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Filter Basics (1)

Filter definition

A filter is a signal processing device that selects or changes the composition of an input signal at a specific frequency, and it achieves the goal of reducing unwanted noise and interference by enhancing or suppressing the amplitude of the signal in a specific frequency range.

There may be various interference sources in the power supply, such as AC voltage noise, high-frequency noise, harmonics, etc., and these interference signals will adversely affect the normal operation of electronic equipment and systems if not filtered out. The basic goal of the power filter is to design appropriate circuits to suppress or filter out these interfering signals, so that the signal output of the power supply is more stable and pure. It is usually composed of capacitance, inductance, resistance, magnetic components, and the inductance and capacitance of distribution parameters, this network allows certain frequencies to pass through, and other frequency components are suppressed and attenuated, and the filter is actually a frequency-selective circuit. Power filter can effectively reduce the noise, fluctuation, harmonics and other unstable factors in the power supply, and provide a more stable and clean power supply. This helps protect the equipment from interference and improves the performance and reliability of the system.

Filter classification

1. According to frequency characteristics (amplitude-frequency characteristics and phase-frequency characteristics)

Low-Pass Filter

Frequency components below the cut-off frequency are allowed to pass through, and frequency components above the cut-off frequency are suppressed. From the frequency of 0~f2, the amplitude-frequency characteristics are straight, which can make the signal lower than that

The frequency component of f2 passes through without attenuation, while the frequency component higher than f2 is greatly attenuated.

The main circuit form of low-pass filter

High-Pass Filter

Frequency components higher than the cut-off frequency are allowed to pass through, and frequency components below the cut-off frequency are suppressed. Contrary to the low-pass filter, the amplitude and frequency characteristics are straight between f1~∞ frequencies, so that the frequency components of the signal higher than f1 pass through almost without attenuation, while the frequency components below f1 will be greatly attenuated.

Band-Pass Filter:

Bandpass filter frequency characteristics

Band-Stop Filter

Allows frequency components located outside a certain frequency range to pass through, and suppresses those located within that range. In contrast to the bandpass filter, the stop band is between f1~f2, which attenuates the frequency components of the signal that are higher than f1 and lower than f2, while the signals of other frequency components pass through almost without attenuation.

Frequency characteristics of the band-stop filter

Low-pass filter and high-pass filter are the two basic forms of filter, other filters can be decomposed into these two types of filters, the series connection of low-pass filter and high-pass filter is a band-pass filter, and the parallel connection of low-pass filter and high-pass filter is a band-stop filter.

2. Classification according to energy loss characteristics

Reflective filter

Reflective filters, also known as lossless filters, work on the principle of forming a large characteristic impedance discontinuity in the transmission path of electromagnetic signals, so that most of the electromagnetic energy is reflected back to the signal source. The reflective filter adopts a passive network composed of energy storage elements such as inductor L and capacitor C, which has good frequency selection characteristics, but is easy to generate resonance.

Absorptive filter

The use of lossy filter elements, so that the energy of the disturbance signal in the filter, in order to achieve the purpose of suppressing interference, also known as lossy filter, absorption filter can avoid the reflection filter due to parasitic parameter effect or impedance mismatch caused by the resonance, but its frequency selectivity is poor. The absorption filter uses ferrite material or other lossy materials to pass or wind wires on ferrite materials of various shapes, and uses its inductance and magnetic field eddy current loss to block the propagation of disturbance signals.

3. Classified according to the standard of "best approximation characteristics".

Butterworth Filter

The requirements are made from the amplitude-frequency characteristics, regardless of the phase-frequency characteristics. The Butterworth filter has a maximum flat amplitude characteristic, which is characterized by a maximally flat frequency response curve in the pass band with no ripple, while the frequency arrest band gradually decreases to zero.

The Butterworth low-pass filter can be expressed by the following formula for the squared frequency of the amplitude:

Chebyshev Filter

The Chebyshev filter, also known as the "Chebyshev filter", is a filter that fluctuates ripples such as the amplitude of the frequency response on the passband or stop band. The Chebyshev filter comes from the Chebyshev distribution and is in honor of the Russia mathematician Bavnity. Lepovich. Chebyshev.

The Chebyshev filter decays faster than the Butterworth filter in the transition zone, but the amplitude-frequency characteristics of the frequency response are not as flat as the latter. The error between the frequency response curves of the cut-ratio filter and the ideal filter is minimal, but there are amplitude fluctuations within the passband.

Type I Chebyshev filter, the relationship between amplitude and frequency of Chebyshev filter can be expressed by the following companies:

Chebyshev filter type II:

Also known as the reciprocal Chebyshev filter, it is less commonly used because the frequency cut-off speed is not as fast as that of Type I and does not require more electronic components. The type II Chebyshev filter has no amplitude fluctuations in the pass band, only in the stop band.

The transfer function of the type II Chebyshev filter is:

Bessel Filter

The Bezier filter is the one with the flattest amplitude and phase response. The phase response of the bandpass is nearly linear. Bessel filters are used in audio equipment because they provide an equal amount of delay to all frequencies below their cut-off frequency, where out-of-band noise must be eliminated without compromising the phase relationship of multiple signals in the band. The transfer function that describes the Bezier filter low-pass filter is as follows:

The non-ideality of the filter Ideal Filter:

An ideal filter is a filter that can make the amplitude and phase of the signal in the passband undistorted, and the frequency component in the stopband is attenuated to zero, and there is a clear dividing line between the passband and the stopband. That is to say, the amplitude-frequency characteristics of an ideal filter in the passband should be constant, the slope of the phase-frequency characteristics should be constant, and the amplitude-frequency characteristics outside the passband should be zero.

Amplitude and phase frequency characteristics of an ideal filter

Actual Filters:

There is no ideal filter, and there should be no strict boundary between the passband and stopband in the amplitude-frequency characteristic diagram of the actual filter. There is a transition band between the passband and the stop band, and the frequencies within the transition band are not completely suppressed, only attenuated. When designing the filter, it is hoped that the transition band is as narrow as possible, that is, the frequency components outside the passband are attenuated as quickly as possible.