Measure vector and area with an oscilloscope X-Y display
Oscilloscopes often include the ability to cross plot the data from two waveforms using X-Y displays. These displays find applications in switched-mode power measurements, baseband quadrature-modulation analysis, and a host of other measurement disciplines. Many oscilloscopes offer measurement tools specifically designed to support X-Y displays. Additionally, math functions can be applied to the elements of X-Y displays to extract key parameters. Here, I'll cover the use of polar-coordinate measurements using X-Y cursors. You can apply these techniques to measuring vector magnitude and phase as well as use waveform math to find the area enclosed by an X-Y plot.
Quadrature modulation techniques employ two baseband signals called the in-phase (I) and quadrature (Q) components, which are combined using vectors to create a composite waveform with phase and amplitude values based on the amplitudes of the I and Q signal components.
Figure 1 shows a dual/X-Y display of the in-phase and quadrature components of a simulated baseband 16QAM signal. Channel 1 (C1, yellow trace) is the in-phase component and channel 2 (C2, pink trace) is the quadrature component. When cross these components plotted on the X-Y display (blue), you can see a traditional state-transition diagram with 16 states. Each state is the result of combining pairs of I and Q amplitude values. There are eight phase states, each with two possible amplitudes. The lower amplitude phase states appear as the higher intensity blue traces in the X-Y display.
An absolute horizontal cursor, indicated by the cross shaped icon in the upper-right corner of the blue display, has been moved to the maximum amplitude state at approximately 45°. Note that the cursor appears on both the X-Y display and the X-T and Y-T components. The cursors track so that the point marked on the X-Y display is created by the vector sum of the points marked on the X-T and Y-T sources. The amplitude readouts of the cursors appear in the waveform descriptor boxes for each trace. In this case the X component (C1, yellow) has an amplitude of 275mV and the Y component (C2, pink) amplitude is 270mV. These are the Cartesian coordinate amplitude values. The cursor readouts under the X-Y display provide the polar coordinate readouts including the Radius (vector magnitude) and Angle (phase) readouts. The marked point has a vector magnitude of 385mV at an angle of 44.5°. So in addition to the Cartesian coordinates which show the component amplitudes, we get a polar readout that provides the magnitude and phase of the resultant vector created by the quadrature sum of the marked X and Y components.
Figure 2 shows a similar 16QAM signal with a simulated error state. Relative horizontal cursors can be used to measure the vector difference between the error state and the correct state
On the X-T and Y-T component waveforms, the relative horizontal cursors measure the time and amplitude difference between two cursors; they are indicated by a down arrow (reference cursor) and an up arrow (difference cursor). Amplitude information appears in the waveform descriptor boxes and time information appears under the timebase and trigger descriptor boxes.
The X-Y cursor polar-coordinate readout field shows the magnitude and phase of the vector connecting the reference and difference cursor locations. If the reference cursor is placed at the desired state and the difference cursor on the error state then the polar cursor readouts shown the magnitude (Radius) and phase (Angle) of the error vector. In this example, the error vector has a magnitude of 192mV at a phase of -155.4°. Again, the cursors track on the X-T and Y-T components so the up arrow cursor marks the error state on the X-T and Y-T waveforms. Thus, the polar cursor readouts on an X-Y display of baseband, quadrature modulation signals enable measurements of state and error vector magnitude and phase.