Above is an enlarged section from a Mullard characteristic curve for a 'typical' ECC81 taken from my BBC Wood Norton training notes (Happy Days) to support the Valve Amplifier/Buffer article ~ During the BBC transmission engineering courses we used these curves to calculate a.c. gains and d.c. operating points for various valve amplifier designs but never at currents as low as 1mA or anode voltages as low as 40V even with the sharpest pencil There are 3 basic parameters that describe a Thermionic Valve ~ They can be read directly from or calculated from the manufacturers characteristic curves ~ In each case the parameter is calculated using 2 values while holding a third value fixed and this 3 dimensional approach to characterisation can be misleading unless you accept that in a practical amplifier the 'fixed' value will change and modify the parameter you used to make a calculation µ ~ Is known as the amplification factor ~ It is the maximum gain a valve can achieve at a particular fixed anode current which in practice means using a constant current anode load and not 'loading' the gain stage ~ so a voltage follower is required ~ The gain of the stage will vary greatly with the valve condition and some form of feedback will be required so a practical amplifier based on using the gain indicated by µ is not (practical) From the graph above µ is calculated by measuring V_{a }between the points where the line I_{a }=1.1mA crosses the curves for V_{g }=0V and V_{g }≈1V to give µ =∆V_{a}/∆V_{g }~ this way µ gets calculated at 46 which I believe is lower than it actually is at this operating point ~ µ becomes greater as V_{a }lowers ~ For 1.1mA at V_{a }=200V µ =45 at V_{a }=170V µ =49 and at V_{a }=100V µ =52 ~ see other ECC81 curves belowg_{m} ~ Is known as the Mutual Conductance and ~ as with other devices ~ is a measure of how much current a Valve will conduct for a given change in control voltage on one of its grids ~ Following the rules the parameter is determined with the anode and other grid voltages held constant so the maximum 'effect' of g_{m} can only be appreciated with a 0Ω or current mirror load or in practical amplifiers a transformer or inductor load From the graph above g_{m }is derived by measuring I_{a} where the line 40V crosses the curves for V_{g }=0V and V_{g }≈1V to give g_{m }=∆I_{a}/∆V_{g }(mA/V) ~ As you can see from the above curves the g_{m} at V_{a }=40V looks about 2.6mA for a 1V change in V_{g} but it is not 2.6mA/V in the region of the operating point due to the asymmetric ~ distortion producing ~ spread along the curve r_{a} ~ Is known as the Anode Slope Resistance or the effective output resistance of a valve ~ It appears as a resistance in series with a voltage source inside the valve or across a current source inside the valve depending on the model used ~ r_{a} is measured with the grid voltages held constant and may appear of no use until you want to make a perfect current sink or output dependant distortion becomes a problem From the graph above r_{a} is µ/g_{m} =∆V_{a}/∆V_{g}/∆I_{a}/∆V_{g} where the two ∆V_{g} cancel and r_{a }=∆V_{a}/∆I_{a }~ But the values for µ and g_{m }derived from the curve above ~ around the point V_{a }=40V are not the most accurate ~ When trying to measure how an ECC81 and other valves performed in the Amplifier/Buffer circuit at low V_{a }and I_{a} I found myself plotting my own curves using a Tektronix 576 Curve Tracer ~ see below The complex interdependencies changing internal gains and impedances within a triode amplifier as V_{a} I_{a }and V_{g} change dynamically cause all kinds of distortion and colouration ~ Simply isolating one cause of distortion such as the non linearity of the I_{a}/V_{g} transfer function cannot fully explain the differences between the sound of similar or even the same type of valves Some valve manufacturers publish other 'typical' curves that plot V_{g} r_{a }g_{m} and µ against I_{a} for a given V_{a }and these can be very useful working at low I_{a} but if the characteristics do not cover the V_{a} you are operating at then interpolation or guesswork is again required It is likely that r_{a }is not measured independently and like the other parameters the results are adjusted to produce smooth regular curves ~ It should also be obvious when looking at valve characteristic curves that the specifications published for many valve amplifier 'designs' are also just 'typical' although many sound better than the design would suggest 

Mullard ECC81 parameters µ gm r_{a }V_{g } plotted at V_{a}= 100V 

Mullard ECC81 parameters µ gm r_{a }V_{g } plotted at V_{a}= 170V 

Mullard ECC81 parameters µ gm r_{a }V_{g } plotted at V_{a}= 200V 

Mullard ECC81 parameters µ gm r_{a }V_{g }plotted at V_{a}= 250V 




The picture on the left is a screen shot from my TEK–576 showing the origin of an ECC81 characteristic curve plot ~ The steps –V_{g }relative to cathode could be made closer together and although only a maximum of 10 uniformly spaced steps are available using the 576 they can be offset up to ±10x the step voltage so more accurate measurements close to an operating point can be made
With an expanded scale and 0.5V steps in –V_{g} this area of the curves now looks 'more linear' than the Mullard curves shown at the top of this page but the parameters µ g_{m} and r_{a} still vary greatly across this reduced area and It should be clear that a slight deviation from an optimum operating point will give less than optimum results and distortion will change with signal level and d.c. conditions and also small changes in the heater voltage 

This screen shot is the same ECC81 as above but with a 27kΩ resistor in the cathode ~ As I say in the Valve amplifier/buffer article the g_{m} with an un–bypassed cathode resistor is reduced to about 1/R_{k }which in this case is about 35µA/V depending on the original g_{m} of the valve
The 'curve' initially looks like a flat line along the bottom of the display until the x scale is decreased to 100µV/div but even then does not look suitable for use as an amplifier because in practice the 27kΩ resistor would 'self bias' the valve to almost 'cut off' unless the grid is raised +ve ~ Using the TEK–576 the effect of the grid being made +ve can be simulated using the step offset control which can be set to a maximum of ±10x the step voltage ~ here the steps are 2V allowing a +20V offset 

The characteristic now looks more like a pentode or even a transistor due to the increase in r_{a} to >1.2MΩ ~ The ∆I_{a} between V_{g} steps is very linear and additional steps above and below those shown will run virtually parallel making interpolation and parameter measurements very easy ~ A load line can be drawn on the curve referenced from 0V as R_{k }is now part of the active device
The load–line for an anode load of 100kΩ (used in the Amplifier/Buffer article) and a 180V supply is drawn onto the curve in the usual way between the points I_{a }=0V where V_{a }=180V and V_{a }=0V where I_{a }=180V/100kΩ =1.8mA ~ Unlike normal triode curves the position of the load–line along the V_{a} axis is not critical for a.c. amplification due to the regular spacing and slope of the V_{g } steps Using this (used but okay) ECC81 the amplifier gain calculated where the loadline crosses V_{g }=2V and V_{g }=20V is about V_{a }=58V/V_{g }=18V giving a gain of 3.22x ~ Due to the regular spacing of the V_{g} steps the operating point can be positioned almost anywhere along the load–line without a change of gain so an optimum point can be chosen for large signals and/or lowest distortion 

An unbypassed cathode resistor_{ }has such a significant effect on the g_{m} of a triode that in the 10dB version of the amplifier/Buffer even an old ECC81 that had failed AVO testing with 20% g_{m }gave good results
Changing the ECC81 for an ECC82 ~ which for the same operating conditions normally has lower g_{m} r_{a} and µ ~ gives an amplifier gain of 9dB ~ If this substitute were done in a traditional design the results would be ... From the ECC82 curves with R_{k }=27kΩ shown on the left the g_{m }is again about 35µA/V but the slope of the V_{g }steps is steeper because r_{a }has only been increased to r_{a}'≈460kΩ ~ The gain calculated from the load–line is V_{a }=52V/V_{g }=18V =2.89x or 9.2dB which correlates well with g_{m}xR_{a}' and measured results 

Changing the ECC81 for an ECC83 ~ which tends to have more than twice the r_{a} and µ but lower g_{m }(and is designed to work at low I_{a}) the amplifier gain is now 11dB ~ As before if this substitute were done in a traditional design the results would be . . . unpredictable From the ECC83 curves with R_{k }=27kΩ shown on the right the g_{m }is once again about 35µA/V but the slope of the V_{g }steps is less because r_{a }has been increased to r_{a}' ≈2.8MΩ The gain calculated from the load–line is about V_{a }=64V/V_{g }=18V =3.55x or 11dB which correlates with the measured results and those of my un–bypassed Rk calculator 


The Amplifier/Buffer project was not specifically 'designed' for an ECC83 or an ECC82 ~ The chosen operating point for the available HT of 180V and gain of 10dB was for an ECC81
As shown above an un–bypassed high value cathode resistor tends to 'normalise' the g_{m} and increase the r_{a} of the gain stage triode so we get predictable gain and operating point for a wide variety of different triode types simply plugged into the same circuit Local negative feedback across an R_{k} of 27kΩ greatly reduces the distortion from this simple amplifier and the reduction of capacitors in the signal path tends to make a 'better sounding' gain stage As the value of R_{k} is reduced so the gain increases as does distortion until a point is reached where R_{k} becomes the value of an auto bias resistor and any further reduction would require a negative grid supply or a bypass capacitor and the ability to simply swap valve types is lost 

To get the maximum gain from an ECCnn in the Amplifier/Buffer configuration R_{k} needs to be an auto bias resistor and the circuit component values need to be chosen for a particular valve working at a particular operating point and of course the valve has to meet its specification which many do not leading to this ECC81 sounds better than this one
Using an ECC81 auto biased for a gain stage I_{a} ≈ 1mA due to R_{k}=1.8kΩ with R_{L}=100k a gain of 27dB with low distortion is possible but not as predictable as when set for lower gains with higher local feedback due to higher values of R_{k} ~ Whether auto bias or higher values of R_{k }are used the cathode follower buffer ensures the gain is not affected by loading 

Manufacturers like Mullard RCA and Brimar published curves of V_{g} r_{a }g_{m} and µ against I_{a} (like those shown here) in addition to the more common I_{a}/V_{a }characteristics but only for limited values V_{a}
The Mullard curves for the ECC83 were supplied for V_{a}=100V and V_{a}=250 and this along with published 'application' circuits led to many similar ECC83 based 'designs' which could have been better optimised with a little effort by investigating other operating conditions especially at lower V_{a} Using a valve tester like the AVO163 g_{m} can be measured reasonably accurately and directly while monitoring I_{a }at low V_{a }(provided the meters have been modified to read correctly or external meters are used) but either µ or r_{a} also need to be determined 



With a valve tester or a Curve Tracer r_{a} can be determined from r_{a }=_{ }∆V_{a}/∆I_{a }by switching the anode voltage steps but at low V_{a} r_{a }is often 10s of kΩ and determining the small change in I_{a} (due to a change in V_{a} alone) may be difficult My un–bypassed Rk calculator does not use g_{m} to determine its results but does calculate µ_{ }from entered values for g_{m} and r_{a} ~ By using all 3 values taken from valve characteristics or measurements a check that µ = g_{m }x r_{a }can be made to confirm the values If you have read this far and have been looking at the graphs of V_{g} r_{a }g_{m} and µ against I_{a} you may notice that the curves change more at low I_{a }which leads some to use higher I_{a} in an attempt to get lower distortion 
