Filter Basis: Functions, Classifications, Parameters

Disclaimer: This is a user generated content submitted by a member of the WriteUpCafe Community. The views and writings here reflect that of the author and not of WriteUpCafe. If you have any complaints regarding this post kindly report it to us.

The function of the filter is to allow the signal of a certain frequency to pass smoothly, while the signal of the other part of the frequency is greatly suppressed. It is essentially a frequency selection circuit.

1. The function of the filter

In the filter, the frequency range through which the signal can pass is called the passband or passband; conversely, the frequency range where the signal is greatly attenuated or completely suppressed is called the stopband; the boundary frequency between the passband and the stopband is called Is the cut-off frequency; the voltage gain of the ideal filter in the pass band is constant, and the voltage gain in the stop band is zero; there is a transition band in a certain frequency range between the pass band and the stop band of the actual filter.

2. Classification of filters

(1) Divided into two kinds of analog filters and digital filters according to the signal processed.

(2) According to the frequency band of the passed signal, it is divided into four types: low-pass, high-pass, band-pass and band-stop filters.

Low-pass filter: It allows low-frequency or DC components in the signal to pass, and suppresses high-frequency components or interference and noise.

High-pass filter: It allows high-frequency components in the signal to pass and suppresses low-frequency or DC components.

Band pass filter: It allows signals of a certain frequency band to pass, and suppresses signals, interference and noise below or above the frequency band.

Band stop filter: It suppresses signals in a certain frequency band and allows signals outside the frequency band to pass.

(3) According to the components used, it is divided into passive and active filters.

Passive filter: A filter composed of only passive components (R, L, and C). It is constructed using the principle that the reactance of capacitance and inductance components changes with frequency. The advantages of this type of filter are: the circuit is relatively simple, does not require a DC power supply, and has high reliability; the disadvantage is: the signal in the passband has energy loss, the load effect is more obvious, and the use of inductive components is likely to cause electromagnetic induction. When L is large, the size and weight of the filter are relatively large, which is not applicable in the low frequency domain.

Active filter: It is composed of passive components (usually R and C) and active components (such as integrated operational amplifiers). The advantages of this type of filter are: the signal in the passband not only has no energy loss, but also can be amplified, the load effect is not obvious, the mutual influence is small when multi-stage is connected, and the simple method of cascade is easy to form a high-order filter The filter is small in size, light in weight, and does not require magnetic shielding (because inductance components are not used); the disadvantage is that the passband range is limited by the bandwidth of active devices (such as integrated operational amplifiers) and requires DC power supply, which is reliable The performance is not as high as passive filters, and it is not suitable for high-voltage, high-frequency, and high-power applications.

3. The main parameters of the filter

(1) Passband gain A0: The voltage amplification factor in the passband of the filter.

(2) Characteristic corner frequency picture and characteristic frequency fn: it is only related to the parameters of the resistance and capacitance elements used for filtering, usually

For band-pass (band-stop) filters, it is called the center angle frequency picture or center frequency f0 of the band-pass (band-stop) filter, which is the frequency of the maximum (minimum) point of voltage gain in the pass-band (stop-band).

(3) Cut-off angular frequency picture and cut-off frequency f0: it is the angular frequency corresponding to the voltage gain when it drops to the picture (ie). It must be noted that pictures are not necessarily equal to pictures. There are two pictures for bandpass and bandstop filters, namely pictures and pictures.

(4) Pass band (stop band) width BW: It is the difference between the two pictures of the band pass (band stop) filter, that is

(5) Equivalent quality factor Q: For low-pass and high-pass filters, the Q value is equal to the ratio of the modulus of the filter circuit voltage gain to the passband gain when the picture is taken; that is, the picture; for the band pass (band stop) filter In other words, the Q value is equal to the ratio of the center angular frequency to the passband (stopband) width BW, that is

4. The order of the active filter

The highest “order” of “S” in the denominator of the active filter transfer function is called the “order” of the filter. The higher the order, the steeper the transition band of the filter amplitude-frequency characteristics, and the closer to the ideal characteristics. In general, the transition band of the first-order filter attenuates at a rate of 20dB per decade; the second-order filter attenuates at a rate of 40dB per decade. High-order filters can be composed of low-order filters in series.

5. The dual relationship between low-pass and high-pass filters

(1) Dual relationship of amplitude-frequency characteristics

When the passband gain A0, cutoff frequency, or f0 of the low-pass filter and the high-pass filter are respectively equal, the amplitude-frequency characteristic curves of the two are symmetrical with respect to the vertical line f=f0.

(2) The dual relationship of the transfer function

If S in the transfer function of the low-pass filter is replaced by 1/S, it becomes the transfer function of the corresponding high-pass filter.

(3) Duality relationship in circuit structure

Replace the filter capacitor C in the low-pass filter with a resistor R, and replace the filter resistor R with a capacitor C, then the low-pass filter is converted into a corresponding high-pass filter.