5/30/2023 0 Comments Vibrating strings theory![]() This method can calculate the eigenvalues and eigencurrents in a large frequency band from a single FDTD run, but it is only valid when one single mode dominates at each resonance. The eigenvalues, on the other hand, are defined as the inner product of the corresponding eigencurrents and eigenpatterns. The eigencurrents are then calculated by discrete Fourier transform (DFT) or fast Fourier transform (FTT) of the surface currents stored at each time step. The main idea is to set up an initial electric field excitation with a random spatial distribution in FDTD, and calculate the induced electric and magnetic fields on the antenna at each time step. proposed to combine the CMA and finite-difference time-domain (FDTD) method to calculate the eigenvalues and eigencurrents of microstrip patch antennas. Therefore, very few works ever consider the modal behaviors in time domain (TD) till now. To obtain CMA results in a frequency band, the eigencurrents and eigenvalues are first computed at discrete sampling frequencies, and then they are processed by some mode tracking routines. CMA is based on the time-harmonic framework, i.e., in frequency domain. Physical insights carried by the eigencurrents and eigenvalues are useful for understanding the radiator and further assisting its design. This work expands largely the field of characteristic mode and may find applications for scattering and antennas.Ĭharacteristic mode analysis (CMA) finds applications in antenna analysis, design, and synthesis. In addition, the temporal modal analysis with excitations is presented, and its potential applications are discussed with emphasis on the analyzing and optimizing transient behaviors of antennas. A frequency-independent condition is discussed and verified for small objects, and it results in a band-limited constraint. To further demonstrate this concept, a rigorous analysis of a sphere is provided. ![]() Temporal modal behaviors of the plate are presented and discussed. Additionally, a narrow plate is selected as an example since it has a similar structure as the vibrating string. Special attentions are paid to the time-domain behaviors of the resonating modes, by following which a temporal modal analysis is proposed. In this paper, resonating modes of a vibrating string are briefly reviewed. Within the regime of electromagnetics, characteristic mode theory is established in frequency domain (FD), and it is doubtful that whether we can find similar modes in time domain (TD). Resonance is a common physical phenomenon in real world, and the modal analysis is a useful tool. ![]()
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