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Hi,
Are you having the issue in simulation(pre tapeout) or in Silicon ?I think bandgap is a self biased circuit and hence the circuit will either operate as desired (with required current mirroring + bg voltage generation etc) or will not startup.
So in general , a startup circuit is added in bandgap so that it does start up.
Now assuming you have a startup circuit and you have a problem with simulation, you can check which transistors have the problem.
As "renwl" said, you can use a .tran statement and run transient simulations. I would suggest you to ru a DC simulation too..
I think the problem may be with your startup circuit..I am not sure how to debug in Silicon.. since some boards are working and some dont may be you can experiment with changing the power supply voltage in the unworking boards...
Simulate the supply ramping with a transient simulation. Use either a positive and a negative offset on your error amplifier. If only one polarity works you get the issue. Startup in CMOS bandgap set the operating point at a value where the PTAT generate enough voltage to overcome offsets.
Also, simulate with worst-case conditions such as -40C and slow mosfets.
Your input supply ramp in transient sim should be very slow, on the order of hundreds of ms.
Using these techniques, you can find why your startup circuit fails to operate on the simulator. In silicon it is hard to check physically since the capacitance and/or leakage of a probe needle will often "kick" the circuit into starting. A picoprobe can probably do it, but the work of probing is much more taxing than just making it fail in sim.
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