Modern mid-range oscilloscopes have more features than most engineers ever use. This article summarizes 10 oscilloscope applications that may surprise you. In any event, you may find them useful.

Use the oscilloscope's fast edge feature and math operations to make frequency response measurements
Frequency response measurements require a source signal that has a flat spectrum. By utilizing the fast edge test signal of the oscilloscope as a step source it is possible to derive the impulse response of the device under test using the scope's derivative function. This can then be applied to the FFT (Fast Fourier Transform) function to obtain the frequency response. Figure 1 shows the steps in the process for both the frequency response of the input signal and that of a 37 MHz low pass filter.

Figure 1. Deriving the frequency response of a filter by applying the fast edge test signal to the filter input (upper left), taking the filter output (upper right trace) differentiating it (right center), and finally taking the average of the FFT (lower right). The spectrum on the lower left trace shows the frequency flatness of the differentiated step input.

The fast edge test signal has a rise time of about 800 ps and a bandwidth of about 400 MHz, which is much greater than the 100 MHz span of this measurement.

This article was originally published on EBN sister publication EDN .

High pass filter your input signal using the oscilloscope's low pass digital filter
If your oscilloscope has provision to apply a low pass filter to a signal using a feature such as the enhanced resolution (ERES) math function then you can high pass filter that same signal. Note that this can only be done if you can access both the input and output of the digital low pass filter. Figure 2 shows the setup.

Figure 2: By subtracting the low pass filtered waveform (trace F1 center) from the input signal (C1, top trace) the resultant signal has a high pass characteristic as shown in the spectrum of the math trace F2 (bottom trace).

The input signal trace C1 is a narrow pulse. Math trace F1 (center trace) filters the signal using the oscilloscope's ERES digital filter. By subtracting the filter trace from the input signal the resultant signal has only higher frequency components. Trace F2 performs the subtraction and also takes the FFT of the high pass signal so you can see the high pass characteristic. The frequency at which the low pass response drops to 0.293 of the maximum response is the -3dB point of the high pass filter.

Selectively average only signals with certain shapes or measured parameters
Oscilloscopes that offer pass/fail testing based on waveform templates or parametric measurements and the ability to store waveforms meeting the pass/fail criteria to internal memory can selectively add those waveforms to the scope’s average function. Set up this function by first entering the pass/fail criteria based either as a waveform template and/or on a measured parameter(s) being within desired limits. The action for a passed test is to store the waveform to an internal storage memory. Set up the averaging function to average the contents of that internal memory. The result is that only waveforms meeting the test criteria will be added to the average content. Figure 3 shows the setup for such a process.

Figure 3. Setup to selectively average only those waveforms that are contained in the waveform template. The channel 1 trace (C1) does not match the template, red circles indicate areas outside the template. The last accepted trace is stored in memory trace M1 and appears within the template. The math trace F1 shows the accumulated average with only waveforms falling within the template being added to the average.

Pass/fail testing is set up to pass waveforms that fall completely within the template (shown in blue). Waveforms that meet the pass criteria are stored to memory M1 and added to the average in function trace F1. Waveforms that do not meet the criteria are rejected and never appear in the average.

Find intermittent events by using exclusion trigger to acquire only on abnormal events
Smart or advanced triggers are based on selected waveform characteristics like width, period, or duty cycle. Several manufactures offer the ability to trigger on smart trigger events that are within or outside a range. Such a trigger is an exclusion trigger in that it can be employed to trigger on only abnormal events, as shown in Figure 4.

Figure 4. An exclusion trigger setup based on the width of a pulse being outside the range of 48±0.8 ns. This resulted in the scope triggering on the large pulse with a 52.6 ns width ignoring all the nominal 48 ns wide pulses.

In this example the scope has been set up to trigger on pulses with widths outside the range of 48±0.8 ns. It doesn't trigger until the large pulse with a width of 52.6 ns occurs. Because the scope only triggers on the pulses with widths outside the nominal 48 ns width there is no issue of update rate. It is literally “lying in wait” for the abnormal pulse widths.

Use the trend functions and trigger hold off as a self-timed data logger
Trend plots are plots of measured parameter values displayed in the order they were taken. An example of just such a setup is shown in Figure 5. The internal temperature of an oscillator is measured with a thermal probe having a sensitivity of 39 µV /°C. Simultaneously, the frequency, taken over a single cycle, is acquired. The 100 measurements in each trend are acquired over 100 acquisitions. The trigger source is the oscillator output. Normally, this would cause the scope to trigger at its nominal update rate.

Figure 5. The trend plots of internal temperature (trace F2) and oscillator output frequency (trace F1) taken over 1000 s show the oscillator's thermal response characteristics.

To keep this from happening and to set a known delay between measurements, trigger hold-off is used. The time between acquisitions is set to 10 s using trigger hold-off so the total measurement interval is 1000 s. The voltage readings of the temperature sensor are converted to degrees Celsius using the parameter math rescale function.

Demodulating amplitude modulated signals
Envelope detection of an amplitude modulated signal involves peak detection of the signal. Peak detection can be implemented by combining the absolute value math function and the digital low pass filter called enhanced resolution (ERES) in this oscilloscope. This makes it easy to accurately extract the shape of modulation envelope. An example is shown in Figure 6. The upper left trace is the acquired AM signal. The absolute value math function is applied as shown in the lower left trace; absolute provides full wave rectification.

Figure 6. The steps in extracting the modulation envelope from an AM signal. Absolute value is used to ‘detect’ the signal. ERES filtering removes the HF carrier yielding a clean modulation envelope.

A combination of the sparsing and ERES functions is used to low pass filter the absolute value, resulting in the modulating envelope shown in the upper right trace.

Sparsing, which selectively reduces the sample rate of an acquired waveform, is used to help set the cutoff frequency of the ERES low pass filter, which is a function of the sampling rate. The low pass filter cutoff frequency must be well below that of the carrier.

The traces in the lower right grid are overlaid zoom traces of the input AM modulated signal and the extracted envelope showing the fidelity of the process. Measurements and further analysis can be applied directly to the extracted envelope.

Detection of frequency, phase, and pulse-width modulated signals
Many midrange oscilloscopes offer a track or time-trend function that generates a waveform based on cycle-by-cycle variations of a measured timing parameter. The track function is time synchronous with the source waveform so that changes in frequency, width, or phase are easily correlated with the source waveform. This provides a way of demodulating FM (frequency modulated), PM (phase modulated), or PWM (pulse width modulated) signals. Figure 7 shows an example of demodulation of a PM waveform using a track of the TIE (time interval error) parameter.

Figure 7. Using the track of the TIE parameter the instantaneous phase of each cycle of the PM waveform is plotted vs. time, thus demodulating the phase-modulated signal.

TIE is the time difference between a threshold crossing on a waveform and that threshold crossing’s ideal position. It is essentially the instantaneous phase of the signal. A track of TIE therefore shows the cycle-to-cycle variation of the carrier's phase and produces a waveform showing the phase variation time synchronous with the original modulated carrier. The vertical scale is in units of time and can be easily converted to phase by a simple rescale operation. In a similar manner, a track of the frequency parameter will show the modulation signal of an FM modulated carrier, and a track of pulse width yields PWM demodulation.

Adding a “Max Hold” function to the oscilloscope's Fast Fourier Transform
Spectrum analyzers offer a peak or max hold feature that is very useful when doing swept sine frequency response measurements. Most oscilloscope FFTs do not offer this feature as part of the FFT function, but they do offer roof or maximum math functions that can be combined with the FFT to hold the maximum amplitude occurring at each frequency cell in the FFT. Figure 8 provides an example of this feature.

Figure 8. The red trace, F2 (center), shows the peak or maximum values for each frequency in the FFT of a swept frequency sine. Trace F1 (bottom) is the FFT without the roof or maximum applied. The F2 descriptor box shows the roof function setup.

The roof (or maximum) function, shown in trace F2 retains the peak amplitude at each frequency cell in the FFT as the input sine wave seeps through a range of frequencies. This allows the user to see the maximum response at each frequency.

Calculating the power spectral density of a waveform in unit of V²/Hz
Oscilloscope FFTs display power spectrum and power spectral density (SPD) logarithmically with units of dBm or dBm/Hz, respectively. Applications such as noise analysis require the power spectral density in linear units such as V²/Hz or V/√ Hz. The measurement of PSD with linear scaling can be accomplished with a little work using the FFT and the rescale math function. Figure 9 shows the FFT setup for this measurement.

The FFT output type is set to Magnitude Squared to display the FFT with vertical units of V². Conversion to PSD requires that the FFT be normalized to the effective resolution bandwidth of the FFT. This is the product of the resolution bandwidth (Δf) and the ENBW (effective noise bandwidth) of the selected weighting function as reported in the FFT setup in Figure 9.

Figure 9. Trace C1 is the acquired band limited noise signal. Trace F3 is the power spectral density with linear vertical scaling in units of V²/Hz. Parameter P7 reads the area under the PSD trace and compares it to the mean squared value of the time waveform, calculated as the square of the standard deviation of trace C1, in parameter P8.

This scope reads the FFT as peak values, so we must also convert this back to mean squared value, which means dividing all amplitude values by a factor of two. The normalization is done using the rescale math function, in this case multiplying each FFT amplitude value by 5×10-6. The resulting trace, F3 in Figure 9, reads PSD in V²/Hz. The parameter P2 is the standard deviation of the input waveform C1. This value is squared in parameter P8 and is the mean squared amplitude of the input signal. The parameter P7 reads the area under the PSD trace (F3) as 23.3 mV². It also reports the mean square amplitude, in this case, derived from the FFT as 23.28 mV² validating the process.

Using zoom-gated FFTs to compare spectral components
Occasionally, you may need to perform an FFT on a small part of an acquired waveform. This often happens when the waveform in question is varying in time. Most oscilloscopes allow you to gate the FFT process either by a gate setup in the FFT controls or via computing the FFT on a zoom of the acquired waveform. Keep in mind that, in either case, the FFT resolution bandwidth will be determined as the reciprocal of the gated signal duration. Since the gated component is shorter than the entire waveform, the resolution bandwidth will increase the resolution bandwidth and decrease the FFT’s frequency resolution. Figure 10 shows an example of gated FFT analysis on a linear sine sweep waveform. The frequency of the sine varies from 1 MHz to 80 MHz over the 10 ms sweep duration (trace M1 upper left).

Two zooms of 5 µs duration are taken at 437 µs and 1.42 ms into the waveform (traces Z1 left center, and Z2 left bottom). The FFT of the entire waveform (F1 upper right) shows a uniform amplitude over the entire sweep range. FFTs of Z1 and Z2 show the frequencies at the selected points in time on the sweep.

Figure 10. Example showing the use of zoom functions to gate the FFT. Two 5 µs zooms taken at 437 µs and 1.42 ms show differences in the frequency as a function of time.

Conclusion
The somewhat unconventional application of existing oscilloscope features allows you to extend the usefulness of this versatile instrument. You paid a good deal for the oscilloscope; you should get your money's worth out of it. Hopefully these hints will allow you to do just that.

This article was originally published on EBN sister publication EDN .