[SI-LIST] Re: Weighting functions for weakly non-linear drivers
- From: David Choe <david.choe@xxxxxxxxxx>
- To: Russell Dill <Russ.Dill@xxxxxxx>, "si-list@xxxxxxxxxxxxx" <si-list@xxxxxxxxxxxxx>
- Date: Fri, 6 May 2011 10:20:32 -0700
Russell,
I'm not versed on the application, but that first equation appears to be some
sort of superimposed Least Squares Fitting.
http://mathworld.wolfram.com/LeastSquaresFittingPolynomial.html
Regards,
David
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Russell Dill
Sent: Thursday, May 05, 2011 7:14 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Weighting functions for weakly non-linear drivers
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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