Characteristic mode analysis
Characteristic modes (CM) form a set of functions which, under specific boundary conditions, diagonalizes operator relating field and induced sources.
Under certain conditions, the set of the CM is unique and complete (at least theoretically) and thereby capable of describing the behavior of a studied object in full.
This article deals with characteristic mode decomposition in electromagnetics, a domain in which the CM theory has originally been proposed.
CM decomposition was originally introduced as set of modes diagonalizing a scattering matrix.
[1][2] The theory has, subsequently, been generalized by Harrington and Mautz for antennas.
[3][4] Harrington, Mautz and their students also successively developed several other extensions of the theory.
[5][6][7][8] Even though some precursors[9] were published back in the late 1940s, the full potential of CM has remained unrecognized for an additional 40 years.
The subsequent boom of CM theory is reflected by the number of prominent publications and applications.
For simplicity, only the original form of the CM – formulated for perfectly electrically conducting (PEC) bodies in free space — will be treated in this article.
The electromagnetic quantities will solely be represented as Fourier's images in frequency domain.
The scattering of an electromagnetic wave on a PEC body is represented via a boundary condition on the PEC body, namely with
representing unitary normal to the PEC surface,
representing incident electric field intensity, and
representing scattered electric field intensity defined as with
The governing equation of the CM decomposition is with
being real and imaginary parts of impedance operator, respectively:
is defined by The outcome of (1) is a set of characteristic modes
Clearly, (1) is a generalized eigenvalue problem, which, however, cannot be analytically solved (except for a few canonical bodies[11]).
Therefore, the numerical solution described in the following paragraph is commonly employed.
and using a set of linearly independent piece-wise continuous functions
to be represented as and by applying the Galerkin method, the impedance operator (2) The eigenvalue problem (1) is then recast into its matrix form which can easily be solved using, e.g., the generalized Schur decomposition or the implicitly restarted Arnoldi method yielding a finite set of expansion coefficients
The properties of the CM decomposition are investigated below.
The properties of CM decomposition are demonstrated in its matrix form.
represents an arbitrary surface current distribution, correspond to the radiated power and the reactive net power,[12] respectively.
The following properties can then be easily distilled: then spans the range of
In reality, the Rayleigh quotient is limited by the numerical dynamics of the machine precision used and the number of correctly found modes is limited.
This last relation presents the ability of characteristic modes to diagonalize the impedance operator (2) and demonstrates far field orthogonality, i.e., The modal currents can be used to evaluate antenna parameters in their modal form, for example: These quantities can be used for analysis, feeding synthesis, radiator's shape optimization, or antenna characterization.
The number of potential applications is enormous and still growing: The prospective topics include CM decomposition has recently been implemented in major electromagnetic simulators, namely in FEKO,[42] CST-MWS,[43] and WIPL-D.[44] Other packages are about to support it soon, for example HFSS[45] and CEM One.
[46] In addition, there is a plethora of in-house and academic packages which are capable of evaluating CM and many associated parameters.
CM are useful to understand radiator's operation better.
