Andrew Beckett wrote on Apr 1st, 2009, 2:10am:
In practice I don't think this would happen. If there are high enough frequencies present in shooting PSS at sufficient magnitude, the timestep will reduce to follow them because of the fact that shooting is using transient - transient would normally reduce the timestep to follow such high frequency transitions. Remember it's the maximum timestep that is being limited, not the minimum timestep.
Of course, I know.
But spectrum resolution(or dynamic range) of Shooting-PSS is very inferior than HB-PSS.
That is one of reason why Cadence Spectre introduced MIC-PSS when Cadence Spectre had only Shooting-PSS.
So if value of "harms" or maximum value of "harmsvec" is not large enough to set small "maxstep",
we can never deny a possibility that accuracies of first 5 harmonics are degraded.Andrew Beckett wrote on Apr 1st, 2009, 2:10am:
Insufficient harmonics in harmonic balance certain can result in aliasing - and can be ameliorated by increasing the oversampling ratio (which is cheaper than increasing the number of harmonics, which would be another way of fixing it). So it's not "incorrect", but maybe "incomplete" would be a better word for it.
No. It is wrong.
Errors due to spectrum truncation are different from errors due to aliasing(or folding).
Even though we make time step small by increasing HB_Oversample but without increasing HB_Order, errors due to spectrum truncation can be never improved at all.
The followings are for HB analysis of Agilent ADSsim.
HB_Order=3, 7, 15, 31, 63, ....
HB_Oversample=1, 2, 4, 8, 16, ....
"tstep" in IFT(Inverse Fourier Transformation) will be small if "HB_Sample_Number" increase.
So errors due to aliasing effects can be improved by "HB_Oversample" ditrectly, although "HB_Order" also affects detemination of "tstep" in HB analysis.
However without increasing HB_Order, errors due to spectrum truncation can be never improved at all.
If we consider "HB_Order", it is directly related to truncation error not aliasing error.
On the other hand, if we consider aliasing error, "HB_Oversample" is directly related to it. Quote:
For HB, besides `reltol', `abstol', `steadyratio' and `lteratio', the number of harmonics has the most impact on the accuracy of simulation results.
When too few harmonics are used, error will be caused by aliasing effect and to obtain accurate results, `harms' should be big enough to cover the signal bandwidth.
”error will be caused by aliasing effect” is not correct.
It has to be ”error will be caused by spectrum truncation”.