New design formulas for microstrip transmission lines using high‐dielectric substrate

Mohamed Lamine Tounsi (Instrumentation Laboratory, Faculty of Electrical Engineering, U.S.T.H.B University, Algiers, Algeria)
Mustapha C.E. Yagoub (School of Information Technology and Engineering (SITE), University of Ottawa, Ottawa, Ontario, Canada)
Brahim Haraoubia (Instrumentation Laboratory, Faculty of Electrical Engineering, U.S.T.H.B University, Algiers, Algeria)



Characterisation and use of dielectric materials with high permittivity are one of the most developed areas of research in microwave circuit simulation. This is mainly because of their various applications in VHF/UHF and microwave frequencies (correlators, instrumentation systems, …). The primary virtue of high‐dielectric substrates for microwave circuits is the reduced size. Since the high dielectric microstrip line also exhibit low loss and useful impedance range, this class of circuits will undoubtedly find wide applications in microwave integrated circuitry.


Owing to the complexity of the electromagnetic problem, numerical methods become an indispensable tool for analysis and modeling of electromagnetic structures. They are the basis to set‐up computer‐aided design (CAD) packages. These models must be accurate, reliable, easily extracted and need limited computational requirements. Since there was a demand for a model able to describe these parameters accurately, an extension of the spectral domain approach (SDA) is proposed for microstrip lines with high permittivity. The analysis is based on the solution of a system of algebraic equations, which are derived from Galerkin's technique in the spectral domain.


Analytical expressions are deduced by curve‐fitting techniques. These expressions can be easily implemented in a CAD simulation tool to design wireless communication components. In this paper, we have developed accurate and suitable general expressions for characteristic parameters for a wide range of εr between 1 and 500. The computed results were compared to those available in the literature when possible. In order to validate our models for high values of dielectric constant (128 < εr<500), neural models were generated for the characteristic impedance and effective permittivity. A very good agreement is demonstrated.


The originality of this paper consists on the development of design formulas to characterise the microstrip lines with high dielectric constant substrate. Closed form equations are almost non‐existent in the technical literature since the available design formulas have been developed only for dielectric media value εr not exceed 128.



Lamine Tounsi, M., Yagoub, M.C.E. and Haraoubia, B. (2005), "New design formulas for microstrip transmission lines using high‐dielectric substrate", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 24 No. 1, pp. 15-34.

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