Low Dispersion Notch Filter for Multi-GHz Frequencies Using Fiber Optics Delays

Although their designs appear simple and straightforward, notch filters for application in stochastic cooling systems are frequently difficult to construct with acceptable characteristics. Problems arise because the components are less than perfect, coaxial cables have loss plus dispersion and other necessary hardware has limitations. Usually it is the delay line, typically a high quality coaxial line, which is the source of most problems. Filter configurations have been produced in many styles. Their purpose is to provide a transmission coefficient with (nearly) zeroes at harmonically related frequencies over a large bandwidth. Specifics of the notch shape (and thus the phase) depend upon the particular filter design. Low dispersion of the notch distribution, that is, the deviation of notch frequencies from ideal, is often difficult to achieve. This is especially true as the operating bandwidths of cooling systems expand. The stochastic cooling systemns used in FNAL´s TEV-I operate in the 12 and 2-4 GHz bands, but future systems at CERN´S ACOL or even an upgraded TEV-I will extend to 8 GHz. A filter developed at FNAL1 solves the dispersion problem by using a small superconducting coaxial cable as the long delay element. Laboratory measurements of its characteristics indicate it to have excellent parameters. Nevertheless it requires substantial support in the way of cryogenic and control equipment for its operation. This f ilter is the one chosen for use in the initial operation of the TeV-I pbar accumulation system.