Drawing one trace on top of another is possible with an X-Y display, sometimes referred to as a scatter plot or cross plot. A plot of this kind can be used to compare two waveforms and demonstrate how they relate to one another. This 2D graphic can be modified to include a third parameter, such as frequency of recurrence, as a variation in color or intensity.
There are numerous traditional and contemporary uses for X-Y display modes, from traditional Lissajous diagrams for calculating phase or frequency ratios to state transition diagrams used in contemporary quadrature communication systems. If there is a relationship between two variables, it can be demonstrated using an X-Y plot. If a relationship is present, it can also indicate whether it is linear or nonlinear as well as its direction. Some of these applications will be discussed in this article.
Ⅰ.Lissajous
Two sine waves are plotted against one another in a Lissajous figure, which is a traditional use of an X-Y display. This graph is used to determine the phase difference between sine waves of the same frequency. It is simpler to obtain the phase difference between the two signals using a contemporary oscilloscope because only one measurement parameter needs to be read. Figure 1 illustrates how to calculate the sine waves' frequency ratio if their frequencies differ.
Figure. 1
Figure 1: An X-Y plot of two harmonically correlated sine waves, in this case, the ratio of the number of horizontal peaks to the number of vertical peaks, representing a 2-to-5 input signal frequency ratio.
The graph shows that the relationship between the frequencies of the two input signals is 2 to 5. The actual measured frequencies are 1MHz and 2.5MHz respectively.
Ⅱ.Curve Tracker
The V-I properties of asemiconductor devicecan be described using an X-Y plot and an oscilloscope and an arbitrary waveform generator (AWG). The measurements for asilicon diodeare displayed in Figure 2.
Figure. 2
Figure 2: V-I curve based on the 12 voltage values generated by the AWG and the current flowing through the silicon diode.
With 12 pulses applied to the diode, the AWG's voltage amplitude increases sequentially from -5V to +5V. To measure the voltage across the diode and the current flowing through it, one pulse per sequence segment, use the oscilloscope's sequence mode. One parameter value per point makes up the trend graph of the recorded voltage and current parameters. The X-Y display's horizontal input axis receives voltage scaled at 1 volt each division, while the vertical axis receives current scaled at 12.4 mA per division. The resulting X-Y map displays the diode's V-I properties. Useful applications for this simple test include matching components.
Ⅲ.Quadrature Signal Measurement
Two signals that are 90 degrees out of phase are combined to create a variable phase signal by the quadrature signal generating algorithm. A vector having magnitude and phase is defined by the addition of two signals in quadrature. Two aspects of the vector are governed by the strength of the input signal. As seen in Figure 3, the X-Y plot made possible by the X-Y cursor enables viewing and monitoring the phase and amplitude of vectors produced by quadrature input signals.
Figure. 3
Figure 3 displays the phase trace of a vector as an X-Y plot of two quadrature signals (sum of squares of the signals). Cartesian coordinates as well as vector magnitude (radius) and phase (angle) can be read by X-Y cursors.
The rotational vector traceroute, which is determined by the sum of the squares of two exponentially weighted RF pulses, may be seen on the X-Y display. The voltage at the source sample points in channels 1 and 2 as well as the vector magnitude (radius) and phase relative to the positive X axis are all read by the X-Y cursors. These cursor readouts follow the waveforms X-Y, X-T, and Y-T. This implies that all cursor measurement vectors' source components are measured simultaneously. The 401mV vector magnitude has an X component of 349.6mV and a Y component of 196.9mV. Since the source of error for these vector parameters can be easily identified, this information is helpful in applications that require quadrature signal production, such as radar and digital communications applications.
A persistence display, which maintains several traces that are covered in the diagram, can also be provided by the X-Y display. Intensity or color is used in persistence displays to indicate how frequently the pixels are shown. A 16QAM signal's in-phase (I) and quadrature (Q) components are shown in Figure 4, along with an X-Y state transition diagram that illustrates how the I component is determined based on the Q component. In this X-Y display, monochromatic persistence is used.
Figure. 4
Figure 4: X-Y plot rendered with monochromatic persistence. Among them, the data states of the state transition diagram are shown as bright spots, while the phase paths of multiple transitions are shown brighter.
State transition diagrams indicate the paths between data states and display the states of the data at each end of each transition path. The data states show up as brighter dots on the X-Y plot because the waveform spends more time in each data state than in the transition route. The two different vector magnitudes are written twice for the four-phase states of 45, 135, 225, and 315 degrees, and they also appear brighter. As a result, the afterglow plot offers further details regarding this measurement, such as a more visible depiction of the overlapping vectors.
Ⅳ.Power-related X-Y measurements
The X-Y display can be used for measurements of power-switching devices. To make sure the device functions within its safe operating range, Figure 5 depicts the voltage against current across the power FET (SOA).
Figure. 5
Figure 5: An X-Y plot used to measure the operating area (SOA) of a power FET, plotting drain current versus drain-source voltage. The Pass/Fail test compares the X-Y plot to the template, with red circles indicating failure.
The drain current is applied to the vertical axis, and the drain-source voltage (VDS) across the FET is applied to the horizontal axis. The FET is on, and the vertical portion of the X-Y diagram shows that VDS is practically constant as the current rises. The FET is off, the current is 0, and the voltage is fluctuating when the horizontal ring is horizontal. The switching transitions that occur when the gadget is losing power are represented by the middle trace. This test confirms that the device's maximum allowable voltage, current, and power have not been reached.
A "pass/fail" template for tracking measurement results is shown in the blue section. The template shouldn't be intersected by the X-Y traces.
Another power-related X-Y measurement is to measure the magnetic properties of inductive devices. Figure 6 shows the measured inductor hysteresis curve.
Figure. 6
Figure 6: Hysteresis graph plotting magnetic flux density as a function of magnetic field strength.
The magnetic field intensity and magnetic flux density are the inputs to the hysteresis diagram. While the magnetic flux density is determined by the integral of the applied voltage, the magnetic field intensity is determined by the current passing through the inductor. These calculations can be made using the oscilloscope utilized in this article's software option for power measurements using the coil geometry (cross-sectional area and magnetic path length), voltage, and current that are all known. The energy loss per cycle, also known as hysteresis loss, occurs inside the hysteresis loop.
Ⅴ.Mechanical measurement
The analysis of mechanical equipment can also be done using X-Y graphs. To translate mechanical data into proportional electrical signals, the right sensors are needed. The pressure-volume diagram of an engine, as depicted in Figure 7, is a nice illustration of an X-Y diagram of a mechanical unit.
Figure. 7
Figure 7: X-Y graph plotting pressure as a function of internal combustion engine cylinder volume.
A pressure sensor attached to the cylinder spark plug measures the pressure value. The measured crank angle is used by the rotary encoder to determine the volume. The oscilloscope's rescaling feature is used by both sensors, enabling measurements in common pressure and volume units, in this case, Pascals and Liters. The PV diagram shows two rings. The one up top is the exhaust stroke, while the one below is the larger one. The area inside the PV map's loop is proportional to the amount of mechanical work the engine produces per cycle. While the exhaust stroke is negative work, the power stroke is positive work.
Ⅵ.Summary
It is obvious that the X-Y display is a highly helpful tool for reading measurements. In addition to comparing signals, it illustrates relationships between plotted variables and displays vector magnitude and phase for quadrature inputs graphically. Additionally, it can reveal any energy gains or losses made while riding. When learning about dual trace applications for digital oscilloscopes, engineers should keep this particular instrument in mind.
