Using an oscilloscope’s time, frequency, and statistical measurement domains

Multiple domains provide designers and test engineers with complementary views of acquired signals.

Oscilloscopes originated as instruments that measure electrical signals in the time domain. The advent of the digital oscilloscope, where input waveforms were digitized and stored in the instrument, opened the door to other analysis domains. In addition to the time domain analysis of the signal, these include the Fast Fourier Transform (FFT) for frequency domain analysis and histograms for statistical analysis. These three measurement domains provide designers and test engineers with three complementary views of the acquired signals. This article reviews the three domains and provides an example of how they interact to facilitate problem diagnosis.

The time domain

The time domain plots the signal’s voltage versus time. This was the original, and still is the primary, function of the oscilloscope (Figure 1).

Figure 1 This time domain view of a sine wave, an oscilloscope’s original and still primary function, also includes some standard time domain measurement tools.

The time domain view shows the waveform as a function of time. The vertical axis is typically measured in volts, but it can be rescaled to measure in any relevant units when used with appropriate sensors. The vertical channel is scaled in volts per division. The horizontal axis is time in seconds, with the scale set to seconds per division. Time-domain measurements can be as simple as counting vertical and horizontal boxes between significant events on the displayed trace and multiplying by the appropriate scale factor, as we did in the “Before Computer (BC)” era.

Most modern oscilloscope users prefer using cursors or automatic measurement parameters. The figure shows the use of both. The cursors (vertical dashed lines) are set to measure the width of the waveform at the half amplitude of a positive half-cycle. Measurement parameters P1 through P4 measure the amplitude, frequency, period, and RMS amplitude of the waveform, respectively.

The frequency domain

A digital oscilloscope acquires and stores the input waveforms. Having the digital representation of the waveform internally allows the oscilloscope’s analysis tools to process the data. One of the most commonly used tools is the Fast Fourier Transform (FFT). The FFT converts the acquired time-domain data into the corresponding frequency-domain data, also known as a spectrum. This enables the oscilloscope to perform most of the common measurements typically found in a spectrum analyzer (Figure 2).

Figure 2 The FFT spectrum of the sine wave plots signal power versus frequency, showing the frequency content of the acquired signal.

The spectrum of a sine wave shows a spectral line at the fundamental frequency, 10 kHz in this example. Due to the large dynamic range of the frequency domain view, it defaults to a logarithmic vertical axis. This scale is calibrated to read in decibels relative to one milliwatt (dBm). If the acquired signal were a perfect sine wave, then the fundamental is all there would be. In the real world, signal sources are not perfect and also show noise and harmonics. This signal has spectral lines at the third (30 kHz), fifth (50 kHz), and seventh (70 kHz) harmonic frequencies.

The frequency domain has the same measurement tools as the time domain, namely, cursors and measurement parameters. The measurement parameters include many that are specific to frequency domain measurements. In this example, the spectral peak amplitudes and frequencies are read out for the fundamental and third harmonics. The fundamental frequency is 10 kHz (P2), and its amplitude is -7.5 dBm (P1). The third harmonic at 30 kHz (P4) has an amplitude of -84.9 dBm (P3), about 77 dB below the fundamental. The dashed lines on the display show the measurement markers for the parameters, indicating what each measures.

The statistical domain

The statistical domain consists mainly of histograms and persistence trace statistical displays. The histogram is the principal tool of statistical analysis. The persistence trace displays show the statistical mean, standard deviation, and range for each point along a trace. The histogram counts the number of amplitude values within a narrow range (called a bin) as a function of amplitude. The vertical axis is the number of samples in a bin, and the horizontal axis is amplitude (Figure 3).

Figure 3 The amplitude histogram of a sine wave is the principal tool of its statistical analysis.

The histogram of a sine wave has a saddle shape, higher on each end and lower in the middle. The reason for this shape lies in the signal’s rate of change. The oscilloscope samples the incoming signal at a fixed rate. If the input signal has a non-uniform rate of change, there will be a greater number of samples where the signal’s rate of change is slower and fewer samples when the rate of change is faster.

In the case of a sine wave, the rate of change is the slowest at both the positive and negative peaks, and greatest at the zero crossings. Hence, the histogram has the greatest concentration of values at the negative (left side) and positive (right side) values. The zero crossings, located in the center of the histogram, have the lowest concentration of values.

The measurement parameters in the statistical domain include the mean, mode, median, standard deviation, and range, among others. The mean, standard deviation, and range of the histogram in the figure are displayed. The mean is the average value of the waveform, the range is the peak-to-peak value, and the standard deviation is the RMS value for a zero mean (some oscilloscope suppliers list it as AC RMS).

Measuring in three domains

Measuring distortion in an amplifier is a common application for an oscilloscope. Consider a measurement of crossover distortion in a push-pull amplifier that uses two transistors to drive a load (Figure 4).

Figure 4 This simplified overview of a push-pull amplifier is accompanied by a diagram of crossover distortion.

The push-pull amplifier uses two complementary transistors to drive a load. The upper NPN transistor supplies current to the load on the positive half of the input signal. The PNP transistor drives the load for the negative half of the input signal. The transistors conduct alternately, based on the polarity of the input signal.

This type of circuit is commonly found in various applications, including amplifiers, half-bridge and full-bridge power supply circuits, and even totem pole output circuits in ICs. The advantage of push-pull operation is that it has no quiescent power dissipation; when the input is zero volts, no power is delivered to the load. A measurement of a properly operating push-pull amplifier (simulated) shows nearly ideal performance (Figure 5).

Figure 5 The analysis of a properly functioning push-pull amplifier shows nearly ideal performance.

Applying a 10 kHz sine wave to a simulated amplifier and analyzing the output yields the expected results across all three measurement domains. The top trace is the time domain view, expanded using horizontal zoom in the trace below it. The trace is a smooth sine wave with no non-monotonic areas. The positive and negative half cycles have a symmetrical shape. There is no obvious clipping or limiting.

The frequency spectrum displays a fundamental spectral line at 10 kHz, accompanied by small odd harmonic distortion products at 30, 50, and 70 kHz, all of which are below -90 dBm. The statistical domain view is a histogram that exhibits a classical, symmetrical saddle-shaped distribution.

One thing that cannot be allowed in this type of amplifier is for both transistors to conduct simultaneously, which would short-circuit the positive and negative power buses. Most amplifiers use a considerable amount of circuitry to prevent this from happening. This compensation can cause one transistor to turn off before the other turns on, resulting in a nonmonotonic flat spot in the output waveform. This situation is described as crossover distortion, which was shown in Figure 4.

What does crossover distortion look like in the three measurement domains? See Figure 6 for an example.

Figure 6 Crossover distortion is evident in all three measurement domain views.

The figure shows a waveform simulating crossover distortion. The distortion is evident in the zoom trace at the zero-crossing points. In this example, the distortion is exaggerated to make it obvious in the time-domain waveform. The frequency spectrum still shows the 10 kHz fundamental, but the levels of the odd harmonics have increased in both number and amplitude.

The FFT spectrum is excellent at showing the presence of distortion as an increase in harmonic amplitudes. The harmonic amplitudes are in the range of -65 to -70 dBm, about 20 to 25 dB higher than the previous levels of normal operation. What the spectrum doesn’t indicate is the source of the distortion.

Look at the histogram in the bottom trace in the figure. Note the large spike at the zero crossing. This indicates a large number of sample values at the 0-volt level, an indicator of crossover distortion. Other forms of distortion would appear in different areas. If the histogram is not symmetric when folded about the zero amplitude axis, then a non-linearity, such as limiting, is suspected. If either peak shows a significantly larger number of values, then clipping is indicated.

Conclusion

The three domain views provide a three-dimensional interpretation of the analyzed waveform. If the distortion is large enough, it is visible as asymmetries and discontinuities, as exemplified by the step in the time-domain zoom trace. Typically, significant distortion does not necessarily produce visible anomalies in the time-domain view.

The increased harmonic levels in the FFT provide a good indicator of any distortion, but it doesn’t indicate the specific type of distortion. The statistical view in the histogram provides information about the type of distortion.

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