Wireless Communications

Characteristic Modes based Antenna Analysis

CMC 2015 (Characteristic Mode Computation):

 

mode_animation

The Characteristic Mode calculation for an arbitrary shaped geometry requires the impedance matrix which can be calculated by the Method of Moments (MoM). In order to investigate and optimized integrated antennas a MATLAB based tool CMC has been programmed. This program has grown in the last years and becomes a power full tool, as it has been proved in certain research projects (e.g. MIMO or Automotive Application – project: KoAMo). The current version exploits the EFIE (Electric Field Integral Equation), MFIE (Magnetic Field Integral Equation) and the PMCHWT formulation for lossy dielectric and magnetic bodies. The surface current is the main quantity, which is used to analyze the radiation mechanism based on the equivalence principle. The popular RWG (Rao-Wilton-Glisson) basis function is used to mesh the entire surfaces into plane triangles.

The graphical user interface is programmed in MATLAB and the aid of the MSDN library. The visualization of the 3D objects and the plots are realized in OpenGL (TaoFramework: freeware, available “www.sourceforge.net/projects/taoframework/”). The software owns a CAD interface and an internal mesh algorithm for the propose of the characteristic mode calculation.

The main features of the software are:

         -          CAD Interface is included

         -          Mesh of the surface into triangles

         -          MoM matrix calculation with EFIE/MFIE and PMCHWT

         -          Import STL and GMSH files

         -          Characteristic Mode Decomposition

         -          Lossy dielectric and magnetic materials

         -          Lumped sources and plane wave excitation

         -          Lumped impedances can be added

         -          Define infinite size ground plane

         -          Q-Factor calculation

         -          Calculate correlation for multi port antenna systems

         -          Lumped impedance matching network can be connected with lumped feed ports

         -          Eigenvalue tracking with correlation and orthogonalization based algorithm

         -          Adaptive frequency control for eigenvalue tracking

         -          Power coefficient

 

 

Theory:

The Theory of Characteristic Modes has been derived by Garbacz in 1971first, and it is a useful method to decompose the complex current distribution of an antenna into its fundamental modes. The radiation properties of these modes are often much simpler to understand than the complex entire current distribution.

tcm1
The numerical evaluation of the characteristic modes requires the impedance matrix, which is typically obtained by the Method of Moments. Once the impedance matrix is available, the generalized eigenvalue equation can be applied.

 

eigenvalue_eq
R and X are the real and imaginary part of the impedance matrix of the structure, respectively.

 

Reconstruction:

As other software, e.g. Empire XCcel, are used for antenna design the characteristic modes cannot be calculated, as the impedance matrix is usually not available. In order to overcome this drawback a reconstruction is needed, which approximates the impact of the characteristic modes by the radiated far field. A mathematical concept to reconstruct the characteristic modes of a complex structure, treated with Empire, and the general knowledge about the modes on a simplified structure, treated with MGUI, has been developed. The approach is based on the assumption that the complex antenna contains the same modes as the simplified structure. The envelope correlation allows for a simple estimation of the coefficients of modes and, therefore, the contribution into the overall power budget.


                          tcm4

 

Reconstruction of a rectangular plate excited by a plane wave polarized along the major axis for six significant characteristic modes. The lines denote the normalized coefficient of the reference calculated with CMC. The dashed lines denote the reconstruction with the method. The result is scaled in |bn| [dB] = 20 log10(|bn|).

 

Impedance Matching Network in CMC:

From earlier publications, it is widely known that the placement of lumped elements, e.g. at the port position, have a significant influence on the mode excitation and the impedance matching of the respective ports. In common antenna designs the input impedance at the front-end of the port is matched with an additional impedance matching network to achieve the required bandwidth at the frequency bands of interest. The reactive network, which is typically designed out of capacitances and inductances, shifts the resonance of the characteristic modes down and up in frequency. The characteristic modes under the influence of such network can be calculated with some MoM impedance matrix modifications.

For this, a simple dipole antenna is assumed, which is placed in free space. The dipole is feed in the center, as denoted in the below figure.

dipole

 The matching network is added in the MoM impedance matrix with:
 matching_network

 

With the aid of this modified matrix the characteristic modes under the influence of the impedance matching network can be analyzed. The same principle can be used if lossy components are included in the network. The next figure shows the eigenvalue of the new modified characteristic modes of the dipole.

eigenvalue

Publications:
 
  1. Safin, E., Martens, R. and Manteuffel, D. , "Modal Source Reconstruction Based on Radiated Far-Field for Antenna Design", In Antennas and Propagation (EUCAP), 2012 6th European Conference on., march, 2012. , pp. 1645 -1649. DOI
    [Abstract]
     
    We present a mathematical technique to reconstruct the modal current distribution on arbitrary antennas from the radiated far-field and general knowledge about the modes involved. The method leads to good results if the radiation mechanism of the actual antenna can be approximated by the current distribution on a simplified structure. The current distribution of the simplified structure is decomposed into its characteristic modes and the related modal far-field is calculated. Assuming that the far-field of the actual antenna contains the same modes, their weighting coefficients are calculated by comparing the far-field of the actual antenna to the modal far-field of the simplified structure. It can be shown that the weighting coefficients of all significant modes can be reconstructed with good accuracy.
    [BibTeX]
     
    @inproceedings{6205814,
      author = {Safin, E. and Martens, R. and Manteuffel, D.},
      title = {Modal source reconstruction based on radiated far-field for antenna design},
      booktitle = {Antennas and Propagation (EUCAP), 2012 6th European Conference on},
      year = {2012},
      pages = {1645 -1649},
      doi = {10.1109/EuCAP.2012.6205814}
    }

  2. Safin E. and Manteuffel, D. , "Resonance Behaviour of Characteristic Modes Due to the Presence of Dielectric Objects", In Antennas and Propagation (EUCAP), 2013 7th European Conference on., April 2013.
    [Abstract]
     
    In this paper we present a modal analysis of dielectric bodies of arbitrary shape. The problem of a dielectric body is reformulated into equivalent electric and magnetic surface currents. Using the weighed eigenvalue equation the characteristic modes of the equivalent problem are calculated. A physical interpretation of the eigenvalue of the dielectric characteristic modes is presented and discussed.

  3. Safin, E. and Manteuffel, D. , "Reconstruction of the Characteristic Modes on an Antenna Based on the Radiated Far Field,", Antennas and Propagation, IEEE Transactions on , vol.61, no.6, pp.2964,2971, June 2013. DOI 
    [Abstract]
     
    In this paper, we present a method to reconstruct the modal current distribution on an antenna from the radiated far field and general knowledge about the modes involved. The method leads to good results if the radiation mechanism of the antenna can be approximated by the current distribution on a simplified structure. The current distribution of the simplified structure is decomposed into its characteristic modes and the related modal far field is calculated. Assuming that the far field of the actual antenna contains the same modes, their weighting coefficients are calculated by comparing the far field of the actual antenna to the modal far field of the simplified structure. It can be shown that the weighting coefficients of all significant modes can be reconstructed with good accuracy even for complex real structures such as mobile phones.
    [BibTeX]
     
    @ARTICLE{6473830,
    author={Safin, E. and Manteuffel, D.},
    journal={Antennas and Propagation, IEEE Transactions on},
    title={Reconstruction of the Characteristic Modes on an Antenna Based on the Radiated Far Field},
    year={2013},
    volume={61},
    number={6},
    pages={2964-2971},
    abstract={In this paper, we present a method to reconstruct the modal current distribution on an antenna from the radiated far field and general knowledge about the modes involved. The method leads to good results if the radiation mechanism of the antenna can be approximated by the current distribution on a simplified structure. The current distribution of the simplified structure is decomposed into its characteristic modes and the related modal far field is calculated. Assuming that the far field of the actual antenna contains the same modes, their weighting coefficients are calculated by comparing the far field of the actual antenna to the modal far field of the simplified structure. It can be shown that the weighting coefficients of all significant modes can be reconstructed with good accuracy even for complex real structures such as mobile phones.},
    keywords={Antennas;Correlation;Current distribution;Eigenvalues and eigenfunctions;Equations;Mathematical model;Surface impedance;Antenna radiation pattern;antenna theory;eigenvalues and eigenfunctions;mobile antennas;numerical analysis},
    doi={10.1109/TAP.2013.2251312},
    ISSN={0018-926X},},
    }