14.1. Current And Voltage Transducers
14.1.1. Average Responding Transducer
14.1.2. r.m.s. Responding Transducer
14.2. ac Current Alarm Transducers
14.3. Frequency Transducer
14.1. Current (acA) and Voltage(acV) Transducers:
14.1.1. Average Responding Transducer
The standard method
for measuring the magnitude of an ac signal is to use a precision rectifier
followed by a filter. This measures the "average" value. A
scale factor is calibrated into the measurement (which is the ratio of r.m.s.
to average for sinewaves).
This is sufficient as long as the input waveform is an undistorted sinewave.
Acceptable results are achieved provided the waveform to be measured has no
greater than a few percent distortion. If the input has high distortion, it
should be measured with an r.m.s. responding instrument. For better accuracy
when measuring non-sinusoidal signals, the measuring instrument should use a r.m.s. technique.
14.1.2. r.m.s. Responding Transducer
Root Mean Square (r.m.s.) is a fundamental measurement of the magnitude
of an ac signal. The r.m.s. value assigned to an ac signal is the amount of
dc required to produce an equivalent amount of heat in the same load.
Mathematically, the r.m.s. value of a voltage is defined as : 
i.e. Square the instantaneous value, average these values over a period of time, and then take the square root of the resultant. The averaging time should be long enough to allow filtering at the lowest frequencies used.
The crest factor of a waveform is defined as the ratio of its peak value to its r.m.s. value. The table below shows the relative differences for r.m.s. and average response to different waveforms.
|
Waveform |
r.m.s. |
average. |
r.m.s./average |
Crest Factor |
|
undistorted sinewave |
|
|
1.11 |
1.414 |
|
symmetrical squarewave |
|
|
1.0 |
1.0 |
|
triangle wave |
|
|
1.155 |
1.73 |
14.2. ac Current Alarm Transducers
AC Current Alarm transducers are important for the protection of a.c. machinery. If faults develop (such as a shorted turn in a motor winding) which cause excessive current to flow, then an a.c. current monitor can detect this over-current and either switch off the faulty machine, or cause alarms to sound before excessive damage is done. Often these current monitors have alarm delays in order to prevent false triggering when machines are turned on which can cause excessive short term turn-on currents to flow.
14.3. Frequency Transducers
A typical method for measurement of frequency is to detect the zero crossings of the input sine wave. This zero crossing signal triggers a monostable multivibrator which produces a pulse of constant width and amplitude for each cycle of the measured signal. This pulse train is converted to a dc value by integration.
Although frequency transducers can be made to operate over a wide frequency range, generally for mains applications we are concerned only for a narrow range about the generation frequency. The most common range is 45...55Hz, although even more sensitive ranges such as 47..53Hz and 48...52Hz are used.