By B.A. Gregory
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Extra resources for An Introduction to Electrical Instrumentation and Measurement Systems: A guide to the use, selection, and limitations of electrical instruments and measurement systems
S. s. s. 414 respectively. Phase relationships When alternating signals are present in a circuit containing a combination of resistive and reactive (inductive or capacitive) components, a time displacement will exist between the signals at various points in the circuit. If the signals are all of one frequency this time displacement is referred to as a phase angle, but this latter term cannot be used if more than a single frequency is present. amplitude I I ,,,_... 28. 28 v = Vm sin () i = Vm sin (() + cp) Thus p = Vm sin () x 1m sin (() = Vm/ m sin () sin (() = Vm/m 2 + cp) + cp) [cos () - cos (2() - cp)] 46 AN INTRODUCTION TO ELECTRICAL INSTRUMENTATION Therefore the mean power over a cycle is the average power P = - 1 J211" -1 VrnIrn [cos cp - cos (2e - cp)] de 21T 0 2 I = -~ 41T 127T [cos cp - cos (2e - cp)] de 0 Examining the terms to be integrated, cos cp is a constant (cp does not change throughout a cycle), and cos (2e - cp) will go through two complete cycles as e goes from 0 to 21T, so its average value must be zero.
Use of a matching transformer INTRODUCTION 41 where R I is the resistance of the circuit on the side of the transformer which has NI turns; R2 and N2 being the resistance and turns on the other side of the trans- former. 001 666 power available from the source = v. 2 ~-- v. 416 V/ v. 833 Vs2 mW 2 x 600 The above shows that the maximum possible (that is 50 per cent) of the power available may be transferred to the instrument using a matching transformer. In practice, there are limitations to this principle.
S. s. current, and the cosine of the phase angle between these quantities. Bias In some measuring situations the signal being measured will be 'biased' or at a potential relative to the zero or earth line. 29. Sinewave signal with a direct bias 47 INTRODUCTION peak and other values characteristic of a signal referred to above will be affected by the presence of a bias; a condition which can create considerable difficulties in some measurement situations. 2 Harmonics It is conveniently assumed that alternating signals are single frequency sinusoidal waveforms.