# Thermal stability of push-pull amplifier

This is a circuit from The Art of Electronics:

To my surprise, the authors try to estimate the increase in quiescent current by assuming that it is constant!

Let us assume the worst and calculate the increase in output-stage quiescent current corresponding to a 30°C temperature rise in output transistor temperature... For that temperature rise, the $$\V_\text{BE}\$$ of each output transistor will decrease by about 63 mV at constant current, raising the voltage across R3 and R4 by about 50% (i.e., the quiescent current will rise by about 50%).

Does it make sense?

• Why not simulate it? Nov 9, 2022 at 10:21
• Are not the diodes and Q2 & Q3 not on the same heatsink? Nov 9, 2022 at 12:10
• @Antonio51, the book says it's better if they are connected to the same heatsink. But for the estimation it is not assumed. Nov 10, 2022 at 3:53
• OK. I don't know if I am wrong with some components at Tamb and some others components at another temperature ... I add in the answer. Seems to work. Nov 10, 2022 at 8:48

As with much of electronics, some approximations and assumptions are being made; their validity or reasonableness can be checked at the end.

1. Yes, 30 C rise will reduce VBE by about 63 mV at constant current.
2. ... if the current increases by 50 %, the VBE will increase by VT.ln(1.5) = 26m*0.4 = 11 mV. This is 17 % of the 63 mV calculated, so you could iterate and find a more self-consistent answer, but the difference between a 50 % rise and a 41 % isn't significant given other approximations (diodes are the same temperature as the transistors; base current is negligible etc.

It does make sense but it should be written more explicitly:

For that temperature rise, the VBE of each output transistor will decrease by about 63 mV at constant base current, raising the voltage across R3 and R4 by about 50% (i.e., the quiescent emitter current will rise by about 50%).

The idea is to do a rough estimation what happens if only the transistor temperature rises by 30°C. The biasing circuit is not affected much in this case. It is the worst case because if the temperature of the diodes in the biasing circuit rises as well, it counteracts the effect of the rise in transistor temperature and the quiescent current does not increase as much.

• This approach is consistent with a philosophy that says that if you have an approach that can economically deal with worse-than-worst-case conditions, you can stop analyzing and start getting things into production. Nov 9, 2022 at 6:12

For reference, here is a simulation showing the effect of temperature (50 °C rise) on ALL components (diodes should be on the same heatsink as output BJTs).
Rise of ~ 10 % currents at quiet point.
NB: modified resistors for Vo ~ 0 V.
Note also that only the current source is constant. Ib currents are not.

Here is a simulation with Q1 & Q2 at 3 temperatures (0 °C, 27 °C, 50 °C).
Diodes are always at 27 °C. Seems to work.

And in the case feedback resistors are 1 mOhm ...