[SI-LIST] Weighting functions for weakly non-linear drivers
- From: Russell Dill <Russ.Dill@xxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Thu, 5 May 2011 19:14:10 -0700
I'm trying to figure out how to calculate weighting functions (sometimes
known as Ku(t)/Kd(t)) for weakly non-linear drivers from IBIS models. By
weighting function, I mean a multiplier to the pulldown and pullup current
sources in the model of a driver that changes the driver from pulldown to
pullup in a ramp-up and vice versa.
B. Mutnury and M. Swaminathan gloss over the calculation of these functions
in quite a few papers[1], but never describe it in detail, in their papers,
it is always given the form:
| w1 | | fa1 fa2 | ^-1 | ia |
| | = | | | |
| w2 | | fb1 fb2 | | ib |
For those who can't see the ascii art, its:
vector [ [w1], [w2] ] = inverse(matrix [ [fa1 fa2] [fb1 fb2] ]) * vector [
[ia] [ib] ]
This is very easy to solve for w1 and w2. However, I have no clue what the
other variables are. The only thing the text makes clear is that f1 and f2
the pullup/pulldown behavior in HIGH and LOW mode respectively in the form
of I vs V. It then talks about testing the driver with two different loads,
which I know as the ramp down and ramp up waveforms in the IBIS file.
I have no clue what exactly they mean by fa1 and fb2. The text also never
mentions ia or ib.
I also found a presentation[2] from Teraspeed Consulting Group that clearly
uses this, but I don't have the associated audio so I'm not sure what they
are trying to communicate. I've worked out the following associations (slide
15)
VUP1 == fa1
VUP2 == fa2
VDN1 == fb1
VDN2 == fb2
V(IN1) - V(PIN1) == ia
V(IN2) - V(PIN2) == ib
They then form the determinate:
CUR='(I(VDN2)*I(VUP1)-I(VDN1)*I(VUP2))/(1E7)'
And then calculate w1 and w2:
CUR='((V(IN1)-V(PIN1))*I(VUP2)-(V(IN2)-V(PIN2))*I(VUP1))/I(VDET)'
CUR='((V(IN2)-V(PIN2))*I(VDN1)-(V(IN1)-V(PIN1))*I(VDN2))/I(VDET)'
But once again, I'm not getting much additional information out of this
besides the fact that I'm on the right track. I am getting confused by their
1E7 term which seems so important to the presentation.
[1] http://smartech.gatech.edu/handle/1853/7459
[2] http://www.vhdl.org/pub/ibis/summits/jun03a/ross.pdf
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