In the previous column, I explained A/D conversion in digital measuring instruments. I hope you, our readers, understood it. In this column, I will continue from where we left off and explain dynamic range, one of the performance characteristics of the input section of digital measuring instruments.
What is dynamic range?
Dynamic range refers to the range within which measuring instruments can produce accurate measurement results without being affected by various types of noise. It is obtained by taking the ratio of the maximum allowable signal level to the noise level and expressing it in dB. In other words, it is the measurable level range when sampling an analog signal with a digital measuring instrument. The larger this value, the wider the range of signal levels that can be measured at once. The origin of the name "dynamic range" is not entirely clear, but it is said that it was originally a term used to describe the signal reproducibility in audio, and then came to be used in the field of measuring instruments. Furthermore, in the field of imaging, such as cameras, this term is used to represent the range of light that a camera can capture.
Relationship with A/D resolution
Readers who remember the content of the previous column may have wondered, "Is there a relationship between A/D resolution and dynamic range?"
As explained in the previous chapter, dynamic range is defined as "the ratio of the minimum value to the maximum value expressed in dB." Here, the ratio of the minimum value to the maximum value is the A/D resolution itself.
For example, if the A/D resolution is 16 bits, the minimum value is 20 = 1 and the maximum value is 216 = 65,536. Since the dynamic range is this ratio expressed logarithmically, it can be calculated as follows.
Similarly, the dynamic range when the A/D resolution is 24 bits can be calculated as follows:
I myself was previously unclear on the relationship between the two, but it becomes clear when you consider A/D resolution as the ratio of the minimum to the maximum value, and its logarithmic representation as dynamic range.
Next, what are the actual dynamic range values of the measuring instruments?
The nominal dynamic range value for our FFT (as listed on our website) is as follows:
| CF-9200/9400 (A/D resolution 24-bit) | 120 dB or more |
| CF-4700 (A/D resolution 24 bits) | 110 dB or more |
| DS-5000 (A/D resolution 24 bits) | 130 dB *1 |
| DS-3000 (A/D resolution 24 bits) | 110 dB or more |
*For 140kHz input units
Looking at this dynamic range value, it's smaller than the theoretical dynamic range calculated earlier for a 24-bit A/D resolution.
What could be the reason for this?
Our digital measuring instruments, including FFTs, are electronic measuring instruments. They have built-in electrical circuits, and electricity flows through the internal circuits when the instrument is in use. In the signal input and A/D conversion sections, if there is no signal, the output will be 0V (Figure 1, ideal waveform). However, in actual electronic measuring instruments, even when there is no signal input, there is electrical noise of its own (called self-noise), so the output is not completely zero (Figure 1, actual waveform). For this reason, the value in the denominator in parentheses in (Equation 1) and (Equation 2) (20=1) is actually greater than 1, and the dynamic range when actually using the measuring instrument will be smaller than the calculated value shown in (Equation 1) and (Equation 2).
While our company and other manufacturers of measuring instruments are working to reduce self-noise, we are currently unable to achieve a completely zero voltage. Therefore, we remeasured the minimum and maximum values (Figure 1, actual waveform, light-colored area), and the ratio is the nominal value shown above, which differs from the theoretical value calculated from the A/D resolution.
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Figure 1: Image of self-noise
Dynamic range of human hearing
The dynamic range of sound intensity that human hearing possesses, that is, the range of sound intensity that can be heard, is said to be approximately 120 dB.
Let's express this 120 dB dynamic range in terms of sound intensity (sound pressure). To represent the range of sound pressure that humans can hear, let P0 be the minimum value (i.e., the smallest sound pressure that humans can hear) and Pmax be the maximum value (i.e., the largest sound pressure that humans can hear). Then the following relationship holds (P0 is also called the minimum audible value).
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(Formula 3)
In other words, the dynamic range of human hearing is 1 million times greater.
For reference, Figure 2 shows a comparison of the dynamic range of human hearing with the levels of common noises in the world. This clearly demonstrates that human hearing is an excellent sensor with a remarkably wide dynamic range.
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Figure 2 Types and magnitudes of noise
In the previous and current articles, we have explained A/D conversion, a fundamental function of the input section of digital measuring instruments, and dynamic range, one of its performance characteristics.
I hope this column helps you understand the image associated with each word.
(Excerpt from the email newsletter issued on November 16, 2022)
