Vector Presentation of Broad Band Wave Filters

The function of a broad-band wave filter of the iterative ladder type in the attenuation band, and outside the attenuation band can be explained very simply when expressed in terms of two characteristic vectors Za and Zb. Drawing the diagram of these vectors, it becomes obvious that the angle between them is the phase shift of the filter and that the natural logarithm of the ratio of their magnitudes is the attenuation. The diagram also shows very plainly the relationship between a mid-series and a mid-shunt structure, and the equations for such filters can be derived in a very simple manner from the geometry of one vector triangle. It is hoped that this simplified presentation of types of filters which are so extensively used in radio, acoustical, and in mechanical engineering will be helpful in understanding their physical meaning.