# Aim at the sore spot

I was trying to figure out which transistors of the whole amp had the most influence on the total memory distortion. Then, the answer struck me as obvious : let's calculate the following two values :

### The Annoyance Factor

• Considering an open-loop amp to which we apply just the right DC input voltage so as to set the output to 0 volts. This is easy to do in simulation, much less so in real life. All results here are in simulation.

In open-loop, the amp is very sensitive, so we can measure F = dV(Output Open Loop)/d(Temp), the variation of open-loop output voltage caused by a 1° variation in the tempearture of a specific transistor. F is in Volts/°C.

• Then, in closed-loop, we can measure H = d(Dissipated Power)/d(VOut Closed Loop), which is the variation of power dissipated in a specific transistor when the output voltage changes by Volt. H is in Watts/Volts.

Therefore, for each transistor, we know

• H : which tells us how much this transistor will heat up (as Temperature variations are proportional to dissipated power variations) ;
• F : which tells us the gravity of the drift induced by this transistor heating.

The product of these two values : A = H*F therefore gives an idea of how Annoying this transistor will be relative to the thermal drifts of the whole amplifier.

### Example 1 : classic Lin amp

click to display schematic (hint : use shift-click)

Sorry for the huge graphics (I always work at 1600x1200). If you use Opera, hit "-" to zoom out. If you use an imperialist browser made by a monopolistic cartel, or a product of a defunct company, hit ctrl-alt-del.

Well well well, this is a standard sand amp, 90 dB open loop gain, 24 dB gain, 66 dB feedback at DC. Close to each transistor, I wrote the corresponding H, F, and A.

• F, in blue : open loop output drift in volts if this transistor heats by 1°C.
• H, in black : power delta for 1 volt Vout change, in micro-watts
• A, in red : annoyance factor, ie. product of above two values.

Now it is pretty obvious that the most annoying transistor is in the input pair, with some help from the VAS and its current sink.

The numbers for H are pretty logical, just think that Power=Voltage*Current and try to explain them.

The numbers for F get worse the closer you get to the input, because they are magnified by the gain of the rest of the amp. ie. a drift occuring in Q25 will not be multiplied by anything, whereas a drift occuring in the input pair will be multiplied by the full OL gain.

In Magenta, I wrote the results for the same technique applied to the power supply. Let's call H' the power variation caused by a 1 volt variation in supply voltage : d(Power)/d(Supply). Then, A'=H*F' relates to the sensitivity of the concerned transistor versus the power supply. The two numbers in magenta are H' : A'.

We can see the input stage is extremely sensitive to power supply variations.

As a side note, the thermal effects in both transistors of the input pair cancel each other, but not completely. The sore spot is therefore not only in the input stage, but also in the VAS and the current sources.

### Example 2 : thermally compensated amp

click to display schematic (hint : use shift-click)

The steps taken to operate critical transistors at constant power make the input stage almost imune to drifts : its annoyance factor dropped dramatically, both relative to signal (red) and to the power supply (magenta).

The current sources also benefitted a lot from cascoding. Same for the VAS.

We can see where the new sore spot is, and where to direct the efforts :

• The current mirror (I'll add a simple JFET cascode, à la Borbely)
• The VAS : under investigation.

A major interest of this method is that the buffer transistor is shown to be quite innocent, where I would have thought the contrary.

Maybe this thing is going to get finished one day ?

All in all, the compensated amp sounds good (euphemish). 94dB feedback, why not ? I have no preconceptions on that.