Reference Phase Angle Research Articles

Development of an advanced industrial metal detector instrumentation

In the normal three-coil balanced detection system for metal contaminants in products, a centrally excited coil provides a symmetric field linking two outer detector coils which are appropriately balanced to produce a zero voltage output for the detector circuit. The product to be inspected is passed on a conveyor belt through the centre of the triple coil system and the presence of any metal causes an imbalance initially on the input coil which is eventually mirrored by an imbalance in the output coil, with the signal being appropriately identified by phase-sensitive detection circuitry. The output signal is a function of many variables, including signal frequency, permeability and resistance of the sample, geometrical position of the sample within the coil cross-sectional area, and coil spacing. The reference phase angle is a crucial adjustment factor which, inter alia, compensates for product factors such as moisture content and other parameters which affect the electrical characteristics. Utilising the work of Poritsky (1960) it was not difficult to solve the fundamental field equations and optimise the various design parameters to maximise the output signal for any coil shape or sample type, and a simple CAD program was written to automate the design process. The performance specifications of new designs could be easily generated without the need for prototype construction and testing and, in addition, the claims of competitive manufacturers could be countered. Another problem addressed was that of long-term drift in the balanced coil system caused by thermal and other effects.

Topologically Independent State Estimation: Part 1 — Theory and Conclusions

The paper develops a novel method for the estimation of the voltage magnitudes and phase angles at the nodes of an interconnected electric power system. The proposed algorithm decomposes the state estimation problem into four sets of linear equations. The first set of linear equations defines the estimates of the active power flows throughout the system in terms of the power flow measurements, the power flow losses in the transmission lines and Kirchoff's first law, similarly the second set defines the reactive power flows through the system. The third set defines the square of the estimates of the voltage magnitudes at all the nodes in the system in terms of the voltage magnitude measurements and the voltage drops across the transmission lines and the fourth set defines the estimates of the phase angles in a similar way to those of the voltage magnitude except that an addtional equation is required which defines the reference phase angle. The solution of the four sets of linear equations is achieved by sparse linear programming. The proposed algorithm is able to operate at the busbar level and it treats the bus couplers in a similar fashion to the transmission lines, however they are deemed to have zero impedance. This feature combined with the excellent bad data rejection property of linear programming methods results in a robust state estimation algorithm which is also able to identify and correct switch status measurement errors.

Determining magnetic anisotropy of rocks with a spinner magnetometer giving in-phase and quadrature data output

A relationship is developed between magnetic anisotropy measurements and the total magnetic susceptibility tensor, in terms of the in-phase and quadrature output components of a two-component spinner magnetometer. Calibration procedures for both signal phase and magnitude are discussed, with reference to remanent magnetization measurement, in terms of a wire loop and mu-metal plate, whose induced magnetizations and anisotropy can be theoretically calculated. The importance of careful reference signal phase adjustment is noted, and the effect on the output amplitude for small systematic errors in simple position and reference phase angle is considered. An average uncertainty in the anisotropy output magnitude is thought to be in the range of 1% to 5%.

An Analysis of the Phase Coherent--Incoherent Output of the Bandpass Limiter

Many applications of the bandpass limiter (BPL) involve coherent demodulation following the limiter. It is shown that as a result of demodulation, the signal mean and the noise variance are direct functions of the phase angle between the signal component passed by the BPL and the coherent reference. As a result, the relationship between the output and input signal-to-noise ratio may be significantly different than that obtained by Davenport for incoherent limiters. A study is also made of the output noise spectral density, and an approximate expressison is derived as a function of the input signal-to-noise ratio, reference phase angle, and the characteristics of the input bandpass filter to the limiter. Also discussed is the first-order signal-plus-noise probability density following coherent demodulation.

A Direct-Reading Acoustical Impedance Meter

A device for the measurement of acoustical impedance is described which employs a high impedance source, monitored by a ribbon element acting as an acoustical ammeter. The output of the ribbon acts through an automatic volume control circuit to maintain constant the volume current injected into the impedance under test. The sound pressure so developed is proportional to the absolute acoustical impedance and is measured by a high impedance probe microphone. The ribbon element also serves as a phase angle reference for the unknown impedance. The total acoustical path length from the ribbon to the diaphragm of the probe microphone is kept to an absolute minimum.