Low-pass filter, high-pass filter, integral circuit, differential circuit

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Low-pass filter, high-pass filter, integral circuit, differential circuit [Copy link]

The circuit whose output signal is proportional to the integral of the input signal: Integral circuit The circuit whose output signal is proportional to the differential of the input signal: Differential circuit 1) First-order RC low-pass filter The circuit of the RC low-pass filter and its amplitude-frequency and phase-frequency characteristics are shown in the figure below. Assume that the input voltage of the filter is ex and the output voltage is ey, the differential equation of the circuit is: This is a typical first-order system. Let =RC, called the time constant, take the Laplace transform of the above formula, and we have: Analysis shows that when f is very small, A(f)=1, and the signal passes without attenuation; when f is very large, A(f)=0, the signal is completely blocked and cannot pass. 2) First-order RC high-pass filter The circuit of the RC high-pass filter and its amplitude-frequency and phase-frequency characteristics are shown in the figure below. Assume that the input voltage of the filter is ex and the output voltage is ey. The differential equation of the circuit is: Analysis shows that when f is very small, A(f)=0, the signal is completely blocked and cannot pass; when f is very large, A(f)=1 and the signal passes without attenuation. 3) RC Bandpass Filter The bandpass filter can be regarded as a series connection of a low-pass filter and a high-pass filter. Its circuit and its amplitude-frequency and phase-frequency characteristics are shown in the figure below. Its amplitude-frequency and phase-frequency characteristics are as follows: H(s) = H1(s) * H2(s) Where H1(s) is the transfer function of the high-pass filter, and H2(s) is the transfer function of the low-pass filter. There are: At this time, both the extremely low and extremely high frequency components are completely blocked and cannot pass through; only the signal frequency components within the frequency passband can pass through. It should be noted that when the high-pass and low-pass stages are connected in series, the mutual influence of the two stages when coupled should be eliminated, because the latter stage becomes the "load" of the former stage, and the former stage is the signal source internal resistance of the latter stage. In fact, emitter followers or operational amplifiers are often used to isolate the two stages. Therefore, the actual bandpass filter is often active. The active filter consists of an RC tuning network and an operational amplifier. The operational amplifier can be used as an isolation between stages and can also amplify the signal amplitude.