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 r_{a} for V_{1} and V_{2} are known for their operating condition ~ For the phase splitter it is assumed that V_{2} grid is at signal ground and using a negative R_{k} 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 R_{k} << R_{1} then R_{2 }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 V_{a} = 170V and –Vbias = 360V ~ see valve characteristics ~ Click on the image above for a pdf copy with space to make notes 

V_{1}–R_{1}

V_{2}–R_{2}  
Internal anode resistances — r_{a}


kΩ 
Amplification factors — µ



Anode load resistors


kΩ 
Additional anode loads


kΩ 
Total anode loads — R_{L}


kΩ 
Common cathode resistor – R_{k}


kΩ 
Calculated results for V_{1 }anode and cathode


R_{k} modified by V_{2} — R_{k1}


kΩ = (r_{a2}+ R_{L2}) / (µ_{2}+1)R_{k} 
Voltage gain at V_{1} anode — A_{V1 }


= µ_{1 }R_{L1 }/ (R_{L1 }+ r_{a1 }+ (µ_{1}+1) R_{k1}) 
Voltage gain


dB = 20log(A_{V1}) 
Output resistance — R_{Out1}


kΩ = r_{a1 }+ (µ_{1}+1) R_{k1}R_{L1} 
Voltage gain at V_{1}_{ }cathode — A_{Rk}


= µ_{1} R_{k1 }/ (R_{L1 }+ r_{a1 }+ (µ_{1+1})_{ }R_{k1}) 
Voltage gain at V_{1}_{ }cathode


dB = 20log(A_{RK}) 
Calculated results for gain at V_{2 }anode


R_{k} modified by V_{1} — R_{k2}


kΩ = (r_{a1}+ R_{L1}) / (µ_{1}+1)R_{k} 
Voltage gain at V_{2 }anode — A_{V2}


^{ }= A_{Rk }R_{L2 }(µ_{2}+1) / (r_{a2} + R_{L2 }) 
Voltage gain


dB = 20log(A_{V2}) 
Output resistance — R_{Out2}


kΩ = r_{a2 }+ (µ_{2}+1) R_{k2}R_{L2} 
V_{1 }/ V_{2 }Balance


Output balance


= A_{V1} /A_{V2} 
For balance make R_{2} =


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 R_{2} for balance is an iterative process ~ The gain of V_{1} is affected by R_{2 }giving another value for R_{2 }until the ratio R_{1}/R_{2} 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 A_{V1 }A_{V2 }and A_{Rk} 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 