Phase difference can be measured on an oscilloscope by determining the time delay between two waveforms along with their period.
All periodic signals can be described in terms of amplitude and phase. We all learned that in basic circuit theory. You surely recall having to calculate signal's phase change when it passed through a network. Fortunately, you can also measure phase with an oscilloscope using several methods.
The phase of a periodic electrical waveform describes a specific position at a point in time. Figure 1 lables some significant phase points: maximum amplitude, minimum amplitude, and both positive and negative going zero crossings. The phase of a waveform is periodic and a complete cycle of the waveform is defined as having 360º or 2π radians of phase.
Phase difference, or phase angle, is the difference in phase between two phase points, usually on two different waveforms with the same frequency. Often, you're interested in the phase difference between a signal before and after it passes through a circuit, cable, connector, or PCB trace. A waveform with a leading phase has a specific phase point occurring earlier in time than the same phase point on its partner. That's the case of when a signal passes through, say, a capacitor: the output current will lead the output voltage by 90º. Conversely, a waveform with lagging phase has phase points occurring later in time than the other paired waveform. Two signals are said to be in opposition if they are 180º out of phase. Signals that differ in phase by ±90º are in phase quadrature.
Phase difference using delay time measurement
Phase difference can be measured on an oscilloscope by finding the time delay between two waveforms and their period. You can accomplish that using the oscilloscope's cursors as shown in Figure 2 where relative cursors measure the time difference between the maxima of the two 10 MHz sine waves. Cursor time readouts in the lower right corner of the screen indicate a delay of 10 ns. The period can also be measured using the cursors. The phase difference, in degrees, can be determined using the equation:
Φ = td/tp × 360 = 10 ns/(100 ns × 360º) = 36º
Where: td is the delay between waveforms and tp is the period of the waveforms.
This technique is a remnant of analog oscilloscope measurements. It works on digital oscilloscopes (DSOs), but the measurement accuracy is very dependent on the manual placement of the cursors.
DSOs simplify phase measurements by offering direct phase measurement, based on measuring the delay and period of the source waveforms. You can select the measurement thresholds and slopes for each waveform. The phase measurement is identical to the method used in the previous section applying an interpolator to assure accurate location of the measured phase points. The advantage of using the oscilloscope's built-in measurement capability is that it removes cursor placement as an error source. Phase can be read out in units of degrees, radians, or percentage of period. Figure 3 provides an example of a phase measurement.
The phase measurement is performed using parameter P1 in the lower left corner of the screen image. This oscilloscope makes "all instance" measurements meaning that the phase is measured for every cycle on the screen for each acquisition. The large number of phase measurements available supports measurement statistics, shown in this Figure 3. Measurement statistics show the most recent measurement, the mean value of all the measurements, maximum and minimum values encountered, the standard deviation, and the number of measurements included in the statistics. The key statistical readouts are the mean value and the standard deviation. The mean is the average value of all the measurements made. The standard deviation is a measure of the uncertainty in the measurement. In this example the mean value is 36º. The standard deviation is 0.747º. Most of the uncertainty in this measurement is a function of the vertical noise on the waveform. The mean value reduces noise by averaging the measured values. Noise can further be reduced by decreasing the bandwidth of the oscilloscope front end.
Dynamic phase measurements
Sometimes the phase difference isn't static and you need to characterize the phase change of a signal—think phase-modulated carrier. This type of measurement relies on the "All Instance" character of parameter-based timing measurements. Phase is measured for every cycle of the waveform. This information can be displayed using a trend or a track plot. The trend plot strings all the measured values together as a waveform where the horizontal axis is measurement event. The track, on the other hand, plots measured values as a function of time. This maintains synchronicity with the source waveform. So if one of the waveforms is phase modulated, you can get a cycle-by-cycle plot of the instantaneous phase as seen in Figure 4.
The upper trace, C1, in Figure 4 is a 10 MHz carrier, phase modulated (PM) by a 100 kHz sine wave. The trace C2 (second from top) is a 10 MHz sine with no modulation. The phase parameter reads the phase difference between the two waveforms. The measured phase difference for each cycle of the source waveforms is plotted in the third trace from the top (F1) as the track of the phase parameter and shows the phase difference versus time. This has, in essence, demodulated the PM waveform.
Note that in addition to having measurement statistics turned on, the oscilloscope also has a histicon (iconic histogram) of the phase parameter displayed. The histicon shows a miniature version of the histogram of phase values. Pointing at the histicon and clicking results in the full-scale histogram of phase difference being displayed in the bottom trace. The histogram breaks the amplitude range into a user set number of "bins." The number of measured values within each bin (vertical scale) is plotted versus the measured values (horizontal scale). The saddle shaped histogram is typical of a sinusoidal signal. Steps in the track plot and gaps in the histogram are the result of the phase difference values holding at fixed values for each cycle of the source waveform.
Figure 4 Dynamic phase difference measurement utilizing the parameter track function (trace F1) to show the cycle to cycle variation in phase difference as a function of time.
The min and max values of the phase parameter readout provide the range of the phase excursion over the full modulation cycle.
[Continue reading on EDN US: Other phase measurement techniques]
Arthur Pini has over 50 years' experience in electronics test and measurement.
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