Unconditionally stable Crank-Nicolson finite-different time-domain method for simulation of three-dimensional microwave circuits

An unconditionally stable Crank-Nicolson finite-difference time-domain (CN-FDTD) algorithm is presented for three-dimensional microwave circuit analysis. First, Mur´s first-order absorbing boundary condition is applied this CN-FDTD algorithm. A symmetric successive over relaxation-preconditioned biconjugate-gradient algorithm is also proposed to solve the large sparse matrix equation obtained in the CN-FDTD method. Resonant cavity and several planar microstrip circuits are presented to illustrate the versatility of this technique. Numerical results indicate that with a time-step size excessively larger than the Courant-Friedrich-Levy limit, the accuracy of CN-FDTD is still much higher than that of the alternating-direction implicit FDTD.