Firas Mohammed Ali
Al-Raie
Department Head
The Polytechnic Higher Institute of Yefren, Libya,
Department of Electronic Engineering,
e-mail: firas@ieee.org

Microstrip lines are commonly used in microwave circuits, although their performance is subject to the type of substrate material selected for a printed-circuit board (PCB). One of the more important material parameters for the substrate is the relative dielectric constant, which should be known before designing a high-frequency, microstrip-based circuit. What follows is a simple and practical method for estimating the relative dielectric constant of a microstrip substrate based on well-known microstrip line empirical equations.

Microstrip transmission lines consist of a strip conductor and a ground metal plane separated by a dielectric medium (Fig. 1). The dielectric material serves as a substrate and it is sandwiched between the strip conductor and the ground plane. Typical substrate materials include alumina, silicon, and polytetrafluoroethylene (PTFE).1 Important physical parameters of the microstrip line include the line width, W, substrate height, h, strip conductor thickness, t, and substrate relative dielectric constant, e_r. Important electrical parameters for microstrip line design are the characteristic impedance, Z_o, the guide wavelength, λ_g, and the attenuation constant, ?.

The electromagnetic (EM) field lines in the microstrip line are not contained entirely in the substrate but also propagate outside of the microstrip (Fig. 2). Therefore, the propagating mode in the microstrip line is not a pure transverse-electromagnetic (TEM) mode but, rather, a quasi-TEM. The phase velocity in the microstrip line is given by:

where:

c = the speed of light and e_re = the effective dielectric constant of the microstrip line.

The value of e_re is significantly lower than that of e_r when the fields external to the substrate are taken into account. The guide wavelength, λ_g is related to the free-space wavelength, λ, as shown by Eq. 2:

Available numerical methods for the characterization of microstrip lines involve extensive computations. Closed-form expressions are necessary for the computer-aided design (CAD) and optimization of microstrip circuits. The closed-form expressions for Z_o and e_re apply to the following two sets of conditions2:

For W/h ≤ 1,

where:

And for W/h ≥ 1,

where:

These expressions provide accuracy of better than 2 percent.