Getting the most from your oscilloscope: part 3

Built-in math operations enable your scope to calculate and display measurement results.

In part 1 of this series, we looked at the features oscilloscopes have offered for the past three-quarters of a century. In part 2, we looked at some of the unique features of modern digital scopes. In this part, we’ll take a closer look at math functions and their use in oscilloscope measurements.

Q: What types of math can oscilloscopes perform?
A: Basically, anything from addition and subtraction to scientific and trigonometric operations — about anything you could do on a scientific calculator, and more.

Q: Could we see an example?
A: Sure. Remember, I am using a PicoScope for this demonstration. Other oscilloscopes offer similar capabilities, but of course, the way you gain access to them will vary. In Figure 1, I’ve clicked the Math channels button on the left of the screen (the upper-case sigma), and the Math channels list appears to the right. You can see some of the built-in operations, including invert channel A, invert channel B, add A and B, and so on.

Figure 1. The average(A) function averages 32 channel A waveforms stored in a buffer. (Image: Rick Nelson)

Q: How does the average function work?
A: The blue trace in Figure 1 shows a 50-mV peak, 1-kHz waveform with some noise. Unlike an analog scope, a digital scope saves waveform data in a buffer. In this case, it stores 32 separate traces. You can see trace thumbnails for waveforms 19 through 32 in the buffer navigator above the main waveform display. (You can scroll horizontally to see the rest.) The average function averages the most recent 32 traces, acting as a filter to minimize noise — specifically, a rolling-average filter. The red trace shows the averaged version with reduced noise. Note that I have offset the red trace vertically by 10% so it’s not hidden behind the blue trace.

Q: How can we perform math on multiple waveforms?
A: The blue trace in Figure 2 shows the input to a simple RC low-pass filter, and the red trace shows the output. I’ve selected the PicoScope Measurements functions for peak-to-peak input and output voltages. For a filter, we would like to see gain and phase shift. PicoScope has a built-in Measurements function for phase, and you can see the result in the bottom right Measurements box below the main display.

Figure 2. A simple RC filter has a gain of -3.96 dB and a phase shift of 58.5 degrees. (Image: Rick Nelson)

It doesn’t, however, provide a built-in measurement for gain (at least not that I could find). In that case, I will build one. Just click the Math channels icon, and a menu of available math functions appears.

To create a new calculation, click the plus sign (circled in blue), and you’ll see the equation-entry pop-up (Figure 3). You can enter an equation employing a variety of operators, including scientific and trigonometric ones. To express the gain in dB, our equation is simply 20 times the base-10 logarithm of the ratio of channel B’s amplitude to channel A’s amplitude. You can see this equation in PicoScope notation in the formula box at the top of Figure 3.

Figure 3. You can enter a formula using various operators. (Image: Rick Nelson)

Now, if we look back at the measurements listed at the bottom of Figure 3, we see that the gain is -3.96 dB and the phase shift is 58.5°. That makes intuitive sense. My RC network uses a 10-kW resistor and 0.1-µF capacitor, for a time constant of RC equals 1 ms. That corresponds to a cutoff frequency of w equals 1/RC equals 1,000 radians per second or 159 Hz. So our 200-Hz input frequency is just higher than the cutoff frequency, so we expect our gain to be slightly less than -3 dB and our phase shift to be more than 45°.

Q: What are some other modern oscilloscope features?
A: We’ll take a further look next time.