frequencies between the first and second resonance), the object will reflect little energy. So, this resonance phenomenon observed with dipoles and patches leads naturally to the notion of modeling them as a resonant circuit connected in parallel across a transmission line - in this case the element is a series connection of a capacitor and inductor, which produces a reflective short circuit at resonance. This type of structure would be known as a band-reject or band-stop filter. Bandpass filters may be constructed using apertures in conducting planes, which are modeled as a shunt element consisting of a parallel connection of an inductor and a capacitor. One-dimensional line gratings can be modeled as shunt inductors (for polarization parallel to the lines) or shunt capacitors (for polarization perpendicular to the lines). Tightly packed "gangbuster" dipole arrays are lowpass structures that can be modeled using shunt capacitors. Resonant circuit R,L,C values must be determined from first principles analysis The exact circuit topology and element values of an equivalent circuit for a FSS sheet have to be determined using first-principles codes. A bandpass mesh-type FSS sheet is a parallel connection of L,C and bandstop patch-type FSS sheet is a series connection of L,C and in both cases, the L,C values are determined from the center frequency and bandwidth of the filter. Reflection and transmission properties of bandpass and bandstop FSS and equivalent circuits – introduction The equivalent transmission line circuit models for FSS came into being from the observation that FSS yield reflection and transmission properties that are very similar to the reflection and transmission properties of inductors and capacitors placed in parallel across a transmission line. Bandstop FSS filter equivalent circuit and reflection response The two fundamental types of FSS are shown in Fig. 2.4.1-1 to the right - the bandpass mesh-type FSS and the bandstop patch-type FSS (Metal-mesh optical filters). The equivalent circuit for a patch-type bandstop FSS is shown in Fig. 2.4.1-2. The impedance of the series connection of the inductor and the capacitor is (Desoer, Kuh [1984]): or, and this series connection of an inductor and capacitor produces a zero impedance (short circuit) condition when At the short circuit condition, all incident energy is reflected, and so this is the equivalent circuit of a resonant patch bandstop filter. The magnitude of the reflection coefficient is: where Z0 is the characteristic impedance of the transmission line. The frequencies for the upper