Oscilloscope measurement parameters provide accurate measurements of acquired waveforms. Most digital oscilloscopes offer around twenty-five standard parameters like frequency, peak-to-peak amplitude, and RMS amplitude. What if you need a measurement parameter that is not in the standard measurement package? Most oscilloscope manufacturers keep alert for these opportunities and offer specialized software analysis packages with optional application-specific parameters. Optional software for power, jitter, serial data, and many more applications, each with specialized measurement parameters, are offered. Another solution is to allow users to create custom measurements using both waveform and parameter math.

Waveform math combines whole waveforms using mathematical functions. Parameter math allows oscilloscope users to create custom measurement parameters based on simple arithmetic relationships between standard measurement parameters. These features allow users to extend the original complement of measurement parameters and to create new parameters based on their measurement needs. This feature can extend the number of available measurements beyond the basic measurement parameters available in the oscilloscope.

This article will examine some commonly used measurements and show how waveform and parameter math can be used to calculate them based on standard measurements.

Setting up a custom measurement using parameter math

Parameter math is controlled in the measurement parameter setup of this oscilloscope and offers eight arithmetic operations to apply to one or more defined measurement parameters (Figure 1).

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

The available arithmetic operations are sum, difference, product, ratio, reciprocal (invert), identity, rescale, and constant. These operations, supplemented by the use of waveform math operations can yield many custom parameters. Parameter math also includes the ability to do these calculations using visual basic scripts. Visual basic scripting is used to internally program the scope and automate selected scope operations.

Measurements based on parameter math share all the characteristics of standard measurement parameters. They can be displayed singly or statistically adding mean, minimum, maximum, and standard deviation values. They can be used as inputs to waveform math functions including histograms, trends, and tracks.

Examples of custom measurement parameters.

Range finder

Measuring distance using ultrasonic signals involves taking a difference between two parameters along with rescaling that measurement from time delay to distance. Figure 2 shows a range measurement using an ultrasonic signal.

Figure 2 Using parameter math to take the time difference between a transmitted and reflected ultrasonic pulse. Source: Arthur Pini

The ultrasonic range finder emits a series of 40 kHz pulses and then detects the time to receive a reflection for each transmitted pulse. The oscilloscope measurement determines the maximum amplitude of the transmitted (parameter P1) and reflected pulses (parameter P3) using gated measurements. It then measures the time at which each maximum occurs using the X@max parameter (parameters P2 and P4). The time difference between these parameters (P5) is the delay between the pulses. This time represents double the distance between the range finder and the target. The final step is to use the parameter math rescale function to multiply the time by one-half of the pulse velocity. The parameter P6 multiplies the time difference by the velocity of the pulse in air divided by two [171.5 meters per second (m/s)]. The rescale function also features the ability to modify the units so that the readout is in units of meters. The resultant distance of 548 millimeters.

Frequency to wavelength

All digital oscilloscopes can read the frequency of a periodic signal. What if you needed to measure the signal’s wavelength? Wavelength is the velocity of the signal divided by its frequency. For a 2.249 GHz sinewave in air, the velocity is 300,000,000 m/s and the wavelength is 0.133 meters (133 mm). The calculation is easy enough to do with a calculator but suppose you wanted to document the measurement and have it available on the oscilloscope screen along with all your other measurements. Using a combination of the constant and ratio arithmetic operations and the measured frequency, the wavelength can be added to the screen as shown in Figure 3.

Figure 3 The constant setup for computing wavelength from frequency using parameter math. The constant is divided by the measured frequency to obtain the signal’s wavelength. Source: Arthur Pini

The calculation of wavelength from frequency starts with entering the velocity of the signal in air at 300M m/s into parameter P2. The setup of the constant includes the ability to enter the physical units of the constant, m/s in this case. The ratio of signal velocity to frequency is accomplished by using the ratio function in parameter P2 to the frequency in P1 as shown in P3. The wavelength of the 2.249 GHz sinewave is 133 mm.

Crest factor

The crest factor is the ratio of the peak amplitude of an RF signal to its RMS value. The oscilloscope measures the peak-to-peak value of a waveform but getting the peak value takes a little math. Figure 4 shows the process using a 40 gigabaud 8PSK signal on a 1-GHz carrier. Determining the peak value of a complex signal is complex. Peaks can be positive or negative in polarity. The peak value is extracted by using the absolute value waveform math function to create a peak detector, converting the acquired bipolar RF signal into a unipolar signal, and then using the maximum measurement parameter to find the greatest peak.

Figure 4 Using the absolute value math function and the maximum measurement parameter to measure the peak value of a modulated RF carrier. Source: Arthur Pini

The math trace F1 performs the computation of the absolute value of the modulated RF carrier in trace M1. Measuring the peak value is done using the maximum value measurement parameter as parameter P1. This process produces a custom measurement of the amplitude using a math function and can be done in any oscilloscope offering the absolute math functions and a maximum or peak measurement, it does not require the use of measurement parameter math. The second half of the crest factor calculation does use parameter math. Continuing with the maximum parameter P1 with the peak value of the RF carrier. The measurement P2 is the RMS value of the RF waveform, a standard measurement. Parameter math is used to complete the calculation of the crest factor by taking the ratio of P1 to P2 and displaying it as parameter P3.

Apparent power and power factor

Although measurements of switched-mode power supplies are generally supported by an application-specific software option in this oscilloscope it is possible to make the same measurements using a combination of waveform and parameter math. Figure 5 provides an example of computing apparent power, real power, and power factor based on the acquired primary voltage and current of a switched-mode power supply.

Figure 5 Using parameter math to calculate apparent power, real power, and power factor based on the input line voltage and line current of a power supply. Source: Arthur Pini

The apparent power P3 is the product of the RMS values of the line voltage P1 and line current P2. The parameter math rescale function P4 is used to convert the reading of apparent power to the correct units of volt-amperes (VA).

To calculate the real power the waveform math product function multiplies the voltage and current waveforms. This is the instantaneous power shown in math trace F1. The parameter P5 measures the mean of the instantaneous power resulting in the real power reading. The ratio of the real to the apparent power is the power factor shown as P6 which used the ratio parameter math function.

FM modulation index

Frequency modulation (FM) is commonly used for applications like frequency shift keying and spread spectrum clocking. One of the key measurements made on an FM signal is its modulation index. The modulation index is the ratio of the FM signal’s frequency deviation from the carrier to its modulation frequency. Neither of these measurements can be made directly from the modulated carrier. The signal has to be demodulated to determine the FM deviation and modulation frequency.

Demodulation is easy to accomplish by using the waveform math track function of the frequency measurement parameter. The track is a time-synchronous plot of the signal’s instantaneous frequency. Figure 6 shows the key measurements made in computing the FM modulation index of an FM signal with a 90-MHz carrier.

Figure 6 Using measurements of the track function of frequency demodulate the 90-MHz FM signal to compute the frequency deviation and modulation frequency needed to calculate the modulation index. Source: Arthur Pini

The FM carrier is shown in the upper left grid. The fast Fourier transform (FFT) of the modulated carrier, in the right-hand grid, shows the dynamics of the variation of the signal frequency about the 90-MHz carrier. The horizontal scale factor of the FFT is 500 kHz per division, frequency deviation can be read approximately from the FFT as ± 250 kHz.   

A more accurate determination of the frequency deviation can be obtained by plotting the track of the signal frequency. This is shown in the lower left-hand grid. The track function plots the instantaneous frequency measured on a cycle-by-cycle basis versus time, synchronous to the source waveform. The vertical axis of the track function is in units of frequency. A parameter measurement of the track’s peak-to-peak amplitude P2 is double the frequency deviation. The parameter math rescale function is used to divide the track by a factor of two with the frequency deviation result in P3 as 251.67 kHz. The frequency of the track P4 is the modulation frequency, 10 kHz in this example. P5 uses the parameter math ratio function 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 other Teledyne LeCroy Windows-based oscilloscopes, includes parameter math. Oscilloscopes that do not include parameter math may be able to use scripting or similar programming capabilities to perform these calculations.

Waveform and parameter math

Using a combination of waveform and parameter math allows oscilloscope users to create custom measurements. These measurements are displayed on-screen just like the standard measurement parameters and can be used as the basis of ongoing analysis including measurement statistics and histograms, trends, and track waveform math functions.

Arthur Pini is a technical support specialist and electrical engineer with over 50 years of experience in electronics test and measurement.

Related Content

• Use waveform math to extend the capabilities of your DSO or digitizer
• Arbitrary waveform generator waveform creation using equations
• Measure vector and area with an oscilloscope X-Y display
• Understanding and applying oscilloscope measurements
• Calculating phase difference with an oscilloscope

The post Custom measurements using waveform and parameter math appeared first on EDN.