Two-path Filter Research Articles

An analysis program, PAMS, for linear signal processing systems containing carrier-actuated modulators as time-varying elements

Linear signal processing systems consisting of time-invariant circuits and carrier-actuated modulators are widely used. An analysis program, PAMS, developed specifically for such systems, and its application for design and analysis (including sensitivity studies) is discussed. Two application examples are given: namely (a) the variation of a single design parameter is shown to vary the response of a two-path filter from that of a lowpass to that of a bandpass filter, and the variation of a hardware parameter is shown to produce 'forbidden' output frequencies; and (b) two versions of a quadrature modulation-type vestigial sideband system are analysed; the suitability of two different filtering symmetry conditions is demonstrated, but the sensitivity of the system amplitude and phase responses to carrier-phase errors is shown to depend on the symmetry condition chosen.

Electronics for the Longitudinal Active Damping System for the CERN PS Booster

Precisely tracking band-pass filters centred at the sixth and seventh harmonic of the revolution frequency are required1). During the accelerating cycle of 0.6 sec the frequency changes by a factor 2.7. The resulting tracking problem is solved by active two-path filters, where the centre frequency is governed by the frequency of a pair of sinusoidal signals in quadrature, which are generated from the accelerating RF frequency (fifth harmonic) by means of a phase-locked loop and a loop-controlled phase shifter. The phase change caused by the large frequency sweep (6 or 7 MHz) in conjunction with the delay in the feedback loop (cables, etc.) is compensated by a digital system, which computes the required phase advance from the value of the RF frequency and controls digitally the phase shift of the two-path filters. A low-frequency quadrature VCO is made to track the synchrotron frequency or harmonics hereof from analogue information about bending magnet field (momentum) and RF voltage. This quadrature pair ensures tracking of single sideband filters which permit each individual mode sideband to be examined throughout the cycle. A drive system can, by means of a similar VCO, generate any desired mode sideband, and thus excite any given mode.

Network Functions of Quadrature N-Path Filters

The general exact time-varying network functions of N-path filters, called quadrature N-path filters (QNF), are obtained in integral and series forms. It is shown that a subclass of the QNF has characteristics similar to previously treated sampled N-path filters (SNF) and that for a given number of paths N, the allowable input signal frequency bandwidth of the QNF is twice as large as that of the SNF. Thus the mimimum N for the QNF is two instead of the three required for the SNF. It is also shown that the well-known networks used in Weaver's "third method" of generating and detecting single-sideband signals correspond to the quadrature two-path filters.