Figure 1 A 33 MHz sine wave sampled at 500 Msps and 31.25 Msps. The properly sampled signal reflects a frequency of 33 MHz, while the signal sampled at 31.25 Msps is aliased and shows an incorrect frequency of 1.75 MHz.
When it comes to making measurements with modular digitizers, it is important to be aware of some common setup problems that will result in bad data and lost time. Setup issues that can arise include aliasing, insufficient amplitude resolution, incorrect amplitude range selection, improper coupling, improper termination, poor trigger setup and excessive noise and spurious pickup. This article will consider each of these issues and provide insight into how to prevent these errors from occurring.
Aliasing, Bane of Sampled Data Systems
Since the advent of sampled data acquisition systems, aliasing has been an ever present problem due to under sampling input signals. Based on the sampling theorem, sampled data instruments such as digitizers and digital oscilloscopes require that analog signals be sampled at greater than two times the highest frequency component present at the input. If this criteria is not met, aliasing can result. Current digitizer designs generally incorporate sampling rates that are greatly in excess of analog bandwidth. By combining this with long acquisition memories, these digitizers minimize this classic problem. Still, users should be aware of aliasing.
Sampled data systems sample the input signals and store the resulting numeric data. If the sample rate meets or exceeds the rule of the sampling theorem, then the signal can be reconstructed without loss of any information. If the analog input waveform is sampled at less than twice its maximum frequency, then the resulting reconstruction of the digital samples results in a waveform at a frequency lower than the original. An example is shown in Figure 1.
The same effect can be seen in the frequency domain (see Figure 2), where the input signal is a sine sweep with a maximum frequency of 2.66 MHz. Sampling is a mixing process that results in the baseband signal (0 to 2.66 MHz) being duplicated about multiples of the sampling frequency. Figure 2ashows the input signal sampled at 15.6 Msps, where the baseband signal appears on the left. The baseband region is duplicated as upper and lower sideband images about the marked 15.6 MHz sample frequency. As the sampling rate is decreased to 6.2 MHz (see Figure 2b), the lower sideband image approaches the baseband signal. Figure 2c shows the spectrum when the sample rate has been reduced to the Nyquist limit (twice the maximum input frequency or 5.2 Msps). At this sampling frequency, the lower sideband image about the sampling frequency interferes with the baseband signal, and aliasing has occurred.
Figure 2 A frequency domain view of a sampled signal, where the sampling rate is well above the Nyquist frequency (a) and approaching the Nyquist frequency (b). Aliasing occurs when the sampling rate is below the Nyquist frequency (c).
Figure 3 A comparison showing how digitizer resolution affects measurement fidelity.
Aliasing generally results in a waveform with a lower frequency than the original signal. It is good practice to know the frequency of the measured signal and then verify it to ensure that it has not been aliased. If the digitizer is triggered from the input signal, then an aliased signal will also appear unstable. This occurs because the digitizer is triggered on the signal and the alias, being at a lower frequency, has multiple trigger points, causing the instability. It is a good procedure to view all unknown signals at the highest sample rate available and then to decrease the sampling rate, if required. If aliasing occurs, the frequency of the signal drop will decrease when a lower sampling rate is selected.
Figure 4 Matching the digitizer’s measurement range with the amplitude of the signal affects the noise of the measurement. Full waveform (a) and magnified low signal region (b).
Insufficient Amplitude Resolution
Digitizers convert the samples of an analog signal into digital values using analog-to-digital converters (ADC). The resolution of the ADC is the number of bits it uses to digitize the input samples. For an n-bit ADC, the number of discrete digital levels that can be produced is 2n. Thus, a 12-bit digitizer can resolve 212 or 4096 levels. The least significant bit (LSB) represents the smallest interval that can be detected; in the case of a 12-bit digitizer, the LSB is 1/4096 or 2.4 × 10-4. To convert the LSB into a voltage, the input range of the digitizer is divided by 2n.
Resolution determines the precision of a measurement; the greater the digitizer resolution, the more precise the measurement values. A digitizer with an 8-bit ADC divides the vertical range of the input amplifier into 256 discrete levels. With a vertical range of 1 V, the 8-bit ADC cannot ideally resolve voltage differences smaller than 3.91 mV, while a 16-bit ADC digitizer with 65,536 discrete levels can resolve voltage differences as small as 15.2 μV.
One reason to use a high resolution digitizer is to measure small signals. Based on the way the minimum voltage level is computed, a lower resolution instrument and a smaller full-scale range can be used to measure smaller voltages. However, many signals contain both small-signal and large-signal components. Thus, for signals with both large and small voltage components, a high resolution instrument with a large dynamic range and a digitizer able to measure small signals and large ones simultaneously is needed.
Figure 3 illustrates how a waveform would look if passed through digitizers with different resolutions, comparing ideal 12-, 14- and 16-bit digitizer responses to a segment of a ±200 mV damped sine waveform. The segment selected is near the end of the waveform and has small amplitude. The 14- and 16-bit digitizers still have sufficient resolution to render the signal accurately. The 12-bit digitizer, with 100 µV resolution (based on a full-scale level of ±200 mV) is unable to resolve levels smaller than 100 µV. The error in reading, for any resolution, will increase with decreasing signal amplitude. This is an ideal case, and noise will limit the accuracy and precision in the real world.
Figure 5 Overloading the digitizer will impair measurement accuracy during the overload and until the instrument recovers.
While signal processing tools like filtering and averaging can improve the resolution of a digitizer, it is still important to consider the dynamic range requirement of any measurement prior to selecting a digitizer; then select one with an appropriate resolution.
Amplitude Range Selection
Quality modular digitizers offer a wide selection of input voltage ranges to accommodate multiple measurement scenarios. The general rule to follow in selecting an amplitude range is to have the signal span the greatest portion of the digitizer’s full scale input range. If possible, aim for utilizing 90 to 95 percent of the available range. Doing so maximizes the available dynamic range and the signal-to-noise ratio. The most common problem is to use only a small percentage of the digitizer’s dynamic range —having a signal with a ±2 V range and acquiring it with a range of ±5 V.
Consider the signals shown in Figure 4. The input is a damped sine with a ±2 V range. It is acquired using the ±2, ±5 and ±10 V ranges. The full signal acquisition using the 2 V range is shown in Figure 4a. A small section of the lower amplitude portion corresponding to the vertical red and blue cursor lines is expanded in Figure 4b. The waveform acquired on the 2 V range (red trace) has the lowest noise level. The waveforms acquired on the 5 V (yellow) and 10 V (blue) ranges have higher noise levels.
One issue that appears when attenuators are in the signal path is that the instrument’s internal noise amplitude scales (relative to the input of the attenuator) with the front-end attenuation. For example, a 10:1 attenuator added to a digitizer with a 58 µV rms noise level has a noise level of 580 µV referenced to the input. The noise level is still the same relative to the percentage of the attenuated full-scale range; however, for a lower signal level – say 5 V on the 10 V range – using one half of the range reduces the dynamic range by 6 dB, and the signal to noise ratio has been decreased.
Figure 6 AC coupling will affect the signal integrity of waveforms with frequency components near or below the lower cutoff frequency (a) and (d), while AC coupling has little to no effect on much higher frequency signals (b) and (c).
Figure 7 Improper matching of digitizer and system impedances can yield measurement artifacts.
The other common setup issue is to acquire the signal on too low a range. If the signal exceeds the full scale range then clipping or limiting will result. If the overload exceeds the maximum voltage range for the digitizer, it may be damaged. Information will be missing in the overloaded areas, and this portion of the waveform is not useful. Some signal processing functions such as the fast Fourier transform (FFT) and digital filtering will produce incorrect results based on overloaded data. Sections of the waveform inside the range may be distorted depending on the overload recovery specifications of the digitizer. If using this technique to see small signals in the presence of larger ones, it is important to verify that the low level signals are not being distorted (see Figure 5). This example shows a 1 V square wave with a 50 mV sine added to it. The digitizer response on the 1 V range is shown as a reference waveform (white trace). The response on the 500 mV range (red trace) shows a slight initial delay but quickly recovers in about 20 ns. When the input is overloaded by 5× (200 mV range, blue trace) the delay is initially about 10 ns with full recovery taking 70 ns. The measured waveform is distorted during the overload recovery time of the digitizer and the distortion depends on the degree of overload. It is better to use a digitizer with greater dynamic range and magnify the acquired signal using zoom than to overload the front end of the digitizer.
Improper Input Coupling
Input coupling in a digitizer offers the ability to AC or DC couple the instrument to the source. DC coupling shows the entire signal, including any DC offset (non-zero mean signals). AC coupling eliminates any steady state mean value (DC). AC coupling is useful for measurements such as ripple on the output of a DC power supply. Without the AC coupling, the DC output would require a large signal attenuation, which would make the ripple harder to measure accurately. With AC coupling, a higher input sensitivity can be used, resulting in a better measurement of the ripple component.
The key specification for AC coupling is its low frequency cutoff (-3 dB point) of the AC coupled frequency response. This determines how much a low frequency signal will be attenuated by the AC coupling. It also relates to the recovery time, the time it takes for the input level to settle after the DC level changes. Generally, the lower the cutoff frequency, the larger the coupling capacitor and the longer the settling time. Problems with AC coupling generally involve trying to measure signals which have low frequency components near or below the lower cutoff frequency of the digitizer’s AC coupling. Consider two square wave input signals with non-zero mean values. One has a frequency of 2 kHz (see Figure 6a), the other 1 MHz (see Figure 6b). Both are applied to a digitizer’s AC coupled input. The 1 MHz square wave has the DC offset removed when using AC coupling (see Figure 6c). The 2 kHz square wave, which is below the 30 kHz cutoff frequency of the digitizer, is differentiated: the coupling circuit passes only the high frequency components, i.e., only the edges of the square wave (see Figure 6d). As the signal frequency is increased, the effect of AC coupling is diminished. Frequencies near the lower cutoff exhibit “tilt,” meaning the top of the square wave will tilt down and to the right.
It is important to know the lower cutoff frequency of the digitizer’s AC coupling. The lower cutoff frequency of the digitizer using the 1 MΩinput termination is 2 Hz and this provides a better range of signal frequencies with good signal fidelity.
Figure 8 The choice of trigger is essential for accurate and stable measurements of noisy signals.
Improper Termination
A measuring instrument should terminate the source properly. For most RF measurements this is a 50 Ω termination. A matching termination minimizes signal losses due to reflections. The figures of merit for matching are return loss or voltage standing wave ratio (VSWR). Either of these indicates the quality of the impedance match. If the source device has a high output impedance then it is more properly matched with a 1 MΩ high impedance termination, which minimizes circuit loading. The 1 MΩ termination also allows the use of high impedance oscilloscope probes, which further increase the load impedance. Impedance matching to other standard terminations, like 75 Ω for video or 600 Ω for audio, can be accomplished by using a 1 MΩ termination combined with a suitable external termination.
Choosing an incorrect termination can cause some interesting effects, as shown in Figure 7. The source for this example is an arbitrary waveform generator (AWG) with a 50 Ω output impedance. When the 50 Ω termination (yellow trace) is selected on the digitizer, the input shows a step voltage going from 1 V down to 0 V. This is the signal amplitude selected in the AWG. When the 1 MΩ termination is selected (red trace), the amplitude doubles (as expected from an unterminated 50 Ω source), with a reflection 32 ns after the negative step. This reflection is due to the mismatch at the digitizer side of the test setup. Selecting the 1 MΩ termination caused two signal integrity errors, which, if observed by an inexperienced engineer, might cause needless troubleshooting. It is best to always terminate the signal being measured with the correct load impedance.
Figure 9 A 10 MHz oscillator (a) contains an unwanted 1 MHz signal (b) from the 5 V power bus (c).
Trigger Setup
Triggering is an essential function for any instrument that acquires and digitizes signals. The most common trigger method uses the signal that is input into one of the digitizer’s channels. The basic principle is that a defined point on the waveform is detected, and this “trigger event” is marked as a known position on the acquired data. The function of triggering is to link the time measurements to a known point in time. For repetitive signals, the trigger must be stable to enable measurements from one acquisition to be compared with others. The wide variation in possible signal waveforms, levels and timing requires that the digitizer’s trigger circuit be extremely flexible. The principal trigger input sources contain dual trigger level comparators and support multiple trigger modes. All modern digitizers include single and dual slope edge triggers, rearm (hysteresis) triggers, window triggers and, for the multiple source trigger, there are related trigger gate generators.
Given the large number of possible trigger modes and settings, it is often difficult to select a good trigger strategy. The most common problems are using the incorrect trigger level and failing to deal with multiple trigger events in a waveform. Both of these issues can be dealt with by actually looking at the trigger signal. Software can aid trigger setup by allowing users to see the trigger levels overlaid on top of the trigger waveform. Viewing the trigger source waveform facilitates selection of the proper trigger levels. A descriptive pop-up window explaining the trigger setup in detail is shown in Figure 8. In this example, a positive rearm or hysteresis trigger mode is being used, as the trigger source is a noisy pulse waveform. The goal is to trigger the digitizer on the signal while minimizing the effects of the noise. There are two trigger levels in this trigger mode: the first (TrigLvl1) arms or enables the trigger; the second (TrigLvl0) will trigger the digitizer acquisition when the waveform exceeds this level with a positive slope. This is explained in the channel trigger pop-up shown in the figure. The rearm trigger is used to trigger reliably in the presence of noise. The difference between the two trigger levels is the trigger hysteresis, which is set to be greater than the typical noise spikes on the waveform. In this case, the digitizer ignores the noise spike between the arm and trigger levels. The digitizer trigger was armed on the lower trigger level but the noise spike amplitude did not exceed the hysteresis, so the digitizer triggered when the waveform resumed its rise.
Noise and Interference
High resolution modular digitizers are designed to minimize internal noise and, because of their large dynamic range, it is important to make sure that extraneous noise and interfering signals do not contaminate the measurements. Interfering signals can be coupled into measurements via either conducted or radiated signal paths.
Conducted noise is most generally due to ground loops in which two or more circuit elements are referenced to different grounds. Proper grounding is essential for accurate measurements. Most commonly, ground loops induce 50 or 60 Hz and related harmonics into a system. These can sometimes be filtered out, but it is better to avoid them if possible. Other conducted paths include spurious signals coupled from power buses. An example of this type of interference is shown in Figure 9, using the output of a 10 MHz oscillator (see Figure 9a). The FFT of the oscillator output (see Figure 9b) shows sidebands spaced at 1 MHz intervals from the 10 MHz carrier, indicating that the oscillator output is being modulated by a 1 MHz source. The 5 V power bus which feeds the oscillator has a 1 MHz ripple with an amplitude of 40 mV peak-to-peak (see Figure 9c), confirming the source of the 1 MHz modulation on the oscillator output.
Radiated noise can be from capacitive, inductive or RF coupling. Interference is “broadcast” from a source directly into the wiring of the circuit under test. The effects of this interference depend on the nature of the coupling and the circuit structure. External noise and interference are not digitizer issues; however, users should be aware that the measurement setup can contribute to uncertainty in the measurement.
Conclusion
Many techniques are useful for reducing noise and spurious pickup in a measurement system. Summarizing the most useful:
- Use low impedance terminations (50 Ω)
- Use the minimum bandwidth necessary for accurate measurements
- Use shielded cables connected to a low noise ground at one end, preferably at the measuring device end
- Use differential cables and digitizers with differential inputs for low speed signals
- Keep radiating sources as far from the circuit under test
- Use magnetic shielding to reduce inductive pickup near motors and other electromagnetic devices
- Ground all measuring instruments to a common, low noise ground
- Use high quality, low loss cables
- Secure cables so that they cannot move or vibrate, to reduce “triboelectric” generation.
- Properly filter all power connections in the circuit under test.
Note: The measured data for the examples in this article were obtained with a Spectrum 14-bit, 500 Msps digitizer. Screenshots were taken using Spectrum’s SBench 6 software
