Sensitivity Analysis

How does each component error impact the spec?

 

 

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OVERVIEW

What is Sensitivity (S)?

• S answers the question:
  • How does a change in component parameter (x) produce a change a circuit spec (y)?
• Or we can ask:
  • How Sensitive is y to changes in x?
  • S = ∆y / ∆x

Examples

• Parameters (x):  Voffset, Ibias, Resistor Tol, etc.
• Circuit Specs (y):  Offset, Gain, Filter Bandwidth, etc.

What is S good for?

• Knowing S, you can calculate the circuit error y from actual device error x.
    y = x * S
  Example:
    vo = voff * S
         = 1mV * 5V/V
         = 5mV
• S depends typically on the circuit only, independent of the actual device or component.
• You can calculate S before choosing any devices / components.
• What does S tell you?
  • Larger S:  select devices with smaller errors (more precise components, higher grade and cost).
  • Smaller S:  select devices with larger errors (less precice components, lower grade and cost)

 

MATHEMATICAL DEFINITIONS

Direct Units	Normalized
Example: Sensitivity of offset voltage to bias current.	Example: Sensitivity of gain to resistor tolerance.
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%

 

NEXT UP

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

 

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