Worst-Case Circuit Analysis – Maple Flow

# Mathematical Tools for Worst-Case Circuit Analysis

• Derive circuit equations
• Analyze circuit tolerances with WCCA, EVA, RSS, Monte-Carlo simulation and sensitivity analysis
• Generate design reports

Using Worst-Case Circuit Analysis
Worst-Case Circuit Analysis (WCCA) is a set of techniques used to determine electronic circuit performance under extremes of environmental or operating conditions. WCCA shows how parameter variations combine to influence circuit performance, and helps the engineer shape the design so the overall system will remain compliant throughout its life-cycle.

Using Maple or Maple Flow to manage your worst-case analysis projects, you can SAVE TIME and REDUCE ERRORS as you identify potential problems that may arise from min-max variations in temperature, voltage, current, and other factors that may affect the performance of the system. Using variables to represent the parameters in your WCCA equations makes it easy to make changes and update the results in your worksheet.
• Use Maple Flow if you need a mathematical scratchpad for efficiently combining calculations and equations into your WCCA reports.
• Use Maple if you want a calculation solution that supports deeper analysis, greater control over report generation, and need to connect to other design tools or codebases.

# Are You a Mathcad® User?

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Do you want to work on mathematically-focused problems, solve larger systems, and develop algorithms? Check out Maple
WCCA using
Maple Flow provides an easy-to-use, freeform, calculation environment for preparing your WCCA reports.
• Format WCCA reports in clear professional layouts, with notes, images and references.
• Derive and use circuit equations, presenting them in readable natural mathematics notation.
• Your math is LIVE. Results update automatically as parameters change during the design project.
What electronics engineers love about Maple Flow:
“It has eliminated unit conversion errors”
Assign units as you define variables and have them cascade through your report.
“The solver commands are ready-to-use at my fingertips”
Access over 5000 efficient math functions, saving time with EVA, Monte Carlo, parametric analysis and RSS analysis.
“I can easily import component reference list data”
Import data from spreadsheets and text for use within WCCA calculations.
WCCA using
Maple is a powerful engineering calculation tool that supports a faster, more efficient WCCA process, working across your existing toolchain.
• Consolidate your calculation steps in one tool by using Maple for the preparation, analysis and presentation of equations and results.
• Perform all the math and calculations you can with Maple Flow and more.
• Connect to your existing electronics engineering toolchain to include circuit netlist data and component property data files in your equations.
What electronics engineers love about Maple:
“Passing results between tools avoids manual entry errors”
Create Maple worksheets that update the parameters from circuit design tools and feed into your stress analysis, derating limits, bill of materials and final results as design specs change.
“I save so much time by creating reusable templates”
Build reusable libraries of circuit equations and specialist functionality in Maple to use in new projects.

### Speeding Up Math Based Analysis

Maple Flow and Maple can combine advanced math commands with plots and equations, making it faster to update your analysis and generate results. Maple also offers a high-level programming language to take your data analysis further. You can easily implement these math based techniques:
• Extreme value analysis (EVA)
• The behaviour of a circuit is simulated for every permutation of extreme component parameters. E.g., a resistor of 5 Ω ± 5% is simulated at 4.75 Ω  and 5.25 Ω, in combination with every permutation of extreme values for all other components.
• Both symmetric and asymmetric tolerances can be implemented.
• Monte Carlo Analysis (MCA)
• Parameters are randomly selected from a distribution, and the circuit simulated, anywhere from 1000 to 100000 times.
• You can generate histograms, calculate the minimum and maximum values, view the statistical distribution of the results and more.
• Sensitivity analysis (SA)
• You can calculate the symbolic or numeric partial derivatives of the circuit with respect to each component parameter. These can be used to perturb the circuit equations.
• You can analyse the frequency-dependent behaviour with phase and magnitude plots.
• This uses a statistical approach, assuming that most of the components fall to the mid of the tolerance zone rather than at the extremes.
• Optimization
• You can optimize the circuit equations by varying the component values within a specific range.

You can also symbolically derive circuit equations, by applying Kirchoff’s current and voltage laws. The resulting equations can be symbolically rearranged and simplified. If the equations are transfer functions, you can generate phase and magnitude plots from the transfer functions.

Given the results, circuits can be redesigned to minimize failures due to parameter variations (or an initially overdesigned circuit could be made cheaper to manufacture with less costly components that have a broader parameter distribution).
See how Maple Flow can improve your design worksheets.

### Applications for Worst-Case Circuit Analysis

Discover how Electrical Engineers use Maple Flow and Maple for the tolerance analysis of components in electronic hardware.

## Improve reliability across unfavourable operating conditions

Use of WCCA aims to assure acceptable operation under the most extreme conditions and during improper application. Prior to procurement of parts, engineers can conduct Extreme Value Analysis (EVA) to determine the mathematical sensitivity of component parameters and document the min/max values in Maple Flow. This avoids the over-reliance on testing alone, which is only valid for a particular batch lot and can overstress the hardware when exposing components to extreme conditions such as temperature, voltage, power, etc.

## Understand the parts with the biggest impact

Some components will have a greater influence over the circuit functional performance than others. Power supplies, connectors and interfaces are expected to vary outputs even in normal operation, but every component has a contributing effect. Sensitivity Analysis (SA) is used to find how much a particular circuit characteristic varies as the component input values change. The results shape design specifications of the circuit and can be used to highlight which parts should be prioritized for quality assurance or for additional testing.

## Control fluctuations in the manufacturing process

Electrical components (such as resistors and capacitors) are manufactured in large quantities. Inconsistencies in raw materials or processing quality can affect component performance. Given the number of components in a circuit and the distribution of their parameters, the circuit may not perform as specified. This risk must be identified, managed and mitigated early in the design process.

The performance fluctuation may have a statistical distribution (e.g., the resistance of a batch of resistors might be described by a normal distribution). Engineers can use the computational power of Maple Flow to perform Root-Sum-Square (RSS) or Monte Carlo Analysis to evaluate the part tolerances and pin down the margins within the circuit design.

## Identify design concerns and performance thresholds

Maple Flow is the ideal tool for compiling the circuit design considerations. Equations and plots can be added alongside design notes using the flexible paper-like worksheet.  Prominent design sections such as safety thresholds, material performance properties, and assumptions about aging and environmental conditions can be clearly presented to create a polished, professional technical document.

## Improving the WCCA process workflow using Maple

The effort to complete a Worst-Case Circuit Analysis assessment and report is high, and the earlier it can be completed the better as the findings can impact key design decisions. As a result, the electrical engineer assigned to WCCA is looking to perform the calculations with speed and accuracy, but also needs to respond quickly as the project scope changes or different parts are substituted in. Since most engineers use a variety of electrical design software apps (AltiumTM, LTSpice and others), there is great benefit in automating and streamlining the design documentation steps.

This is where the world-class Maple engineering calculation software can help to manage the underlying equations and expressions. Maple offers flexible options for integrating electrical engineering data and component property lists from multiple sources, and offers built-in scripting and data analysis features that speed up the creation of WCCA reports.

The overall process can be sped up by applying these principles:

• Capture circuit design information such as netlist, subsystem variables and source load information, and use Maple (along with the free Syrup add-on package) to parse the information ready for analysis.
• The workflow is greatly simplified by reducing the number of calculation tools used to pass results back and forward. If the engineer defines the parameters and conducts all the stress analysis and derating limit calculations in Maple, then the results and key design information such as the Bill of Materials can be presented together in a report in the same tool.
• Creating a repository to store component data and procedures on a network drive available for all users, allows Maple to dynamically link to the property tables so that the parameter values (min, nom, max) can be fed into equations and further analyses.
• The Optimization and Parameter Sweep apps included in Maple greatly save time when working with equations and command line solvers can be called from within the analysis. This saves time when working with subcircuits and when generating Stress Analysis and finding the Derating Limits.
• Clear presentation of the data and analysis makes it easier for peers to review or to share project work with other teams. Creating Section Summary tables in the Maple worksheet will highlight key findings and will stay up-to-date even if the design criteria or component selection is changed further up the worksheet.

Once the electronics engineer is familiar with Maple and using it regularly in their toolchain, they will experience a great reduction in errors from unit conversions and manual data entry and find that WCCA reports are greatly accelerated – reports that previously took 3-4 weeks to prepare can now be run in a matter of days.

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