PLC , or Programmable Logic Controller, works on the following conversion principle:
1. An analog-to-digital converter is a system that converts analog signals into digital signals. It involves filtering, sampling and holding, and encoding.
The analog signal is band-limited filtered and sample-and-holded to become a stepped signal. Then, it is encoded by an encoder to convert each level in the stepped signal into binary code.
2. A digital-to-analog converter (DAC) is a system that converts digital signals into analog signals, typically achieved using low-pass filtering. The digital signal is first decoded, converting the digital code into corresponding voltage levels to form a stepped signal, and then low-pass filtered.
According to signal and system theory, a digital stepped signal can be viewed as the convolution of an ideal impulse sampled signal and a rectangular pulse signal. Therefore, by the convolution theorem, the spectrum of the digital signal is the product of the spectrum of the impulse sampled signal and the spectrum of the rectangular pulse (i.e., the Sa function). Thus, by using the reciprocal of the Sa function as spectral characteristic compensation, the sampled signal can be recovered from the digital signal. By the sampling theorem, the spectrum of the sampled signal can be ideally low-pass filtered to obtain the spectrum of the original analog signal.
In general implementation, these principles are not directly applied because sharp sampling signals are difficult to obtain. Therefore, these two filters (Sa function and ideal low-pass) can be combined (cascaded). Since the filtering characteristics of this system are physically unrealizable, they can only be approximated in real systems.
