The process of sampling analog signals, such as voltage signals obtained from sensors, at a specific frequency and converting them into digital values is called AD conversion.
(analogue-to-digital conversion)
The precision of AD conversion is expressed in terms of the number of digits in the numerical value, and is generally expressed as the number of binary digits, such as 8 bits.
One of the eight bits is used for the sign (polarity), so if the maximum amplitude is 1, the smallest step size is 2^-7 (1/128). If we consider this smallest step size as the smallest unit, we can represent a numerical value by multiples of this unit. This can be likened to a quantum, and AD conversion is sometimes called quantization (amplitude quantization) in the sense that it is represented by the number of quanta.
Furthermore, if we use the term resolution, AD conversion can decompose an amplitude of up to 1 into several levels, so a resolution of 8 bits is expressed as 256 levels, a resolution of 10 bits as 1024 levels, and so on.
Now, when a continuous waveform is converted using AD conversion, the quantized data cannot be made finer than the smallest step size, so a difference arises between the quantized data and the actual value.
The difference is called the quantization error, and the distortion of the waveform caused by this error is called quantization distortion. From the perspective of the original waveform, this can be thought of as noise equal to the quantization error being added. It is clear that increasing the number of digits reduces the quantization error.
The signal-to-noise ratio (S/N, usually expressed in dB) is used to represent the degree of noise, as it is the ratio of signal power to noise power.
The quantization error, expressed as the signal-to-noise ratio (S/N), can be calculated using the following formula.
S/N = 6b + 4.8 - 20LogP
b: Number of binary digits (including 1 polarity bit)
P: Ratio of maximum amplitude to average amplitude of the signal
For a sine wave, P = √2 (understand this as taking the square root of 2).
When calculating with b=16 bits:
S/N=97.8 dB
Generally, a higher signal-to-noise ratio (S/N ratio) is said to result in higher sound and image quality. Audio CDs typically have a S/N ratio of 90dB, while VHS tapes for video use are said to have an S/N ratio of 45dB.
Dynamic range is similar to signal-to-noise ratio (S/N), but it is defined as "the ratio of the magnitude of the largest signal and the smallest signal that can be handled in an amplification circuit, etc., and is expressed in units of dB."
For example, in an AD converter, signals smaller than the quantization distortion and the self-noise inherent in the amplification circuit itself are buried in noise, making it impossible to distinguish between a signal and noise. The ratio of the smallest signal that is larger than the self-noise and clearly recognizable as a signal to the maximum amplitude of 1 is the key.
Now, I've written at length about some rather confusing things, but the keywords for the answer in the previous issue are "dynamic range and a large signal-to-noise ratio." Measuring instruments such as digital oscilloscopes allow you to change the voltage range to match the waveform amplitude. This means setting the voltage range so that the waveform amplitude fills the screen as much as possible (AD conversion amplitude 1), and setting an appropriate voltage range to achieve a large dynamic range and signal-to-noise ratio. When viewing only the AC component of a DC and AC mixed signal, selecting AC coupling and setting the voltage range to suit its maximum amplitude will result in the best measurement conditions.
(Excerpt from the email newsletter published on December 21, 2001)
