Software simulation has largely taken the place of "trial-and-error" prototypes in fine-tuning high-frequency designs. Two of the types of software tools often used by RF and microwave engineers are mathematical and electromagnetic (EM) field simulators. Although math tools can be applied for analysis in almost all scientific fields, they can also be run with electrical engineering modules. And EM simulators have leveraged the increased computing power of improved microprocessors to provide greater insight into planar and three-dimensional (3D) circuits and structures.

MATLAB from The MathWorks, one of the best known math software tools, is used for everything from cancer research to waveguide analysis. The software combines a powerful numeric engine with a technical programming environment and practical visualization capabilities to serve as a versatile analysis tool. The firm offers a student version with various tools from the full-featured version, including a symbolic math toolbox, a signal-processing toolbox, and an optimization toolbox. In addition, the company provides a free interactive user's kit on its web site (upon registration), with data sheets, customer comments, and recorded product presentations.

SOLVING EQUATIONS
Mathsoft, the developer of Mathcad software, was acquired by PTC (www. ptc.com) in 2006. Version 14.0 of Mathcad features a long list of improvements, including full Unicode support for displaying worksheets across many different operating systems and the capability to perform inline numerical evaluations to simplify substituting values for variables in equations.

Version 13 is the latest iteration of the Maple math software from Maple- Soft. In addition to its powerful equation editors and equation-solving engines, the program can recognize handwritten symbols to simplify data entry. It supports symbolic and numeric math operations, linear algebra, and provides full connectivity to MATLAB.

Mathematica from Wolfram Research is now in Version 7, with built-in image processing, vector and field visualization, discrete symbolic calculus capabilities, and support for delay differential equations (DDEs). It is now written for computers with parallel processors and can readily handle differential and difference equations, perform Boolean analysis, and analyze integer sequences.

For those seeking a lower-cost math software, Sage is an open-source mathematical modeling system licensed under the GNU General Public License (GPL) program. It is an open-source alternative to such tools as Maple, MATLAB, and Mathematica and is composed of nearly 100 open-sourced packages with a unified interface.

EM SIMULATION TOOLS
EM simulators can be thought of as mathematical solvers devoted to Maxwell's equations. Programs such as the Sonnet Suite of tools from Sonnet Software operate with a physical description of an antenna or planar circuit and apply a method-of-moments (MoM) analysis based on Maxwell's equations to develop models of those subjects. The models include all parasitic, cross-coupling, enclosure and package resonance effects and can be used to produce S-, Y-, or Z-parameters for the antenna or circuit for further modeling and analysis. The company also offers a feature-limited version of its planar EM simulation software called Sonnet Lite for free download on its web site.

The RF Module in the COMSOL Multiphysics suite of programs from COMSOL also provides EM simulation capabilities for modeling antennas, waveguide, microwave components, and even highspeed optical components. It includes a host of advanced post-processing capabilities, including far-field analysis and S-parameter computation.

Zeland Software, the developer of the popular IE3D 3D EM simulator, was acquired by Mentor Graphics earlier this year. Zeland's EM simulator is now integrated with Mentor's HyperLynx product suites and adds the capability to perform full-wave EM analysis on 3D structures in circuits and packages, including viaholes, solder bumps, and wire bonds. Last year, Zeland had introduced its IE3D-SI version for signal integrity (SI) analysis, which is now also available as part of the Mentor HyperLynx.

One of the standards in EM simulation, the High-Frequency Structure Simulation (HFSS) software from ANSYS, is now available as release 12.1. This version introduces a new integral equation EM solver option based on full-wave MoM computation. It is suitable for large-scale radiating and scattering studies, such as radar-crosssection (RCS) and antenna analyses.

In many cases, EM simulation tools are included as part of larger software suites. CST Microwave Studio from Computer Simulation Technology, for example, is a software suite that includes 3D EM simulation capability. Two other leading simulation suites, Microwave Office from AWR and the Advanced Design System (ADS) from Agilent Technologies, feature powerful EM simulation tools, AXIEM and Momentum, respectively.

AWR's AXIEM handles 3D planar applications, including printed-circuit boards and monolithic microwave integrated circuits (MMICs). It integrates with the firm's Microwave Office and Analog Office suites of software tools and uses advanced hybrid meshing technology and proprietary full-wave planar EM solver technology.

The latest version of Agilent's Momentum, the second-generation Momentum G2, is seamlessly integrated into the firm's ADS platform, which is also well integrated with the company's test equipment. Momentum is a 3D planar MoM EM simulator with multithreading algorithms that take advantage of the processing speed of modern computers and microprocessors.

For those looking for low-cost EM simulation, Version 0.2 of Arpeggio is a general-purpose EM simulator that performs true 3D simulations that will provide processing speed in proportion to the capabilities of a computer's memory and microprocessors.