Simulating a high-frequency device before it is built can help avoid pitfalls in its design and manufacturing. Fortunately, engineers faced with predicting the behavior of RF and microwave circuits have a wide array of electromagnetic (EM) solvers to choose from, although selecting an optimum simulation tool should require consideration of some practical guidelines.

There are several classes of solvers, with each best suited to a particular class of problems. Some computer- aided-engineering (CAE) tools, such as solvers based on the finite-element method (FEM) or the finite-difference method (FDM), or closely related approaches such as the transmission-linematrix (TLM) method, are suitable for analyzing complex arbitrary threedimensional (3-D) geometries. But if a reasonable hypothesis can be applied to reduce the complexity of this class of structures, and some known properties of the structures can be exploited in the solver, then other approaches, such as integral-equation/ method-of-moments (MoM) solvers, can be used with fairly close results. These differences essentially highlight programs that have been developed for multipurpose use versus software dedicated to a specific set of problems. Another contrast to consider is that time-domain analysis is well suited for broadband projects, especially when nonlinear effects must be considered, whereas frequency-domain analysis is ideal for strongly resonant, high-Q structures.

In some ways, a commercial highfrequency simulator is akin to "black magic," since it is based on a set of algorithms not often publicly known, although results using the simulator may often be published. One of the few exceptions is the EM3DS (ElectroMagnetic 3D Solver) program. In 2000, researchers at the University of Ancona, Italy (now Universit Politecnica delle Marche), developed and published new ideas for an EM simulator. At that time, their approaches had only been implemented in non-commercial, academic software aimed at specific problems. Some of their ideas had been published in a text1>; the theory was further developed and subsequently published in technical articles.

At the time, the researchers were seeking a company interested in implementing their algorithms in a commercial product, although they discovered it would not be a straightforward matter because of the readily availability of the intellectual property (IP) in the published text. As a result, the researchers started their own company, Microwave and ElectroMagnetics (MEM) Research, mainly to develop and commercialize a new product embedding the results of their work: the EM3DS software. MEM Research was also founded to provide services, such as research and development (R&D) and design, for companies wishing to outsource these functions, blending the capabilities of the new company's talented young engineers with the experience of its academic staff.

Since its earliest versions, EM3DS has grown in performance and usability, becoming a tool of choice for many MMIC designers, even though the basic philosophy behind the program remains.2> The Ancona researchers have shared the belief of philosopher Karl R. Popper,3> that scientific theory should be submitted to the largest possible audience for "falsification," in order to identify weaknesses and possible failure scenarios. The Ancona researchers reasoned that the best way to seek falsification for their theories was by embedding those theories in a user-friendly software program and allowing the software's users to put those theories to the test.

This approach has worked effectively. Customers for the software, whether small or large, have alerted the software's developers to key issues, linking work performed in an academic environment to the needs of working designers. MEM Research did the rest as part of the software development, testing and linking the algorithms in EM3DS.

As a result, many EM3DS features are unique among EM electromagnetic simulators, such as the capability to couple EM and acoustical/ mechanical models in order to handle such devices as bulk-acoustic-wave (BAW) resonators, or use a transconductive controlled-current source for modeling linear active devices, such as high-electron-mobility transistors (HEMTs) and metal-epitaxialsemiconductor field-effect transistors (MESFETs)4>.

EM3DS (*Fig. 1*) implements a technique known as the Generalized Transverse Resonance/Diffraction Approach (GTRD). It is a frequencydomain technique that involves solving an integral equation by means of an MoM approach. It exploits the Green's function for a metal box and defines metal and dielectric discontinuities by using volume currents. Owing to the use of volume currents, it is basically a 3-D tool; however, a user can shrink volume currents to surface currents to achieve a two-andone- half-dimension (2.5-D) mode of operation. The 2.5-D mode, which is obtained as a limiting case of the 3-D mode, retains many capabilities of the 3-D mode while simplifying the model and significantly reducing the computational load. For some cases, however, such as modeling dielectric resonators (DRs), BAW resonators, or dielectric discontinuities, the 3-D mode is still needed (*Fig. 2*).

For a BAW resonator, for example, EM3DS defines a special kind of dielectric material, where the permittivity and losses are functions of frequency. The frequency behavior of the special material is calculated preliminarily by an acoustic analysis, in which equivalent transmission lines are used to model the acoustic wave propagation. As part of this analysis, a user specifies the mechanical properties of the piezoelectric material, as well as those of the surrounding material stack, in a dialog window, creating a parametric reference to the effective permittivity of the piezoelectric material. Once specified, these parameters can be used in the EM3DS EM solver (*Fig. 3* and *Fig. 4*).

EM3DS allows anything to be parametric. It also allows materials to be defined by entering frequencydependent expressions, with an internal parser helping to create the models. This provides a user with the freedom necessary to create original models. EM3DS analyzes a structure by enclosing it in a metal box. This makes it possible to model shielded structures, and makes the simulation engine extremely accurate, since the enclosed boundary approach provides a high dynamic range. For modeling antennas, absorbing boundaries can be used in place of enclosure top and bottom covers. The 2007 version of EM3DS includes several new graphical charts (polar plots, far-field 2-D charts, far-field 3-D plots) to aid in designing antennas (*Fig. 5*). In addition, top, bottom, and two lateral walls can be replaced with ideal magnetic walls, to be used when modeling symmetric structures. A post-processing tool called "Symmetry Wizard" helps to model symmetrical multiport structures, by combining two simpler simulations in which the symmetry plane is replaced in turn by magnetic and electric planes. Also, the top and bottom of an enclosure in EM3DS can be replaced by an infinite rectangular waveguide, filled with arbitrary materials.

Although structures that are analyzed with EM3DS are enclosed in a box, they are not forced to fit a grid. This makes it possible to more easily import structures from other software programs since GDSII and DXF bidirectional filters are implemented to aid in the transfer of those computeraided- design (CAD) files. This is also useful when using the embedded optimizer, acting directly and continuously on the parameters defining the geometry (*Fig. 6*).

Most MoM programs use specialized Fast Fourier Transform (FFT) methods to quickly fill the Green's function; the price paid is a fixed grid, over which FFT is performed. On the other hand, EM3DS extracts some frequency-independent information from the calculation of the first frequency point (the so-called asymptotic behavior), and reuses it for all other frequency points. As a result, calculation of the first frequency point in EM3DS usually requires more time than when using an FFTbased program, although calculation of the remaining frequencies is faster but nonetheless accurate. This feature is quite useful when using EM3DS's "SmartFit" tool: the software automatically selects the frequencies for performing an EM calculation, searching for the poles and zeros of the frequency response. Once this is performed, the full-band response is recovered by means of the correct rational polynomial for the circuit or structure of interest. This approach also provides an interpretation of the applied polynomials in terms of equivalent circuits, with automated extraction of a wideband lumped-element circuit representation (*Fig. 7*)6> Lumped and distributed elements can be connected to an EM simulation in EM3DS by means of an integrated basic linear circuit simulator (*Fig. 8*).

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Ports in EM3DS are standard "delta gap" ports, namely unit voltage generators are applied across artificial gaps in conductors, and the input admittance is evaluated. Once the admittance (Y) matrix is known, all of the other parameters are calculated from it. There are several kind of ports that can be considered in EM3DS, namely edge ports, via ports, via internal ports, planar internal ports, and differential ports. Edge ports are those defined between a conductor and the metal enclosure; via ports are similar, but defined across vias, namely along the dielectric stack (in a sense, vertical). Internal ports are generally offground ports, useful for a number of functions (such as exciting dipole and slot antennas, characterizing packages, and connecting active devices).

In any case, a port represents a discontinuity to an EM simulator like EM3DS, and in most cases, it is important to remove the discontinuity. For this purpose, EM3DS's developers used a multiport short-open-calibration (SOC) approach that allows a general treatment of a discontinuity without requiring a hypothesis about the kind of port discontinuity.7>

Moreover, if the port is attached to a transmission line, or a set of mutually coupled transmission lines, information about propagation characteristics are recovered according to a previously published algorithm8> Differential ports are handled by a post-processing algorithm, so that they can be defined over existing simulations performed with standard ports. Since the EM3DS enclosure was implemented as a general waveguide calibration approach, it can be used to model some rectangular waveguide components, such as resonant cavities and filters9> A waveguide can be excited by any standard port, to be used as a "strip-to-waveguide" transition. The response of the latter is recovered, and eventually removed, by a calibration process. In EM3DS 2007, this process is also generalized to the case of multiple accessible modes, providing the Generalized Admittance Matrix (GAM) of the transition. The latter has a number of possible intriguing uses as noted in the literature.10> This kind of calibration algorithm is at the early stage of development, and in the near future should lead to a new tool to assist laboratory measurements.

Strategic partnerships and working closely with users are vital to the success of MEM Research. For example, EM3DS is the tool of choice for MEMS developer Coventor (Cary, NC), used in conjunction with the multiphysics tool, Coventorware. Because of the close linking between the two programs, some customers consider EM3DS as part of Coventorware, with data exchanges by means of GDSII code.

MEM Research's partnership with Applied Wave Research (AWR, El Segundo, CA) led to a seamless integration with that firm's Microwave Office software. Common customers of AWR and MEM Research often view EM3DS as an alternative EM simulator to the EM engine in Microwave Office, while exploiting the Microwave Office editor and integrated capabilities with the other programs of the AWR family. Results can be compared, exported and imported using the Touchstone format. Moreover there is the possibility of importing directly in a chart a bitmap coming from scanning any document (useful for direct comparison or data recovery from literature.

EM3DS offers a wide array of charts and plots of currents/fields for data analysis. All plots can be animated over frequency or phase while modifying excitation and termination conditions. Animations can be exported for reuse in presentations or stored in EM3DS documents. This use of animation greatly aids in understanding the results, the quality of mesh, the origin of issues related to undesired couplings, and also in teaching the principles of electromagnetics in microwave design. In fact, EM3DS is used for this last purpose in a number of universities and institutions around the world, due to its intuitive interface and effective post-processing features.

EM3DS was developed to be flexible and, with this in mind, EM3DS 2007 introduces a script engine to access most of the EM3DS features, including the main EM3DS menu. The program employs Object Oriented Pascal scripting, which is intuitive, with an embedded debugger.

When choosing a high-frequency simulator, cost should be considered. Since EM3DS is affordable, small companies can take advantage of its simulation capabilities, while larger companies can add it to their design tools with negligible financial impact. To add to its appeal, EM3DS is available to universities and non-profit organizations on a discounted basis.

Further details about EM3DS can be found on the MEM Research web site at www.memresearch.com.

REFERENCES

1. Tullio Rozzi and Marco Farina, Full-Wave Analysis of Passive and Active Planar Devices, IEE Press, 1999.

2. Steve Marsh, Practical MMIC Design, Artech House, Norwood, MA, 2006, p. 75.

3. Karl R. Popper, The Logic of Scientific Discovery, 1935.

4. Marco Farina, L. Pierantoni, and T. Rozzi, "3D Full-Wave Model of pHEMT in Linear Regime," IEEE Transactions on Microwave Theory & Techniques, Vol. 52, No. 2, February 2004.

5. Marco Farina and Tullio Rozzi, "Electromagnetic Modeling of Thin-Film Bulk Acoustic Resonators," IEEE Transactions on Microwave Theory & Techniques, Vol. 52, No. 11, November 2004, pp. 2496-2502.

6. Marco Farina, Antonio Morini, and Tullio Rozzi, "Broadband Frequency-Domain Electromagnetic Analysis and Automatic Extraction of SPICE-Compatible Equivalent Circuits," IEEE Electron Letters, Vol. 41, No. 22, October 2005.

7. Marco Farina and Tullio Rozzi, "A Short- Open De-Embedding Technique for Method of Moments Based Electromagnetic Analysis," IEEE Transactions on Microwave Theory & Techniques, Vol. 49, No. 4, April 2001, pp. 624-628.

8. Marco Farina, Antonio Morini, and Tullio Rozzi, "On the Derivation of Coupled-Line Models From EM Simulators and Application to MoM Analysis," IEEE Transactions on Microwave Theory & Techniques, Vol. 53, No. 11, November 2005, pp. 3275-3280.

9. Marco Farina and Tullio Rozzi, "On the Extension of Commercial Lanar Circuit CAD Packages to the Analysis of Two-Port Waveguide Components," International Journal of RF and Microwave CAE, Vol. 13, No. 2, February 2003.

10. Marco Farina, A. Morini, and Tullio Rozzi, "A Calibration Approach for the Segmentation and Analysis of Microwave Circuits," IEEE Transactions on Microwave Theory & Techniques, Vol. 55, No. 10, 2007, pp. 2124-2134.