Digital to Analog Voltage Conversion? Learn about Quantization!

About quantization

When quantized at 1 bit

Let's assume that the target analog data fluctuates between 0 and 5V, and that the AD converter can also input the same range.
The range that can be entered is called the full scale.
It is digitized in 1 bit, 2 stages, so 5V is divided into 2. 0 to 2.5V → 0, 2.5 to 5V → 1.

The period information of the original data is correct, but the fine voltage and duty (the ratio of "1" to "0" intervals) have changed, resulting in a different waveform. Therefore, we will try increasing the number of bits.

When quantized at 2 bits

It is digitized in 2 bits and 4 stages, so 5V is divided into 4 parts in 1.25V increments.
0 to 1.25V → 00, 1.25 to 2.5V → 01, 2.5 to 3.75V → 10, 3.75 to 5V → 11.

By increasing the bit count from 1 to 2, we have come much closer to the original waveform. Let's add another bit.

When quantized at 3 bits

It is digitized in 3 bits and 8 steps, so 5V is divided into 8 parts in 0.625V increments.
0~0.625V → 000, 0.625~1.25V → 001, 1.25~1.875V → 010, 1.875~2.5V → 011, 2.5~3.125V → 100
3.125 to 3.75V → 101, 3.75 to 4.375V → 110, 4.375 to 5V → 111.

The result is very close to the original data.
As you can see, the more bits you add, the closer you get to the original analog data.

Resolution and LSB (Smallest Change)

The number of bits used to represent digital data is called resolution, and the larger the number, the more accurately the data can be reproduced.
In the case of 3 bits, 5V is divided by 8, so the minimum change is 5V/8=0.625V.
Digital data can express a minimum change of 0.625V compared to continuous analog data, and any change below this is treated as the same data. This minimum change is called the LSB (Least Significant Bit).

Actual AD converter resolution example

For the purposes of explanation, we have shown an example of a low resolution, but in reality, even low-precision ADCs are around 8 bits, with the majority of products being around 12 to 16 bits, and there are also high-precision products with 24 or 32 bits.

If the full-scale voltage is 5V, the following is a typical example of the LSB relative to the number of bits. It is calculated as 5/(2^number of bits).

You can see that increasing the resolution decreases the LSB exponentially. Simply put, higher resolution is preferable, but just like with sampling frequency, increasing the resolution increases the number of digits that represent one piece of data, which increases the amount of data. This leads to increased costs, such as an increase in the circuit scale of the AD converter itself and faster communication speeds.

Relationship between resolution and sampling frequency

It is also important to note that the amount of data acquired per unit time is the product of the resolution and sampling frequency.
Here is an example of allocating resolution and sampling frequency.

With high resolution and high sampling frequency, you can see that you get a lot of data.

Types and selection of AD converters

There are various types of AD converters, each with their own unique characteristics, such as those that are specialized for sampling frequencies and can be made faster depending on the circuit configuration, and those that can easily increase the number of bits and achieve higher resolution.
It is important to select an AD converter that is suitable for your application.