X-Y Shows, also referred to as scatter or cross plots, present a method of plotting one hint towards one other. Such a show exhibits comparisons and relationships between the 2 waveforms. A 3rd parameter, equivalent to frequency of incidence, could also be launched by including it as a variation of coloration or depth to the two-dimensional plot.
The X-Y show mode finds many classical and present purposes. From the basic Lissajous sample to measure section or frequency ratios, to state transition diagrams for contemporary quadrature communications techniques. X-Y plots can present if there’s a relationship between two variables. If such a relationship is discovered it might probably present if the connection is linear or nonlinear and the course of the connection. This text will have a look at a few of these purposes.
Lissajous Patterns
The basic introduction to X-Y plots is the Lissajous plot. Two sine waves are plotted towards one another. For sine wave of the identical frequency the plot is used to measure the section distinction between the sine waves. With fashionable oscilloscopes it’s simpler to only learn the relative section with a measurement parameter. If the sine waves are at completely different frequencies the ratio of their frequencies may be decided as proven in Determine 1.
Determine 1 An X-Y plot of two harmonically associated sine waves the ratio of the variety of horizontal peaks to the variety of vertical peaks exhibits the frequency ratio of the inputs on this case 2 to five.
This plot exhibits the connection between the frequencies of the 2 inputs is 2 to five. The measured frequencies are 1 and a couple of.5 MHz.
Curve tracer
Utilizing an oscilloscope together with an arbitrary waveform generator (AWG) you’ll be able to characterize semiconductor gadget utilizing the X-Y show to plot their V-I traits. Determine 2 exhibits the results of measuring a silicon diode.
Determine 2 The V-I curve for a silicon diode based mostly on twelve utilized voltage values generated by an AWG and the resultant present by way of the gadget.
The AWG generated twelve pulses with voltage amplitudes incremented from -5 to +5 Volts which was utilized to the diode. The voltage throughout the diode and the present by way of the diode have been acquired utilizing the oscilloscope’s sequence mode with one pulse per sequence phase. Measurement voltage and present parameters have been summarized in a pattern plot with one parameter worth per level. The voltage pattern was utilized to the X-Y show horizontal enter with a scale issue of 1 Volt per division whereas the present pattern was utilized to the vertical axis at 12.4 mA per division. The ensuing X-Y show exhibits the diode V-I attribute. A fast check like that is helpful for issues like matching elements.
Quadratic sign measurements
Quadratic sign era makes use of two alerts with a ninety-degree section distinction to generate a sign with a variable section. Two alerts added in quadrature outline a vector with a magnitude and a section. The magnitude of the enter alerts determines each vector attributes. X-Y plots, supported by X-Y cursors can help you view and measure the vector section and magnitude as it’s generated by the quadrature inputs as proven in Determine 3.
Determine 3 The X-Y show of two quadrature alerts exhibits the section trajectory of the vector generated because the quadratic sum of the alerts. X-Y cursors learn the vector magnitude (Radius) and the section (Angle) in addition to the Cartesian coordinates.
The X-Y show permits you to visualize the trail traced by a rotating vector outlined by the quadratic sum of the 2 exponentially weighted RF pulses. The X-Y cursors learn the vector magnitude (Radius) and Part relative to the constructive X axis along with the voltages within the supply pattern factors in channel 1 and a couple of. These cursor readings observe throughout the X-Y and X-T and Y-T waveform shows. Which means the supply elements for any cursor measured vector are measured on the similar time. The 401mV vector magnitude is the results of the 349.6mV X element and the 196.9 mV Y element. This info is beneficial in purposes that use quadratic sign era equivalent to radar and digital communications the place an error within the vector parameters may be traced simply to the supply elements.
The X-Y show can be rendered as persistence show which retains a number of traces overlaid on the show. Persistence shows present the frequency of incidence of the displayed pixels both utilizing displayed depth or coloration. Determine 4 exhibits the in-phase(I) and quadrature (Q) elements of a 16QAM sign together with the X-Y show exhibiting I plotted towards Q, the state transition diagram. Monochrome persistence is used on the X-Y show.
Determine 4 Rendering the X-Y show in monochrome persistence exhibits the information states of the state transition diagram as brighter dots whereas the a number of transitioned section paths are also proven as brighter.
The state transition diagram exhibits the information states on the finish of every transition path in addition to marking the trail between information the states. The waveform spends extra time at every information state than on the transition path and due to this fact the information states are proven as brighter factors on the X-Y show. The 4 section states at 45, 135, 225, and 315 levels are written over twice with two completely different vector amplitudes and likewise seem brighter. Persistence thus offers further details about this measurement together with extra clearly exhibiting the overlapping vectors.
Energy associated X-Y measurements
X-Y shows are additionally used for measurements on switched mode energy gadgets. One instance plots the voltage throughout an influence FET versus the present by way of it to be able to guarantee that the gadget operates inside its protected working space (SOA) as proven in Determine 5.
Determine 5 An X-Y show used to measure the SOA of an influence FET by plotting drain present versus drain to supply voltage. Move/Fail testing compares the X-Y show towards a masks, purple circles point out failures.
The drain to supply voltage (VDS) throughout the FET is utilized to the horizontal axis and the drain present is utilized to the vertical axis. The vertical part of the X-Y show represents the FET in conduction, the VDS is sort of fixed whereas the present will increase. The horizontal loops present the time when the FET is off, present is zero and the voltage is oscillatory. The traces in between symbolize the switching transitions the place energy is dissipated by the gadget. Testing can confirm that the gadgets voltage, present, and energy limits are usually not exceeded.
The blue space is a Move/Fail masks which is used to watch the measurement. The X-Y hint shouldn’t intersect the masks. If it does, it signifies a failure, it’s marked as a failure by a purple circle. Moreover, Move/Fail testing has a number of response choices, each {hardware} and software program to point the state of the check for response actions.
One other energy associated X-Y measurement is measuring the magnetic properties of inductive gadgets. Determine 6 exhibits a magnetic hysteresis plot of an inductor.
Determine 6 The magnetic hysteresis plot plots magnetic flux density as a operate of magnetic discipline energy.
The hysteresis plot inputs are magnetic discipline energy and flux density. Magnetic discipline energy is calculated from the present by way of the inductor whereas flux density is derived from the integral of the utilized voltage. The oscilloscope used on this article has a software program possibility for energy measurements which performs these calculations based mostly on the know coil geometry (cross sectional space and magnetic path size), voltage and present. The world contained in the hysteresis loop is the vitality misplaced per cycle known as, appropriately, the hysteresis loss.
Mechanical measurements
X-Y shows can be utilized to research mechanical gadgets. This requires acceptable transducers to transform mechanical parameters into proportional electrical alerts. An instance of an X-Y show of a mechanical gadget is a pressure-volume plot for an engine as proven in Determine 7.
Determine 7 An X-Y show plotting stress as a operate of cylinder quantity in an inside combustion engine.
The stress is learn utilizing a stress transducer ported by way of the spark plug for the cylinder. The amount is calculated based mostly on the measured crank angle utilizing a rotary encoder. Each transducers use the oscilloscope’s rescale operate to permit measurements in commonplace models of stress and quantity on this case Pascals and liters. There are two loops within the PV plot. The higher, bigger, one represents the facility stroke and the decrease one is the exhaust stroke. The mechanical work generated for every cycle of the engine is proportional to the areas contained in the PV diagram loops. The ability stroke being constructive work and the exhaust stroke is unfavorable work.
Conclusion
It ought to be apparent that the X-Y show is a particularly great tool for deciphering measurements. It permits you to examine alerts, it exhibits the relationships between the plotted variables, and it graphically shows the vector magnitude and section for quadratic inputs. It can also present info of vitality contributions or losses in cyclic processes. It’s a device that you must take into accout for finding out twin hint purposes.
Arthur Pini is a technical assist specialist and electrical engineer with over 50 years expertise in electronics check and measurement.
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