Electronic filter - AbsoluteAstronomy.com

Electronic filters
Filter (signal processing)
In signal processing, a filter is a device or process that removes from a signal some unwanted component or feature. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal...

are electronic circuit

Electronic circuit

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...

s which perform signal processing

Signal processing

Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...

functions, specifically to remove unwanted frequency components from the signal, to enhance wanted ones, or both. Electronic filters can be:

passive or active
Active filter
An active filter is a type of analog electronic filter that uses an amplifier stage. Amplifiers included in a filter design can be used to improve the performance, stability and predictability of a filter. An amplifier prevents the impedance of source or load stages from affecting the...
analog or digital
Digital filter
In electronics, computer science and mathematics, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is...
high-pass
High-pass filter
A high-pass filter is a device that passes high frequencies and attenuates frequencies lower than its cutoff frequency. A high-pass filter is usually modeled as a linear time-invariant system...

, low-pass
Low-pass filter
A low-pass filter is an electronic filter that passes low-frequency signals but attenuates signals with frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called a high-cut filter, or treble cut filter...

, bandpass
Band-pass filter
A band-pass filter is a device that passes frequencies within a certain range and rejects frequencies outside that range.Optical band-pass filters are of common usage....

, band-reject
Band-stop filter
In signal processing, a band-stop filter or band-rejection filter is a filter that passes most frequencies unaltered, but attenuates those in a specific range to very low levels. It is the opposite of a band-pass filter...

(band reject; notch), or all-pass
All-pass filter
An all-pass filter is a signal processing filter that passes all frequencies equally, but changes the phase relationship between various frequencies. It does this by varying its propagation delay with frequency...

.
discrete-time (sampled) or continuous-time
linear
Linear filter
Linear filters in the time domain process time-varying input signals to produce output signals, subject to the constraint of linearity.This results from systems composed solely of components classified as having a linear response....

or non-linear
Non-linear filter
A nonlinear filter is a signal-processing device whose output is not a linear function of its input. Terminology concerning the filtering problem may refer to the time domain showing of the signal or to the frequency domain representation of the signal. When referring to filters with adjectives...
infinite impulse response
Infinite impulse response
Infinite impulse response is a property of signal processing systems. Systems with this property are known as IIR systems or, when dealing with filter systems, as IIR filters. IIR systems have an impulse response function that is non-zero over an infinite length of time...

(IIR type) or finite impulse response
Finite impulse response
A finite impulse response filter is a type of a signal processing filter whose impulse response is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response filters, which have internal feedback and may continue to respond indefinitely...

(FIR type)

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.

History

The oldest forms of electronic filters are passive analog linear filters, constructed using only resistors and capacitor

Capacitor

A capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...

s or resistors and inductor

Inductor

An inductor is a passive two-terminal electrical component used to store energy in a magnetic field. An inductor's ability to store magnetic energy is measured by its inductance, in units of henries...

s. These are known as RC and RL single-pole filters respectively.
More complex multipole LC filters have also existed for many years, and their operation is well understood.

Hybrid filters are also possible, typically involving a combination of analog amplifiers with mechanical resonators or delay lines. Other devices such as CCD

Charge-coupled device

A charge-coupled device is a device for the movement of electrical charge, usually from within the device to an area where the charge can be manipulated, for example conversion into a digital value. This is achieved by "shifting" the signals between stages within the device one at a time...

delay line

Delay line

Delay line may refer to:* Propagation delay, the length of time taken for something to reach its destination* Analog delay line, used to delay a signal...

s have also been used as discrete-time filters. With the availability of digital signal processing, active digital filters have become common.

Passive filters

Passive implementations of linear filters are based on combinations of resistor

Resistor

A linear resistor is a linear, passive two-terminal electrical component that implements electrical resistance as a circuit element.The current through a resistor is in direct proportion to the voltage across the resistor's terminals. Thus, the ratio of the voltage applied across a resistor's...

s (R), inductor

Inductor

s (L) and capacitor

Capacitor

s (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 capacitor

Capacitor

s do the reverse. A filter in which the signal passes through an inductor

Inductor

, or in which a capacitor provides a path to ground, presents less attenuation to low-frequency signals than high-frequency signals and is a low-pass filter
Low-pass filter
A low-pass filter is an electronic filter that passes low-frequency signals but attenuates signals with frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called a high-cut filter, or treble cut 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 is a high-pass filter
High-pass filter
A high-pass filter is a device that passes high frequencies and attenuates frequencies lower than its cutoff frequency. A high-pass filter is usually modeled as a linear time-invariant system...

. Resistor

Resistor

s 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

LC circuit

An LC circuit, also called a resonant circuit or tuned circuit, consists of an inductor, represented by the letter L, and a capacitor, represented by the letter C...

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

Hertz

The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....

), 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

The simplest passive filters, RC

RC circuit

A resistor–capacitor circuit ', or RC filter or RC network, is an electric circuit composed of resistors and capacitors driven by a voltage or current source...

and RL

RL circuit

A resistor-inductor circuit ', or RL filter or RL network, is one of the simplest analogue infinite impulse response electronic filters. It consists of a resistor and an inductor, either in series or in parallel, driven by a voltage source.-Introduction:The fundamental passive linear circuit...

filters, include only one reactive element, except hybrid LC filter

Hybrid LC Filter

Hybrid LC filter is a kind of LC filter, which typically contains two conductive foil layers, separated by an insulation material and coiled on a core. One layer, which is placed between the voltage source, such as inverter, and a load, is called “the main foil”; this layer forms filter inductance....

which is characterized by inductance and capacitance integrated in one element.

T and π filters

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

M-derived filter

m-derived filters or m-type filters are a type of electronic filter designed using the image method. They were invented by Otto Zobel in the early 1920s. This filter type was originally intended for use with telephone multiplexing and was an improvement on the existing constant k type filter...

sections with correct termination impedances, the input impedance can be reasonably constant in the pass band.

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 filter

An active filter is a type of analog electronic filter that uses an amplifier stage. Amplifiers included in a filter design can be used to improve the performance, stability and predictability of a filter. An amplifier prevents the impedance of source or load stages from affecting the...

s are implemented using a combination of passive and active (amplifying) components, and require an outside power source. Operational amplifier

Operational amplifier

An operational amplifier is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output...

s are frequently used in active filter designs. These can have high Q factor

Q factor

In physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how under-damped an oscillator or resonator is, or equivalently, characterizes a resonator's bandwidth relative to its center frequency....

, and can achieve resonance

Electrical resonance

Electrical resonance occurs in an electric circuit at a particular resonance frequency where the imaginary parts of circuit element impedances or admittances cancel each other...

without the use of inductors. However, their upper frequency limit is limited by the bandwidth of the amplifiers used.

Digital filters

Digital signal processing

Digital signal processing is concerned with the representation of discrete time signals by a sequence of numbers or symbols and the processing of these signals. Digital signal processing and analog signal processing are subfields of signal processing...

allows the inexpensive construction of a wide variety of filters. The signal is sampled and an analog-to-digital converter

Analog-to-digital converter

An analog-to-digital converter is a device that converts a continuous quantity to a discrete time digital representation. An ADC may also provide an isolated measurement...

turns the signal into a stream of numbers. A computer program running on a CPU

Central processing unit

The central processing unit is the portion of a computer system that carries out the instructions of a computer program, to perform the basic arithmetical, logical, and input/output operations of the system. The CPU plays a role somewhat analogous to the brain in the computer. The term has been in...

or a specialized DSP

Digital signal processor

A digital signal processor is a specialized microprocessor with an architecture optimized for the fast operational needs of digital signal processing.-Typical characteristics:...

(or less often running on a hardware implementation of the algorithm

Algorithm

In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

) calculates an output number stream. This output can be converted to a signal by passing it through a digital-to-analog converter

Digital-to-analog converter

In electronics, a digital-to-analog converter is a device that converts a digital code to an analog signal . An analog-to-digital converter performs the reverse operation...

. 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

Aliasing

In signal processing and related disciplines, aliasing refers to an effect that causes different signals to become indistinguishable when sampled...

will occur.

Quartz filters and piezoelectrics

In the late 1930s, engineers realized that small mechanical systems made of rigid materials such as quartz

Quartz

Quartz is the second-most-abundant mineral in the Earth's continental crust, after feldspar. It is made up of a continuous framework of SiO4 silicon–oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall formula SiO2. There are many different varieties of quartz,...

would acoustically resonate at radio frequencies, i.e. from audible frequencies (sound

Sound

Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...

) up to several hundred megahertz.
Some early resonators were made of steel

Steel

Steel is an alloy that consists mostly of iron and has a carbon content between 0.2% and 2.1% by weight, depending on the grade. Carbon is the most common alloying material for iron, but various other alloying elements are used, such as manganese, chromium, vanadium, and tungsten...

, but quartz quickly became favored. The biggest advantage of quartz is that it is piezoelectric

Piezoelectricity

Piezoelectricity is the charge which accumulates in certain solid materials in response to applied mechanical stress. The word piezoelectricity means electricity resulting from pressure...

. 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

Crystal oscillator

A crystal oscillator is an electronic oscillator circuit that uses the mechanical resonance of a vibrating crystal of piezoelectric material to create an electrical signal with a very precise frequency...

filters have much higher quality factors than LCR filters. When higher stabilities are required, the crystals and their driving circuits may be mounted in a "crystal oven

Crystal oven

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 in the frequency due to variations in ambient temperature...

" to control the temperature. 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

Analog delay line

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 signal and its output signal. An example is a bucket-brigade device....

" reinforces the desired frequencies as the sound waves flow across the surface of the quartz crystal.
The tapped delay line has become a general scheme of making high-Q filters in many different ways.

SAW filters

SAW (surface acoustic wave

Surface acoustic wave

]A surface acoustic wave is an acoustic wave traveling along the surface of a material exhibiting elasticity, with an amplitude that typically decays exponentially with depth into the substrate.-Discovery:...

) filters are electromechanical devices commonly used in radio frequency

Radio frequency

Radio frequency is a rate of oscillation in the range of about 3 kHz to 300 GHz, which corresponds to the frequency of radio waves, and the alternating currents which carry radio signals...

applications. Electrical signals are converted to a mechanical wave in a device constructed of a piezoelectric crystal or ceramic; this wave is delayed as it propagates across the device, before being converted back to an electrical signal by further electrode

Electrode

An electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit...

s. The delayed outputs are recombined to produce a direct analog implementation of a finite impulse response

Finite impulse response

A finite impulse response filter is a type of a signal processing filter whose impulse response is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response filters, which have internal feedback and may continue to respond indefinitely...

filter. This hybrid filtering technique is also found in an analog sampled filter

Analog sampled filter

An analog sampled filter an electronic filter that is a hybrid between an analog and a digital filter. The input signal is analog, and usually stored in capacitors. The time domain is discrete, however. Distinct analog samples are shifted through an array of holding capacitors as in a bucket brigade...

.
SAW filters are limited to frequencies up to 3 GHz.

BAW filters

BAW (Bulk Acoustic Wave) filters are electromechanical devices. BAW filters can implement ladder or lattice filters.
BAW filters typically operate at frequencies from around 2 to around 16 GHz, and may be smaller or thinner than equivalent SAW filters. Two main variants of BAW filters are making their way into devices, Thin film bulk acoustic resonator

Thin film bulk acoustic resonator

Thin Film Bulk Acoustic Resonator is a device consisting of a piezoelectric material sandwiched between two electrodes and acoustically isolated from the surrounding medium. FBAR devices using piezoelectric films with thicknesses ranging from several micrometres down to tenth of micrometres...

or FBAR and Solid Mounted Bulk Acoustic Resonators.

Garnet filters

Another method of filtering, at microwave

Microwave

Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...

frequencies from 800 MHz to about 5 GHz, is to use a synthetic single crystal

Single crystal

A single crystal or monocrystalline solid is a material in which the crystal lattice of the entire sample is continuous and unbroken to the edges of the sample, with no grain boundaries...

yttrium iron garnet

Yttrium iron garnet

Yttrium iron garnet is a kind of synthetic garnet, with chemical composition 323, or Y3Fe5O12. It is a ferrimagnetic material with a Curie temperature of 550 K....

sphere made of a chemical combination of yttrium

Yttrium

Yttrium is a chemical element with symbol Y and atomic number 39. It is a silvery-metallic transition metal chemically similar to the lanthanides and it has often been classified as a "rare earth element". Yttrium is almost always found combined with the lanthanides in rare earth minerals and is...

and iron

Iron

Iron is a chemical element with the symbol Fe and atomic number 26. It is a metal in the first transition series. It is the most common element forming the planet Earth as a whole, forming much of Earth's outer and inner core. It is the fourth most common element in the Earth's crust...

(YIGF, or yttrium iron garnet filter). The garnet sits on a strip of metal driven by a transistor

Transistor

A transistor is a semiconductor device used to amplify and switch electronic signals and power. It is composed of a semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current...

, and a small loop antenna

Antenna (radio)

An antenna is an electrical device which converts electric currents into radio waves, and vice versa. It is usually used with a radio transmitter or radio receiver...

touches the top of the sphere. An electromagnet

Electromagnet

An electromagnet is a type of magnet in which the magnetic field is produced by the flow of electric current. The magnetic field disappears when the current is turned off...

changes the frequency that the garnet will pass. 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

Magnetic field

A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

Atomic filters

For even higher frequencies and greater precision, the vibrations of atoms must be used. Atomic clock

Atomic clock

An atomic clock is a clock that uses an electronic transition frequency in the microwave, optical, or ultraviolet region of the electromagnetic spectrum of atoms as a frequency standard for its timekeeping element...

s use caesium

Caesium

Caesium or cesium is the chemical element with the symbol Cs and atomic number 55. It is a soft, silvery-gold alkali metal with a melting point of 28 °C , which makes it one of only five elemental metals that are liquid at room temperature...

maser

Maser

A maser is a device that produces coherent electromagnetic waves through amplification by stimulated emission. Historically, “maser” derives from the original, upper-case acronym MASER, which stands for "Microwave Amplification by Stimulated Emission of Radiation"...

s as ultra-high Q filters to stabilize their primary oscillators. Another method, used at high, fixed frequencies with very weak radio signals, is to use a ruby

Ruby

A ruby is a pink to blood-red colored gemstone, a variety of the mineral corundum . The red color is caused mainly by the presence of the element chromium. Its name comes from ruber, Latin for red. Other varieties of gem-quality corundum are called sapphires...

maser tapped delay line.

The transfer function

see also Filter (signal processing)
Filter (signal processing)
In signal processing, a filter is a device or process that removes from a signal some unwanted component or feature. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal...

for further analysis

The transfer function

Transfer function

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 system. With optical imaging devices, for example, it is the Fourier transform of the point spread function i.e...

of a filter is the ratio of the output signal

to that of the input signal

as a function of the complex frequency

with

.

The transfer function of all linear time-invariant filters, when constructed of discrete components, will be the ratio of two polynomials in

, i.e. a rational function

Rational function

In mathematics, a rational function is any function which can be written as the ratio of two polynomial functions. Neither the coefficients of the polynomials nor the values taken by the function are necessarily rational.-Definitions:...

. 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

Active filter

technology can be further classified by the particular electronic filter topology

Electronic filter topology

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....

used to implement them.

Any given filter transfer function may be implemented in any electronic filter topology

Electronic filter topology

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....

.

Some common circuit topologies are:

Cauer topology - Passive
Sallen Key topology
Sallen Key filter
The Sallen–Key topology is an electronic filter topology used to implement second-order active filters that is particularly valued for its simplicity. It is a degenerate form of a voltage-controlled voltage-source filter topology...

- Active
Multiple Feedback topology - Active
State Variable Topology - Active
Biquadratic topology biquad filter - Active

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

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

Image impedance

Image impedance is a concept used in electronic network design and analysis and most especially in filter design. The term image impedance applies to the impedance seen looking in to the ports of a network. Usually a two-port network is implied but the concept is capable of being extended to...

point of view, mostly being driven by the requirements of telecommunications. After World War II

World War II

World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...

the dominant methodology was network synthesis

Network synthesis filters

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...

. The higher mathematics used originally required extensive tables of polynomial coefficient values to be published but modern computer resources have made that unnecessary.

Direct circuit analysis

Low order filters can be designed by directly applying basic circuit laws such as Kirchhoff's laws

Kirchhoff's circuit laws

Kirchhoff's circuit laws are two equalities that deal with the conservation of charge and energy in electrical circuits, and were first described in 1845 by Gustav Kirchhoff...

to obtain the transfer function. This kind of analysis is usually only carried out for simple filters of 1st or 2nd order.

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.

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.

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.

External links and references

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.

History

Passive filters

Single element types

T and π filters

Multiple element types

Active filters

Digital filters

Quartz filters and piezoelectrics

SAW filters

BAW filters

Garnet filters

Atomic filters

The transfer function

Classification by topology

Classification by design methodology

Direct circuit analysis

Image impedance analysis

Network synthesis

See also

External links and references