Cascaded R–C Networks and Phase-shift Oscillators

Abstract

This article briefly describes the salient features of the simple three section C–R phase-shift oscillator which is met quite early in electronics laboratory courses. The frequency of operation and the gain required for oscillation are shown to depend on the output impedance of the amplifier which feeds the C–R network. By using a directly coupled cathode follower, the C–R network can be driven under almost ideal conditions where the C–R network determines the frequency and gain requirement. A simple and rapid method for calculating the frequency and gain for a cascade of ‘n’ identical sections is given, in general form, along with a graph of gain and frequency/no. of sections. A three section C–R network with tapered sections is analysed from the point of view of the gain required for the limiting case of extremely steep taper. The R–C transmission line with distributed parameters is considered and the gain required for the open-circuit line type of oscillator is shown to be – coshπ. The limiting gain required for a large number of identical sections appears to approach — coshπ, but this is not proved.

Backgrounds to Sensitive Experiments Underground

“…For the thorium chain, the important alpha emitters are 216 Po (6.8 MeV alpha) and 212 Po (8.8 MeV alpha), and for the uranium chain are 218 Po (6.0 MeV alpha), 214 Po (7.7 MeV alpha), and 210 Po (5.3 MeV alpha). Detailed information including tables of (α, n) yields from light nuclides as a function of alpha energy are given by References (137,138).…”

Simulations of neutron background in a time projection chamber relevant to dark matter searches

“…Our calculations with SOURCES show that spontaneous fission dominates the neutron production from uranium in iron. We compared our results for a total neutron yield from U and Th in iron and stainless steel with a calculation carried out by Heaton [26] for iron on the basis of the measurements by West and Sherwood [27]. We found that for equal contamination levels of U and Th, Heaton's yield for iron is 57% higher than our result for iron.…”

“…We can interpret this difference as an estimate for the systematic uncertainty in our calculations. Unfortunately, the calculations of Heaton [26] cannot be used to generate recoil spectra since they do not contain information about neutron energies and the cross-sections of (α,n) reactions are not available from the measurements quoted above.…”