required which can be 'lumped' together to add to each
output ~ If Rk << R1 then R2
will need to be adjusted to obtain a balanced output so the degree
of imbalance is also indicated by the calculator

Input values can be changed to calculate other
parameters like the cathode follower gain of V1 reduced by R1 by making µ2
–1 ~ For calculations of triode gain and follower output impedance this
may be better ~ The default values are for two sections of an ECC81
both with Ia ≈ 1mA at Va = 170V and –Vbias = 360V ~
see valve
characteristics ~ Click on the image above for a pdf copy with space
to make notes

V1–R1

V2–R2

Internal anode resistances — ra

kΩ

Amplification factors — µ

Anode load resistors

kΩ

Additional anode loads

kΩ

Total anode loads — RL

kΩ

Common cathode resistor – Rk

kΩ

Calculated results for V1
anode and cathode

Rk modified by V2 —
Rk1

kΩ = (ra2+ RL2) / (µ2+1)||Rk

Voltage gain at V1 anode — AV1

= µ1 RL1 / (RL1 +
ra1 + (µ1+1) Rk1)

Voltage gain

dB = 20log(AV1)

Output resistance — ROut1

kΩ =  ra1 + (µ1+1) Rk1||RL1

Voltage gain at
V1 cathode — ARk

= µ1 Rk1 / (RL1 + ra1 +
(µ1+1) Rk1)

Voltage gain at
V1 cathode

dB = 20log(ARK)

Calculated results for gain at
V2 anode

Rk modified by V1 —
Rk2

kΩ = (ra1+ RL1) / (µ1+1)||Rk

Voltage gain at V2 anode —
AV2

= ARk
RL2 (µ2+1) / (ra2 +
RL2 )

Voltage gain

dB  =  20log(AV2)

Output resistance — ROut2

kΩ =  ra2 + (µ2+1)
Rk2||RL2

V1 / V2
Balance

Output balance

= AV1 /AV2

For balance make R2 =

kΩ

In practice with standard value components perfect
balance may not be achieved or even desired because this would lead to
cancellation of even harmonics leaving "nasty" odd harmonics ~ Changing
the value of R2 for balance is an iterative process ~ The gain
of V1 is affected by R2 giving another value for
R2 until the ratio R1/R2 is correct ~ for
this reason it is important that the loading of the outputs ~ both
resistive and reactive is taken into account

The three voltage gains
AV1 AV2 and ARk have also been expressed
as dB gains ~ This is useful if you use a meter with a dB function and
relative offset ~ If the meter is 'zeroed' when connected to the phase
splitter input the gain to each of these points can be easily checked to
confirm the circuit and/or the valves are working correctly

I normally use PSpice modelling or just a
calculator for circuit design but now that I have made these calculators I
tend to use them more ~ PSpice however is much quicker and more accurate
for a.c. and transient analysis or when a frequency plot is required ~
Click Here for
other calculators