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Electronic filter

Television signal splitter consisting of a high-pass filter (left) and 

a low-pass filter (right). The antenna is connected to the screw

terminals to the left of center.

Electronic filters   are   analog circuits   which performsignal processing   functions, specifically to remove un-wanted frequency components from the signal, to en-hance wanted ones, or both. Electronic filters can be:

•   passive or active

•   analog or digital

•   high-pass,   low-pass,   band-pass,  band-stop   (band-rejection; notch), or all-pass.

•   discrete-time (sampled) or continuous-time

•   linear or non-linear

•   infinite impulse response (IIR type) or finite impulseresponse (FIR type)

The most common types of electronic filters are   linearfilters, regardless of other aspects of their design. Seethe article on linear filters for details on their design andanalysis.

1 History

Main article: Passive analogue filter development

The oldest forms of electronic filters are passive ana-log linear filters, constructed using only   resistors   andcapacitors or resistors and  inductors. These are known

as RC and RL single-pole filters respectively. More com-plex multipole LC filters have also existed for many years,and their operation is well understood.

Hybrid filters are also possible, typically involving a com-bination of analog amplifiers with mechanical resonatorsor delay lines. Other devices such as  CCD delay lineshave also been used as discrete-time filters. With theavailability of digital signal processing, active digital fil-ters have become common.

2 Classification by technology

2.1 Passive filters

Passive implementations of linear filters are basedon combinations of   resistors   (R),   inductors   (L) andcapacitors (C). These types are collectively known as pas-

sive filters , because they do not depend upon an externalpower supply and/or they do not contain active compo-nents such as transistors.

Inductors block high-frequency signals and conduct low-frequency signals, while capacitors do the reverse. A fil-ter in which the signal passes through an inductor, or in

which a capacitor provides a path to ground, presents lessattenuation to low-frequency signals than high-frequencysignals and is therefore a   low-pass filter . If the sig-nal passes through a capacitor, or has a path to groundthrough an inductor, then the filter presents less attenua-tion to high-frequency signals than low-frequency signalsand therefore is a high-pass filter .  Resistors on their ownhave no frequency-selective properties, but are added toinductors and capacitors to determine the  time-constants 

of the circuit, and therefore the frequencies to which itresponds.

The inductors and capacitors are the reactive elements of

the filter. The number of elements determines the orderof the filter. In this context, an LC tuned circuit beingused in a band-pass or band-stop filter is considered a sin-gle element even though it consists of two components.

At high frequencies (above about 100 megahertz), some-times the inductors consist of single loops or strips ofsheet metal, and the capacitors consist of adjacent stripsof metal. These inductive or capacitive pieces of metalare called stubs.

2.1.1 Single element types

The simplest passive filters,  RC and RL filters, includeonly one reactive element, except hybrid LC filter which

1

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2   2 CLASSIFICATION BY TECHNOLOGY 

vin

  vout

 R

C

A low-pass electronic filter realised by an RC circuit 

is characterized by inductance and capacitance integratedin one element.[1]

2.1.2 L filter

An L filter consists of two reactive elements, one in seriesand one in parallel.

2.1.3 T and π filters

Main article: Capacitor-input filterThree-element filters can have a 'T' or 'π' topology and

vin

  vout

 L

CC

Low-pass π filter 

vin

  vout

 L

CC

High-pass T filter 

in either geometries, a   low-pass,   high-pass,  band-pass,

or band-stop characteristic is possible. The componentscan be chosen symmetric or not, depending on therequired frequency characteristics. The high-pass T filter

in the illustration, has a very low impedance at highfrequencies, and a very high impedance at low frequen-cies. That means that it can be inserted in a transmissionline, resulting in the high frequencies being passedand low frequencies being reflected. Likewise, for theillustrated low-pass π filter, the circuit can be connected

to a transmission line, transmitting low frequenciesand reflecting high frequencies. Using m-derived filtersections with correct termination impedances, the inputimpedance can be reasonably constant in the pass band.[2]

2.1.4 Multiple element types

Multiple element filters are usually constructed as a laddernetwork. These can be seen as a continuation of the L,Tand π designs of filters. More elements are needed whenit is desired to improve some parameter of the filter such

as stop-band rejection or slope of transition from pass-band to stop-band.

2.2 Active filters

Active filters   are implemented using a combination ofpassive and active (amplifying) components, and requirean outside power source.   Operational amplifiers are fre-quently used in active filter designs. These can have highQ factor, and can achieve resonance without the use of in-ductors. However, their upper frequency limit is limited

by the bandwidth of the amplifiers.

2.3 Other filter technologies

2.3.1 Digital filters

Main article: digital filterDigital signal processing allows the inexpensive construc-

d1

  d2

  d3

  dn

a1

  a2

  a3

  an

OUT 

 IN 

Σ   Summation

 Ampli fication

 Delay 

A general finite impulse response filter with n  stages, each with

an independent delay, di and amplification gain, ai.

tion of a wide variety of filters. The signal is sampled

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2.3 Other filter technologies    3

and an analog-to-digital converter turns the signal into astream of numbers. A computer program running on aCPU  or a specialized DSP (or less often running on ahardware implementation of the algorithm) calculates anoutput number stream. This output can be converted to asignal by passing it through a digital-to-analog converter.

There are problems with noise introduced by the conver-sions, but these can be controlled and limited for manyuseful filters. Due to the sampling involved, the input sig-nal must be of limited frequency content or aliasing willoccur.

2.3.2 Quartz filters and piezoelectrics

Main article: Crystal filterSee also: Mechanical filter

In the late 1930s, engineers realized that small mechani-cal systems made of rigid materials such as quartz wouldacoustically resonate at radio frequencies, i.e. from audi-ble frequencies (sound) up to several hundred megahertz.Some early resonators were made of   steel, but quartzquickly became favored. The biggest advantage of quartzis that it is  piezoelectric. This means that quartz res-onators can directly convert their own mechanical motioninto electrical signals. Quartz also has a very low coeffi-cient of thermal expansion which means that quartz res-onators can produce stable frequencies over a wide tem-perature range.   Quartz crystal filters have much higher

quality factors than LCR filters. When higher stabilitiesare required, the crystals and their driving circuits may bemounted in a "crystal oven" to control the temperature.For very narrow band filters, sometimes several crystalsare operated in series.

Engineers realized that a large number of crystals couldbe collapsed into a single component, by mounting comb-shaped evaporations of metal on a quartz crystal. In thisscheme, a “tapped delay line" reinforces the desired fre-quencies as the sound waves flow across the surface of thequartz crystal. The tapped delay line has become a gen-eral scheme of making high-Q  filters in many differentways.

2.3.3 SAW filters

SAW (surface acoustic wave) filters areelectromechanical   devices commonly used in   radiofrequency  applications. Electrical signals are convertedto a mechanical wave in a device constructed of apiezoelectric crystal or ceramic; this wave is delayed asit propagates across the device, before being convertedback to an electrical signal by further  electrodes. Thedelayed outputs are recombined to produce a direct

analog implementation of a finite impulse response filter.This hybrid filtering technique is also found in an analogsampled filter. SAW filters are limited to frequencies up

Crystal filter with a centerfrequency of45 MHz anda bandwidth

B3dB of 12 kHz.

to 3 GHz. The filters were developed by Professor TedPaige and others.[3]

2.3.4 BAW filters

BAW (bulk acoustic wave) filters are electromechanicaldevices. BAW filters can implement ladder or lattice fil-

ters. BAW filters typically operate at frequencies fromaround 2 to around 16 GHz, and may be smaller or thin-ner than equivalent SAW filters. Two main variants of

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4   5 CLASSIFICATION BY DESIGN METHODOLOGY 

BAW filters are making their way into devices:  thin-filmbulk acoustic resonator or FBAR and solid mounted bulkacoustic resonators.

2.3.5 Garnet filters

Main article: YIG sphere

Another method of filtering, at   microwave frequenciesfrom 800 MHz to about 5 GHz, is to use a synthetic singlecrystal yttrium iron garnet  sphere made of a chemicalcombination of yttrium and iron (YIGF, or yttrium irongarnet filter). The garnet sits on a strip of metal drivenby a transistor, and a small loop antenna touches the topof the sphere. An electromagnet changes the frequencythat the garnet will pass. The advantage of this method isthat the garnet can be tuned over a very wide frequency

by varying the strength of the magnetic field.

2.3.6 Atomic filters

For even higher frequencies and greater precision, thevibrations of atoms must be used.   Atomic clocks   usecaesium masers  as ultra-high  Q  filters to stabilize theirprimary oscillators. Another method, used at high, fixedfrequencies with very weak radio signals, is to use a  rubymaser tapped delay line.

3 The transfer function

see also   Filter (signal processing)   for further 

analysis 

The transfer function   H (s) of a filter is the ratio of theoutput signal   Y  (s) to that of the input signal   X (s) as afunction of the complex frequency   s :

H (s) =  Y  (s)

X (s)with   s =  σ  +  jω  .

The transfer function of all linear time-invariant filters,when constructed of discrete components, will be the ra-tio of two polynomials in   s  , i.e. a rational function ofs . The order of the transfer function will be the highestpower of   s  encountered in either the numerator or thedenominator.

4 Classification by topology

Electronic filters can be classified by the technology usedto implement them. Filters using passive filter and active

filter technology can be further classified by the particularelectronic filter topology used to implement them.

Any given filter transfer function may be implemented inany electronic filter topology.

Some common circuit topologies are:

•   Cauer topology – passive

•  Sallen–Key topology – active

•  Multiple Feedback topology – active

•  State Variable Topology – active

•  Biquadratic topology biquad filter – active

5 Classification by design method-

ology

Historically, linear analog filter design has evolvedthrough three major approaches. The oldest designs aresimple circuits where the main design criterion was theQ factor of the circuit. This reflected the radio receiverapplication of filtering as Q was a measure of the fre-quency selectivity of a tuning circuit. From the 1920s fil-ters began to be designed from the image point of view,mostly being driven by the requirements of telecommu-nications. After World War II the dominant methodol-ogy was network synthesis. The higher mathematics used

originally required extensive tables of polynomial coef-ficient values to be published but modern computer re-sources have made that unnecessary.[4]

5.1 Direct circuit analysis

Low order filters can be designed by directly applyingbasic circuit laws such as Kirchhoff’s laws to obtain thetransfer function. This kind of analysis is usually onlycarried out for simple filters of 1st or 2nd order.

RL filter frequency response

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5

5.2 Image impedance analysis

Main article: Composite image filters

This approach analyses the filter sections from the point

of view of the filter being in an infinite chain of identicalsections. It has the advantages of simplicity of approachand the ability to easily extend to higher orders. It has thedisadvantage that accuracy of predicted responses relieson filter terminations in the image impedance, which isusually not the case.[5]

Constant k filter response with 5 elements 

Zobel network (constant R) filter, 5 sections 

5.3 Network synthesis

Main article: Network synthesis filters

The network synthesis approach starts with a requiredtransfer function and then expresses that as a polynomial

equation of the input impedance of the filter. The actualelement values of the filter are obtained by continued-fraction or partial-fraction expansions of this polynomial.

m-derived filter response, m=0.5, 2 elements 

m-derived filter response, m=0.5, 5 elements 

Unlike the image method, there is no need for impedancematching networks at the terminations as the effects ofthe terminating resistors are included in the analysis fromthe start.[5]

Here is an image comparing Butterworth, Chebyshev, andelliptic filters. The filters in this illustration are all fifth-order low-pass filters. The particular implementation –analog or digital, passive or active – makes no difference;

their output would be the same.As is clear from the image, elliptic filters are sharper thanall the others, but they show ripples on the whole band-width.

6 See also

7 Notes, references and external

links

[1] Dzhankhotov V.,   Hybrid LC filter for power electronic 

drives: Theory and Implementation, 2009

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6   7 NOTES, REFERENCES AND EXTERNAL LINKS 

0

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Butterworth

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Chebyshev type 1

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Chebyshev type 2

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Elliptic

[2] The American Radio Relay League, Inc.: “The ARRL

Handbook, 1968” page 50

[3] Ash, Eric A; E. Peter Raynes (December 2009). “Edward

George Sydney Paige. 18 July 1930 — 20 February 2004”

(PDF). Biographical Memoirs of Fellows of the Royal So-

ciety 55: 185–200. doi:10.1098/rsbm.2009.0009.

[4] Bray, J,  Innovation and the Communications Revolution,

Institute of Electrical Engineers

[5] Matthaei, Young, Jones  Microwave Filters, Impedance-

Matching Networks, and Coupling Structures McGraw-Hill

1964

•  Zverev, Anatol, I (1969).   Handbook of 

Filter Synthesis . John Wiley & Sons.ISBN 0-471-98680-1. Catalog of passivefilter types and component values. TheBible for practical electronic filter design.

•   Williams, Arthur B & Taylor, Fred J(1995).   Electronic Filter Design Hand-

book . McGraw-Hill.   ISBN 0-07-070441-4.

•   National Semiconductor AN-779application note describing analog filtertheory

•  Fundamentals of Electrical Engineeringand Electronics – Detailed explanation ofall types of filters

•  BAW filters (in French; PDF)

•  Some Interesting Filter Design Configu-rations & Transformations

•  Analog Filters for Data Conversion

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8 Text and image sources, contributors, and licenses

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