To confirm that the thermal coupling suggested would give something reasonably close to the required derating the calculation I did assumed a conventional circuit rather than the 'improved' version I suggested, with 300mV Vbe for the sensor transistor with no amplifier output, and 600mV needed to switch it on at 20deg C. At higher temperature this 600mV will reduce by about 2mV per deg, so it will fall to 300mV at about 170deg, and so the sensor transistor will switch on even with no signal and prevent further dissipation in the power device when 170deg is reached. Looking at power transistor derating specifications the case temperature at which they are derated to zero seems to vary between 150 and 200deg, so we are in the right area. Hopefully the heatsink temperature will be limited to something like 70deg by a thermal cutout, but the derating is a linear function of temperature, so if it is about right at 170 deg it should be fairly close at 70 also. In practice there are other factors to take into account, such as the difference between the power transistor case temperature and the sensor transistor junction temperature.
A bigger problem is that the straight line approximation to constant power is already inaccurate, and changing the sensor temperature makes it even worse. What we really need is for the sensor transistor to have Vbe = 300mV + kVI, where k is some constant and V and I are the collector-emitter voltage and current of the power transistor. What we have in the standard circuit is Vbe = aV + bI where a and b are constants. The next diagram shows what happens if we design for the best straight line at 20deg, and then use thermal coupling to reduce the maximum power at higher temperatures. Supply voltages of plus and minus 30V are again used.
At 170deg the power is reduced to zero at zero output voltage, corresponding to 30V power transistor voltage, but a current of several amps is still theoretically possible at reduced voltage. More serious is the reduction of output current to zero at 70deg before reaching the maximum output voltage into reactive loads. A better result would be the line shown in red, but this is not so easy to achieve in practice.
A better alternative is to design for the best straight line approximation at the derated power at 70deg, and this result is shown next:
The 70deg line is what we would have to use if no thermal coupling was used and we wanted to keep the power transistors within their safe operating area up to 70deg. (As mentioned before the question of what temperature the sensor transistor operates at is difficult to predict if it is just mounted somewhere on the circuit board, so this is probably a bad idea anyway.) With the thermal coupling there is now at 20deg an extra 50% current available at Vo = 0, plus 24% greater peak current into low resistive loads. The higher current at higher voltages will help with highly reactive loads. The only negative effect is that the maximum power reaches 156W, slightly over the 150W limit, but not enough to worry about.
The same approach could be tried for more complex circuits designed to increase permitted current at high and low voltages to give a better approximation to constant power. (e.g. see Becker, 'High-power Audio Amplifier Design', Wireless World, Feb 1972, p81.) Designing for optimum results at 70deg with thermal coupling will give improved maximum output current at lower temperature, but the result for the single line approximation suggests that care may then be needed to avoid allowing the maximum power limit to be exceeded.
The calculation in the first paragraph assumed a 2mV per deg.C fall in Vbe, but looking at data sheets for a more accurate value I found that for any given transistor the value is a function of collector current. For example the BC546 is specified as 2mV/deg.C at Ic=5mA, 2.2mV/deg.C at Ic=1mA and 1.8mV/deg.C at Ic=20mA. To add further complication the value is different for other transistor types. The currents at which Vbe falls by 2mV per deg.C are 10mA for a BC486, 20mA for a BC485, and 40mA for a MPSA05. These figures are taken from Motorola data sheets, and there is no certainty that the same types from other manufacturers will have identical specifications. It is also not clear how far the values can vary between samples, the figures appear to be only 'typical'. It is fortunate that exact figures are not essential, and even approximate compensation can give a worthwhile increase in available output at low temperatures.
