### Custom Measurement Parameters using Parameter Math

Parameter math allows oscilloscope users to create custom parameters based on simple arithmetic relationships between existing parameters. It allows you to add, multiply, subtract, rescale, or divide parameters. This feature allows users to extend the original complement of measurement parameters based on measurement needs.

For example, consider measurement of the crest factor of a waveform. Crest factor is the ratio of a waveform’s peak value to its rms value. Teledyne LeCroy oscilloscopes do not list crest factor as a parameter, but by combining some simple math with existing parameters, we can calculate and display crest factor.

Figure 1 shows the steps in creating a crest factor measurement. #### Figure 1:

The setup for computing crest factor using parameter math

The source waveform in this example is a noise waveform shown in channel 1. Because the definition of crest factor is the peak value divided by the rms value, we must account for both positive and negative peaks by using the absolute value math function. Math function F1 accomplishes this task. The peak value is measured using the absolute value math function. Math function F1 accomplishes this task. The peak value is measured using the maximum parameter (P1) applied to F1. The rms value is measured using the standard deviation (sdev) parameter (P2). Sdev ignores any DC offset in the signal, which is sometimes called AC rms.

The crest factor is the ratio of maximum to sdev and is computed using parameter P3. The dialog box for setting up parameter math in P3 is shown in Figure 1. The numeric readout of P3 is the crest factor (4.23)

Another example of parameter math is measuring the modulation index of an FM signal. The modulation index is the ratio of the peak frequency deviation to the FM modulation frequency. We can determine both the modulation frequency and peak deviation of a sinusoidally-modulated FM carrier using a track function of the frequency parameter. The track function is a plot of the parameter value as a function of time, synchronous with the source waveform. Figure 2 provides an example. #### Figure 2:

Measuring the modulation index of an FM signal

Start by measuring the frequency of the source channel. Teledyne LeCroy oscilloscopes offer all-instance measurements, so we see the frequency of each cycle of the source waveform. The function F1 is the low-pass filtered track of frequency. You can see the sinusoidal shape of the modulating signal. The frequency of F1 is the modulation frequency. The amplitude of F1 is the peak-to-peak frequency deviation. The goal is to divide the ratio of the peak frequency deviation by the modulation frequency. We start the process by measuring the peakto-peak amplitude of F!. Using parameter math, we divide this by two to get the peak frequency deviation. The setup for parameter rescale is shown in the dialog box at the bottom of figure 2. The value of peak-to-peak amplitude (P3) is multiplied by 0.5. This is the peak frequency deviation. Parameter math is again used in P5 to take the ratio of peak frequency deviation to the frequency of F1, yielding the FM modulation index of 5.17.

Parameter math is a valued adjunct to measurements made with Teledyne LeCroy oscilloscopes.