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)

g_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

~ Plotting Characteristic curves using Tektronix 576 Curve Tracer ~

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

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 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 load-line 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

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_mxR_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

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

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

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