Composite Image Filter - The Image Method

The Image Method

The image analysis starts with a calculation of the input and output impedances (the image impedances) and the transfer function of a section in an infinite chain of identical sections. This can be shown to be equivalent to the performance of a section terminated in its image impedances. The image method, therefore, relies on each filter section being terminated with the correct image impedance. This is easy enough to do with the internal sections of a multiple section filter, because it is only necessary to ensure that the sections facing the one in question have identical image impedances. However, the end sections are a problem. They will usually be terminated with fixed resistances that the filter cannot match perfectly except at one specific frequency. This mismatch leads to multiple reflections at the filter terminations and at the junctions between sections. These reflections result in the filter response deviating quite sharply from the theoretical, especially near the cut-off frequency.

The requirement for better matching to the end impedances is one of the main motivations for using composite filters. A section designed to give good matching is used at the ends but something else (for instance stopband rejection or passband to stopband transition) is designed for the body of the filter.