What's an Error Budget Analysis
Anyway?

 

 

Financial Budget

• An itemized list and total of dollar expenses versus the maximum allocated budget for a particular purpose.

Circuit Design Budget

• An itemized list and total of circuit errors versus the maximum allocated budget for the system requirements..

 

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OVERVIEW

 

Take a fast track preview of an Error Budget Analysis.

MAX BUDGET

• Max allowable error budget from requirements, typically
  • Offset Error (∆Voffset)
  • Gain Error (∆K)
  • Total Error = ±∆Voffset + (±∆K x Reading)
• NOTE! Other specs may be analyzed:
  •  Filter Response, Settling Time, Noise, Linearity, etc.

 

ERROR SOURCES

• Identify all error sources in your circuit.
• Amplifiers
  • Input Offset Voltage, Input Bias Current
• Resistors: 
  • Tolerance, Tempco
• ADCs, DACs:
  • Resolution, Gain Error, Offset error, Non-linearity

 

SENSITIVITY ANALYSIS

• Calculate how sensitive is the Offset / Gain to each Error Source.
• Offset Sensitivity Example (how ibias affects the offset)
    S = ∆Voffset / ∆ibias
• Gain Sensitivity Example (how R Tolerance affects gain error):
    S = ∆K / ∆R

 

ACTUAL OFFSET / GAIN ERRORS

• Calculate Offset / Gain Errors using actual values of component errors.
• Offset Error:
    ∆Voffset = ibias_U1 x S
• Gain Error:
    ∆K  = ∆R1 x S

 

TOTAL ERROR

• Worst Case Analysis (WCA)
  • Total = | Error1 | + | Error2 | + ...
  • Assumes all errors at max limit and in same polarity.
  • May OVER estimate total error.
• Root Sum Square (RSS)
  • Total = √( Error1² + Error2² + ...)
  • More realistic total - considers statistical variation of errors.
  • May UNDER estimate total error.

 

BUDGET CHECK

• If Total Error < Max Budget?
  • PASS - Gain confidence that the circuit design will meet spec when built and tested.

• If Total Error > Max Budget?
  • FAIL - Investigate higher grade components or a more optimal circuit topology.

 

 

NEXT UP

Which are the critical errors? Let's take a look at a Basic Circuit Block - Ideal and Actual (with Errors).

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