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APRIL 2021 I DESIGN007 MAGAZINE 63 Conclusion In summary (and how I typically use these programs), I will use the closed form equation soware as an approximate tool and use the field solver for doing the detailed design work. I use the closed form calculators in the begin- ning of the design phase to go through the vari- ous tradeoffs when considering different high frequency circuit materials, thicknesses, con- ductor widths, RF structures, etc. Once I have the basic circuit defined from using the closed form equation soware, the detailed work will be done using a field solver. However, when using MWI-2019 closed form equation soware, and if I am just evaluating a simple microstrip transmission line circuit, I usually do not need a field solver because MWI-2019 is very accurate for that type of circuit and for many years I have received good correlation between the soware and measured results. DESIGN007 References 1. 2. "Accurate models of computer aided microstrip design," E. Hammerstad and O. Jensen, IEEE MTT-S Symposium Digest, p. 407, May 1980. 3. "Multi-GHz, Causal Transmission Line Modeling Methodology with a Hemispherical Surface Rough- ness Approach," S.H. Hall, S.G. Pytel, P.G. Huray, D. Hua, A. Moonshiram, G. Brist, and E. Sijercic, IEEE Transactions on Microwave Theory and Techniques, December 2007, pp 2614–2624. 4. "Measurements of microstrip effective relative permittivities," S. Deibele and J.B. Beyer, IEEE Trans. Microwave Theory Tech., vol. MTT-35, pp. 535-538, May 1987. 5. "Accurate model for effective dielectric con- stant of microstrip with validity up to millimeter- wave frequencies," M. Kirschning and R.H. Jansen, Electronics Letters, Vol. 18, No. 6, p. 272-273, March 1982. John Coonrod is technical marketing manager at Rogers Corporation. To read past columns or contact Coonrod, click here. ate accurate results. However, the connector transition, from the connector(s) to the PCB, is a 3D problem to solve and a 3D field solver would be the right choice. For the experiments that I do, I understand the connector transition quite well (usually) from many years of experi- ence; because of that I can use a 2D field solver to solve my design issues on the PCB that I'm evaluating. e 2D field solvers nowadays are typically referred to as 2.5D or planar 3D and the true 3D field solvers are typically referred to as arbi- trary 3D field solving. Again, these descrip- tions are admittedly simplified but a planar 3D field solver will solve Maxwell's equations using method of moments (MoM) and an arbi- trary 3D field solver will also solve Maxwell's equations but the soware may use finite ele- ment Analysis (FEA), using a mesh that is three-dimensional. e mesh is the analysis grid of the circuit to be modeled and is used to solve Maxwell's equations at discrete points, as well as how each of these points can inter- act with its neighboring point. ese points make up the grid or mesh. An arbitrary 3D field solver will use a three-dimensional grid that will have the shape of a tetrahedron (four- sided) or maybe a hexahedron (six-sided) grid element. e arbitrary 3D solver will use these connected grid elements for everything in the circuit such as conductor layers, dielectric lay- ers, air, etc. However, a planar 3D solver will use a planar grid (mesh) and it will be applied for the conductor layers only. e fields will still be solved in 3D for the planar 3D so- ware, but solutions will be between the differ- ent conductor features, and so the dielectric material between these conductors will cer- tainly have an influence. ere are tricks that can be done with planar 3D field solving to get a circuit solution similar to arbitrary 3D so- ware, such as for a circuit conductor; one can build up layers of conductors to form the over- all circuit conductor which may be very thick and coupled to another thick conductor, as an example.

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