1970s Design Indulgence

The Meters and the Maths

Bob Cordell's modified SPICE models for the MJL21193 and MJL21194 output transistors gives slightly different betas (BF) and adds base resistance (RB).

This makes it possible to calculate the quiescent voltage (Vq) reasonably accurately.

The exact figure would have to be arrived at through iteration, but here we are talking about fractions of a millivolt which, even if we could set the voltage to, would be ephemeral due to minute changes in ambient temperature, and tiny mains voltage variations.

Estimating 60mA quiescent current in the output stage and betas of 70 (NPN) and 110 (PNP), the base current will be 0.86mA (NPN) and 0.55mA (PNP).

Considering the NPN upper EF2, the driver has half the resistance of the inter-emitter resistor (0.5 x 220R), and 0.625V is dropped across it, which is 5.7mA (this will be the same for the PNP lower EF2).

Now add the bias: 5.7 + 0.86 = 6.56.

The emitter resistance of the upper driver will be the thermal voltage divided by the current: 26mV/6.56 = 4 ohms.

Cordell gives MJL21194 base resistance as 3.4 ohms, to which we add 4 ohms to give a total input resistance of 7.4 ohms.

This is then divided by the beta: 7.4/70 = 0.106 ohms

This appears in series with the real emitter resistance of 0R33 making 0.436 ohms, and for 26mV to appear across it, then 59.63mA will need to flow.

This is extremely close to the estimated 60mA.

Multiplying 59.63mA by 0R33 ohms, we find the optimum voltage is 19.7 mV.

Considering the PNP lower EF2, we know from above the driver current is 5.7mA. The power transistor base current is 0.55mA, making a total quiescent driver current of 6.25mA.

The driver's thermal voltage is 26mV, so 26mV/6.25mA = 4.16 ohms.

Cordell gives base resistance as 2 ohms, to which we add 4.16 to give 6.16 ohms.

This is divided by the beta of 110 to give 0.056 ohms, which is added to the real emitter resistor value of 0R33 to give 0R386 ohms.

If 26mV is developed across 0R386, then 67.4mA must be flowing. Obviously, it cannot if the upper NPN has 59.63mA.

But continuing, 67.4mA x 0R33 = 22.23 mV.

This difference is noted by Oliver as beta difference distortion, but there is little we can do to compensate for it, except to average out the resulting voltages and adjust the meters to read the average.

(19.7 + 22.23) / 2 = 20.965 mV.

By setting the meter midway between 20 and 22 gradations we approximate the correct quiescent voltage (Vq).

It should be noted that this is the meter reading with the amplifier at a steady comfortable room temperature of say between 20 and 27 C.

The amplifier should have been left to settle for several hours before the final adjustment.

It will be noted that if ambient temperature changes by a few degrees the meters will indicate a variation of about +/- 1mV; and if the amplifier is left a long time under no-signal conditions, the meter will indicate a graduation low.

The images below show the distortion products when setting to the above approximation.



Edited by Graham Slee - 21 Feb 2020 at 2:36pm

The less than optimum matching exhibited by beta differences between the MJL21193 and MJL21194 output transistors meant that exact quiescent voltage was unable to be set.

The importance of quiescent voltage must not be underestimated as it has a more direct effect on sound quality than most other distortions.

Taking note of Bob Cordell's comment:

"one must also bear in mind that the internal resistances and betas of the PNP and NPN output transistors may not be the same, in some cases possibly calling for slightly different optimal values of emitter resistors top and bottom."

(https://www.diyaudio.com/forums/solid-state/105934-biasing-thermal-compensation-thermal-trak-transistors-14.html)

Hopefully I have calculated in the right direction (sometimes I can get things wrong), and reducing the upper emitter resistor to 0R27 makes the quiescent voltage the same for both halves.

I was about to write about optimising class AB output stage bias, but decided to do some further tests to support it. Surprisingly I found that class B bias gave the best test results, and all class AB did was to pronounce upper odd-harmonics - the ones which cause listening fatigue.

True, overall distortion rose to 0.2% THD 1kHz at half a watt, but mainly second order with the third much lower. At full output (42 watts) 1kHz THD fell to 0.05%.