compare the ABCD matrix of a series inductor with the ABCD matrix of a short transmission line (Ramo [1994]), in order to obtain the proper length of transmission line between the shunt capacitors (sub-resonant FSS layers) to produce a Butterworth filter response. It is well known that a series inductor represents an approximate lumped circuit model of a short transmission line, and we'll exploit this equivalence to determine the required thickness of the air spacers. With the thickness of the air spacers between sheets now determined, the equivalent circuit now takes on the form shown in Fig. 3.1.4-1: Second transformation: Replace shunt capacitors with capacitive patch FSS below resonance Now the only thing left to do is to find the lowpass FSS that yields the shunt capacitance values called out in Fig. 2.3.1-4. This is usually done through trial and error. Fitting a shunt capacitor to a real FSS is done by repeated running of a first principles code to match the reflection response of the shunt capacitor with the reflection from a capacitive FSS. Patch-type FSS below resonance will produce a capacitive shunt admittance equivalent circuit, with closer packing of elements in the FSS sheet yielding higher shunt capacitance values in the equivalent circuit. Examples FSS can seemingly take on a nearly infinite number of forms, depending on the application. And now FSS are being used in the development of certain classes of meta-materials. Classification: by form or by function FSS are typically resonance region structures (wavelength comparable to element size and spacing). FSS can be classified either by their form or by their function. Morphologically, Munk (Munk [200]) classified FSS elements into 2 broad categories: those that are "wire-like" (one-dimensional) and those that are "patch-like" (two-dimensional) in appearance. His lifelong preference was for the one-dimensional wire-like FSS structures, and they do seem to have advantages for many applications. Frequency selective surfaces, as any type of filter, may also be classified according to their function, and these usually fall into 3 categories: low-pass, high-pass and bandpass, in addition to band-stop filters. FSS may be made to be absorptive as well, and absorption is usually over some frequency band. Elements A number of FSS scatterer configurations are now known, ranging from early types such as resonant dipoles, disks and squares to crossed dipoles, Jerusalem crosses, four-legged loaded slots and tripoles, Low-pass The FSS reflection and transmission properties are determined by