AW: [Re: thermal tips re expo converters:]

[Haible Juergen]

Hi Ian,

thanks for explaining it again. I still think I understood it after your 
previous mail - otherwise I fear I still haven't understood it yet ..

	>The lower the loop gain, the larger this error is. 

Yes. That's why I have only considered integral type regulation from the
start.

	>Another approach would be to use "proportional plus integral"
control,
	>where the integral of the error signal is also fed back, in order
to
	>eliminate the equilibrium error signal. 

That's in fact the only thing I considered. And my conclusion was that
one might be able to get a precise, stable regulation in theory, but the
settling time of the whole system would be so slow that it would be
of no practical use.
The general problem is with introducing a second pole in the loop
(integral part of the control). The first pole is determined by the
thermal system. Good isolation = low bleed rate = low frequency
of thermal pole.
With an I (or PI control) your overall system has two poles, and you
will have to design it for low Q. That results in a very slow regulation,
i.e. no use in the real world.

I've hacked a crude example into PSpice to get a feeling for the
involved time constants.
I tried the following system: 

Time constant of cooling (i.e. bleeding thru isolation): 1000 seconds
(1F cap + 1k resistor, as electrical analogy)
Heater was a unidirectional VC current source (can only heat, not cool)
(Note: "current" equals heat, not electrical current, here !)

Ambient temperature is coupled in over the 1k (thermal isolation) resistor.
I modelled it with a rectangle wave that changes betwen 25 and 30 degrees,
period 200 seconds, PW = 50% (voltage source)

The reference temperature for heating was set to 40 degrees.
The control amp was an opamp integrator (dc gain 25.000, R = 10k,
C=100nF)

Heat flow was limited to the "number" 100m (there is a factor between
thermal
and electrical units, set by choosing the electrical capacitance to model
the thermal capacitance)

This example system shows a dynamic error of  0.4 degrees (the static error
should be zero; the 0.4 degrees are the overshot from regulating a 5 degree
200second rectangle)

This is fairly reasonable, so far. But now comes the knockout: This example
system takes 10 minutes (!) to warm up from 0 degrees to the 40 degrees 
working state.

So I don't think the *static* error is a problem at all. You can get rid of
that
with an integral control. But the dynamic error can only be made small when
you have a lot of time. 

	>If the arguments about not needing a fast cooling rate were true,
	>designers would not be heating their chips to the 60-80 deg C
range.

I fully agree, as I did in my previous mail !

It's just that we started from different points (proportional control vs.
integral control).
Unfortunately, neither will lead to a good solution.

So, either high temp and high bleed, or compensation rather than heating.

JH.