Electronic filters are electronic circuits which perform signal processing functions, specifically intended to remove unwanted signal components and/or enhance wanted ones. An electronic circuit is a closed path formed by the interconnection of Electronic components through which an Electric current can flow Signal processing is the analysis interpretation and manipulation of signals Signals of interest include sound, images, biological signals such as Electronic filters can be:
The most common types of electronic filters are linear filters, regardless of other aspects of their design. Passivity is a property of engineering systems most commonly used in electronic engineering and control systems An active filter is a type of analog Electronic filter, distinguished by the use of one or more Active components i Analogue electronics (or analog in American English) are those electronic systems with a continuously Variable signal In Electronics, Computer science and Mathematics, a digital filter is a system that performs mathematical operations on a sampling, A discrete signal or discrete-time signal is a Time series, perhaps a signal that has been sampled from a continuous-time signal. A continuous signal or a continuous-time signal is a varying quantity (a signal) that is expressed as a function of a real-valued domain usually time A linear filter applies a Linear operator to a time-varying input signal A nonlinear filter is a signal-processing device whose output is not a Linear function of its input IIR redirects here For the conference company IIR see Informa. A finite impulse response (FIR filter is a type of a Digital filter. A linear filter applies a Linear operator to a time-varying input signal 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. |- align = "center"| |width = "25"| | |- align = "center"| || Potentiometer |- align = "center"| | | |- align = "center"| Resistor| | A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors An inductor is a passive electrical component designed to provide Inductance in a circuit These are known as RC and RL single pole filters respectively. In Complex analysis, a pole of a Meromorphic function is a certain type of singularity that behaves like the singularity at z = 0 More complex multipole LC filters have also existed for many years and the operation of such filters is well understood with many books having been written about them.
Hybrid filters have also been made, typically involving combinations of analog amplifiers with mechanical resonators or delay lines. Other devices such as CCD delay lines have also been used as discrete-time filters. A charge-coupled device ( CCD) is an analog Shift register, that enables the transportation of analog signals (electric charges through successive stages (capacitors With the availability of digital signal processing, active digital filters have become common.
Passive implementations of linear filters are based on combinations of resistors (R), inductors (L) and capacitors (C). |- align = "center"| |width = "25"| | |- align = "center"| || Potentiometer |- align = "center"| | | |- align = "center"| Resistor| | An inductor is a passive electrical component designed to provide Inductance in a circuit A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors These types are collectively known as passive filters, because they do not depend upon an external power supply.
Inductors block high-frequency signals and conduct low-frequency signals, while capacitors do the reverse. A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors A filter in which the signal passes through an inductor, or in which a capacitor provides a path to earth, presents less attenuation to low-frequency signals than high-frequency signals and is a low-pass filter. An inductor is a passive electrical component designed to provide Inductance in a circuit A low-pass filter is a filter that passes low- Frequency signals but Attenuates (reduces the Amplitude of signals with frequencies 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 is a high-pass filter. A high-pass filter is a filter that passes high frequencies well but attenuates (reduces the amplitude of frequencies lower than the Cutoff frequency 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. |- align = "center"| |width = "25"| | |- align = "center"| || Potentiometer |- align = "center"| | | |- align = "center"| Resistor| |
At very 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. The hertz (symbol Hz) is a measure of Frequency, informally defined as the number of events occurring per Second. These inductive or capacitive pieces of metal are called stubs. Electronics "? Perhaps "In MMICs quot ? Or is that *too* specific?
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. An LC circuit is a variety of resonant circuit or tuned circuit and consists of an Inductor, represented by the letter L and a Capacitor, represented
The simplest passive filters consist of a single reactive element. These are constructed of RC, RL, LC or RLC elements. A resistor–capacitor circuit (RC circuit, or RC filter or RC network, is an Electric circuit composed of resistors and capacitors driven by A resistor-inductor circuit (RL circuit, or RL filter or RL network, is one of the simplest analogue Infinite impulse response An LC circuit is a variety of resonant circuit or tuned circuit and consists of an Inductor, represented by the letter L and a Capacitor, represented An RLC circuit (also known as a Resonant circuit tuned circuit or LCR circuit is an Electrical circuit consisting of a Resistor (R an
The quality or "Q" factor is a measure that is sometimes used to describe simple band-pass or band-stop filters. For other uses of the terms Q and Q factor see Q value. In Physics and Engineering the quality A filter is said to have a high Q if it selects or rejects a range of frequencies that is narrow in comparison to the centre frequency. Q may be defined as the ratio of centre frequency divided by 3dB bandwidth. It is not commonly employed with higher order filters where other parameters are of more concern.
Consists of two elements, one in series and one in parallel.
Three element filters in a 'T' configuration can be constructed for low-pass, high-pass, band-pass or band-stop.
Three element filters in a 'π' configuration can be constructed for low-pass, high-pass, band-pass or band-stop.
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 speed of transition from pass-band to stop-band.
Active filters are implemented using a combination of passive and active (amplifying) components, and require an outside power source. An active filter is a type of analog Electronic filter, distinguished by the use of one or more Active components i Operational amplifiers are frequently used in active filter designs. An operational amplifier, often called an op-amp, is a DC - coupled high- Gain electronic voltage amplifier with differential These can have high Q, and can achieve resonance without the use of inductors. Electrical resonance occurs in an electric circuit at a particular resonance frequency when the impedance between the input and output of the However, their upper frequency limit is limited by the bandwidth of the amplifiers used.
Digital signal processing allows the inexpensive construction of a wide variety of filters. Digital signal processing ( DSP) is concerned with the representation of the signals by a sequence of numbers or symbols and the processing of these signals The signal is sampled and an analog to digital converter turns the signal into a stream of numbers. An analog-to-digital converter (abbreviated ADC, A/D or A to D) is an electronic integrated circuit which converts continuous signals to A computer program running on a CPU or a specialized DSP (or less often running on a hardware implementation of the algorithm) calculates an output number stream. A digital signal processor ( DSP or DSP micro) is a specialized Microprocessor designed specifically for Digital signal processing, generally In Mathematics, Computing, Linguistics and related subjects an algorithm is a sequence of finite instructions often used for Calculation This output can be converted to a signal by passing it through a digital to analog converter. In Electronics, a digital-to-analog converter ( DAC or D-to-A) is a device for converting a digital (usually binary code to an Analog signal There are problems with noise introduced by the conversions, but these can be controlled and limited for many useful filters. Due to the sampling involved, the input signal must be of limited frequency content or aliasing will occur. This article applies to signal processing including computer graphics See also: Digital filter. In Electronics, Computer science and Mathematics, a digital filter is a system that performs mathematical operations on a sampling,
In the late 1930s, engineers realized that small mechanical systems made of rigid materials such as quartz would acoustically resonate at radio frequencies, i. The 1930s were described as an abrupt shift to more radical and conservative lifestyles as countries were struggling to find a solution to the Great Depression. Quartz (from German) is the most abundant Mineral in the Earth 's Continental crust (although Feldspar is more common in e. from audible frequencies (sound) up to several hundred megahertz. Sound' is Vibration transmitted through a Solid, Liquid, or Gas; particularly sound means those vibrations composed of Frequencies Some early resonators were made of steel, but quartz quickly became favored. Steel is an Alloy consisting mostly of Iron, with a Carbon content between 0 The biggest advantage of quartz is that it is piezoelectric. Piezoelectricity is the ability of some materials (notably Crystals and certain Ceramics including bone to generate an Electric potential in response to This means that quartz resonators can directly convert their own mechanical motion into electrical signals. Quartz also has a very low coefficient of thermal expansion which means that quartz resonators can produce stable frequencies over a wide temperature range. Quartz crystal filters have much higher quality factors than LCR filters. A crystal oscillator is an Electronic circuit that uses the mechanical Resonance of a vibrating Crystal of piezoelectric material to create an When higher stabilities are required, the crystals and their driving circuits may be mounted in a "crystal oven" to control the temperature. A crystal oven is a temperature-controlled chamber used to maintain the quartz crystal in electronic Crystal oscillators at a constant temperature in order to prevent changes For very narrow band filters, sometimes several crystals are operated in series.
Engineers realized that a large number of crystals could be collapsed into a single component, by mounting comb-shaped evaporations of metal on a quartz crystal. In this scheme, a "tapped delay line" reinforces the desired frequencies as the sound waves flow across the surface of the quartz crystal. An analog delay line is a network of electrical components connected in series where each individual element creates a time difference or phase change between its input The tapped delay line has become a general scheme of making high-Q filters in many different ways.
SAW (surface acoustic wave) filters are electromechanical devices commonly used in radio frequency applications. A surface acoustic wave ( SAW) is an Acoustic wave traveling along the surface of a material having some elasticity, with an Amplitude that In Engineering, electromechanics combines the Sciences of Electromagnetism of Electrical engineering and mechanics. Radio frequency ( RF) is a Frequency or rate of Oscillation within the range of about 3 Hz to 300 GHz Electrical signals are converted to a mechanical wave in a piezoelectric crystal; this wave is delayed as it propagates across the crystal, before being converted back to an electrical signal by further electrodes. Piezoelectricity is the ability of some materials (notably Crystals and certain Ceramics including bone to generate an Electric potential in response to An electrode is an Electrical conductor used to make contact with a nonmetallic part of a circuit (e The delayed outputs are recombined to produce a direct analog implementation of a finite impulse response filter. A finite impulse response (FIR filter is a type of a Digital filter. This hybrid filtering technique is also found in an analog sampled filter. An analog sampled filter an Electronic filter that is a hybrid between an analog and a Digital filter. SAW filters are limited to frequencies up to 3GHz.
BAW (Bulk Acoustic Wave) filters are electromechanical devices. In Engineering, electromechanics combines the Sciences of Electromagnetism of Electrical engineering and mechanics. These filters are in the research state for the moment. BAW filters can implement ladder or lattice filters. BAW filters seem to be smaller than SAW filters, and can operate at frequencies up to 16 GHz.
Another method of filtering, at microwave frequencies from 800MHz to about 5 GHz, is to use a synthetic single crystal yttrium iron garnet sphere made of a chemical combination of yttrium and iron (YIGF, or yttrium iron garnet filter). Yttrium iron garnet filter ( YIG filter) is a magnetically tunable Filter for Microwave frequencies Microwaves are electromagnetic waves with Wavelengths ranging from 1 mm to 1 m or frequencies between 0 A single crystal, also called monocrystal, is a Crystalline Solid in which the Crystal lattice of the entire sample is continuous and unbroken Yttrium iron garnet ( YIG) is a kind of synthetic Garnet, with chemical composition 32(Fe43 or Y3Fe5O12 Yttrium (ˈɪtriəm is a Chemical element with symbol Y and Atomic number 39 Iron (ˈаɪɚn is a Chemical element with the symbol Fe (ferrum and Atomic number 26 The garnet sits on a strip of metal driven by a transistor, and a small loop antenna touches the top of the sphere. In Electronics, a transistor is a Semiconductor device commonly used to amplify or switch electronic signals An antenna is a Transducer designed to transmit or Receive electromagnetic waves In other words antennas convert electromagnetic waves into An electromagnet changes the frequency that the garnet will pass. An electromagnet is a type of Magnet in which the Magnetic field is produced by the flow of an electric current. The advantage of this method is that the garnet can be tuned over a very wide frequency by varying the strength of the magnetic field. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges
For even higher frequencies and greater precision, the vibrations of atoms must be used. Atomic clocks use caesium masers as ultra-high Q filters to stabilize their primary oscillators. An atomic clock is a type of Clock that uses an Atomic resonance Frequency standard as its timekeeping element Caesium or cesium (ˈsiːziəm is the Chemical element with the symbol Cs and Atomic number 55 A maser is a device that produces coherent Electromagnetic waves through amplification due to Stimulated emission. Another method, used at high, fixed frequencies with very weak radio signals, is to use a ruby maser tapped delay line. A Ruby is a pink to blood-red Gemstone, a variety of the Mineral Corundum ( Aluminium oxide)
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 :
with . A transfer function is a mathematical representation in terms of spatial or temporal frequency of the relation between the input and output of a ( linear time-invariant)
The transfer function of all linear time-invariant filters generally share certain characteristics:
The proper construction of a transfer function involves the Laplace transform, and therefore it is needed to assume null initial conditions, because
And when f(0)=0 we can get rid of the constants and use the usual expression
An alternative to transfer functions is to give the behavior of the filter as a convolution. In Mathematics, the Laplace transform is one of the best known and most widely used Integral transforms It is commonly used to produce an easily soluble algebraic In Mathematics and in particular Functional analysis, convolution is a mathematical operation on two functions f and The convolution theorem, which holds for Laplace transforms, guarantees equivalence with transfer functions. In Mathematics, the convolution theorem states that under suitableconditions the Fourier transform of a Convolution is the Pointwise product
Filters may be specified by family and passband. A transfer function is a mathematical representation in terms of spatial or temporal frequency of the relation between the input and output of a ( linear time-invariant) A filter's family is specified by certain design criteria which give general rules for specifying the transfer function of the filter. Some common filter families and their particular design criteria are:
Generally, each family of filters can be specified to a particular order. The Butterworth filter is one type of Electronic filter design Chebyshev filters are analog or Digital filters having a steeper Roll-off and more Passband ripple (type I or Chebyshev filters are analog or Digital filters having a steeper Roll-off and more Passband ripple (type I or In Electronics and Signal processing, a Bessel filter is a variety of Linear filter with a maximally flat Group delay (linear Phase response An elliptic filter (also known as a Cauer filter, named after Wilhelm Cauer) is an Electronic filter with equalized ripple ( Equiripple The Optimum "L" filter (also known as a Legendre filter) was proposed by Athanasios Papoulis in 1958 In Electronics and Signal processing, a Gaussian filter is a filter whose Filter window is the Gaussian function x The raised-cosine filter is a particular Electronic filter, frequently used for Pulse-shaping in digital Modulation due to its ability to minimise The higher the order, the more the filter will approach the "ideal" filter. The ideal filter has full transmission in the pass band, and complete attenuation in the stop band, and the transition between the two bands is abrupt (often called brick-wall).
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.
As is clear from the image, elliptic filters are sharper than all the others, but they show ripples on the whole bandwidth.
Each family can be used to specify a particular pass band in which frequencies are transmitted, while frequencies in the stop band (i. e. outside the pass band) are more or less attenuated.
The family and passband of a filter completely specify the transfer function of a filter. The transfer function completely specifies the behavior of a linear filter, but not the particular technology used to implement it. In other words, there are a number of different ways of achieving a particular transfer function when designing a circuit.
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. Passivity is a property of engineering systems most commonly used in electronic engineering and control systems An active filter is a type of analog Electronic filter, distinguished by the use of one or more Active components i An electronic filter topology is an electronic Analog filter circuit in which the values of the components remain undefined
Any given filter transfer function may be implemented in any electronic filter topology. An electronic filter topology is an electronic Analog filter circuit in which the values of the components remain undefined
Some common circuit topologies are:
|Linear analog electronic filters|
Historically, linear analog filter design has evolved through three major approaches. Multiple feedback topology is an Electronic filter topology which is used to implement an Electronic filter by adding two poles to the Transfer function State Variable Topology refers to filters with two pole filter topology. For the digital implementation of a biquad filter check digital biquad filter The Butterworth filter is one type of Electronic filter design Chebyshev filters are analog or Digital filters having a steeper Roll-off and more Passband ripple (type I or An elliptic filter (also known as a Cauer filter, named after Wilhelm Cauer) is an Electronic filter with equalized ripple ( Equiripple In Electronics and Signal processing, a Bessel filter is a variety of Linear filter with a maximally flat Group delay (linear Phase response In Electronics and Signal processing, a Gaussian filter is a filter whose Filter window is the Gaussian function x The Optimum "L" filter (also known as a Legendre filter) was proposed by Athanasios Papoulis in 1958 A Linkwitz-Riley (L-R filter is an infinite impulse response filter used in Linkwitz-Riley Audio crossovers named after its inventors Siegfried Linkwitz Electronic filters designed from the Image impedance point of view are called image filters Constant k filters are a type of Electronic filter designed using the image method m-type filters or m-derived filters are a type of Electronic filter designed using the image method For the wave filter invented by Zobel and sometimes named after him see M-derived filters. Electronic filters designed from the Image impedance point of view are called image filters A resistor-inductor circuit (RL circuit, or RL filter or RL network, is one of the simplest analogue Infinite impulse response A resistor–capacitor circuit (RC circuit, or RC filter or RC network, is an Electric circuit composed of resistors and capacitors driven by An RLC circuit (also known as a Resonant circuit tuned circuit or LCR circuit is an Electrical circuit consisting of a Resistor (R an An LC circuit is a variety of resonant circuit or tuned circuit and consists of an Inductor, represented by the letter L and a Capacitor, represented The oldest designs are simple circuits where the main design criterion was the Q factor of the circuit. For other uses of the terms Q and Q factor see Q value. In Physics and Engineering the quality 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. Image impedance is a concept used in electronic network design and analysis and most especially in filter design After WW2 the dominant methodology was network synthesis. World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including The higher mathematics used originally required extensive tables of polynomial coefficient values to be published but modern computer resources have made that unnecessary. 
Low order filters can be designed by directly applying basic circuit laws such as Kirchoff'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 rely on filter terminations in the image impedance, which is usually not the case. 
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.