# Phase-angle measurement

## Phase-angle measurement

Measurement of the time delay between two periodic signals. The phase difference between two sinusoidal waveforms that have the same frequency and are free of a dc component can be conveniently described as shown in the illustration. It can be seen that the phase angle can be considered as a measure of the time delay between two periodic signals expressed as a fraction of the wave period. This fraction is normally expressed in units of angle, with a full cycle corresponding to 360°. For example, in the illustration, where the voltage v1 passes through zero cycle before a second voltage v2, it leads by 360°/8 or 45°. Phase angle is usually defined from the fundamental component of each waveform; therefore distortion of either or both signals can give rise to errors, the extent of which depends on the nature of the distortion and the method of measurement.

Phase angle Θ between voltages v1 and v2

The majority of modern phase-measuring devices are based on the use of zero-crossing detectors. The time at which each signal crosses the zero-voltage axis is determined, usually by means of a squaring-up circuit (for example, an overdriven amplifier) followed by a high-speed comparator. This produces, in each channel, a trigger pulse that is used to drive a bistable flip-flop. The output from the bistable is a rectangular wave, the duty cycle of which is proportional to the phase difference between the input signals. If this signal is integrated by means of a suitable filter, a dc voltage is produced that is an analog representation of the phase angle. This voltage is then displayed on a panel meter (analog or digital) suitably scaled in degrees or radians. Instrumentation using this principle is capable of measuring phase differences to approximately ±0.05° over a wide range of amplitudes and frequencies.

Conventional phase meters have an upper frequency limit of a few hundred kilohertz. This limit is imposed mainly by the ability of the arrangement consisting of a comparator and a flip-flop to maintain a clean and precise rectangular waveform under conditions of high-speed operation. In order to measure phase angle at frequencies between about 100 kHz and several gigahertz, it is necessary to down-convert the radio-frequency signals to a frequency that can be handled correctly by the phase meter. At microwave frequencies, instruments such as slotted lines, air lines, and vector network analyzers are also used for phase-angle measurements. See Microwave measurements

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.
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