Microwave Circuit Time-domain Spectroscopy Quick Analysis

Numerical simulation is very important to design the appliance such as the resonators and the waveguides. Because of this, lots of numerical methods had developed. Among all these methods, the finite-element method (FEM) has become a more popular numerical technique because of its superior versatility in geometry and material modeling. But there is an inevitable problem in-FEM, that is each time it must solve a linear equation, and the quantity of this computation is very huge, just because of this, FEM wastes time very much.The SETD (spectral-element method in time domain) talked in this thesis is a special FEM. It is combined by FEM and spectral method. The biggest difference between SEM and FEM is its basic function. The basic function used in SEM is orthogonal polynomial which is used in spectral method, so SEM has the trait of high-order accuracy. This trait is that the computation error decreases along with the order of basic function increases. Besides, if the thought of FEM is used to solve the differential equation, we can get a diagonal mass matrix when the model is dispersed by rectangular hexahedron or mass-diagonal matrix if the model is dispersed by curving hexahedron, all these are because the basic function is orthogonal. When SEM is used in time domain, this trait is materialized adequately. When the time discrete format is middle-difference scheme,Runge-Kutta scheme or Symplectic scheme, the coefficient matrix of equation is only mass matrix, and it is easy to get the contrary matrix, so the solving complexity of equation is reduced largely, and the solving time is also decreased.When SETD is used to analyze micro circuits, it is needed to set appropriate boundary condition at the truncation of the domain. By studying the numerical examples, we find that this method is not only implemented easily but also has very good performance. But there is a defect of this method that is unknowns is very large. So, the first order ABCs is introduced to SETD. It not only decreases the number of unknowns but also has very good performance at low frequency. For some problems at high frequency, we can use ABCs instead of PEC to truncate the outside of PML, it can reduce at least 10dB of the reflection errors.In the methods of time domain, there are FETD (Finite Element Time-Domain Method,FDTD(Finite-Difference Time-Domain Method), we analyze some examples compared with this two methods to validate the high-accuracy and fast solving time of SETD.