Alexander Sychev, Mikhail Chekalin, Vasily Shestakov


Computer aided microstrip structures modeling has been performed by conformal mapping technique. A new approach to reduce the connectivity order of the original cross-section geometry of the structure is proposed. The multiply connected domain
is reduced to simply connected ones by implementation of magnetic slits concept. The microstrip structures analysis is carried out by numerical conformal transformations technique realized in Schwarz–Christoffel toolbox for MATLAB. This technique is applied to the quasi-static analysis of coupled microstrip lines taking into account the conductor thickness. Described approach ensures high numerical efficiency and can be used for accurate analysis of complex microstrip structures.

Full Text:



Field modeling of a multiconductor digital bus / H. Yordanov, M. Ivrlac, J. Nossek, P. Russer // Proceedings of the 37th European Microwave Conference, October 8─12, 2007. ─ Munich, Germany, 2007. ─ P. 1377─1380.

Sychev A. N., Chekalin M. E. Numerical conformal transformations technique for analysis of the microstrip structures // Proceedings of 21st International Crimean Conference “Microwave & Telecommunication Technology”, September 12─16, 2011. ─ Sevastopol: Weber, 2011. ─ P. 216─218.

Sychev A. N., Dolgushin M. E. Analysis of the broadside coupled lines on the vertical substrate using the numerical conformal transformations // Proceedings of 20th International Crimean Conference “Microwave & Telecommunication Technology”, September 13─17, 2010. ─ Sevastopol:

Weber, 2010. ─ P. 636─638.

Ghione G., Goano M. Revisiting the partial-capacitance approach to the analysis of coplanar transmission lines on multilayered substrates // IEEE Transactions on Microwave Theory and Techniques. ─ 2003. ─ Vol. 51, N. 9. ─ P. 2007─2014.

A general conformal-mapping approach to the optimum electrode design of coplanar waveguides with arbitrary cross section / M. Goano, F. Bertazzi, P. Caravelli, G. Ghione, T. Driscoll // IEEE Transactions on Microwave Theory and Techniques. ─ 2001. ─ Vol. 49, N. 9. ─ P.


Teppati V., Goano M., Ferrero A. Conformal-mapping design tools for coaxial coupler with complex cross section // IEEE Transactions on Microwave Theory and Techniques. ─ 2002. ─ Vol. 50, N. 10. ─ P. 2339─2345.

Sychev A. N. A simple technique of enclosed subregions for CAD models of shielded multilayer/multiconductor coplanar coupled lines // Proceedings of Asia-Pacific Microwave Conference, December 2002 ─ Kyoto, Japan, 2002. ─ Vol. 1. ─ P. 85─88.

Sychev A. N. Combined method of partial capacitances and conformal mapping for analysis of multimode stripline structures. ─ Tomsk: TUSUR Publisher, 2007. ─ 138 p. [in Russian].

Zehentner J. Characteristic impedance and effective permittivity of modified microstrip line for high power transmission // IEEE Transactions on Microwave Theory and Techniques. ─ 1987. ─ Vol. 35, N. 7. ─ P. 615─620.

Wheeler H. A. Transmission line properties of parallel strip separated by dielectric sheet // IEEE Transactions on Microwave Theory and Techniques. ─ 1965. ─ Vol. 13, N. 3. ─ P. 172─185.

Wan С. Analytically and accurately determinated quasi-static parameters of coupled microstrip lines // IEEE Transactions on Microwave Theory and Techniques. ─ 1996. ─ Vol. 44, N. 1. ─ P. 75─80.

Callarotti R., Gallo A. On the solution of a microstripline with two dielectrics // IEEE Transactions on Microwave Theory and Techniques. ─ 1984. ─ Vol. 32, N. 4. ─ P. 333─339.

Lavrik V. I., Fil’chakova V. P., Yashin A. A. Conformal mapping of physic-topological models / Ed. by Yu. A. Mitropol’sky. ─ Kiev: Naukova Dumka, 1990. ─ 376 p. [in Russian].

Driscoll T. SC toolbox for MATLAB. http://

Driscoll T. A. Algorithm 756: A MATLAB toolbox for Schwarz–Christoffel mapping // AMC Transactions on Mathematical Software. ─ June 1996. ─ Vol. 22, N. 2. ─ P. 168─186.

Driscoll T. A. Algorithm 843: Improvements to the Schwarz–Christoffel Toolbox for MATLAB // ACM Transactions on Mathematical Software. ─ June 2005. ─ Vol. 31, N. 2. ─ P. 239─251.

Crowdy D. G. The Schwarz–Christoffel mapping to bounded multiply connected polygonal domains // Proceedings of the Royal Society, A 461. ─ 2005. ─ P. 2653─2678.

Crowdy D. G. The Schottky–Klein prime function on the Schottky double of planar domains // Computational Methods and Function Theory. ─ 2010. ─ Vol. 10, N. 2. ─ P. 501─517.

LINPAR for Windows: Matrix parameters for multiconductor transmission lines / A. Djiordjevic, M. B. Bazdar, T. K. Sarkar, R. F. Harrington // Software and user’s manual. ─ 1995.



  • There are currently no refbacks.