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Electronic filters are a type of signal processing filter in the form of electrical circuits. This article covers those filters consisting of lumped electronic components, as opposed to distributedelement filters. That is, using components and interconnections that, in analysis, can be considered to exist at a single point. These components can be in discrete packages or part of an integrated circuit.
Electronic filters remove unwanted frequency components from the applied signal, enhance wanted ones, or both. They can be:
The most common types of electronic filters are linear filters, regardless of other aspects of their design. See the article on linear filters for details on their design and analysis.
The oldest forms of electronic filters are passive analog linear filters, constructed using only resistors and capacitors or resistors and inductors. These are known as RC and RL singlepole filters respectively. However, these simple filters have very limited uses. Multipole LC filters provide greater control of response form, bandwidth and transition bands. The first of these filters was the constant k filter, invented by George Campbell in 1910. Campbell's filter was a ladder network based on transmission line theory. Together with improved filters by Otto Zobel and others, these filters are known as image parameter filters. A major step forward was taken by Wilhelm Cauer who founded the field of network synthesis around the time of World War II. Cauer's theory allowed filters to be constructed that precisely followed some prescribed frequency function.
Passive implementations of linear filters are based on combinations of resistors (R), inductors (L) and capacitors (C). These types are collectively known as passive filters, because they do not depend upon an external power supply and/or they do not contain active components such as transistors.
Inductors block highfrequency signals and conduct lowfrequency signals, while capacitors do the reverse. A filter in which the signal passes through an inductor, or in which a capacitor provides a path to ground, presents less attenuation to lowfrequency signals than highfrequency signals and is therefore a lowpass filter . If the signal passes through a capacitor, or has a path to ground through an inductor, then the filter presents less attenuation to highfrequency signals than lowfrequency signals and therefore is a highpass filter . Resistors on their own have no frequencyselective properties, but are added to inductors and capacitors to determine the timeconstants of the circuit, and therefore the frequencies to which it responds.
The inductors and capacitors are the reactive elements of the filter. The number of elements determines the order of the filter. In this context, an LC tuned circuit being used in a bandpass or bandstop filter is considered a single element even though it consists of two components.
At high frequencies (above about 100 megahertz), sometimes the inductors consist of single loops or strips of sheet metal, and the capacitors consist of adjacent strips of metal. These inductive or capacitive pieces of metal are called stubs.
The simplest passive filters, RC and RL filters, include only one reactive element, except hybrid LC filter which is characterized by inductance and capacitance integrated in one element.^{ [1] }
An L filter consists of two reactive elements, one in series and one in parallel.
Threeelement filters can have a 'T' or 'π' topology and in either geometries, a lowpass, highpass, bandpass, or bandstop characteristic is possible. The components can be chosen symmetric or not, depending on the required frequency characteristics. The highpass T filter in the illustration, has a very low impedance at high frequencies, and a very high impedance at low frequencies. That means that it can be inserted in a transmission line, resulting in the high frequencies being passed and low frequencies being reflected. Likewise, for the illustrated lowpass π filter, the circuit can be connected to a transmission line, transmitting low frequencies and reflecting high frequencies. Using mderived filter sections with correct termination impedances, the input impedance can be reasonably constant in the pass band.^{ [2] }
Multipleelement filters are usually constructed as a ladder network. These can be seen as a continuation of the L,T and π designs of filters. More elements are needed when it is desired to improve some parameter of the filter such as stopband rejection or slope of transition from passband to stopband.
Active filters are implemented using a combination of passive and active (amplifying) components, and require an outside power source. Operational amplifiers are frequently used in active filter designs. These can have high Q factor, and can achieve resonance without the use of inductors. However, their upper frequency limit is limited by the bandwidth of the amplifiers.
There are many filter technologies other than lumped component electronics. These include digital filters, crystal filters, mechanical filters, surface acoustic wave (SAW) filters, bulk acoustic wave (BAW) filters, garnet filters, and atomic filters (used in atomic clocks).
The transfer function of a filter is the ratio of the output signal to that of the input signal as a function of the complex frequency :
The transfer function of all linear timeinvariant filters, when constructed of lumped components (as opposed to distributed components such as transmission lines), will be the ratio of two polynomials in , i.e. a rational function of . The order of the transfer function will be the highest power of encountered in either the numerator or the denominator.
Electronic filters can be classified by the technology used to implement them. Filters using passive filter and active filter technology can be further classified by the particular electronic filter topology used to implement them.
Any given filter transfer function may be implemented in any electronic filter topology.
Some common circuit topologies are:
Linear analog electronic filters 


Simple filters 
Historically, linear analog filter design has evolved through three major approaches. The oldest designs are simple circuits where the main design criterion was the Q factor of the circuit. This reflected the radio receiver application of filtering as Q was a measure of the frequency selectivity of a tuning circuit. From the 1920s filters began to be designed from the image point of view, mostly being driven by the requirements of telecommunications. After World War II the dominant methodology was network synthesis. The higher mathematics used originally required extensive tables of polynomial coefficient values to be published but modern computer resources have made that unnecessary.^{ [3] }
Low order filters can be designed by directly applying basic circuit laws such as Kirchhoff's laws to obtain the transfer function. This kind of analysis is usually only carried out for simple filters of 1st or 2nd order.
This approach analyses the filter sections from the point of view of the filter being in an infinite chain of identical sections. It has the advantages of simplicity of approach and the ability to easily extend to higher orders. It has the disadvantage that accuracy of predicted responses relies on filter terminations in the image impedance, which is usually not the case.^{ [4] }
The network synthesis approach starts with a required transfer function and then expresses that as a polynomial equation of the input impedance of the filter. The actual element values of the filter are obtained by continuedfraction or partialfraction expansions of this polynomial. Unlike the image method, there is no need for impedance matching networks at the terminations as the effects of the terminating resistors are included in the analysis from the start.^{ [4] }
Here is an image comparing Butterworth, Chebyshev, and elliptic filters. The filters in this illustration are all fifthorder lowpass 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 than all the others, but they show ripples on the whole bandwidth.
Wikimedia Commons has media related to Electronic filters . 
An electrical network is an interconnection of electrical components or a model of such an interconnection, consisting of electrical elements. An electrical circuit is a network consisting of a closed loop, giving a return path for the current. Linear electrical networks, a special type consisting only of sources, linear lumped elements, and linear distributed elements, have the property that signals are linearly superimposable. They are thus more easily analyzed, using powerful frequency domain methods such as Laplace transforms, to determine DC response, AC response, and transient response.
Linear filters process timevarying input signals to produce output signals, subject to the constraint of linearity. In most cases these linear filters are also time invariant in which case they can be analyzed exactly using LTI system theory revealing their transfer functions in the frequency domain and their impulse responses in the time domain. Realtime implementations of such linear signal processing filters in the time domain are inevitably causal, an additional constraint on their transfer functions. An analog electronic circuit consisting only of linear components will necessarily fall in this category, as will comparable mechanical systems or digital signal processing systems containing only linear elements. Since linear timeinvariant filters can be completely characterized by their response to sinusoids of different frequencies, they are sometimes known as frequency filters.
A lowpass filter (LPF) is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter design. The filter is sometimes called a highcut filter, or treblecut filter in audio applications. A lowpass filter is the complement of a highpass filter.
A gyrator is a passive, linear, lossless, twoport electrical network element proposed in 1948 by Bernard D. H. Tellegen as a hypothetical fifth linear element after the resistor, capacitor, inductor and ideal transformer. Unlike the four conventional elements, the gyrator is nonreciprocal. Gyrators permit network realizations of two(ormore)port devices which cannot be realized with just the conventional four elements. In particular, gyrators make possible network realizations of isolators and circulators. Gyrators do not however change the range of oneport devices that can be realized. Although the gyrator was conceived as a fifth linear element, its adoption makes both the ideal transformer and either the capacitor or inductor redundant. Thus the number of necessary linear elements is in fact reduced to three. Circuits that function as gyrators can be built with transistors and opamps using feedback.
An active filter is a type of analog circuit implementing an electronic filter using active components, typically an amplifier. Amplifiers included in a filter design can be used to improve the cost, performance and predictability of a filter.
The Butterworth filter is a type of signal processing filter designed to have a frequency response as flat as possible in the passband. It is also referred to as a maximally flat magnitude filter. It was first described in 1930 by the British engineer and physicist Stephen Butterworth in his paper entitled "On the Theory of Filter Amplifiers".
An electronic component is any basic discrete device or physical entity in an electronic system used to affect electrons or their associated fields. Electronic components are mostly industrial products, available in a singular form and are not to be confused with electrical elements, which are conceptual abstractions representing idealized electronic components.
Foster's reactance theorem is an important theorem in the fields of electrical network analysis and synthesis. The theorem states that the reactance of a passive, lossless twoterminal (oneport) network always strictly monotonically increases with frequency. It is easily seen that the reactances of inductors and capacitors individually increase with frequency and from that basis a proof for passive lossless networks generally can be constructed. The proof of the theorem was presented by Ronald Martin Foster in 1924, although the principle had been published earlier by Foster's colleagues at American Telephone & Telegraph.
Electronic filter topology defines electronic filter circuits without taking note of the values of the components used but only the manner in which those components are connected.
An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces through which electric current can flow. To be referred to as electronic, rather than electrical, generally at least one active component must be present. The combination of components and wires allows various simple and complex operations to be performed: signals can be amplified, computations can be performed, and data can be moved from one place to another.
Zobel networks are a type of filter section based on the imageimpedance design principle. They are named after Otto Zobel of Bell Labs, who published a muchreferenced paper on image filters in 1923. The distinguishing feature of Zobel networks is that the input impedance is fixed in the design independently of the transfer function. This characteristic is achieved at the expense of a much higher component count compared to other types of filter sections. The impedance would normally be specified to be constant and purely resistive. For this reason, Zobel networks are also known as constant resistance networks. However, any impedance achievable with discrete components is possible.
Dual impedance and dual network are terms used in electronic network analysis. The dual of an impedance is its reciprocal, or algebraic inverse . For this reason the dual impedance is also called the inverse impedance. Another way of stating this is that the dual of is the admittance .
A lattice phase equaliser or lattice filter is an example of an allpass filter. That is, the attenuation of the filter is constant at all frequencies but the relative phase between input and output varies with frequency. The lattice filter topology has the particular property of being a constantresistance network and for this reason is often used in combination with other constant resistance filters such as bridgeT equalisers. The topology of a lattice filter, also called an Xsection is identical to bridge topology. The lattice phase equaliser was invented by Otto Zobel. using a filter topology proposed by George Campbell.
Network synthesis is a method of designing signal processing filters. It has produced several important classes of filter including the Butterworth filter, the Chebyshev filter and the Elliptic filter. It was originally intended to be applied to the design of passive linear analogue filters but its results can also be applied to implementations in active filters and digital filters. The essence of the method is to obtain the component values of the filter from a given rational function representing the desired transfer function.
An equivalent impedance is an equivalent circuit of an electrical network of impedance elements which presents the same impedance between all pairs of terminals as did the given network. This article describes mathematical transformations between some passive, linear impedance networks commonly found in electronic circuits.
Analogue filters are a basic building block of signal processing much used in electronics. Amongst their many applications are the separation of an audio signal before application to bass, midrange, and tweeter loudspeakers; the combining and later separation of multiple telephone conversations onto a single channel; the selection of a chosen radio station in a radio receiver and rejection of others.
In signal processing, a filter is a device or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. However, filters do not exclusively act in the frequency domain; especially in the field of image processing many other targets for filtering exist. Correlations can be removed for certain frequency components and not for others without having to act in the frequency domain. Filters are widely used in electronics and telecommunication, in radio, television, audio recording, radar, control systems, music synthesis, image processing, and computer graphics.
A distributedelement filter is an electronic filter in which capacitance, inductance, and resistance are not localised in discrete capacitors, inductors, and resistors as they are in conventional filters. Its purpose is to allow a range of signal frequencies to pass, but to block others. Conventional filters are constructed from inductors and capacitors, and the circuits so built are described by the lumped element model, which considers each element to be "lumped together" at one place. That model is conceptually simple, but it becomes increasingly unreliable as the frequency of the signal increases, or equivalently as the wavelength decreases. The distributedelement model applies at all frequencies, and is used in transmissionline theory; many distributedelement components are made of short lengths of transmission line. In the distributed view of circuits, the elements are distributed along the length of conductors and are inextricably mixed together. The filter design is usually concerned only with inductance and capacitance, but because of this mixing of elements they cannot be treated as separate "lumped" capacitors and inductors. There is no precise frequency above which distributed element filters must be used but they are especially associated with the microwave band.
Passivity is a property of engineering systems, used in a variety of engineering disciplines, but most commonly found in analog electronics and control systems. A passive component, depending on field, may be either a component that consumes but does not produce energy or a component that is incapable of power gain.
A frequency dependent negative resistor (FDNR) is a circuit element that exhibits a purely real negative resistance 1/(ω^{2}kC) that decreases in magnitude at a rate of 40 dB per decade. The element is used in implementation of lowpass active filters modeled from ladder filters. The element is usually implemented from a generalized impedance converter (GIC) or gyrator. The impedance of a FDNR is