There are billions of these critters around the world : think about all the opamps in your TV, CD player, portable phone, etc. This circuit topology has become so common that almost everybody takes it for granted. With the very notable exception of Tubes, audio amplifiers almost universally use a differential pair. Those which don't have a differential are often exotic designs, like zero-feedback, single-ended class A oddities.
If you read the previous article, you remember that the Memory distortion theory states that thermal pulses in the transistors, caused by the audio signal, upset the global DC operating point. Feedback hides the bias variations : as one stage gets imbalanced, the other stages will tend to get imbalanced too, but the opposite way, in a desperate effort to compensate. Therefore, the distortion spectrum, which is dependent on the operating point, varies according to the signal which passed through the amplifier in the last few seconds. Tubes are insensitive to this phenomena, which could be the explanation of why transistors and tubes sound "different".
Fig. 2-1 is the schematic, in which the two voltage sources taken in the emitters represent the Vbe shifts with temperatures. The output is taken as I(R1)-I(R2). The input, or error signal, is the voltage between the two bases. RE=100R, ITail=8 mA.
Fig. 2-2 shows the dissipated power in both transistors versus error signal (which is simply the differential signal betwen the two bases). The high rail voltage makes them dissipate quite a lot ; the maximum value (at clipping) is around 250 mW. I modified the thermal model for small TO92 transistors, BC550 for instance, which are much easier to heat up than the bigger ones we use as VAS.
Fig.1 : The differential pair.
Fig.2 : Dissipated power in Q1 and Q2 vs error signal.
Consider an amplifier with the following parameters as an example :
We will suppose for a moment that we have an amplifier with large openloop bandwidth, in which FB is constant with frequency, to simplify. Now, let's suppose this amp is asked to produce the same transient as in the last article (30V for 20ms) : Vout = 30V at the ouput corresponds to Vout/Ao = 150 mV between the transistor bases.
In Fig. 2-3, I plot the die temperature of the two transistors. The black curve is the output voltage, the green and blue are the temperature of both transistors.
Fig. 2-3a : Temperature of Q1 and Q2 versus Time
Fig. 2-3b : Output Signal (zoomed)
In this example, the transient generated a temperature delta of 0.016°C, which is pretty small. It translates as a 3uA difference in the output currents, which is 50 dB smaller than the audio signal. This thermal signal is quite small. However, these thermal drifts have importance regarding sound quality, as we will se later.
Before I forget, let me mention the interesting fact that, no matter what values we have for FB and Ao, this 50dB between thermal signal and error signal is likely to be a constant, as thermal dissipation is proportional to error signal (see Fig. 2-2). So, we have not found an explanation on why the low-feedback amps seem to sound better.
Of course, we forgot the audio signal itself. The error signal is differential, but the audio signal, which comes at the input of the amplifier, is common mode. Fig. 2-4 shows what happens when both transistors have the same base voltages : the purple curve is their dissipated power vs. common mode voltage, and the green one is their junction temperatures, while processing the same transient as before.
Fig. 2-4 : Thermal variations in common mode
Their temperature varies of 0.046°C on the transient. This is much higher than the variation caused by the error signal.
Much has been said on clipping. A fact is that amplifier behaviour at clipping seems to be an important factor for sound quality.
At clipping, feedback no longer maintains a low error signal : the error signal is simply the difference between the actual Input Voltage and the maximum input voltage that can be amplified without clipping. The same transient as before, driven into clipping with a 1 Volt error signal, generates a delta of 0.1°C between Q1 and Q2.
Unlike in the last article, where the numbers clearly showed that there was something happening, this time the thermal effects seem rather small. Effects caused by the error signal really seem negligible. The other two, common mode audio signal and clipping, might not. Let's see what happens when the openloop gain changes.
In a low feedback amp (Ao=200 or 46dB), the error signal for a full scale output (Vout=30V) is around Vout/Ao = 150mV. A delta of 0.1°C, offsets the error signal by 200uV, which is very little indeed.
In a high feedback amp (Ao=50000 or 90dB), the error signal will be 600uV for a full scale output. Then, 200uV generated by one tenth of a degree of thermal imablance do not appear to be negligible anymore. It is actually one third of the actual audio signal !
High-feedback amps have a low open-loop bandwidth, as low as 10-100Hz. This is associated with the notion of them being "slow", i.e. incapable of reproducing transients, while in fact they have very good speed and slew rate. The reason why they often sound "slow" on transients might be that, when they clip, the tiny thermal imbalance that is generated will be enough to offset the operating point of the input stage, and then the other stages, by a noticeable margin, for several seconds after the instant when clipping has occured. The quasi-religious question of feedback is not solved, but we know a little more.
The clipping behaviour of tubes vs transistors, has been compared many times, especially in amplifiers which have to deal with original signals coming from microphones, which have much more dynamics than recorded ones. However no really conclusive evidence of why tubes clip more gracefully has appeared. This thermal imbalance theory might be the answer to that old question...
Finally, it has appeared in this page that the input stage did not generate much thermal drift (except on clipping). It is, however, sensitive to the drifts generated in the other parts of the amplifier, especially the VAS (see last article). We will take this into account in the input stage design.
Next part : How to measure Memory