Is there any reason not to short the input pins of an op amp? i.e. such as in the image:
Bandgaps have an unavoidable curve over temperature with 0ppm/ºC resistors from 0 - 100ºC, which can be compensated for to a great degree in different ways, and are basically "supply independent," the above image has no temperature curve with 10ppmºC resistors over the same range, but you could say it is highly supply dependent...
(although I think both designs are in fact supply dependent in different ways, bandgap for a known current source needed - itself to a degree dependent on a roughly known voltage source, and this for the precise known voltage source needed)
Is there some reason, or several, why the above circuit isn't typically used? Apart from there being no skill needed or joy in designing two op amps shoved together, whereas bandgaps look like a fine art?
One reason might be, that it cannot possibly work.
Shorting the pins of an op amp will just drive the output to one extreme or another.
You have a much better chance of balancing a ball bearing on the edge of a razor blade than getting the output of an op amp to sit half way between the supply rails with the inputs shorted together.
That's funny, nice analogy, thanks, that means metastable? ...the simulation software appears to contradict you, Warpspeed, which shows that simulations can be really useful or terribly misleading.
Is it so that the Brokaw is more temperature stable than the Widlar 4 transistor bandgap?
Ambient magnetic/EM fields (example, AC mains hum) can reach the wire joining the inputs. Although it is a common mode signal to the op amp, nevertheless it is an unwanted signal. It can cause unwanted response from the op amp. This is one reason that guidelines tell us to tie inputs (separate or joined) to some definite volt level.
To add a little more detail every opamp has an offset error. So when the leads are shorted the opamp 'sees' the offset of say 1mV. Then that gets multiplied by the open-loop gain of say 100,000 which is guaranteed to result in the output going to one rail.
It will never stay in between though it might occasionally flip if the offset changes signs due to, say, temperature variations.
If you actually want the opamp to put out zero volts set it up as a unity gain buffer and tie the (+) pin to ground.