Electrical Engineering Software - Math Software for Electrical Engineers

# Math Software for Electrical Engineers

From stub matching and circuit analysis to transmission line modeling and semiconductor math, Maple delivers a robust, auditable environment for the types of analyses performed by Electrical Engineers.

## Six Applications of Math Software for Electrical Engineers

Electrical engineers are a unique breed. Their work is mathematically demanding, and they constantly face challenging technical problems. Maplesoft understands these challenges, and they built features into Maple that address them such as an easy-to-use mathematical engine, support for units, impactful visualizations, and rich documentation. Given these powerful features (and more), it’s no surprise that many electrical engineers use Maple. In this video, 6 specific applications are examined as examples of the kinds of tasks that electrical engineers perform within Maple. These examples include: (1) circuit analysis using transfer functions; (2) equivalent circuit models for MOSFETs; (3) worst case circuit analysis; (4) stub matching on a transmission line; (5) antenna design, and; (6) digital signal processing. For more information, visit us at: http://www.maplesoft.com/products/maple/?ref=youtube

### Maple has a feature-set that is perfect for Electrical Engineers

Electrical engineers are a unique breed. Their work is mathematically demanding, and they constantly face challenging technical problems. Maplesoft understands these challenges, and has built a features that specifically address them, such as:

A Maple document combines live math, text, images and plots in a single document. In effect, Maple captures the inherent assumptions and thought process behind an analysis, as well as the calculations.

## High-Level Symbolic and Numeric Math

Maple offers practical high-level tools for numeric and symbolic math, data analysis, and programming. These tools are designed for both simple and complex engineering problems.

• Numerically solve the equations for stub matching
• Symbolically manipulate the transfer functions that arise from circuit analysis

The symbolic and numeric math engines are seamlessly connected; parameters, equations and calculations can fluidly flow between the two. This means you can derive and numerically evaluate your equations in a single cohesive workflow.

Moreover, Maple’s programming language benefits from an interactive development environment and can use any of Maple’s high-level math tools.

• Code is faster to develop, debug and verify
• Can use Maple’s high level math functions, and
• Is easier to read by humans

## Reduce Calculation Risk with Units

Nearly every single quantity an electrical engineer encounters – whether it’s a resistance, voltage or a length - has a unit. Units are fluidly integrated into Maple, and can be used in simple calculations as well as numeric equation solving, optimization and visualization.

volt := 5.2V :
curr := 3.2A :
power := curr volt= 16.64 W

Using units in calculations removes the risk of introducing unit conversion errors, and also acts as a check on the physical validity of the equations.

# Application Example

## Circuit Analysis Using Transfer Functions and Laplace Transforms

You can use Maple to derive and manipulate transfer functions of electric circuits using Kirchoff’s current and voltage laws. Transfer functions can be converted to differential equations or discretized, and you can easily generate Phase and Magnitude plots.

Transfer functions can contain symbolic coefficients; these parameters can be optimized to match a target response.

Maple contains many features to help you symbolically manipulate transfer functions. These include:

• solve – rearrange transfer functions and nodal equations
• simplify – simplify circuit transfer functions to the most concise form.
• indets – identify unknown parameters in a set of equations
• eval – substitute numeric values into a symbolic equation
• Free SYRUP addon to Maple – convert netlist-like descriptions of circuits into transfer functions
• DynamicSystems – Generate phase and magnitude plots

A free package for Maple lets you convert SPICE netlists to transfer functions. This transfer can be analyzed in Maple’s symbolic and numeric math environment. For example, you can do AC and DC analysis, generate phase and magnitude plots, rearrange the transfer function for specific parameters or convert it to a differential equation and more.

# Application Example

## Mathematical Modeling of Semiconductor Devices

Semiconductors are complex devices, but Maple helps you derive the math models to accurately describe their characteristics.

MOSFETs are a critical component of modern electronics such as smartphones and other portable devices. Low power MOSFETS are critical to switching in power supply systems.

With Maple, you can turn equivalent circuit models of MOSFETS into analytical equations by writing down and manipulating the basic relationships.

These applications, for example, will help you model the effect of source inductance and cross conduction in modern power MOSFETs.

Deriving the equations for the gate voltage of a MOSFET

# Application Example

## Worst Case Circuit Analysis

Electrical components are manufactured in large quantities. Inconsistencies in the materials and the manufacturing process mean that component parameters have a statistical distribution. That is, the resistance of a batch of resistors might be described by a normal distribution.

Given the number of components in a circuit and the distribution of their parameters, the circuit may not perform as specified. This is a risk that must be identified, managed and mitigated early in the design process.

Electrical engineers often use Maple for worst case circuit analysis. You can either employ:

• Monte Carlo analysis, in which parameters are randomly selected from a distribution, and the circuit simulated, anywhere from 1000 to 100000 times
• This uses Maple’s tools for
• sampling probability distributions
• element-wise calculations for fast numeric evaluation
• generating histograms and statistical analysis
• or evaluate the circuit equations at the extreme value of all circuit components
• This uses Maple’s tools for
• generating permutations of parameters
• element-wise calculations

Once prepared, you can automatically generate a table of results and populate it with the results of your analysis, including conditional coloring for out-of-specification parameters.

# Application Example

## Stub Matching on a Transmission Line

RF and microwave engineers often need to match load to the impedance of a transmission line. This known as stub matching, and involves numerically solving a nonlinear set of equations.

This requires strong numerical solvers, found in fsolve. This supersedes traditional approaches using Smith charts

The parameters in these problems usually have dimensions (for example, resistances are in ohms and distances are in meters etc).  Maple can carry units from parameter definitions through to the final numerical solution of equations.

# Application Example

Practitioners in antenna and radar design use Maple to create executable design documents that capture the spatial, temporal and spectral aspects of their designs. The documents can contain both the equations, programming and visualizations necessary for the design.

The design documents can be deployed to the web or the desktop.

# Application Example

## Digital Signal Processing

Maple offers many tools for analyzing and manipulating signals and images

• Use FFTs, wavelets, Lomb-Scargle analyses for irregularly sampled data and more
• Signals can be upsampled or downsampled, and missing gaps filled by interpolation
• Generate periodograms, spectrograms, phase and magnitude plots and more
• Import and export many types of data, including Excel, text, audio and images
• Symbolic math helps you understand concepts such as convolution
• Units-aware numeric solvers help you solve iterative problems, such as those that arise in antenna design
• Many examples and applications for you to explore
• Do and document your analyses in a single interface, and deploy to the desktop and web

Designing an FIR Filter and generating a spectrogram and periodogram