most of the electric lines reside in the substrate and parts of some lines exist in air. As W/h1 and 1, the electric lines concentrate mostly in the substrate. Fringing in this case field makes the microstrip line look wider electrically compared to its physical dimensions. Since some of the waves travel in the substrate and some in air, an effective dielectric constant is introduced to account for fringing and the wave propagation in the line [1]. Figure 2.3 Microstrip line and its electric field lines, and effective dielectric constant The effective dielectric constant is defined as the dielectric constant of the uniform dielectric material so that the line of Figure 2.3(c) has identical electrical characteristics, particularly propagation constant, as the actual line of Figure 2.2(a). Effective Length, Resonant Frequency, and Effective Width Because of the fringing effects, electrically the patch of the microstrip antenna looks greater than its physical dimensions. For the principal E-plane ( plane), this is demonstrated in Figure 2.4(a) where the dimensions of the patch along its length have been extended on each end by a distance , which is a function of the effective dielectric constant and the width-to height ratio (w/h) [1]. Figure 2.4 Physical and effective lengths of rectangular microstrip patch Since the length of the patch has been extended by on each side, the effective length of the patch is now (L= for for dominant mode with no fringing) For the dominant mode, the resonant frequency of the microstrip antenna is a function of its length. Usually given by is the speed of light in free-space. Since (2-5) does not account for fringing, it must be modified to include edge effects and should be computed using where
field most of the electric lines reside in the substrate and parts of some lines exist in air. As W/h1 and 1, the electric lines concentrate mostly in the substrate. Fringing in this case makes the microstrip line look wider electrically compared to its physical dimensions. Since some of the waves travel in the substrate and some in air, an effective dielectric constant is introduced to account for fringing and the wave propagation in the line [1]. Figure 2.3 Microstrip line and its electric field lines, and effective dielectric constant The effective dielectric constant is defined as the dielectric constant of the uniform dielectric material so that the line of Figure 2.3(c) has identical electrical characteristics, particularly propagation constant, as the actual line of Figure 2.2(a). Effective Length, Resonant Frequency, and Effective Width Because of the fringing effects, electrically the patch of the microstrip antenna looks greater than its physical dimensions. For the principal E-plane ( plane), this is demonstrated in Figure 2.4(a) where the dimensions of the patch along its length have been extended on each end by a distance , which is a function of the effective dielectric constant and the width-to height ratio (w/h) [1]. Figure 2.4 Physical and effective lengths of rectangular microstrip patch Since the length of the patch has been extended by on each side, the effective length of the patch is now (L= for for dominant mode with no fringing) For the dominant mode, the resonant frequency of the microstrip antenna is a function of its length. Usually given by is the speed of light in free-space. Since (2-5) does not account for fringing, it must be modified to include edge effects and should be computed using where
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