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Error Budget Analysis

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Sensitivity Analysis

How does each component error
impact the circuit error?

 

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OVERVIEW

What is Sensitivity (S)?

Examples

What is S good for?

 

 

MATHEMATICAL DEFINITIONS

Direct Units Normalized
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Example: Sensitivity of offset voltage to bias current. Example: Sensitivity of gain to resistor tolerance.
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Offset Error Calc Gain Error Calc
Example:
ibias = 100nA
S = 1000 (V/A)

∆Voffset = ibias * S
           = 100nA * 1000 (V/A)
           = 100uV
Example:
R1_Tol = 0.1%
S = 0.5

∆K/K = R1_Tol * S
      = 0.1% * 0.5
      = 0.05%

 

GAIN ERROR EXAMPLE

Suppose you have an amplfier defined by a gain of K = R2/R1+1. How does a change in R2 cause a change in K?

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The gain error is defined as a ratio where K is the ideal gain and K' is the actual gain with errors.

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The Ideal Gain K and Actual Gain K’ can be written as

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For a numerical example check out the next topic (link below).

THE MATH: ALGEBRA VS. CALCULUS

 

NEXT UP

Let's apply Sensitivity Analysis to a simple Offset and Gain Error Example.

 

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