**Authors:** Giacomo Bianconi and Raj Mittra

**Source:** FERMAT, Volume 2, Article 4, Mar.-Apr., 2014

**Abstract:** In this paper we present an efficient
numerical technique, called the Characteristic Basis
Function Method (CBFM), for the electromagnetic
analysis of planar microstrip structures as well as for a
class of three-dimensional scattering problems. In this
method, the original problem geometry is segmented into
smaller regions called blocks, and high-level basis
functions are generated to represent the electromagnetic
characteristics of these sections. These basis functions are
referred to as the Characteristic Basis Functions (CBFs),
and their use leads to a reduced matrix equation system.
Since the method only requires the solution of relatively
small-size matrix equation, both in the process of
generating the CBFs and in the solution of the reduced
matrix, the overall computational burden is reduced in
terms of the memory requirement relative to the
conventional Method of Moments (MoM) approach, and
an acceleration of the solve time is also achieved. The
Characteristic Basis Function Method is next combined
with the Equivalent Medium Approach (EMA) for fast
and efficient design of microstrip circuits etched on
layered media. In particular, the developed EMA method
substitutes the stratified environment with an equivalent
“homogeneous” medium whose Dyadic Green's
Functions (DGF's) can be evaluated analytically. The
above technique yields reliable results and reduces the
computational time in comparison with the conventional
Method of Moments. In the second part of the paper, the
CBFM will be applied to the solution of electromagnetic
scattering problems involving plasmonic nano-rod array
antennas operating in the Terahertz regime. In
particular, the formulation necessary for the analysis of a
single nano-rod is introduced and subsequently
generalized to the case of a double-periodic array and to
the case of a finite randomly tilted array. Several
numerical examples which demonstrate the accuracy and
the efficiency of the described procedures are included,
both for the case of microstrip structures as well as for
the nano-rod antennas.

**Index Terms:** Method of Moments (MoM),
Characteristic Basis Function Method (CBFM), Dyadic
Green's Function (DGF's).

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