Many of our readers use digital measuring instruments in their daily work, such as digital oscilloscopes, digital recorders, and FFT analyzers. In this and the next column, we will explain the basic functions of their input sections, namely A/D conversion and one of their performance characteristics, namely dynamic range.
A/D Conversion (Analog/Digital Conversion)
Signals associated with physical phenomena such as sound, electricity, and radio waves are inherently continuous quantities and therefore cannot be directly handled by electronic circuits such as digital measuring instruments. For this reason, a method is used in which the horizontal axis (time) is discretized at regular intervals, and the vertical axis (intensity) is further discretized at regular levels to represent the waveform as a point cloud. This operation is called A/D conversion. Digital measuring instruments receive signals from connected sensors continuously, but the instrument itself measures them at a period specified by the user and treats them as two-dimensional coordinate point data. In the past, if the only purpose was to monitor the observed waveform, there were measuring instruments that displayed the waveform continuously as is (such as analog oscilloscopes), but nowadays, there is a growing need to record measurement results numerically, so digital measuring instruments have become mainstream, and A/D conversion has become essential in data processing.
-
Figure 1: Image of A/D conversion
Discretization of the time axis = sampling.
Next, we will explain the elements necessary for A/D conversion using digital measuring instruments. To represent the signal input to a measuring instrument in two dimensions, the horizontal axis is treated as time and the vertical axis as amplitude. Discretizing an analog signal at regular time intervals is called sampling. This regular time interval is called the sampling period, and its reciprocal is called the sampling frequency. In measurements of sound, electricity, etc., the sampling period is often much shorter than 1 second, so for ease of reading in notation, the sampling frequency, which is its reciprocal, is used.
For example, with a sampling frequency of 1 kHz (1000 Hz), continuous values are replaced with discrete values (discontinuous values) every 0.001 seconds. Incidentally, as readers are probably well aware, music CDs, unlike analog records, are digitally sampled media. The sampling frequency for CDs is 44.1 kHz (44,100 Hz), so the reciprocal of that frequency, approximately 0.0000227 seconds (22.7 μs), is used for sampling and recording. Furthermore, high-resolution digital audio sources, which are considered to have even higher sound quality, use a sampling frequency of 96 kHz (96,000 Hz), meaning that samples are taken approximately every 0.0000104 seconds (10.4 μs). Setting a higher sampling frequency allows for tracking finer fluctuations in the original analog signal, but it also increases the number of data points per unit time (doubling the frequency doubles the number of data points). Therefore, in actual measurements, selecting a sampling frequency appropriate for the purpose avoids increasing unnecessary data capacity.
It will disappear.
-
Figure 2: Image of sampling.
Discretization of the amplitude axis = quantization
In the previous section, sampling frequency was defined as the step size (time interval) on the horizontal axis when converting an analog signal to digital.
As explained above, discretizing the vertical axis with constant amplitude steps is called quantization.
Furthermore, this indicates how many numerical steps the amplitude of the original analog signal will be represented by using the step size at this time.
This value is called the A/D resolution (quantization bit depth).
Electronic circuits use binary representation, where "0" and "1" represent OFF and ON states. This means that with 1 bit, the amplitude intensity is represented in two stages: 0 or 1. With 2 bits, since 2²=4, the waveform is plotted using four divisions on the vertical axis. Today, 16 bits are becoming the mainstream for digital measuring instruments, but 16 bits = 2 16 = 65,536, which means that the vertical axis scale is divided into 65,536 divisions, and the original analog signal is applied to these divisions.
If the range is ±1 V, the 2 V span from +1 V to -1 V is divided into 65,536 divisions.
Since this is the applied value, the resolution is approximately 0.00003 V = approximately 30 μV.
As mentioned earlier, music CDs have a quantization bit depth of 16 bits, while digital high-resolution audio sources have an even finer 24 bits. Taking the ±1 V range as an example, the quantization bit depth of digital high-resolution audio sources is 24 bits = 2²⁴ = 16,777,216 divisions. Dividing the 2 V span by this number, the signal is quantized by applying it to a vertical axis scale of approximately 0.00000012 V = approximately 120 n V.
Similar to sampling frequency, a higher quantization bit depth allows for more faithful digital conversion (quantization) of the original analog signal. However, high-bit A/D converters generally have more complex processing and are more expensive.
-
Figure 3: Image of quantization
That concludes our discussion on A/D resolution. Next time, we will explain dynamic range, another fundamental performance indicator for digital measuring instruments.
(Excerpt from the email newsletter issued on September 21, 2022)
