7 Variable conversion elements

 

7.7 Phase measurement

Instruments that convert the measured variable into a phase change in a sinusoidal electrical signal include the transit-time ultrasonic flowmeter, the radar level sensor, the LVDT and the resolver. The most accurate instrument for measuring the phase difference between two signals is the electronic counter-timer. However, two other methods also exist that are less accurate but are nevertheless very useful in some circumstances. One method involves plotting the signals on an X–Y plotter and the other uses a dual beam oscilloscope.

 

7.7.1 Electronic counter-timer

In principle, the phase difference between two sinusoidal signals can be determined by measuring the time that elapses between the two signals crossing the time axis. However, in practice, this is inaccurate because the zero crossings are susceptible to noise contamination. The normal solution to this problem is to amplify/attenuate the two signals so that they have the same amplitude and then measure the time that elapses between the two signals crossing some non-zero threshold value.

The basis of this method of phase measurement is a digital counter-timer with a quartz-controlled oscillator providing a frequency standard that is typically 10 MHz. The crossing points of the two signals through the reference threshold voltage level are applied to a gate that starts and then stops pulses from the oscillator into an electronic counter, as shown in Figure 7.20. The elapsed time, and hence phase difference, between the two input signals is then measured in terms of the counter display.

 

7.7.2 X–Y plotter

This is a useful technique for approximate phase measurement but is limited to low frequencies because of the very limited bandwidth of an X–Y plotter. If two input

signals of equal magnitude are applied to the X and Y inputs of a plotter, the plot obtained is an ellipse, as shown in Figure 7.21. If the X and Y inputs are given by:

V_X = V sin(ωt);  V_Y = V sin(ωt + )

At t = 0, V_X = 0 and V_Y = V sin . Thus, from Figure 7.21, for V_X = 0, V_Y = ±h:

                          sin = ±h/V                                                                         (7.16)

Solution of equation (7.4) gives four possible values for  but the ambiguity about which quadrant  is in can usually be solved by observing the two signals plotted against time on a dual-beam oscilloscope.

7.7.3 Oscilloscope

Approximate measurement of the phase difference between signals can be made using a dual-beam oscilloscope. The two signals are applied to the two oscilloscope inputs and a suitable timebase chosen such that the time between the crossing points of the two signals can be measured. The phase difference of both low- and high-frequency signals can be measured by this method, the upper frequency limit measurable being dictated by the bandwidth of the oscilloscope (which is normally very high).

 

7.7.4 Phase-sensitive detector

The phase-sensitive detector described earlier in section 5.5.9 can be used to measure the phase difference between two signals that have an identical frequency. This can be exploited in measurement devices like the varying-phase output resolver (see Chapter 20).