ECE 3150
Spring 2009
Week 8 Recitation
There is only Lab 2 report due.
I got the most questions from least square fit and
standard deviation.
Introduce the fitting algorithm behind:
Given a measurement of
f
i
(x
i
)
, for example, this can be
I
D
(V
GS
)
where you have measured
I
D
for every given
V
GS
under a given low
V
DS
.
For a range of VGS (corresponding say the
10
th
to 20
th
measured point), you would like to fit to
f(x) = ax + b
.
We will define the
standard deviation from the fitting function as:
(
29
(
29
(
29
11
20
10
2
∑
=

=
i
i
i
i
x
f
x
f
S
The best fitting coefficient can be given as minimizing S with respect to the choice of
a
and
b
:
0
;
0
;
0
;
0
2
2
2
2
∂
∂
∂
∂
=
∂
∂
=
∂
∂
b
S
a
S
b
S
a
S
This will give unique
a
and
b
for the fitting function
f(x) = ax + b
.
Notice that we can fit
to any function with arbitrary coefficients, since each coefficient will have its own
equation to obtain its value.
However, the closer
f
i
(x
i
)
is to
f(x)
, the least error and
uncertainty there will be.
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