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In the field of data acquisition, an RC low-pass filter is the most common signal conditioning circuit used to suppress high-frequency interference or noise. The following figure is the simplest schematic diagram of a passive RC low-pass filter.Only one resistor and capacitor can be implemented, and its cut-off frequency Fc=1/(2πRC)Hz, allowing signals below Fc Hz to pass, and signals above Fc Hz not passing,The first-order RC filter has a wider transition band, and the signal does not attenuate so drastically.
However, we also heardRC integrator, its structure and RC low-pass filter are exactly the same, what is the difference between the two parameters? When is a low pass filter? When is the high pass filter again?
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First look at the low pass filter,The resistance of the low-pass filter in the figure is 33 ohms, the capacitance is 500nF, the cutoff frequency is calculated to be 10KHz, and the cutoff frequency is the frequency point where the gain is -3dB (the magnification is 0.707 times). It is a signal with a frequency of Fc Hz. After passing through the filter, the amplitude becomes 0.707 times the original.
Let's look at the response curve in the frequency domain. At 10Khz, the gain is -3dB, which is the same as the previous calculation.
Look at the time domain waveform again,Red Vi is the input 1V 10Khz sinusoidal signal,The green Vo output is a 0.7V sinusoidal signal,The signal becomes 0.7 times the original, which is consistent with the previous calculation result.
If the signal frequency increases, such as from 10KHz to 100Khz, it will be difficult to pass the high frequency due to the low pass.A 100Khz signal will be severely attenuated. A 1V input, after low pass filtering, is only 100mV.
After talking about the low-pass filter, let's talk about the integrator.
Let's re-look at the 100Khz input sinusoidal signal and the corresponding output signal. will find,The crossing point of Vi sine signal is exactly the minimum value of Vo. Careful observation found that the output Vo and Vi are exactly 180° different. At this time, the input sin signal becomes the output -cos signal, and the effect of integration is realized, but the amplitude is slightly difference.
In fact, in the final analysis, the RC circuit is also a process of charging and discharging the capacitor. If Vi>>Vo, it will play a role similar to the integral, in other words, the RC time constant τ is very large,If Vi is changed to a square wave signal of 100KHz, then the integral effect is more obvious. When Vi is at a high level, Vo keeps accumulating and rises linearly; when Vi is at a low level, Vo keeps decreasing and falls linearly.
The integrator can change from square wave to triangular wave,The passive integrator has a relatively large error,If an operational amplifier is added to form an active low-pass filter, it is another way of playing, which will not be discussed here for the time being.
After we talk about hardware, let's talk about software.
The average filter is a very simple low-pass filter, and its operation process is the process of summing the input signal and dividing it by the coefficient n for weighting, so as to achieve average filtering. There is a summation calculation in its molecule, and it can also realize the function of integration under certain conditions.
Therefore, the hardware circuit design must be rigorous, and the circuit parameters should be set reasonably according to the target signal to avoid the expected effect.
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