Log-ratio signal-processing technique for beam position monitors

Two basic signal-processing techniques are presently in wide use for the processing of signals from beam position monitors (BPM's); difference-over-sum, and amplitude-modulation-to-phase-modulation (AM-PM) conversion. Difference-over-sum offers simplicity and low cost, but poor real-time normalized response and amplitude dynamic range. AM-PM offers fast real-time response and large dynamic range, but is costly and difficult to implement. Logarithmic-ratio processing, a technique using newly available inexpensive hybrid circuits, appears to offer the advantages of both, and the disadvantages of neither. The features of all three processing techniques are reviewed, and the features of the log-ratio technique are highlighted. Among the advantages of log-ratio is a beam-displacement response linearity that is superior to either difference-over-sum or AM-PM for circular-aperture BPM's.