Design of lumped constant delay lines

Lumped constant delay lines are lowpass filters which are valued for their delay characteristics. The delay is relatively long, in some cases tremendously long. It must also be very constant over a lowpass band. This type of filter is very old, going back to the 1920's. It arises from Zobel's image parameter theory, which is generally considered obsolete in regard to any other species of filter. Indeed, the modern methods can make delay lines that have better performance than the image parameter type, but they cannot begin to compete, in regard to cost, with the repetitious element values of the m-derived delay line.Without going into the details of image parameter theory, we shall simply say that delay lines consist of a number-sometimes a very large number of cascaded sections which consist of a center-tapped coil having a series resonant circuit connected from the center tap to ground. All sections are identical except for a single Z,-section at the ends, the purpose of which is to "match" the image impedance of the line to the resistive terminations. These are standard half sections having m = 0.6. One size fits all. The dominant m parameter, however, is central to the design, appearing in the design formulas of all elements in the dominant section. Our purpose here is to show how, given the number of sections, we can calculate an optimum value of m. We then summarize the design procedure, which turns out to be very simple and easy to do.