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~ Cathode Coupled Amplifier / Phase Splitter Calculator ~

Push-Pull Phase splitter

This is an 'a.c. only' which can be used to calculate the gain of a cathode coupled amplifier provided µ and ra for V1 and V2 are known at their operating current

Here it is shown with V1 and V2 grids connected to 0V ground and the cathodes to a negative supply [a.c. ground] via Rk forming a Long Tail Pair but Rk could be 2 series resistors to ground for 'auto–bias' as seen in many designs like this or this [where R13 should be 51kΩ not 57kΩ as drawn]

The calculation takes into account additional anode loads for each output due to the input impedance of following stages and bias components which can be 'lumped together' ~ If Rk<R1 then R2 will need to be adjusted [increased] to obtain a balanced output which is also calculated

Input variables 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 calculator default values are for two sections of an ECC81 both with Ia ≈ 1mA at Va = 170V and –VHT = 360V ~ see valve characteristics

Input variables in Yellow for V1 — R1       V2 — R2
Internal anode resistances — ra   kΩ
Amplification factors — µ
Anode load resistors — R   kΩ
Additional anode loads   kΩ
Total anode loads — RL   kΩ
Common cathode resistor — Rk kΩ        Output Significant Figures 
Calculated results for V1 anode and cathode
Rk modified by V2 — Rk1 kΩ = (ra2+RL2) / (µ2+1)∥Rk
Voltage gain at V1 anode — AV1 V/V = µ1RL1 / (RL1+ra1+ (µ1+1) Rk1)
AV1 dB = 20log (AV1)
Output resistance — ROUT1 kΩ = ra1+(µ1+1) × Rk1∥RL1
Voltage gain at V1 cathode — ARk V/V = µ1Rk1 / (RL1+ra1+(µ1+1) Rk1)
ARk 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 V/V = ARk RL2(µ2+1) / (ra2+RL2 )
AV2 dB  =  20log (AV2)
Output resistance — ROUT2 kΩ = ra2+(µ2+1) × Rk2∥RL2
V1 / V2 Balance
Output balance = AV1 / AV2
For balance make R2 = kΩ

No Silicon Heaven ~ Then where do all the Calculators go 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 sounding 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 is taken into account

Cathode coupled Triode Amplifier PSpice schematic

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

The valves are modelled with voltage controlled voltage sources so Rk can be retutned to Gnd and not a negative supply ~ In fact no power supplies are needed when using this method

Click Here for other calculators ~ Click image for the PSpice plot

 

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