Transient and DC operating point are different

Unknown said:

They are actually very closed to each other (2pA difference) but should they be exact the same?

You're really worried about 1 part in 40 million? Circuit simulators solve nonlinear differential equations. It's not possible to get an exact solution to such equations, so numerical methods are employed (e.g. Newton Raphson) which iterate towards a solution and determine that the solution has converged when the error is small (this is all part of a tradeoff between speed and reasonable accuracy). The criteria used to determine the error is generally in the form reltol*quantity+abstol (so this might be the change between two iterations, or the error in the sum of currents into a node).  reltol defaults to 1e-3, and vabstol is 1e-6V and iabstol is 1e-12A. The absolute tolerances are for when the signal levels are close to zero - because otherwise you'd have an ever increasing accuracy for tiny (insignificant) signals. So a difference of only 2pA is remarkably small (it's close to the abstol), especially in a current of 800uA. I didn't actually see that difference. Even if I had, the starting point for the two DC solutions may have been slightly different (it typically starts from whatever set of numbers were used previously - or it may have been that there was a small difference in the number of iterations - either way, the differences are well within the accuracy tolerances).

There is a small amount of inaccuracy that appears in the DC solution with reltol=1e-3, which reduces if you tighten it to 1e-5 (note, I seriously doubt you need this level of accuracy for this circuit) - and if you compare the three operating points, they are very close:

DC : M0:id = 0.00079999999976654 M1:id = 0.00079999999976654
TRAN 0: M0:id = 0.00079999999976654 M1:id = 0.00079999999976654
FINAL : M0:id = 0.00080000135675758 M1:id = 0.00079999851611377

This was with this script:

openResults("forum_oppoint.raw")
;println(results())
;println(results(?noAlias t))
selectResult("dcOpInfo")
printf("DC : M0:id = %.14g M1:id = %.14g\n" getData("M0:id") getData("M1:id"))
selectResult("tran_info-tran_info")
printf("TRAN 0: M0:id = %.14g M1:id = %.14g\n" value(getData("M0:id") 0) value(getData("M1:id") 0))
selectResult("finalTimeOP-info")
printf("FINAL : M0:id = %.14g M1:id = %.14g\n" getData("M0:id") getData("M1:id"))

Note I did this with MMSIM14.1 ISR18 so your results may be slightly different (although not significantly different). All the results there are well within the tolerances. There's probably some longer term settling effect - I found this reduced if I ran a much longer simulation with a lower frequency sine wave too. There's also some error that occurs (local truncation error) during transient which also will give a small error in each instantaneous time point, but this won't accumulate over time.

So I would say you're worrying about a level of accuracy that really isn't warranted.

Regards,

Andrew.

Unknown said:

They are actually very closed to each other (2pA difference) but should they be exact the same?

You're really worried about 1 part in 40 million? Circuit simulators solve nonlinear differential equations. It's not possible to get an exact solution to such equations, so numerical methods are employed (e.g. Newton Raphson) which iterate towards a solution and determine that the solution has converged when the error is small (this is all part of a tradeoff between speed and reasonable accuracy). The criteria used to determine the error is generally in the form reltol*quantity+abstol (so this might be the change between two iterations, or the error in the sum of currents into a node).  reltol defaults to 1e-3, and vabstol is 1e-6V and iabstol is 1e-12A. The absolute tolerances are for when the signal levels are close to zero - because otherwise you'd have an ever increasing accuracy for tiny (insignificant) signals. So a difference of only 2pA is remarkably small (it's close to the abstol), especially in a current of 800uA. I didn't actually see that difference. Even if I had, the starting point for the two DC solutions may have been slightly different (it typically starts from whatever set of numbers were used previously - or it may have been that there was a small difference in the number of iterations - either way, the differences are well within the accuracy tolerances).

There is a small amount of inaccuracy that appears in the DC solution with reltol=1e-3, which reduces if you tighten it to 1e-5 (note, I seriously doubt you need this level of accuracy for this circuit) - and if you compare the three operating points, they are very close:

DC : M0:id = 0.00079999999976654 M1:id = 0.00079999999976654
TRAN 0: M0:id = 0.00079999999976654 M1:id = 0.00079999999976654
FINAL : M0:id = 0.00080000135675758 M1:id = 0.00079999851611377

This was with this script:

openResults("forum_oppoint.raw")
;println(results())
;println(results(?noAlias t))
selectResult("dcOpInfo")
printf("DC : M0:id = %.14g M1:id = %.14g\n" getData("M0:id") getData("M1:id"))
selectResult("tran_info-tran_info")
printf("TRAN 0: M0:id = %.14g M1:id = %.14g\n" value(getData("M0:id") 0) value(getData("M1:id") 0))
selectResult("finalTimeOP-info")
printf("FINAL : M0:id = %.14g M1:id = %.14g\n" getData("M0:id") getData("M1:id"))

Note I did this with MMSIM14.1 ISR18 so your results may be slightly different (although not significantly different). All the results there are well within the tolerances. There's probably some longer term settling effect - I found this reduced if I ran a much longer simulation with a lower frequency sine wave too. There's also some error that occurs (local truncation error) during transient which also will give a small error in each instantaneous time point, but this won't accumulate over time.

So I would say you're worrying about a level of accuracy that really isn't warranted.

Regards,

Andrew.