Figure 2: Derivative of S11 with respect to the septum width. (©2006 IEEE)

(Image from "Sensitivity analysis of scattering parameters with

electromagnetic time-domain simulators," by N.K. Nikolova, Ying Li, Yan

Li, and M.H. Bakr, /IEEE Trans. Microwave Theory Tech/., vol. 54, No. 4,

April 2006, pp. 1598-1610.)

Figure 2 shows the derivatives of the real part of S11 with respect to the

width of the spectrum in the frequency band from 3.5 to 4.5 GHz. The curve

generated by the new method closely follows the conventional method

estimates.

H-plane filter validation study

Figure 3: Six-resonator H-plane filter. (©2006 IEEE) (Image from

"Sensitivity analysis of scattering parameters with electromagnetic time-

domain simulators," by N.K. Nikolova, Ying Li, Yan Li, and M.H. Bakr,

/IEEE Trans. Microwave Theory Tech/., vol. 54, No. 4, April 2006, pp.

1598-1610.)

The H-plane filter shown in figure 3 was previously modeled using by an in-

house method which solved an additional adjoint problem. Then, in a single

XFDTD simulation, the researchers obtained the S-parameters and their

derivatives with respect to all design variables. The grid of size 56 by 1 by

301 is uniform. The excitation is a Gaussian modulated sine with a spectrum

from 5 to 10 GHz. Five current sources are placed uniformly across the port

conforming to the half-sine modal distribution. Figure 4 shows the derivative

of the insertion loss |S21| with respect to the width of the septum (W4) for a

parameter sweep at 7.0 GHz. The agreement between the finite difference

sensitivity curves and the new method is very good.