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~ 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
Calculated results for V1 anode and cathode
Rk modified by V2 — Rk1
kΩ = (ra2+ RL2) / (µ2+1)||Rk
Voltage gain at V1 anode — AV1
= µRL1 / (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 2+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 =
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

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