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# Passive RC filter circuit and how it works

2023-11-11【Archive】

The test system usually uses RC filters. Because in this field, signal frequency is relatively low. The RC filter has a simple circuit, strong anti-interference performance, good low-frequency performance, and standard resistance and capacitance components that are easy to obtain, so most commonly used filter in field of technical testing is RC filter.

First Order RC Low-Pass Filter

The RC low-pass filter circuit and its amplitude-frequency and phase-frequency characteristics are shown in figure below.

Assuming input voltage of filter is ex and output voltage is ey, differential equation of circuit is:

This is a typical first order system. Let =RC, called time constant, take Laplace transform of above formula, is:

or

Formulas of its amplitude-frequency and phase-frequency characteristics:

The analysis shows that for small f, A(f)=1, signal passes without attenuation, for large f, A(f)=0, signal is completely blocked and cannot pass.

Second first-order RC high-pass filter

The circuit of RC high-pass filter and its amplitude-frequency and phase-frequency characteristics are shown in figure below.

Assuming input voltage of filter is ex and output voltage is ey, differential equation of circuit is:

Similarly, let =RC, take Laplace transform of above formula, is:

or

Formulas of its amplitude-frequency and phase-frequency characteristics:

The analysis shows that for small f, A(f)=0, signal is completely blocked and cannot pass; for large f, signal A(f)=1 passes without attenuation.

Three, RC bandpass filter

A band-pass filter can be considered as a series connection of a low-pass filter and a high-pass filter, its circuit, amplitude-frequency and phase-frequency characteristics are shown in figure below.

The formula for its amplitude-frequency and phase-frequency characteristics: H(s) = H1(s) * H2(s)In formula, H1(s) is transfer function of high-pass filter, and H2(s) is low-pass filter frequencies. Transfer function of a transmission filter. Yes:

At this time, extremely low frequency and extremely high frequency components are completely blocked and cannot pass through; only frequency components of signal within frequency bandwidth can pass.

It should be noted that when two stages of high-frequency and low-pass are connected in series, mutual influence of two-stage communication must be eliminated, since last stage becomes "load" of first stage. , and first stage is signal of internal resistance of source of second stage. In fact, an emitter follower or op amp is usually used for decoupling between two stages. Therefore, practical bandpass filters are often active. The active filter consists of an RC tuning circuit and an operational amplifier. The operational amplifier can be used not only as an interstage decoupler, but can also amplify signal amplitude

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