Filter (electronic)

See also: Filter, Converter

A filter is a electronic Circuit which carries out an operation of Treatment of the signal. In other words, it attenuates certain components of a Signal and lets some pass from others. A known example of the general public is the audio equalizer.

A filter modifies (or filters) certain parts of an entry signal in the time field and the frequency field. According to the Theory of Fourier, any real signal can be regarded as made up of a sum of sinusoidal signals (of infinite number if necessary) at different frequencies; the role of the filter is to modify the phase and the amplitude of these components.

Linear filters invariants by the shift

See also: linear electric Filter

In general, when one speaks about filter in electronics, it is about an operator (or circuit) having two quite precise mathematical properties:

  • the Linearity: the sum of the response of the filter to two entry signals is equal to its answer to the sum of these two signals.

  • invariance in the shift: the response of a filter to a given signal is an identical but delayed signal of a time T (it is said that the signal underwent a time or shift). This last is invariable.

When an operator (or circuit) has these two basic properties, it is easily shown, by the Théorie of Fourier, that one can characterize it by his Impulse response or his Transfer function transfer.

Any signal which can be broken up into a sum of sinusoidal signals of various frequencies (and which constitute its frequential Specter), simple means of characterizing a filter is to give its transfer transfer function, obtained by comparing the frequential spectrum of the entry signals and exit of the filter.

Another means of characterizing a filter is its impulse response, i.e. the signal at exit of the filter when the entry signal is a Impulsion of Dirac, i.e. when all the frequencies are present at its entry.

When the signal is discrete, one uses the Transformée into Z rather than the Transformée of Fourier.

Classification

One can classify the filters starting from the form of their Transfer function transfer or the behavior of the passive elements which compose the filter. The most current filters are one of the four following types: low-pass, high-pass, band pass or rejector of band.

  • a high-pass Filtre lets pass only the frequencies above a determined frequency, called Frequency cut-off. It attenuates the others (low frequencies). In other words, it “lets pass what is high”. It is a low register attenuator for an audio signal. One could also call it cut-low.
  • a low-pass Filtre lets pass only the frequencies below its cut-off frequency. It is an attenuator of acute for an audio signal. One could call it cut-high.
  • a Filtre band pass lets pass only one certain waveband (and all attenuates that is above or in lower part). It is very much used in the radio operator receivers, TV… to insulate the signal which one wishes to collect.
  • a filter rejector, also called filter trap door, bell or band suppressor, is complementary to band pass. It attenuates a beach of frequencies. That can be useful to decrease certain parasites for example.

Technically, a filter can be carried out various manners: passivate, active or numerical.

Passive filters

A passive filter is characterized by the exclusive use of component passive (resistances, condensers, reels coupled or not). Consequently, their profit (relationship of power between the exit and the entry) cannot excéder  1. In other words, they can only attenuate signals partly, but not amplify them.

The simplest achievements are based on circuits RC, RL, LLC or Circuit RLC. But it is of course allowed to increase the complexity of the filter (and the component count). The less there will be components, the more it will be delicate to be selective: the attenuation will be done gradually. With more components, one can hope more brutally to cut a frequency by touching the neighbors less.

The passive filters are seldom prone to phenomena of saturation (except some cases of reels with core) from where for example their use in the enclosures of loudspeakers. Moreover they can exist in all the frequency bands (from where their use in certain circuits high frequency as out of radio for example). However, the same circuit can with difficulty cover with him only a very broad frequency band because the choice of a type of reel or condenser depends on the frequency. It is feasible but more complex. Let us quote the example of the electrochemical condenser: adapted well to the low frequencies, it rather quickly becomes inductive with the increase in the frequency (it loses its capacitive behavior).

A reel consists of a wire and is thus very conducting in low frequency. On the other hand, she is opposed in the passing high frequencies. The condensers make the reverse (insulating in low frequency, driver in high frequency). Resistances do not select the frequencies alone, but make it possible to define the time-constant of a circuit by limiting the currents more or less. Thus resistances determine the frequency to which the filter will act and its attenuation.

Beyond 100  MHz: inductances are often consisted a simple sinuous wire or metal bands, and the condensers by superimposed metal bands ( stubs ). For example on the two opposite faces of a printed circuit.

For the filters of the second order, i.e. being able to be described by a differential equation (linear very often) of the second order, it is possible to define a Facteur of quality, i.e. the relationship between their center frequency and them Band-width, attention this is valid only for one band pass. A filter having a very fine band compared to its center frequency will be considered very selective or of great quality.

The circuit is subjected to more or less unwanted noise appearing in the signals. That depends on the components employed. Very weak thermal noise in resistances, rather weak noise in the condensers, but more important sensitivity to the magnetic fields with the reels.

To be complete, it is advisable to mention the quartz filters, the wave filters of surface ( Surface Acoustic Waves filters or SAW), the mechanical filters ceramics and filters, which form also part of the passive filters.
They can be regarded in the most general case as quadripoles.

Active filters

The active filters are characterized by the use of at least a active Composant (for example transistor, operational amplifier, or another integrated circuit…).

These filters have the advantage of being able to do without reels which are expensive, not easily able to be miniaturized and imperfect (angles loss, resonances clean, sensitivity to the parasites). Moreover they have a profit which can be higher à  1 (they can amplify).

This type of filter is appropriate well for the signals of low amplitude and low power. The active filters thus are largely used in the audio amplifiers and electronic instruments of all kinds.

Side disadvantages, contrary to the passive filters, they require a power supply and are limited in amplitude (saturation). Today they can cover broad wavebands. The active components (as well as resistances to a lesser extent) can introduce unwanted noise, which, beyond of a certain threshold, can be awkward. However this noise can often be controlled.

In this category of filters one can with the rigor arrange the filters commutated capacities, which are halfway between the passive and active filters.

Numerical filters

analog-to-digital Converter. It is then treated by a Microprocesseur or a numerical processor of signal DSP (which carry out filtering itself), then reconverted in analogical signal by a Digital-to-analog converter.

This system makes it possible to produce changeable filters, working on multiple and inevitably not fixed frequencies. The chain of sampling/conversion causes the appearance of Bruit, but this one can be eliminated with the suitable filters. On the other hand, the frequency band is limited by the sampling and the phenomena of Aliasing . -->

A numerical Filtre is characterized by the entirely digital processing of the signal. Au préalable, the signal is digitized by a analog-to-digital Converter (EDGE), i.e. with regular intervals (called period of sampling) the instantaneous amplitude of the signal is observed then quantified. The signal is thus not observed permanently and these filters thus react rather badly vis-a-vis signals (even parasitic) of frequency higher than that envisaged.

A numerical filter treats a continuous flood of information (such as for example that read on audio CD) and calculates in real-time a new flood of outgoing data, which correspond to the desired filtered signal. The output data can appear at the same rate/rhythm or intervals different from the entering data.

At the end of the chain, the analogical signal is rebuilt by a Digital-to-analog converter (CNA). These filters have the advantage of being able to be integrated in able to be miniaturized circuits digital into the extreme, such of the processors ( DIGITAL Signal Processors , DSP in particular) and not to require quasi any analogical component, which guarantees strictly reproducible characteristics of one apparatus to the autre : in other words the precision is much better since there is less of analogical components.

However, the numerical filters have obviously limitations (rounded calculation, limited amplitude, folding up of spectrum…). On the other hand they offer the advantage of being able to be reprogrammed (possibly with stolen) to change characteristics quickly, without changing material circuit.

The numerical filters produce also noise (in addition to the noise introduced into the signal by the converters YEAR and NA) called noise of Quantification. There exist techniques to try to reduce this last.

They make it possible to obtain spectral characteristics of which some can be reproduced by no analogical filter (active or not): for example, they can be very selective or eliminate a whole series from harmonic components (filter out of comb). It is only one question of mathematical calculation.

Let us note how the maximum frequency of the spectrum of the signal which treats a numerical filter must remain quite lower than half of the sampling rate (Théorème of sampling of Nyquist-Shannon), and that consequently the numerical filter is not adapted for signals spread out over a too large tape of fréquences. It was necessary to await the rise to power of the capacities of calculation of the processors to see appearing these large scales filters. They henceforth are very much used in modern electronics where the analogical one yields the step to the numerical one. The majority of the signals being numerical they are treated directly like such.

Other technologies

Crystal filters

Piezoelectric qualities of certain materials, like the quartz, can be used in the design of filters. The filters quartz have a high factor of quality and a very good stability in temperature.

Filters SAW

A Filtre SAW (of English Surface Acoustic Wave , “acoustic wave of surface”) is an electromechanical system used generally in applications using the waves radio. The electrical signals are converted into mechanical wave by a piezoelectric crystal . This wave is delayed during its propagation in the crystal, then reconverted in electrical signal. The delayed exits are recombined to produce an implementation of a finished Impulse response filter.

Atomic filters

For higher frequencies and a precision, it is possible to use the oscillatory modes of Atome S. the atomic clocks use Maser S with Césium like factor filters very high of quality in order to stabilize their primary education oscillators. Another method, used for high and fixed frequencies on very weak radio operator signals, is to use a maser with Rubis.

Applications

  • Telecommunications
    • radio Station: selection of the frequency of each transmitting station.
    • Television: selection of the television channels or channels.
    • Telephone with keys: each key sends a signal of 2 precise frequencies which “sign” a figure; with 10 digits, one composes the call number of his correspondent
    • ADSL: on the same phone line can pass all at the same time a phone conversation BF (low frequency: typically audio frequencies), the signal of a tele chain (broad band HF), and the signal of the IP (InternetProtocol).

See too

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