A characteristic mode (CM) formulation is developed for the modal analysis of microstrip antennas. It is derived from the mixed-potential integral equation (MPIE) with spatial-domain Green’s functions for multilayered media, where spatial-domain Green’s functions take into account the effect of the multilayered media. The resultant characteristic currents and fields are orthogonal with each other among different orders of modes. Together with the eigenvalues and their deduced indicators, the CMs provide deep physical insights into the radiation mechanisms of microstrip antennas. Numerical results are presented to confirm CM formulation’s effectiveness and accuracy in determining the resonant frequencies, radiating mode currents, and modal fields of microstrip antennas. As opposed to the very popular CM formulation for conducting bodies, comparative studies are presented to show the quite different modal analysis results by considering the multilayered media.

Microstrip antennas (MSAs) have gained great interest in modern wireless communications due to their attractive features such as low profile, light weight, and ease of fabrication. Nevertheless, MSAs usually have narrow bandwidths and can only operate effectively in the vicinity of resonant frequencies. Therefore, it is important to accurately determine the resonant frequencies of MSAs. Moreover, obtaining the radiating modes of MSAs is also of great importance for practical designs. A number of methods have been proposed to determine resonant frequencies of MSAs. These methods can be generally classified into analytical and numerical methods. Analytical methods such as cavity models [

Recently, the characteristic mode (CM) theory [_{10} mode for rectangular patch antennas with air substrate is analyzed using the CM theory for conducting bodies. Similarly, U-slot and E-shaped MSAs with air substrate were also analyzed using the CM theory for conducting bodies [

This paper develops a CM formulation from the mixed-potential integral equation (MPIE). Spatial-domain Green’s functions (GFs) of multilayered media are used in the MPIE to account for the effect of multilayered media. Numerical results are given to show the accuracy of the proposed CM formulation. Comparative studies are also given to show the limitations of the CM theory of conducting bodies in the modal analysis of MSAs with nonair dielectric substrate.

The conventional CM theory was initially developed by Garbacz and Turpin [

The MPIE with spatial-domain GFs of multilayered media (infinite in transverse directions) allows accurate modeling surface currents in multilayered media environment [

After the spatial-domain GFs is calculated, the MPIE can be easily discretized using the MoM procedure. By applying the standard Galerkin’s procedure to the MPIE with using the RWG basis functions

The characteristic current is generally normalized according to

The electric field

In practical radiation problems, the radiating field of a microstrip antenna is of finite extent. If we choose the radiation surface

Let

Apparently, characteristic mode with

Other than the eigenvalues tell how the mode can be efficiently excited for radiation purpose, modal significance is also a popular indicator in understanding resonant behaviors:

To confirm the validity of the MPIE based CM theory, MSAs with single layered and three-layered dielectric substrates are investigated. Comparative study is performed to intuitively show the differences between the CM theory of conducting bodies and the MPIE based CM theory for multilayered media.

A rectangular MSA with dimensions of ^{2} was analyzed from 0.8 GHz to 2.2 GHz. The patch is printed on a grounded dielectric substrate with relative permittivity _{10}, TM_{01}, TM_{11}, and TM_{20} resonate at 1.075 GHz, 1.605 GHz, 1.955 GHz, and 2.145 GHz, respectively. These modes have proved to be the natural radiating modes that can be physically excited at their own resonant frequencies.

To clearly demonstrate the effectiveness of the proposed approach, a comparison study among three different models is carried out. In the first model, only an isolated rectangular patch in free space is considered. This model has been used for CM analysis of MSA in [

Modal significances for the same rectangular patch but with different dielectric substrate and ground plane configurations.

Modal significances for isolated rectangular patch in free space

Modal significances for rectangular patch with ground plane. The space between the patch and the ground plane is filled with air (

Modal significances for rectangular patch with grounded dielectric substrate (

To investigate the effect of the ground plane, the second model which consists of a rectangular patch and an infinite ground plane is considered for CM analysis. The patch size is the same as that in the first model. The space between the patch and the ground plane is filled with air and the distance between them is 1.524 mm. Figure

To fully consider the true configurations of the MSA, the dielectric material (

However, rectangular MSAs with grounded dielectric substrates were previously analyzed using the CM formulation of conducting bodies [

Figure

The characteristic currents and fields of the rectangular patch with grounded dielectric substrate (

TM_{10} (1st mode)

TM_{01} (2nd mode)

TM_{11} (3rd mode)

TM_{20} (4th mode)

For comparison purpose, the characteristic currents and fields solved from the first model (an isolated rectangular patch in free space) are plotted in Figure _{10}, TM_{01}, TM_{11}, and TM_{20}, respectively. This is the reason that the CM theory of conducting bodies can be used to roughly predict the modal behavior of MSAs. On the other hand, the 3rd and 6th modes do not appear in the MPIE based CM analysis results. They are defined as the inductive modes in [

The characteristic currents and fields of the rectangular patch in free space.

1st mode

2nd mode

3rd mode

4th mode

5th mode

6th mode

Although CM theory for PEC bodies [

Modal significances (a) and characteristic angles (b) for the dual-band CP antenna.

Figures

Figure

Characteristic currents and fields for (a) 1st mode, (b) 2nd mode, (c) 3rd mode, and (d) 4th mode. In figures (a)–(d), the left figure shows the characteristic currents on the top patch, while the right figure shows the characteristic currents on the bottom patch.

In summary, the modal significance, characteristic angle, and characteristic currents clearly illustrate that CP radiation can be realized by properly exciting and combining coresonant CMs. Dual-band performance is also observed from the CM analysis results.

The CM theory based on the MPIE with spatial-domain GFs for multilayered media is proposed for the modal analysis of microstrip antennas with multilayered media. Against the conventional CM theory in [

The authors declare no conflict of interests regarding the publication of this paper.

This work is supported by the Natural Science Foundation of China under Grant no. 61671127.