We then consider the same substrate with a fixed thickness b equal to [[lambda].sub.0]/70 at the frequency f = 1GHz (i.e., b = 4.28 mm); according to (5), in order to have maximum broadside radiation at f = 1GHz a normalized susceptance [[bar.B].sub.f] = 11.14 is required, which can be obtained, for example, with a ferroelectric film having t = 2 mil and [[epsilon].sub.r2] = 6.68 x [10.sup.3] .
More directive beams can be obtained with thinner substrates (and, accordingly, larger values of the normalized susceptance).
Step 1: Determine the required normalized susceptance slope
where [X.sub.1i]/[Y.sub.0] and [DELTA][f.sub.1-3dBi] are the normalized susceptance slope parameters and 3-dB bandwidths of each T-shaped DMS correspondingly, [X.sub.2i]/[Y.sub.0] and [DELTA][f.sub.2-3dBi] represents the normalized susceptance slope parameters and 3-dB bandwidths of each U-shaped DGS respectively, [C.sub.1i] and [C.sub.2i] are the equivalent capacitances of the defected structures, [L.sub.1i] and [L.sub.2i] are the equivalent inductances of the defected structures, [g.sub.i] are the element values of lowpass prototype, [[OMEGA].sub.c] is the normalized cutoff frequency.
Figure 5 shows the normalized susceptance [B.sub.t]/[A.sub.k] obtained for [f.sub.sk]/[f.sub.pk] 1.1 and [alpha] = 1.
If an equiripple response is imposed both in the passband and in the stopband a suitable placement of the resonators poles is required, However, assume initially that and are not depending on k, so that only two frequenvies -- [f.sub.p] and [f.sub.s] -- specify the susceptance zero and pole for all the resonators If a suit able frequency transformation is found the normalized susceptance [b'.sub.k] [B.sub.k]/[Y.sub.R] of each resonator can be derived from a standard low pass prototype Biter (that is defined once the number n of the resonators and the maximum bandpass attenuation [A.sub.1]m are given)
Hence, the above discussed design methodology can be also applied to implement another stopband design using the MS-DMSs if we can obtain proper dimensions of each MS-DMS unit cell to satisfy the required normalized susceptance
slop parameter of each resonator.
Figure 5 shows the calculated values of the normalized susceptances
anti Figure 6 shows the transmission phases.