Homework assignment
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3 analog inputs from 0 to 5 volts
1 output from 0 - 5 volts
3 inputs defined as i1,i2,i3
1 output defined as o1
notation: i1,i2,i3 => o1
0,4,0.1 => 1.1
0,2,0.1 => 1.2
3,4,0.2 => 3.1
1,4,0.3 => 2.1
many of these
contraint: no DAC or microprocessor. Obviously they want an OPA solution.
That means inputs are weighted.
Weight can be negative, actually 2nd weight is negative and exactly -0.05 =(1.1-1.2)/(4-2) as it's obvious from 1st and 2nd line where input vector just differs in 2nd input variable .
I expected to find a linear relationship which is damn easy with OPA-s:\nÿ1ÿ
No luck, 3.9333 != 2.1.
The trick is to make an additive offset.
Step1: find additive offset: output for 0 inputvector
0,0,0 => ?
This is done by linearly combining the 4 input vectors.
I start it for you, by making first number 0:
0,4,0.1 => 1.1
0,2,0.1 => 1.2
From 3d line we subtract 3*(4th line):
3,4,0.2 => 3.1
-3*
1,4,0.3 => 2.1
=0,-8,-0.7 => -3.2
While from 4th line we subtract 1/3*(3d line):
1,4,0.3 => 2.1
-1/3*
3,4,0.2 => 3.1
=0,...,... => ...
Now our equations are:
0,4,0.1 => 1.1
0,2,0.1 => 1.2
0,-8,-0.7 => -3.2
0,...,... => ...
Just continue eliminating 2nd and 3d column to get output for 0 input vector.
Step2 : subtract the offset from the output
Step3 : calculate the a1 weights
Same as
a1=inverse(x1) * o1'
above, that is with matrix inversion. This time you'll see that 4th line will match the weights just fine.