Determination Of Phase Angle Research Articles

Microprocessor Determination of Phase Angle in the Presence of Harmonics

An instrument based on the look-up table technique in a microprocessor is developed to measure the phase angle between the fundamental components of two nonsinusoidal periodic signals. In real-time mode, the phase angle is measured with a resolution of 1°, while a resolution of 0.10° is achieved in the steady-state mode. Additional hardware is also incorporated to ensure that frequency variation in the range 45-55 Hz does not introduce any additional error in measurement.

Relaxation effects in monolayers and their contribution to water wave damping: I. Wave-induced phase shifts

The newly developed experimental approach of measuring surface potential variations over propagating water waves cover with monolayers allows direct determination of phase angles θ between the hydrodynamic surface area variation and the surface film concentration (surface tension, surface potential) variation depending on the chemical structure and the relaxation behavior of the film molecules. These phase shift data and independently measured laboratory surface viscosity values determined by means of the canal method are used for calculating dilational modulus E values which turn out to be lower than E values obtained by classical Langmuir-trough measurements. As shown in Part II of this work (H. Hühnerfuss, P. A. Lange, and W. Walter, J. Colloid Interface Sci. 108, 442, 1985) these E values obtained under dynamic conditions are much more suitable for describing quantitatively the wave damping effects of monolayers.

Phase-angle determination by anomalous X-ray scattering with a four-circle SSD diffractometer

By the use of a four-circle diffractometer with a solid- state detector, the integrated Bragg reflexion intensities from hemimorphite [Zn4Si2O7(OH)2.H2O] have been measured by energy-dispersive diffractometry at three energy values, including the region very near the Zn Kα absorption edge. The anomalous difference Patterson map obtained indicated Zn-Zn peaks. By the use of the anomalous-scattering effect to the maximum extent, the phases of one hundred reflexions have been deter- mined with a mean error of 15.4°

Improved-accuracy phase angle measurement

A method for phase angle determination from measurement of three magnitudes, described in a recent paper (Middlebrook 1975), is extended to provide improved accuracy.

Improved Reactive Power Measurement through Precision Phase Angle Determination

In the past, the accuracy of reactive measurement has been substantially limited by the precision with which two voltages in quadrature could be generated. A technique employing a commercially available electronic phasemeter has been developed whereby phase angles may be established very precisely. This technique is described in the context of reactive measurements, and other applications are suggested as well.

The structure of vitamin B 12 . IX. The crystal structure of cobyric acid, factor V 1 a

The structure of cobyric acid (factor V 1 a ), the aquocyanide of the natural nucleus of the B 12 vitamins, has been determined by X-ray crystallographic analysis. The crystals are monoclinic, space group, P2 1 ; the asymmetric unit has the contents, C 46 H 66 O 9 N 11 Co. 11H 2 O. The intensities of the X-ray spectra recorded with CuK α radiation were measured visually; they showed marked intensity differences between kkl and kkl reflexions due to anomalous dispersion, which permitted the calculation of phase angles for 1994 reflexions; the ambiguity in phase angle determination from the differences was resolved by choosing the one nearer to the phase of the cobalt atom. The first electron density map obtained revealed the structure almost completely. It has been refined by successive structure factor and difference electron density maps and block diagonal least squares calculations; in the later stages adjustments were made to the individual observed F values, 6188 reflexions in all. Many details of the geometry of the cobyric acid nucleus and of the attached side chains are well defined; one acetamide group, that on ring B, is rotated from its usual position to make a hydrogen bonded contact with a water molecule attached to the cobalt atom.

The Structure of haemoglobin - VII. Determination of phase angles in the non-centrosymmetric [100] zone

In the last paper in this series a Fourier projection down the [010] axis of horse haemoglobin was given (Bragg & Perutz 1954). This projection was centrosymmetric. As a first step towards the three-dimensional analysis, the projection down [100] has now been attacked. This projection is non-centrosymmetric, and arbitrary phase angles have had to be determined. All the fundamental problems of a three-dimensional study are met, but only a small number of reflexions need be dealt with. The isomorphous replacement method has been used successfully with three mercury derivatives of haemoglobin. This provided a test of new methods for finding the vectors relating heavy atoms. Particular attention has been given to estimation of errors, and to their effect on the results. Further information about the phases has been derived from anomalous scattering by the mercury atoms, using CrKα and CuKα radiation. By combining these results, the phases of most reflexions out to a spacing of about 6 Å have been determined with a standard error of about 25°. Ambiguous results are obtained for a few reflexions. The resulting electron density projection shows peaks up to four times the estimated standard error. The prospects for three-dimensional structure analysis at 6 Å resolution are favourable. If the polypeptide chain is coiled in the α-form, the contrast should be sufficient for it to show up throughout its length.

Determination of Absolute Intensities of X-Ray Reflexions from Relative Intensity Data

RECENTLY, owing to the advent of various methods1 of direct determination of phase angles of Bragg reflexions from a crystal, a convenient method of determination of absolute intensities of Bragg reflexions seems urgently needed2. In 1942 I proposed a simple method of determination of absolute from relative intensities3, which has since been made rigorous and so should be reliable in general cases if used properly. Accordingly, I present here the final result of the method, which is applicable to practical cases immediately.

The determination of phase angle by cathode-ray oscillograph

The determination of phase angle by cathode-ray oscillograph