Detailed Description of Analog Signal Sampling and AD Conversion

Here are some points:

Band limited

After the sampling frequency is greater than twice the maximum frequency of the signal, the original signal can be recovered without distortion

In practice, the signal is often wireless bandwidth. How to ensure the limited bandwidth? Therefore, we should add a low-pass filter at the analog signal input to make the signal bandwidth limited, and then use 2.5 3 times the highest signal frequency for sampling. About this, we will see the analog-to-digital conversion process below.

Although it cannot be less than or equal to 2 times, is it good to choose 2 times? In theory, the higher the sampling frequency, the more distortion free recovery of the original signal, but the higher the sampling frequency, the higher the processing speed and storage requirements of the back-end digital system. Therefore, a compromise value should be selected.

If the window in the back-end digital signal processing is too narrow and the sampling rate is too high, it is difficult to accommodate even one cycle of the signal in one window, which makes the signal unrecognizable in some way. For example, if the window size of digital signal processing is 1024 points and the sampling rate is 50KHz, the window can accommodate a signal length of 1024 * (1 / 50KHz) = 20.48ms at most. If a period of the signal is 30ms (20.48ms), it makes it impossible for the digital signal processing window to accommodate a periodic signal, The solution is to reduce the sampling rate or increase the window length on the premise of meeting the requirements.

1 Analog to digital conversion

I remember once taking part in the internship written examination of the Institute of computing of the Chinese Academy of Sciences. There was such a question: what two steps do you have to go through to convert analog signals to digital signals? Fortunately, I was prepared and immediately filled in sampling and quantification. Let's analyze these two processes in detail, but before analysis, let's give a flow chart of the whole process. You can think about why you need each module first.

Programmable amplifier

Our actual analog signals are collected through sensors. People who have done single chip microcomputer should be familiar with DS18B20 temperature sensor. Sorry, it is a digital sensor, that is to say, when people do sensors, they put AD conversion into the sensor. But this is not a common situation, because the temperature is the easiest to measure in the analog signal, and most sensors do not integrate the AD conversion process, such as most acceleration sensors, vibration sensors, sound sensors, electronic compass, and even some GPS (don't be confused, GPS is also a kind of sensor) are analog output. Moreover, due to physical manufacturing, the electrical signal returned by the sensor is very small, generally in a few MV (in case of current, it is also generally in a few MA). Such a weak signal is easy to annihilate in the noise if it is transmitted through wires or cables. Therefore, we often see that the output line of analog sensor will use a line covered with a layer of plastic, which is called shielded wire (as shown in the figure).

Shielded wire can only ensure the minimum interference before the signal is transmitted to the system, but the signal still needs to be processed before it can be used for digital system. At the input end of analog signal (especially high-frequency signal), first use a low-noise amplifier to amplify the signal. This amplifier has special requirements, which must be low noise. We already know that the analog signal signal is very weak. If there is a certain noise in the amplifier, the amplified signal after noise superposition may no longer be the original signal. Since it comes to low noise, how to measure low noise? This can be determined by the amplifier noise figure (NF).

The noise figure is defined as the signal-to-noise ratio between the input signal and the output signal of the amplifier. Its physical meaning is: after the signal passes through the amplifier, the signal-to-noise ratio deteriorates due to the noise generated by the amplifier; The multiple of signal-to-noise ratio reduction is the noise coefficient. The noise figure is usually expressed in dB.

In practice, in addition to considering the low noise figure, we should also consider the bandwidth and frequency range of the amplifier and the most important amplification gain. Since the strength of the input signal may vary from time to time, the programmable amplification gain is used to ensure that the signal can reach full degree without saturation (it is still difficult to do this in practice).