Affirma Spectre DC Device Matching Analysis Tutorial - Cadence ...

Affirma Spectre DC Device Matching Analysis Tutorial
200
∂ ⎛ ⎛ p1 p2 ⎞⎞
error = 2 yi ------------
∂ p ∑ ⎜ – ⎜ + ------------- + p
3
W iL 2 3⎟⎟(
– 1)
=
⎝ ⎝ i W iL ⎠⎠
i = 1
i
The Equations (16), (17), and (18) can be rearranged in normal form as:
∑
∑
∑
1
--------------
2 2
W i
Li
1
--------------
2 3
W i
Li
1
------------
W iLi ∑
∑
∑
1
--------------
2 3
W i
Li
1
--------------
2 4
W i
Li
1
-------------
2
W iLi (EQ 18)
(EQ 19)
Assuming that the matrix in the Equation (19) is not singular, then (19) can be solved
for p1, p2, and p3, using standard LU decomposition and backsubstitution. If the
matrix is singular, then different method such as singular value decomposition can be
used. The model parameters mvtwl, mvtwl2, and mvt0 are simply the square root of
the p1, p2, and p3, respectively.
As for illustration, we attach a sample C program here. The first half portion of the
program is to cook up 200 sample data points of yi to mimic measurement data. We
also create the right hand side vector rhs
as in Equation (19). The last half portion
creates the matrix, and calls dense matrix solver routines dgeco and dgesl from
LINPACK (a popular dense matrix package) to obtain the fitted parameters. Upon
executing the program, we got this result:
model parameter mvtwl = 0.01
model parameter mvtwl2 = 0.003
model parameter mvt0 = 0
∑
∑
1
------------
W iLi 1
-------------
2
W iLi ∑1
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p 1
p 2
p 3
=
∑
∑
yi ------------
W iLi yi -------------
2
W iLi ∑ yi 0