![]() The test uses a sine wave as the test signal because high-quality sine waves are relatively easy to generate and characterize. The basic test process involves applying a known, high-quality signal to the digitizer and then analyzing the digitized waveform (Figure 3). This approach provides an easily understood and universal figure of merit for comparisons. A good place to start is by determining the digitizing system’s SNR and the resulting effective bits according to the preceding equations. ![]() Understanding the impact of digitizer noise on oscilloscope measurements figure 3It is often easier to measure overall performance instead of trying to distinguish and measure each error source in a digitizing system. ![]() If you do not meet bandwidth requirements, quickly changing lesser bits can be dropped, lowering the ENOB. ![]() This requirement increases bandwidth requirements for data lines and buffer inputs for these lesser bits. For example, in high-speed real-time digitizing without sample-and-hold or track-and-hold tracking, the LSBs must change at high rates to follow a quickly changing signal. This error is an inherent part of digitizing (Figure 2).īeyond these error sources, still other possible sources of digitizing error exist. Even in an ideal digitizer, quantizing causes a minimum noise or error level amounting to ±½ LSB. Noise or error relating to digitizing can come from a number of sources. Improved ENOB results can improve this result, so comparisons of ENOB specifications or testing must account for both test-signal amplitude and frequency. Actual testing may use test signals at less than full-scale-50 or 90% of full-scale, for example. These equations employ full-scale signals. This assumption allows you to replace the ideal quantization error term with FS/(2 N √1¯2¯), where FS is the digitizer’s full-scale input range. An alternative for the third equation assumes that the ideal quantization error is uniformly distributed over one LSB (least-significant bit) peak to peak. The IEEE Standard for Digitizing Waveform Recorders (IEEE Standard 1057) defines the first two equations (Reference 1). In the second equation above for EB, the ideal quantization error term is the rms error in the ideal, N-bit digitizing of the input signal. These equations employ a noise, or error, level that the digitizing process generates. Where N is the nominal, or static, resolution of the digitizer, and, EB=−log2(rmsERROR)×√1¯2¯/FS. Where EB represents the effective bits, A is the peak-to-peak input amplitude of the digitized signal, and FS is the peak-to-peak full-scale range of the digitizer’s input.ĮB=N−log 2 (rms ERROR / IDEAL_QUANTIZATION_ERROR) The following equation yields the relationship to effective bits: Where rms SIGNAL is the root-mean-square value of the digitized signal and rmsERROR is the root-mean-square value of the noise error. You can express this noise on a digitized signal in terms of SNR (signal-to-noise ratio): Noise in this case refers to any random or pseudorandom error between the input signal and the digitized output. This decline in digitizer performance manifests itself as an increasing level of noise on the digitized signal. As the signal you are digitizing increases in frequency or speed, performance drops to lower and lower values of effective bits. In this case, an 8-bit digitizer provides 8 effective bits of accuracy only at dc and low frequencies. The figure illustrates that effective digitizing accuracy falls off as the frequency of the digitized signal increases. It also can cause waveforms to appear “fat” in contrast to analog oscilloscopes. Noise can make it challenging to find the true voltage of a signal, and it can increase jitter, making timing measurements less accurate. In test and measurement, noise can make it difficult to make measurements on a signal in the millivolt range, such as in a radar transmission or a heart-rate monitor. Unfortunately, when an ENOB specification is provided, it is often at just one or two points rather than across all frequencies. Resolution typically degrades significantly as frequency increases, so ENOB versus frequency is a useful specification. The ENOB figure summarizes the noise and frequency response of a system. You can use ENOB (effective-number-of-bits) testing to more accurately evaluate the performance of digitizing systems, including oscilloscopes. One of the most common sources of errors in measurements is the presence of vertical noise, which can decrease the accuracy of signal measurement and lead to such problems as inaccurate measurements as frequencies change.
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