پروژه در برنامه متلب در مورد روشهای عددی در الکترومغناطیس

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شرح پروژه

You are required to compute the resonance frequencies of a 2D rectangular cross section cavity bound by PEC walls using a 2D-FDTD (TE or TM) simulation.

a) First, derive the analytical expressions for the resonance frequencies and eigenmodes in a 2D rectangular cross section cavity bound by PEC walls and obtain the resonance frequencies for both TE and TM.

(Hint: Solve the Helmholtz equation for 𝐸𝑧/𝐻𝑧 using boundary conditions to show that 𝑘2=(𝑚𝜋𝑎)2+(𝑛𝜋𝑏)2, where (𝑎,𝑏) are cavity dimensions)

b) Choose the dimensions (𝑎,𝑏) of the rectangular cross-section cavity. Excite the cavity with a modulated Gaussian pulse. Next, appropriately choose your spatial and time discretization (use a CFL number of 0.99) and simulate the fields in the cavity over a large number of iterations (say 10,000). Accumulate the time response for any electric field at a discrete point. Using Fourier transform, compute the Fourier response of the cavity and detect the resonant frequencies.

i) Plot the Fourier response.

ii) Compare the numerically calculated resonance frequencies results with the ones obtained via analytical solution in (a).

iii) Comment on the results.

c) Assume that the 2D cavity is fully-filled with a lossless dielectric. Repeat (b) to observe the sliding of the resonance frequencies at the frequency spectrum with respect to relative dielectric permittivity.

i) Plot the Fourier response.

ii) Compare the numerically calculated resonance frequencies results with the ones obtained via analytical solution in (a).

iii) Comment on the results.

d) Can you use a cavity resonator to find the relative dielectric permittivity of a material? Explain.

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