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Solving for SMALL numbers

Microelectronics is (apparently) one of few fields where we routinely have to calculate very small numbers - numbers so small that modern calculators and programs tend to round them to zero!

Here are two ways to get around this problem:

 

1) Remembering "Taylor Series," if "small" is a very small number,

1 / (1+small) ~ 1-small

1/(1-small) ~ 1+small

So, for example if we realize that e-33 is a very small number,

1 - 1/(1+e-33) ~ 1 - (1-e-33) ~ e-33

And THIS our calculators CAN handle

e-33 = 4.65 x 10-15

 

2) For MATHCAD users,
Go to FORMAT

Select RESULT

hit the TOLERANCE tab

set the "zero threshold" to 20 (i.e. display numbers as small as 10-20)