Monte Carlo Analysis

Monte Carlo Analysis (Premium) #

Monte Carlo analysis simulates your circuit multiple times with random component variations within their specified tolerances. This statistical approach reveals how manufacturing variations affect circuit performance in the real world.

What It Does #

Monte Carlo analysis:

  1. Assigns random values to components based on their tolerances
  2. Runs multiple simulations (typically 100-1000)
  3. Shows statistical distribution of results
  4. Identifies worst-case scenarios and yield rates

When to Use #

Use Monte Carlo Analysis for:

  • Production Design: Ensure circuits work with real components
  • Yield Prediction: Estimate percentage of working boards
  • Tolerance Allocation: Identify critical components needing tighter specs
  • Worst-Case Analysis: Find extreme operating conditions
  • Cost Optimization: Balance performance vs. component cost

Setting Component Tolerances #

Resistors #

Resistance: 10kΩ
Tolerance: 5%
Distribution: Gaussian (6-sigma)

Capacitors #

Capacitance: 100nF
Tolerance: 10%
Distribution: Gaussian

Other Components #

  • Inductors: Typically 10-20% tolerance
  • Voltage Sources: 1-5% for references
  • Transistor Beta: Can vary 2:1 or more

Configuration Parameters #

Simulation Settings #

  • Number of Runs: 100-1000 (more = better statistics)
  • Distribution Type:
    • Gaussian (normal) - Most common
    • Uniform - Equal probability across range
    • Worst-case - Corners only

Analysis Types #

Monte Carlo works with:

  • DC Operating Point: Bias point variations
  • AC Analysis: Frequency response spread
  • Transient: Time-domain variations
  • DC Sweep: Parameter sensitivity

Understanding Results #

Statistical Plots #

Histogram

  • Shows distribution of results
  • Peak indicates most likely value
  • Width shows variation range
  • Multiple peaks suggest design issues

Box Plot

  • Median (50th percentile)
  • Quartiles (25th, 75th)
  • Whiskers (5th, 95th)
  • Outliers beyond whiskers

Key Statistics #

Mean (μ)

  • Average value across all runs
  • Should match nominal design

Standard Deviation (σ)

  • Measure of spread
  • Smaller = more consistent

Yield

  • Percentage meeting specifications
  • Industry targets: 95-99%

Cp/Cpk

  • Process capability indices
  • Cpk > 1.33 considered good

Example Applications #

Voltage Divider Analysis #

* 5V to 3.3V divider with 5% resistors
V1 vcc 0 DC 5
R1 vcc out 10k tolerance=5%
R2 out 0 18k tolerance=5%

.mc 1000 dc V(out) tolerance=gauss

Results might show:

  • Nominal: 3.214V
  • Mean: 3.215V
  • Std Dev: 0.045V
  • 3-sigma range: 3.08V to 3.35V

Op-Amp Gain Circuit #

* Non-inverting amp with gain = 11
X1 in 0 out vcc vee OPAMP
R1 n1 0 10k tolerance=1%
R2 out n1 100k tolerance=1%

.mc 500 ac V(out) tolerance=gauss

Gain variations:

  • Nominal: 20.8 dB
  • Spread: ±0.17 dB
  • Affects frequency response

Filter Cutoff Frequency #

* RC low-pass filter
V1 in 0 AC 1
R1 in out 10k tolerance=5%
C1 out 0 100n tolerance=10%

.mc 1000 ac V(out) tolerance=gauss

Cutoff frequency spread:

  • Nominal: 159 Hz
  • Range: 135-185 Hz
  • Important for filter specs

Design Guidelines #

Component Selection #

Critical Components

  • Use 1% or better tolerance
  • Consider temperature coefficients
  • May need selection/trimming

Non-Critical Components

  • 5-10% tolerance acceptable
  • Standard values fine
  • Cost optimization opportunity

Sensitivity Analysis #

Identify which components most affect output:

  1. Run baseline Monte Carlo
  2. Tighten one component tolerance
  3. Compare improvement vs. cost
  4. Iterate for optimization

Design Centering #

Adjust nominal values for best yield:

  • If distribution skewed high, reduce nominals
  • If failures at one extreme, shift center
  • Balance all specifications

Advanced Techniques #

Correlation #

Some parameters correlate:

  • Matched resistors in same package
  • Temperature tracking
  • Process variations

Worst-Case Corners #

Combine extremes systematically:

  • All resistors high, all capacitors low
  • Temperature extremes
  • Supply voltage limits

Design for Manufacturability #

Rules of thumb:

  • 3-sigma design: 99.7% yield
  • 4-sigma design: 99.99% yield
  • Consider assembly variations too

Interpreting Results #

Red Flags #

Bimodal Distribution

  • Two peaks in histogram
  • Indicates instability
  • Circuit may have two operating modes

Wide Spread

  • Large standard deviation
  • Poor tolerance to variations
  • Redesign recommended

Low Yield

  • Many failures
  • Tighten tolerances
  • Or redesign for robustness

Success Indicators #

Tight Distribution

  • Small sigma relative to spec
  • High Cpk values
  • Robust design

High Yield

  • 99%+ meeting specs
  • Cost-effective production
  • Reliable in field

Export and Reporting #

Premium features include:

  • Export all run data to CSV
  • Statistical summary reports
  • Histogram/distribution plots
  • Worst-case identification
  • Correlation matrices

Tips for Effective Monte Carlo #

  1. Start Simple: Run with few components first
  2. Realistic Tolerances: Use actual component specs
  3. Sufficient Runs: 500+ for good statistics
  4. Check Assumptions: Gaussian may not always apply
  5. Temperature Too: Combine with temperature analysis
  6. Validate Results: Build and measure prototypes

See Also #