Oscilloscope measurement parameters present correct measurements of acquired waveforms. Most digital oscilloscopes supply round twenty-five customary parameters like frequency, peak-to-peak amplitude, and RMS amplitude. What if you happen to want a measurement parameter that’s not in the usual measurement bundle? Most oscilloscope producers preserve alert for these alternatives and supply specialised software program evaluation packages with non-compulsory application-specific parameters. Non-obligatory software program for energy, jitter, serial knowledge, and lots of extra purposes, every with specialised measurement parameters, are provided. One other resolution is to permit customers to create customized measurements utilizing each waveform and parameter math.

Waveform math combines complete waveforms utilizing mathematical features. Parameter math permits oscilloscope customers to create customized measurement parameters primarily based on easy arithmetic relationships between customary measurement parameters. These options enable customers to increase the unique complement of measurement parameters and to create new parameters primarily based on their measurement wants. This characteristic can prolong the variety of accessible measurements past the essential measurement parameters accessible within the oscilloscope.

This text will study some generally used measurements and present how waveform and parameter math can be utilized to calculate them primarily based on customary measurements.

Organising a customized measurement utilizing parameter math

Parameter math is managed within the measurement parameter setup of this oscilloscope and provides eight arithmetic operations to use to a number of outlined measurement parameters (Determine 1).

Determine 1 A typical measurement parameter math setup takes the ratio of parameter P3 to parameter P4. Supply: Arthur Pini

The accessible arithmetic operations are sum, distinction, product, ratio, reciprocal (invert), identification, rescale, and fixed. These operations, supplemented by way of waveform math operations can yield many customized parameters. Parameter math additionally contains the power to do these calculations utilizing visible primary scripts. Visible primary scripting is used to internally program the scope and automate chosen scope operations.

Measurements primarily based on parameter math share all of the traits of ordinary measurement parameters. They are often displayed singly or statistically including imply, minimal, most, and customary deviation values. They can be utilized as inputs to waveform math features together with histograms, tendencies, and tracks.

Examples of customized measurement parameters.

Vary finder

Measuring distance utilizing ultrasonic indicators includes taking a distinction between two parameters together with rescaling that measurement from time delay to distance. Determine 2 reveals a variety measurement utilizing an ultrasonic sign.

Determine 2 Utilizing parameter math to take the time distinction between a transmitted and mirrored ultrasonic pulse. Supply: Arthur Pini

The ultrasonic vary finder emits a sequence of 40 kHz pulses after which detects the time to obtain a mirrored image for every transmitted pulse. The oscilloscope measurement determines the utmost amplitude of the transmitted (parameter P1) and mirrored pulses (parameter P3) utilizing gated measurements. It then measures the time at which every most happens utilizing the X@max parameter (parameters P2 and P4). The time distinction between these parameters (P5) is the delay between the pulses. This time represents double the space between the vary finder and the goal. The ultimate step is to make use of the parameter math rescale operate to multiply the time by one-half of the heart beat velocity. The parameter P6 multiplies the time distinction by the speed of the heart beat in air divided by two [171.5 meters per second (m/s)]. The rescale operate additionally options the power to switch the items in order that the readout is in items of meters. The resultant distance of 548 millimeters.

Frequency to wavelength

All digital oscilloscopes can learn the frequency of a periodic sign. What if you happen to wanted to measure the sign’s wavelength? Wavelength is the speed of the sign divided by its frequency. For a 2.249 GHz sinewave in air, the speed is 300,000,000 m/s and the wavelength is 0.133 meters (133 mm). The calculation is simple sufficient to do with a calculator however suppose you needed to doc the measurement and have it accessible on the oscilloscope display together with all of your different measurements. Utilizing a mix of the fixed and ratio arithmetic operations and the measured frequency, the wavelength will be added to the display as proven in Determine 3.

Determine 3 The fixed setup for computing wavelength from frequency utilizing parameter math. The fixed is split by the measured frequency to acquire the sign’s wavelength. Supply: Arthur Pini

The calculation of wavelength from frequency begins with coming into the speed of the sign in air at 300M m/s into parameter P2. The setup of the fixed contains the power to enter the bodily items of the fixed, m/s on this case. The ratio of sign velocity to frequency is achieved through the use of the ratio operate in parameter P2 to the frequency in P1 as proven in P3. The wavelength of the two.249 GHz sinewave is 133 mm.

Crest issue

The crest issue is the ratio of the height amplitude of an RF sign to its RMS worth. The oscilloscope measures the peak-to-peak worth of a waveform however getting the height worth takes just a little math. Determine 4 reveals the method utilizing a 40 gigabaud 8PSK sign on a 1-GHz service. Figuring out the height worth of a fancy sign is advanced. Peaks will be optimistic or detrimental in polarity. The height worth is extracted through the use of absolutely the worth waveform math operate to create a peak detector, changing the acquired bipolar RF sign right into a unipolar sign, after which utilizing the utmost measurement parameter to seek out the best peak.

Determine 4 Utilizing absolutely the worth math operate and the utmost measurement parameter to measure the height worth of a modulated RF service. Supply: Arthur Pini

The mathematics hint F1 performs the computation of absolutely the worth of the modulated RF service in hint M1. Measuring the height worth is completed utilizing the utmost worth measurement parameter as parameter P1. This course of produces a customized measurement of the amplitude utilizing a math operate and will be carried out in any oscilloscope providing absolutely the math features and a most or peak measurement, it doesn’t require using measurement parameter math. The second half of the crest issue calculation does use parameter math. Persevering with with the utmost parameter P1 with the height worth of the RF service. The measurement P2 is the RMS worth of the RF waveform, a typical measurement. Parameter math is used to finish the calculation of the crest issue by taking the ratio of P1 to P2 and displaying it as parameter P3.

Obvious energy and energy issue

Though measurements of switched-mode energy provides are usually supported by an application-specific software program choice on this oscilloscope it’s attainable to make the identical measurements utilizing a mix of waveform and parameter math. Determine 5 supplies an instance of computing obvious energy, actual energy, and energy issue primarily based on the acquired major voltage and present of a switched-mode energy provide.

Determine 5 Utilizing parameter math to calculate obvious energy, actual energy, and energy issue primarily based on the enter line voltage and line present of an influence provide. Supply: Arthur Pini

The obvious energy P3 is the product of the RMS values of the road voltage P1 and line present P2. The parameter math rescale operate P4 is used to transform the studying of obvious energy to the right items of volt-amperes (VA).

To calculate the true energy the waveform math product operate multiplies the voltage and present waveforms. That is the instantaneous energy proven in math hint F1. The parameter P5 measures the imply of the instantaneous energy leading to the true energy studying. The ratio of the true to the obvious energy is the ability issue proven as P6 which used the ratio parameter math operate.

FM modulation index

Frequency modulation (FM) is usually used for purposes like frequency shift keying and unfold spectrum clocking. One of many key measurements made on an FM sign is its modulation index. The modulation index is the ratio of the FM sign’s frequency deviation from the service to its modulation frequency. Neither of those measurements will be made instantly from the modulated service. The sign must be demodulated to find out the FM deviation and modulation frequency.

Demodulation is simple to perform through the use of the waveform math observe operate of the frequency measurement parameter. The observe is a time-synchronous plot of the sign’s instantaneous frequency. Determine 6 reveals the important thing measurements made in computing the FM modulation index of an FM sign with a 90-MHz service.

Determine 6 Utilizing measurements of the observe operate of frequency demodulate the 90-MHz FM sign to compute the frequency deviation and modulation frequency wanted to calculate the modulation index. Supply: Arthur Pini

The FM service is proven within the higher left grid. The quick Fourier rework (FFT) of the modulated service, within the right-hand grid, reveals the dynamics of the variation of the sign frequency in regards to the 90-MHz service. The horizontal scale issue of the FFT is 500 kHz per division, frequency deviation will be learn roughly from the FFT as ± 250 kHz.   

A extra correct willpower of the frequency deviation will be obtained by plotting the observe of the sign frequency. That is proven within the decrease left-hand grid. The observe operate plots the instantaneous frequency measured on a cycle-by-cycle foundation versus time, synchronous to the supply waveform. The vertical axis of the observe operate is in items of frequency. A parameter measurement of the observe’s peak-to-peak amplitude P2 is double the frequency deviation. The parameter math rescale operate is used to divide the observe by an element of two with the frequency deviation end in P3 as 251.67 kHz. The frequency of the observe P4 is the modulation frequency, 10 kHz on this instance. P5 makes use of the parameter math ratio operate to compute the modulation index by dividing the frequency deviation by the modulation frequency. The modulation index is 25.2.

The oscilloscope used for these examples is a Teledyne LeCroy WaveMaster 8Zi-A which, like different Teledyne LeCroy Home windows-based oscilloscopes, contains parameter math. Oscilloscopes that don’t embody parameter math might be able to use scripting or comparable programming capabilities to carry out these calculations.

Waveform and parameter math

Utilizing a mix of waveform and parameter math permits oscilloscope customers to create customized measurements. These measurements are displayed on-screen similar to the usual measurement parameters and can be utilized as the idea of ongoing evaluation together with measurement statistics and histograms, tendencies, and observe waveform math features.

Arthur Pini is a technical assist specialist and electrical engineer with over 50 years of expertise in electronics take a look at and measurement.

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