Figure 4: Derivative of |S21| for the H-plane filter at 7 GHz 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.)

The memory requirements of the sensitivity analysis are mostly due to the

field waveforms recorded at the perturbation points. The number of these

points is roughly equal to the number of cells surrounding a perturbation

surface or line. XFDTD can export the field recorded at user-defined points

or probes, which is usually done through text files. XFDTD updates these

text files after every iteration of the time-stepping algorithm, resulting in

very small memory requirements. The memory and read/write time

requirements can be practically eliminated if the sensitivity solver is

integrated with the electromagnetic simulator for direct data exchange

through random access memory (RAM).

Versatile and computationally efficient method

The researchers have developed a versatile and computationally efficient

method for S-parameter sensitivity analysis with transient EM solutions. The

method is based on the finite-difference E-field vector wave equation and

the second-order discrete sensitivity analysis approach. It is developed for,

but not limited to, structured-grid field solutions such as those provided by

FDTD-based simulators. With the new method, the S-parameter matrix and

its derivatives with respect to all design parameters are obtained through a

single system analysis with XFDTD. The overhead of the sensitivity

computation is negligible compared to the computational intensity of the