Electronic filter

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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. Hilofilter.agr.jpg
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 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 distributed-element 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 single-pole 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.

Classification by technology

Passive filters

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 high-frequency signals and conduct low-frequency 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 low-frequency signals than high-frequency signals and is therefore a low-pass filter . If the signal passes through a capacitor, or has a path to ground through an inductor, then the filter presents less attenuation to high-frequency signals than low-frequency signals and therefore is a high-pass filter . Resistors on their own have no frequency-selective properties, but are added to inductors and capacitors to determine the time-constants 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 band-pass or band-stop 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.

Single element types

A low-pass electronic filter realised by an RC circuit 1st Order Lowpass Filter RC.svg
A low-pass electronic filter realised by an RC circuit

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]

L filter

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

T and π filters

Low-pass p filter Lowpass Pi Filter.svg
Low-pass π filter
High-pass T filter Highpass T Filter.svg
High-pass T filter

Three-element filters can have a 'T' or 'π' topology and in either geometries, a low-pass, high-pass, band-pass, or band-stop characteristic is possible. The components can be chosen symmetric or not, depending on the required frequency characteristics. The high-pass 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 low-pass π filter, the circuit can be connected to a transmission line, transmitting low frequencies and reflecting high frequencies. Using m-derived filter sections with correct termination impedances, the input impedance can be reasonably constant in the pass band. [2]

Multiple-element types

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

Active filters

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.

Other filter technologies

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

see also Filter (signal processing) for further analysis

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 time-invariant 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.

Classification by topology

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:

Classification by design methodology

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]

Direct circuit analysis

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.

RL filter frequency response RL filter response.png
RL filter frequency response

Image impedance analysis

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]

Constant k filter response with 5 elements Constant k order 5.png
Constant k filter response with 5 elements
Zobel network (constant R) filter, 5 sections Zobel 5 sections.png
Zobel network (constant R) filter, 5 sections
m-derived filter response, m=0.5, 2 elements M-derived order 1.png
m-derived filter response, m=0.5, 2 elements
m-derived filter response, m=0.5, 5 elements M-derived order 5.png
m-derived filter response, m=0.5, 5 elements

Network synthesis

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 continued-fraction or partial-fraction 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 fifth-order low-pass filters. The particular implementation – analog or digital, passive or active – makes no difference; their output would be the same.

Electronic linear filters.svg

As is clear from the image, elliptic filters are sharper than all the others, but they show ripples on the whole bandwidth.

See also

Notes and references

  1. Dzhankhotov V., Hybrid LC filter for power electronic drives: Theory and Implementation, 2009
  2. The American Radio Relay League, Inc.: "The ARRL Handbook, 1968" page 50
  3. Bray, J, Innovation and the Communications Revolution, Institute of Electrical Engineers
  4. 1 2 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.CS1 maint: multiple names: authors list (link) Catalog of passive filter types and component values. The Bible for practical electronic filter design.
  • Williams, Arthur B; Taylor, Fred J (1995). Electronic Filter Design Handbook . McGraw-Hill. ISBN   0-07-070441-4.

Related Research Articles

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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 time-varying 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. Real-time 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 time-invariant filters can be completely characterized by their response to sinusoids of different frequencies, they are sometimes known as frequency filters.

A low-pass 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 high-cut filter, or treble-cut filter in audio applications. A low-pass filter is the complement of a high-pass filter.

Gyrator analog circuit

A gyrator is a passive, linear, lossless, two-port 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 non-reciprocal. Gyrators permit network realizations of two-(or-more)-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 one-port 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 op-amps using feedback.

Active filter active filter

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.

Butterworth filter type of signal processing filter designed to have a frequency response as flat as possible in the passband

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".

Electronic component basic discrete device or physical entity in an electronic system used to affect electrons or their associated fields

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Electronic filter topology electronic filter circuits without taking note of the values of the components used but only the manner in which those components are connected

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Zobel network type of filter section based on the image-impedance design principle

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Lattice phase equaliser

A lattice phase equaliser or lattice filter is an example of an all-pass 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 constant-resistance network and for this reason is often used in combination with other constant resistance filters such as bridge-T equalisers. The topology of a lattice filter, also called an X-section 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.

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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.

Distributed-element filter type of electronic filter circuit

A distributed-element 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 distributed-element model applies at all frequencies, and is used in transmission-line theory; many distributed-element 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.

Frequency dependent negative resistor

A frequency dependent negative resistor (FDNR) is a circuit element that exhibits a purely real negative resistance -1/(ω2kC) that decreases in magnitude at a rate of -40 dB per decade. The element is used in implementation of low-pass 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