Mechanical filter
Encyclopedia
A mechanical filter is a signal processing filter
usually used in place of an electronic filter
at radio frequencies
. Its purpose is the same as that of a normal electronic filter: to pass a range of signal frequencies, but to block others. The filter acts on mechanical vibrations which are the analogue of the electrical signal. At the input and output of the filter there are transducer
s which convert the electrical signal into, and then back from, these mechanical vibrations.
The components of a mechanical filter are all directly analogous to the various elements found in electrical circuits. The mechanical elements obey mathematical functions which are identical to their corresponding electrical elements. This makes it possible to apply electrical network analysis and filter design methods to mechanical filters. Electrical theory has developed a large library of mathematical forms that produce useful filter frequency responses and the mechanical filter designer is able to make direct use of these. It is only necessary to set the mechanical components to appropriate values to produce a filter with an identical response to the electrical counterpart.
Steel
and nickel
–iron
alloys are common materials for mechanical filter components; nickel is sometimes used for the input and output couplings. Resonators in the filter made from these materials need to be machined to precisely adjust their resonance frequency before final assembly.
While the meaning of mechanical filter in this article is one that is used in an electromechanical
role, it is fully possible to use a mechanical design to filter mechanical vibrations or sound waves (which are also essentially mechanical) directly. For example, filtering of audio frequency response in the design of loudspeaker cabinets
can be achieved with mechanical components. In the electrical application, in addition to mechanical components which correspond to their electrical counterparts, transducers are needed to convert between the mechanical and electrical domains. There are a wide variety of component forms and topologies for mechanical filters, a representative selection of which are presented in this article.
The theory of mechanical filters was first applied to improving the mechanical parts of phonograph
s in the 1920s. By the 1950s mechanical filters were being manufactured as self-contained components for applications in radio transmitters and high-end receivers. The high "quality factor", Q
, that mechanical resonators can attain, far higher than that of an all-electrical LC circuit, made possible the construction of mechanical filters with excellent selectivity. Good selectivity, being important in radio receivers, made such filters highly attractive. Contemporary researchers are working on microelectromechanical filters, the mechanical devices corresponding to electronic integrated circuits.
linear electrical network consist of inductor
s, capacitor
s and resistor
s which have the properties of inductance
, elastance (inverse capacitance
) and resistance
, respectively. The mechanical counterparts of these properties are, respectively, mass
, stiffness
and damping
. In most electronic filter designs, only inductor and capacitor elements are used in the body of the filter (although the filter may be terminated with resistors at the input and output). Resistances are not present in a theoretical filter composed of ideal components and only arise in practical designs as unwanted parasitic element
s. Likewise, a mechanical filter would ideally consist only of components with the properties of mass and stiffness, but in reality some damping is present as well.
The mechanical counterparts of voltage
and electric current
in this type of analysis are, respectively, force
(F) and velocity
(v) and represent the signal waveforms. From this, a mechanical impedance
can be defined in terms of the imaginary angular frequency
, jω, which entirely follows the electrical analogy.
The scheme presented in the table is known as the impedance analogy. Circuit diagrams produced using this analogy match the electrical impedance of the mechanical system seen by the electrical circuit, making it intuitive from an electrical engineering standpoint. There is also the mobility analogy,The impedance analogy is the more common approach,(Gatti & Ferrari, pp.630–632) but amongst those using the mobility analogy is Rockwell Collins
Inc, a principal manufacturer of mechanical filters. (Johnson, 1968, p.41) in which force corresponds to current and velocity corresponds to voltage. This has equally valid results but requires using the reciprocals of the electrical counterparts listed above. Hence, M → C, S → 1/L, D → G where G is electrical conductance, the inverse of resistance. Equivalent circuits produced by this scheme are similar, but are the dual impedance forms whereby series elements become parallel, capacitors become inductors, and so on. Circuit diagrams using the mobility analogy more closely match the mechanical arrangement
of the circuit, making it more intuitive from a mechanical engineering standpoint. In addition to their application to electromechanical systems, these analogies are widely used to aid analysis in acoustics.
Any mechanical component will unavoidably possess both mass and stiffness. This translates in electrical terms to an LC circuit, that is, a circuit consisting of an inductor and a capacitor, hence mechanical components are resonators and are often used as such. It is still possible to represent inductors and capacitors as individual lumped elements in a mechanical implementation by minimising (but never quite eliminating) the unwanted property. Capacitors may be made of thin, long rods, that is, the mass is minimised and the compliance is maximised. Inductors, on the other hand, may be made of short, wide pieces which maximise the mass in comparison to the compliance of the piece.
Mechanical parts act as a transmission line
for mechanical vibrations. If the wavelength
is short in comparison to the part then a lumped element model
as described above is no longer adequate and a distributed element model
must be used instead. The mechanical distributed elements are entirely analogous to electrical distributed elements and the mechanical filter designer can use the methods of electrical distributed element filter
design.
(in particular, acoustic resonance
) was very familiar to engineers. This situation was not to last for long; electrical resonance
had been known to science for some time before this, and it was not long before engineers started to produce all-electric designs for filters. In its time, though, the harmonic telegraph was of some importance. The idea was to combine several telegraph signals on one telegraph line by what would now be called frequency division multiplexing thus saving enormously on line installation costs. The key
of each operator activated a vibrating electromechanical reed which converted this vibration into an electrical signal. Filtering at the receiving operator was achieved by a similar reed tuned to precisely the same frequency, which would only vibrate and produce a sound from transmissions by the operator with the identical tuning.
Versions of the harmonic telegraph were developed by Elisha Gray
, Alexander Graham Bell
, Ernest MercadierErnest Mercadier article in French Wikipedia and others. Its ability to act as a sound transducer
to and from the electrical domain was to inspire the invention of the telephone.
theories were carried over into mechanics by analogy. Kennelly, who was also responsible for introducing complex impedance, and Webster
were the first to extend the concept of impedance into mechanical systems in 1920. Mechanical admittance and the associated mobility analogy came much later and are due to Firestone in 1932.
It was not enough to just develop a mechanical analogy. This could be applied to problems that were entirely in the mechanical domain, but for mechanical filters with an electrical application it is necessary to include the transducer in the analogy as well. Poincaré
in 1907 was the first to describe a transducer as a pair of linear algebra
ic equations relating electrical variables (voltage and current) to mechanical variables (force and velocity). These equations can be expressed as a matrix relationship in much the same way as the z-parameters
of a two-port network
in electrical theory, to which this is entirely analogous:
where V and I represent the voltage and current respectively on the electrical side of the transducer.
Wegel, in 1921, was the first to express these equations in terms of mechanical impedance as well as electrical impedance. The element
is the open circuit mechanical impedance, that is, the impedance presented by the mechanical side of the transducer when no current is entering the electrical side. The element 
, conversely, is the clamped electrical impedance, that is, the impedance presented to the electrical side when the mechanical side is clamped and prevented from moving (velocity is zero). The remaining two elements, 
and 
, describe the transducer forward and reverse transfer functions respectively. Once these ideas were in place, engineers were able to extend electrical theory into the mechanical domain and analyse an electromechanical system as a unified whole.
ic sound reproduction. A recurring problem with early phonograph designs was that mechanical resonances in the pickup and sound transmission mechanism caused excessively large peaks and troughs in the frequency response, resulting in poor sound quality. In 1923, Harrison of the Western Electric Company filed a patent for a phonograph in which the mechanical design was entirely represented as an electrical circuit. The horn of the phonograph is represented as a transmission line, and is a resistive load for the rest of the circuit, while all the mechanical and acoustic parts—from the pickup needle through to the horn—are translated into lumped components according to the impedance analogy. The circuit arrived at is a ladder topology of series resonant circuits coupled by shunt capacitors. This can be viewed as a bandpass filter circuit. Harrison designed the component values of this filter to have a specific passband corresponding to the desired audio passband (in this case 100 Hz to 6 kHz) and a flat response. Translating these electrical element values back into mechanical quantities provided specifications for the mechanical components in terms of mass and stiffness, which in turn could be translated into physical dimensions for their manufacture. The resulting phonograph has a flat frequency response in its passband and is free of the resonances previously experienced. Shortly after this, Harrison filed another patent using the same methodology on telephone transmit and receive transducers.
Harrison used Campbell
's image filter
theory, which was the most advanced filter theory available at the time. In this theory, filter design is viewed essentially as an impedance matching
problem. More advanced filter theory was brought to bear on this problem by Norton
in 1929 at Bell Labs
. Norton followed the same general approach though he later described to Darlington
the filter he designed as being "maximally flat". Norton's mechanical design predates the paper by Butterworth
who is usually credited as the first to describe the electronic maximally flat filter
. The equations Norton gives for his filter correspond to a singly terminated Butterworth filter, that is, one driven by an ideal voltage source with no impedance, whereas the form more usually given in texts is for the doubly terminated filter with resistors at both ends, making it hard to recognise the design for what it is. Another unusual feature of Norton's filter design arises from the series capacitor, which represents the stiffness of the diaphragm
. This is the only series capacitor in Norton's representation, and without it, the filter could be analysed as a low-pass prototype
. Norton moves the capacitor out of the body of the filter to the input at the expense of introducing a transformer into the equivalent circuit (Norton's figure 4). Norton has used here the "turning round the L" impedance transform to achieve this.
The definitive description of the subject from this period is Maxfield and Harrison's 1926 paper. There, they describe not only how mechanical bandpass filters can be applied to sound reproduction systems, but also apply the same principles to recording systems and describe a much improved disc cutting head.
, which in turn leads to the ability to squeeze more telephone channels into the same cable. This same feature is useful in radio transmitters for much the same reason. Mechanical filters quickly also found popularity in VHF/UHF radio intermediate frequency
(IF) stages of the high end radio sets (military, marine, amateur radio
and the like) manufactured by Collins. They were favoured in the radio application because they could achieve much higher Q-factors than the equivalent LC filter. High Q allows filters to be designed which have high selectivity, important for distinguishing adjacent radio channels in receivers. They also had an advantage in stability over both LC filters and monolithic crystal filters. The most popular design for radio applications was torsional resonators because radio IF typically lies in the 100 to 500 kHz band.
s used with mechanical filters: magnetostrictive and piezoelectric. Piezoelectric is favoured in more recent designs since the piezoelectric material can also be used as one of the resonators of the filter, thus reducing the number of components and thereby saving space. They also avoid the susceptibility to extraneous magnetic fields from which the magnetostrictive type suffers.
current superimposed on the signal, but this approach would detract from the generality of the filter design.
The usual magnetostrictive materials used for the transducer are either ferrite
or compressed powdered iron
. Mechanical filter designs often have the resonators coupled with steel or nickel-iron wires, but on some designs, especially older ones, nickel wire may be used for the input and output rods. This is because it is possible to wind the transducer coil directly on to a nickel coupling wire since nickel is slightly magnetostrictive. However, it is not strongly so and coupling to the electrical circuit is weak. This scheme also has the disadvantage that there are no measures taken to prevent eddy current
s, a problem that is avoided if ferrites are used instead of nickel.
The coil of the transducer adds some inductance on the electrical side of the filter. It is common practice to add a capacitor in parallel with the coil so that an additional resonator is formed which can be incorporated into the filter design. While this will not improve performance to the extent that an additional mechanical resonator would, there is some benefit and the coil has to be there in any case.
s on to the piezoelectric material. Early piezoelectric materials used in transducers such as barium titanate
had poor temperature stability. This precluded the transducer from functioning as one of the resonators; it had to be a separate component. This problem was solved with the introduction of lead zirconate titanate
(abbreviated PZT) which is stable enough to be used as a resonator. Another common piezoelectric material is quartz
, which has also been used in mechanical filters. However, ceramic
materials such as PZT are preferred for their greater electromechanical coupling coefficient
.
One type of piezoelectric transducer is the Langevin type, named after a transducer used by Paul Langevin
in early sonar
research. This is good for longitudinal modes of vibration. It can also be used on resonators with other modes of vibration if the motion can be mechanically converted into a longitudinal motion. The transducer consists of a layer of piezoelectric material sandwiched transversally into a coupling rod or resonator.
Another kind of piezoelectric transducer has the piezoelectric material sandwiched in longitudinally, usually into the resonator itself. This kind is good for torsional
vibration modes and is called a torsional transducer.
|}
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...
usually used in place of an electronic filter
Electronic filter
Electronic filters are electronic circuits which perform signal processing functions, specifically to remove unwanted frequency components from the signal, to enhance wanted ones, or both...
at radio frequencies
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...
. Its purpose is the same as that of a normal electronic filter: to pass a range of signal frequencies, but to block others. The filter acts on mechanical vibrations which are the analogue of the electrical signal. At the input and output of the filter there are transducer
Transducer
A transducer is a device that converts one type of energy to another. Energy types include electrical, mechanical, electromagnetic , chemical, acoustic or thermal energy. While the term transducer commonly implies the use of a sensor/detector, any device which converts energy can be considered a...
s which convert the electrical signal into, and then back from, these mechanical vibrations.
The components of a mechanical filter are all directly analogous to the various elements found in electrical circuits. The mechanical elements obey mathematical functions which are identical to their corresponding electrical elements. This makes it possible to apply electrical network analysis and filter design methods to mechanical filters. Electrical theory has developed a large library of mathematical forms that produce useful filter frequency responses and the mechanical filter designer is able to make direct use of these. It is only necessary to set the mechanical components to appropriate values to produce a filter with an identical response to the electrical counterpart.
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...
and nickel
Nickel
Nickel is a chemical element with the chemical symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel belongs to the transition metals and is hard and ductile...
–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...
alloys are common materials for mechanical filter components; nickel is sometimes used for the input and output couplings. Resonators in the filter made from these materials need to be machined to precisely adjust their resonance frequency before final assembly.
While the meaning of mechanical filter in this article is one that is used in an electromechanical
Electromechanics
In engineering, electromechanics combines the sciences of electromagnetism, of electrical engineering and mechanics. Mechanical engineering in this context refers to the larger discipline which includes chemical engineering, and other related disciplines. Electrical engineering in this context...
role, it is fully possible to use a mechanical design to filter mechanical vibrations or sound waves (which are also essentially mechanical) directly. For example, filtering of audio frequency response in the design of loudspeaker cabinets
Loudspeaker enclosure
A loudspeaker enclosure is a purpose-engineered cabinet in which speaker drivers and associated electronic hardware, such as crossover circuits and amplifiers, are mounted...
can be achieved with mechanical components. In the electrical application, in addition to mechanical components which correspond to their electrical counterparts, transducers are needed to convert between the mechanical and electrical domains. There are a wide variety of component forms and topologies for mechanical filters, a representative selection of which are presented in this article.
The theory of mechanical filters was first applied to improving the mechanical parts of phonograph
Phonograph
The phonograph record player, or gramophone is a device introduced in 1877 that has had continued common use for reproducing sound recordings, although when first developed, the phonograph was used to both record and reproduce sounds...
s in the 1920s. By the 1950s mechanical filters were being manufactured as self-contained components for applications in radio transmitters and high-end receivers. The high "quality factor", Q
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....
, that mechanical resonators can attain, far higher than that of an all-electrical LC circuit, made possible the construction of mechanical filters with excellent selectivity. Good selectivity, being important in radio receivers, made such filters highly attractive. Contemporary researchers are working on microelectromechanical filters, the mechanical devices corresponding to electronic integrated circuits.
Elements
The elements of a passivePassivity (engineering)
Passivity is a property of engineering systems, used in a variety of engineering disciplines, but most commonly found in analog electronics and control systems...
linear electrical network consist of 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, 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 and 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 which have the properties of inductance
Inductance
In electromagnetism and electronics, inductance is the ability of an inductor to store energy in a magnetic field. Inductors generate an opposing voltage proportional to the rate of change in current in a circuit...
, elastance (inverse capacitance
Capacitance
In electromagnetism and electronics, capacitance is the ability of a capacitor to store energy in an electric field. Capacitance is also a measure of the amount of electric potential energy stored for a given electric potential. A common form of energy storage device is a parallel-plate capacitor...
) and resistance
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...
, respectively. The mechanical counterparts of these properties are, respectively, mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
, stiffness
Stiffness
Stiffness is the resistance of an elastic body to deformation by an applied force along a given degree of freedom when a set of loading points and boundary conditions are prescribed on the elastic body.-Calculations:...
and damping
Damping
In physics, damping is any effect that tends to reduce the amplitude of oscillations in an oscillatory system, particularly the harmonic oscillator.In mechanics, friction is one such damping effect...
. In most electronic filter designs, only inductor and capacitor elements are used in the body of the filter (although the filter may be terminated with resistors at the input and output). Resistances are not present in a theoretical filter composed of ideal components and only arise in practical designs as unwanted parasitic element
Parasitic element (electrical networks)
In electrical networks, a parasitic element is a circuit element that is possessed by an electrical component but which it is not desirable for it to have for its intended purpose. For instance, a resistor is designed to possess resistance, but will also possess unwanted parasitic...
s. Likewise, a mechanical filter would ideally consist only of components with the properties of mass and stiffness, but in reality some damping is present as well.
The mechanical counterparts of voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...
and electric current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...
in this type of analysis are, respectively, force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
(F) and velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
(v) and represent the signal waveforms. From this, a mechanical impedance
Mechanical impedance
Mechanical impedance is a measure of how much a structure resists motion when subjected to a given force. It relates forces with velocities acting on a mechanical system. The mechanical impedance of a point on a structure is the ratio of the force applied at a point to the resulting velocity at...
can be defined in terms of the imaginary angular frequency
Angular frequency
In physics, angular frequency ω is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity...
, jω, which entirely follows the electrical analogy.
| Mechanical element | Formula (in one dimension) | Mechanical impedance | Electrical counterpart |
|---|---|---|---|
| Stiffness, S |  |
 |
Elastance, 1/C, the inverse of capacitance |
| Mass, M |  |
 |
Inductance, L |
| Damping, D |  |
 |
Resistance, R |
The scheme presented in the table is known as the impedance analogy. Circuit diagrams produced using this analogy match the electrical impedance of the mechanical system seen by the electrical circuit, making it intuitive from an electrical engineering standpoint. There is also the mobility analogy,The impedance analogy is the more common approach,(Gatti & Ferrari, pp.630–632) but amongst those using the mobility analogy is Rockwell Collins
Rockwell Collins
Rockwell Collins, Inc. is a large United States-based international company headquartered in Cedar Rapids, Iowa, primarily providing aviation and information technology systems and services to governmental agencies and aircraft manufacturers.- History :...
Inc, a principal manufacturer of mechanical filters. (Johnson, 1968, p.41) in which force corresponds to current and velocity corresponds to voltage. This has equally valid results but requires using the reciprocals of the electrical counterparts listed above. Hence, M → C, S → 1/L, D → G where G is electrical conductance, the inverse of resistance. Equivalent circuits produced by this scheme are similar, but are the dual impedance forms whereby series elements become parallel, capacitors become inductors, and so on. Circuit diagrams using the mobility analogy more closely match the mechanical arrangement
Topology (electronics)
The topology of an electronic circuit is the form taken by the network of interconnections of the circuit components. Different specific values or ratings of the components are regarded as being the same topology....
of the circuit, making it more intuitive from a mechanical engineering standpoint. In addition to their application to electromechanical systems, these analogies are widely used to aid analysis in acoustics.
Any mechanical component will unavoidably possess both mass and stiffness. This translates in electrical terms to an LC circuit, that is, a circuit consisting of an inductor and a capacitor, hence mechanical components are resonators and are often used as such. It is still possible to represent inductors and capacitors as individual lumped elements in a mechanical implementation by minimising (but never quite eliminating) the unwanted property. Capacitors may be made of thin, long rods, that is, the mass is minimised and the compliance is maximised. Inductors, on the other hand, may be made of short, wide pieces which maximise the mass in comparison to the compliance of the piece.
Mechanical parts act as a transmission line
Transmission line
In communications and electronic engineering, a transmission line is a specialized cable designed to carry alternating current of radio frequency, that is, currents with a frequency high enough that its wave nature must be taken into account...
for mechanical vibrations. If the wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
is short in comparison to the part then a lumped element model
Lumped element model
The lumped element model simplifies the description of the behaviour of spatially distributed physical systems into a topology consisting of discrete entities that approximate the behaviour of the distributed system under certain assumptions...
as described above is no longer adequate and a distributed element model
Distributed element model
In electrical engineering, the distributed element model or transmission line model of electrical circuits assumes that the attributes of the circuit are distributed continuously throughout the material of the circuit...
must be used instead. The mechanical distributed elements are entirely analogous to electrical distributed elements and the mechanical filter designer can use the methods of electrical distributed element filter
Distributed element filter
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...
design.
Harmonic telegraph
Mechanical filter design was developed by applying the discoveries made in electrical filter theory to mechanics. However, a very early example (1870s) of acoustic filtering was the "harmonic telegraph", which arose precisely because electrical resonance was poorly understood but mechanical resonanceMechanical resonance
Mechanical resonance is the tendency of a mechanical system to absorb more energy when the frequency of its oscillations matches the system's natural frequency of vibration than it does at other frequencies...
(in particular, acoustic resonance
Acoustic resonance
Acoustic resonance is the tendency of an acoustic system to absorb more energy when it is forced or driven at a frequency that matches one of its own natural frequencies of vibration than it does at other frequencies....
) was very familiar to engineers. This situation was not to last for long; electrical 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...
had been known to science for some time before this, and it was not long before engineers started to produce all-electric designs for filters. In its time, though, the harmonic telegraph was of some importance. The idea was to combine several telegraph signals on one telegraph line by what would now be called frequency division multiplexing thus saving enormously on line installation costs. The key
Telegraph key
Telegraph key is a general term for any switching device used primarily to send Morse code. Similar keys are used for all forms of manual telegraphy, such as in electrical telegraph and radio telegraphy.- Types of keys :...
of each operator activated a vibrating electromechanical reed which converted this vibration into an electrical signal. Filtering at the receiving operator was achieved by a similar reed tuned to precisely the same frequency, which would only vibrate and produce a sound from transmissions by the operator with the identical tuning.
Versions of the harmonic telegraph were developed by Elisha Gray
Elisha Gray
Elisha Gray was an American electrical engineer who co-founded the Western Electric Manufacturing Company...
, Alexander Graham Bell
Alexander Graham Bell
Alexander Graham Bell was an eminent scientist, inventor, engineer and innovator who is credited with inventing the first practical telephone....
, Ernest MercadierErnest Mercadier article in French Wikipedia and others. Its ability to act as a sound transducer
Transducer
A transducer is a device that converts one type of energy to another. Energy types include electrical, mechanical, electromagnetic , chemical, acoustic or thermal energy. While the term transducer commonly implies the use of a sensor/detector, any device which converts energy can be considered a...
to and from the electrical domain was to inspire the invention of the telephone.
Mechanical equivalent circuits
Once the basics of electrical network analysis began to be established, it was not long before the ideas of complex impedance and filter designFilter design
Filter design is the process of designing a filter , often a linear shift-invariant filter, that satisfies a set of requirements, some of which are contradictory...
theories were carried over into mechanics by analogy. Kennelly, who was also responsible for introducing complex impedance, and Webster
Arthur Gordon Webster
Arthur Gordon Webster was the founder of the American Physical Society.Arthur Gordon Webster was born on 28 November, 1863 at Brookline, Massachusetts to William Edward Webster and Mary Shannon Davis...
were the first to extend the concept of impedance into mechanical systems in 1920. Mechanical admittance and the associated mobility analogy came much later and are due to Firestone in 1932.
It was not enough to just develop a mechanical analogy. This could be applied to problems that were entirely in the mechanical domain, but for mechanical filters with an electrical application it is necessary to include the transducer in the analogy as well. Poincaré
Henri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
in 1907 was the first to describe a transducer as a pair of linear algebra
Linear algebra
Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...
ic equations relating electrical variables (voltage and current) to mechanical variables (force and velocity). These equations can be expressed as a matrix relationship in much the same way as the z-parameters
Impedance parameters
Impedance parameters or Z-parameters are properties used in electrical engineering, electronic engineering, and communication systems engineering to describe the electrical behavior of linear electrical networks. They are also used to describe the small-signal response of non-linear networks...
of a two-port network
Two-port network
A two-port network is an electrical circuit or device with two pairs of terminals connected together internally by an electrical network...
in electrical theory, to which this is entirely analogous:
where V and I represent the voltage and current respectively on the electrical side of the transducer.
Wegel, in 1921, was the first to express these equations in terms of mechanical impedance as well as electrical impedance. The element
is the open circuit mechanical impedance, that is, the impedance presented by the mechanical side of the transducer when no current is entering the electrical side. The element , conversely, is the clamped electrical impedance, that is, the impedance presented to the electrical side when the mechanical side is clamped and prevented from moving (velocity is zero). The remaining two elements, and , describe the transducer forward and reverse transfer functions respectively. Once these ideas were in place, engineers were able to extend electrical theory into the mechanical domain and analyse an electromechanical system as a unified whole.Sound reproduction
An early application of these new theoretical tools was in phonographPhonograph
The phonograph record player, or gramophone is a device introduced in 1877 that has had continued common use for reproducing sound recordings, although when first developed, the phonograph was used to both record and reproduce sounds...
ic sound reproduction. A recurring problem with early phonograph designs was that mechanical resonances in the pickup and sound transmission mechanism caused excessively large peaks and troughs in the frequency response, resulting in poor sound quality. In 1923, Harrison of the Western Electric Company filed a patent for a phonograph in which the mechanical design was entirely represented as an electrical circuit. The horn of the phonograph is represented as a transmission line, and is a resistive load for the rest of the circuit, while all the mechanical and acoustic parts—from the pickup needle through to the horn—are translated into lumped components according to the impedance analogy. The circuit arrived at is a ladder topology of series resonant circuits coupled by shunt capacitors. This can be viewed as a bandpass filter circuit. Harrison designed the component values of this filter to have a specific passband corresponding to the desired audio passband (in this case 100 Hz to 6 kHz) and a flat response. Translating these electrical element values back into mechanical quantities provided specifications for the mechanical components in terms of mass and stiffness, which in turn could be translated into physical dimensions for their manufacture. The resulting phonograph has a flat frequency response in its passband and is free of the resonances previously experienced. Shortly after this, Harrison filed another patent using the same methodology on telephone transmit and receive transducers.
George Ashley Campbell
George Ashley Campbell was a pioneer in developing and applying quantitative mathematical methods to the problems of long-distance telegraphy and telephony. His most important contributions were to the theory and implementation of the use of loading coils and the first wave filters designed to...
's image filter
Constant k filter
Constant k filters, also k-type filters, are a type of electronic filter designed using the image method. They are the original and simplest filters produced by this methodology and consist of a ladder network of identical sections of passive components...
theory, which was the most advanced filter theory available at the time. In this theory, filter design is viewed essentially as an impedance matching
Impedance matching
In electronics, impedance matching is the practice of designing the input impedance of an electrical load to maximize the power transfer and/or minimize reflections from the load....
problem. More advanced filter theory was brought to bear on this problem by Norton
Edward Lawry Norton
Edward Lawry Norton was an accomplished Bell Labs engineer and scientist famous for developing the concept of the Norton equivalent circuit. He attended the University of Maine for two years before transferring to M.I.T. and received a S.B. degree in 1922. He received an M.A...
in 1929 at Bell Labs
Bell Labs
Bell Laboratories is the research and development subsidiary of the French-owned Alcatel-Lucent and previously of the American Telephone & Telegraph Company , half-owned through its Western Electric manufacturing subsidiary.Bell Laboratories operates its...
. Norton followed the same general approach though he later described to Darlington
Sidney Darlington
Sidney Darlington was an electrical engineer and inventor of a transistor configuration in 1953, the Darlington pair...
the filter he designed as being "maximally flat". Norton's mechanical design predates the paper by Butterworth
Stephen Butterworth
Stephen Butterworth was a British physicist who invented the Butterworth filter, a class of electrical circuits that are used to separate different frequencies of electrical signals....
who is usually credited as the first to describe the electronic maximally flat filter
Butterworth filter
The Butterworth filter is a type of signal processing filter designed to have as flat a frequency response as possible in the passband so that it is also termed a maximally flat magnitude filter...
. The equations Norton gives for his filter correspond to a singly terminated Butterworth filter, that is, one driven by an ideal voltage source with no impedance, whereas the form more usually given in texts is for the doubly terminated filter with resistors at both ends, making it hard to recognise the design for what it is. Another unusual feature of Norton's filter design arises from the series capacitor, which represents the stiffness of the diaphragm
Diaphragm (acoustics)
In the field of acoustics, a diaphragm is a transducer intended to faithfully inter-convert mechanical motion and sound. It is commonly constructed of a thin membrane or sheet of various materials. The varying air pressure of the sound waves imparts vibrations onto the diaphragm which can then be...
. This is the only series capacitor in Norton's representation, and without it, the filter could be analysed as a low-pass prototype
Prototype filter
Prototype filters are electronic filter designs that are used as a template to produce a modified filter design for a particular application. They are an example of a nondimensionalised design from which the desired filter can be scaled or transformed. They are most often seen in regards to...
. Norton moves the capacitor out of the body of the filter to the input at the expense of introducing a transformer into the equivalent circuit (Norton's figure 4). Norton has used here the "turning round the L" impedance transform to achieve this.
The definitive description of the subject from this period is Maxfield and Harrison's 1926 paper. There, they describe not only how mechanical bandpass filters can be applied to sound reproduction systems, but also apply the same principles to recording systems and describe a much improved disc cutting head.
Volume production
The first volume production of mechanical filters was undertaken by Collins Radio Company starting in the 1950s. These were originally designed for telephone frequency-division multiplex applications where there is commercial advantage in using high quality filters. Precision and steepness of the transition band leads to a reduced width of guard bandGuard band
-Radio and electronic signalling:In radio, a guard band is an unused part of the radio spectrum between radio bands, for the purpose of preventing interference....
, which in turn leads to the ability to squeeze more telephone channels into the same cable. This same feature is useful in radio transmitters for much the same reason. Mechanical filters quickly also found popularity in VHF/UHF radio intermediate frequency
Intermediate frequency
In communications and electronic engineering, an intermediate frequency is a frequency to which a carrier frequency is shifted as an intermediate step in transmission or reception. The intermediate frequency is created by mixing the carrier signal with a local oscillator signal in a process called...
(IF) stages of the high end radio sets (military, marine, amateur radio
Amateur radio
Amateur radio is the use of designated radio frequency spectrum for purposes of private recreation, non-commercial exchange of messages, wireless experimentation, self-training, and emergency communication...
and the like) manufactured by Collins. They were favoured in the radio application because they could achieve much higher Q-factors than the equivalent LC filter. High Q allows filters to be designed which have high selectivity, important for distinguishing adjacent radio channels in receivers. They also had an advantage in stability over both LC filters and monolithic crystal filters. The most popular design for radio applications was torsional resonators because radio IF typically lies in the 100 to 500 kHz band.
Transducers
There are two general types of transducerTransducer
A transducer is a device that converts one type of energy to another. Energy types include electrical, mechanical, electromagnetic , chemical, acoustic or thermal energy. While the term transducer commonly implies the use of a sensor/detector, any device which converts energy can be considered a...
s used with mechanical filters: magnetostrictive and piezoelectric. Piezoelectric is favoured in more recent designs since the piezoelectric material can also be used as one of the resonators of the filter, thus reducing the number of components and thereby saving space. They also avoid the susceptibility to extraneous magnetic fields from which the magnetostrictive type suffers.
Magnetostrictive
A magnetostrictive material is one which changes shape when a magnetic field is applied. In reverse, it produces a magnetic field when distorted. The magnetostrictive transducer requires a coil of conducting wire around the magnetostrictive material. The coil either induces a magnetic field in the transducer and sets it in motion or else picks up an induced current from the motion of the transducer at the filter output. It is also usually necessary to have a small magnet to bias the magnetostrictive material into its operating range. It is possible to dispense with the magnets if the biasing is taken care of on the electronic side by providing a d.c.Direct current
Direct current is the unidirectional flow of electric charge. Direct current is produced by such sources as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type. Direct current may flow in a conductor such as a wire, but can also flow through...
current superimposed on the signal, but this approach would detract from the generality of the filter design.
The usual magnetostrictive materials used for the transducer are either ferrite
Ferrite (magnet)
Ferrites are chemical compounds consisting of ceramic materials with iron oxide as their principal component. Many of them are magnetic materials and they are used to make permanent magnets, ferrite cores for transformers, and in various other applications.Many ferrites are spinels with the...
or compressed powdered 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...
. Mechanical filter designs often have the resonators coupled with steel or nickel-iron wires, but on some designs, especially older ones, nickel wire may be used for the input and output rods. This is because it is possible to wind the transducer coil directly on to a nickel coupling wire since nickel is slightly magnetostrictive. However, it is not strongly so and coupling to the electrical circuit is weak. This scheme also has the disadvantage that there are no measures taken to prevent eddy current
Eddy current
Eddy currents are electric currents induced in conductors when a conductor is exposed to a changing magnetic field; due to relative motion of the field source and conductor or due to variations of the field with time. This can cause a circulating flow of electrons, or current, within the body of...
s, a problem that is avoided if ferrites are used instead of nickel.
The coil of the transducer adds some inductance on the electrical side of the filter. It is common practice to add a capacitor in parallel with the coil so that an additional resonator is formed which can be incorporated into the filter design. While this will not improve performance to the extent that an additional mechanical resonator would, there is some benefit and the coil has to be there in any case.
Piezoelectric
A piezoelectric material is one which changes shape when an electric field is applied. In reverse, it produces an electric field when it is distorted. A piezoelectric transducer, in essence, is made simply by plating electrodeElectrode
An electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit...
s on to the piezoelectric material. Early piezoelectric materials used in transducers such as barium titanate
Barium titanate
Barium titanate is the inorganic compound with the chemical formula BaTiO3. Barium titanate is a white powder and transparent as larger crystals...
had poor temperature stability. This precluded the transducer from functioning as one of the resonators; it had to be a separate component. This problem was solved with the introduction of lead zirconate titanate
Lead zirconate titanate
Lead zirconate titanate , also called PZT, is a ceramic perovskite material that shows a marked piezoelectric effect. PZT-based compounds are composed of the chemical elements lead and zirconium and the chemical compound titanate which are combined under extremely high temperatures. A filter is...
(abbreviated PZT) which is stable enough to be used as a resonator. Another common piezoelectric material is 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,...
, which has also been used in mechanical filters. However, ceramic
Ceramic
A ceramic is an inorganic, nonmetallic solid prepared by the action of heat and subsequent cooling. Ceramic materials may have a crystalline or partly crystalline structure, or may be amorphous...
materials such as PZT are preferred for their greater electromechanical coupling coefficient
Electromechanical coupling coefficient
Electromechanical coupling coefficient is a numerical measure of the conversion efficiency between electrical and acoustic energy in piezoelectric materials.Qualitatively the electromechanical coupling coefficient, k, can be determined as:...
.
One type of piezoelectric transducer is the Langevin type, named after a transducer used by Paul Langevin
Paul Langevin
Paul Langevin was a prominent French physicist who developed Langevin dynamics and the Langevin equation. He was one of the founders of the Comité de vigilance des intellectuels antifascistes, an antifascist organization created in the wake of the 6 February 1934 far right riots...
in early sonar
Sonar
Sonar is a technique that uses sound propagation to navigate, communicate with or detect other vessels...
research. This is good for longitudinal modes of vibration. It can also be used on resonators with other modes of vibration if the motion can be mechanically converted into a longitudinal motion. The transducer consists of a layer of piezoelectric material sandwiched transversally into a coupling rod or resonator.
Another kind of piezoelectric transducer has the piezoelectric material sandwiched in longitudinally, usually into the resonator itself. This kind is good for torsional
Torsion (mechanics)
In solid mechanics, torsion is the twisting of an object due to an applied torque. In sections perpendicular to the torque axis, the resultant shear stress in this section is perpendicular to the radius....
vibration modes and is called a torsional transducer.
Resonators
depending on composition|}
It is possible to achieve an extremely high Q
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....
with mechanical resonators. Mechanical resonators typically have a Q of 10,000 or so, and 25,000 can be achieved in torsional resonators using a particular nickel-iron alloy. This is an unreasonably high figure to achieve with LC circuits, whose Q is limited by the resistance of the inductor coils.
Early designs in the 1940s and 1950s started by using steel as a resonator material. This has given way to nickel-iron alloys, primarily to maximise the Q since this is often the primary appeal of mechanical filters rather than price. Some of the metals that have been used for mechanical filter resonators and their Q are shown in the table.
Piezoelectric crystals are also sometimes used in mechanical filter designs. This is especially true for resonators that are also acting as transducers for inputs and outputs.
One advantage that mechanical filters have over LC electrical filters is that they can be made very stable. The resonance frequency can be made so stable that it varies only 1.5 parts per billion
Parts-per notation
In science and engineering, the parts-per notation is a set of pseudo units to describe small values of miscellaneous dimensionless quantities, e.g. mole fraction or mass fraction. Since these fractions are quantity-per-quantity measures, they are pure numbers with no associated units of measurement...
(ppb) from the specified value over the operating temperature range , and its average drift with time can be as low as 4 ppb per day. This stability with temperature is another reason for using nickel-iron as the resonator material. Variations with temperature in the resonance frequency (and other features of the frequency function) are directly related to variations in the Young's modulus
Young's modulus
Young's modulus is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds. In solid mechanics, the slope of the stress-strain...
, which is a measure of stiffness of the material. Materials are therefore sought that have a small temperature coefficient
Temperature coefficient
The temperature coefficient is the relative change of a physical property when the temperature is changed by 1 K.In the following formula, let R be the physical property to be measured and T be the temperature at which the property is measured. T0 is the reference temperature, and ΔT is the...
of Young's modulus. In general, Young's modulus has a negative temperature coefficient (materials become less stiff with increasing temperature) but additions of small amounts of certain other elements in the alloySee, for instance, "Thermelast 4002", a proprietary example of such an alloy, retrieved 2010. (in German). The first alloy to be discovered with this property was Elinvar
Elinvar
Elinvar is a nickel steel alloy with a modulus of elasticity which does not change much with temperature changes. The name is a contraction of the French elasticité invariable. It was invented in the late 1890s by Charles Édouard Guillaume, a Swiss physicist who also invented Invar, another...
for which, together with Invar
Invar
Invar, also known generically as FeNi36 , is a nickel steel alloy notable for its uniquely low coefficient of thermal expansion . The name, Invar, comes from the word invariable, referring to its lack of expansion or contraction with temperature changes.It was invented in 1896 by Swiss scientist...
, Charles Edouard Guillaume
Charles Edouard Guillaume
Charles Édouard Guillaume was a Swiss physicist who received the Nobel Prize in Physics in 1920 in recognition of the service he had rendered to precision measurements in physics by his discovery of anomalies in nickel steel alloys.Guillaume is known for his discovery of nickel-steel alloys he...
received the Nobel Prize
Nobel Prize
The Nobel Prizes are annual international awards bestowed by Scandinavian committees in recognition of cultural and scientific advances. The will of the Swedish chemist Alfred Nobel, the inventor of dynamite, established the prizes in 1895...
in 1920. The original application was for temperature compensation of scientific measuring instruments, clocks and marine chronometers. (Gould, p.201.) can produce a material with a temperature coefficient that changes sign from negative through zero to positive with temperature. Such a material will have a zero coefficient of temperature with resonance frequency around a particular temperature. It is possible to adjust the point of zero temperature coefficient to a desired position by heat treatment of the alloy.
Resonator modes
It is usually possible for a mechanical part to vibrateVibration
Vibration refers to mechanical oscillations about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road.Vibration is occasionally "desirable"...
in a number of different modes, however the design will be based on a particular vibrational mode and the designer will take steps to try to restrict the resonance to this mode. As well as the straightforward longitudinal mode some others which are used include flexural
Flexural strength
Flexural strength, also known as modulus of rupture, bend strength, or fracture strength, a mechanical parameter for brittle material, is defined as a material's ability to resist deformation under load...
mode, torsional mode
Torsional vibration
Torsional vibration is angular vibration of an object—commonly a shaft along its axis of rotation. Torsional vibration is often a concern in power transmission systems using rotating shafts or couplings where it can cause failures if not controlled....
, radial mode and drumhead mode
Vibrations of a circular drum
The vibrations of an idealized circular drum, essentially an elastic membrane of uniform thickness attached to a rigid circular frame, are solutions of the wave equation with zero boundary conditions....
.
Modes are numbered according to the number of half-wavelengths in the vibration. Some modes exhibit vibrations in more than one direction (such as drumhead mode which has two) and consequently the mode number consists of more than one number. When the vibration is in one of the higher modes, there will be multiple nodes on the resonator where there is no motion. For some types of resonator, this can provide a convenient place to make a mechanical attachment for structural support. Wires attached at nodes will have no effect on the vibration of the resonator or the overall filter response. In figure 5, some possible anchor points are shown as wires attached at the nodes. The modes shown are (5a) the second longitudinal mode fixed at one end, (5b) the first torsional mode, (5c) the second torsional mode, (5d) the second flexural mode, (5e) first radial expansion mode and (5f) first radially symmetric drumhead mode.
Circuit designs
There are a great many combinations of resonators and transducers that can be used to construct a mechanical filter. A selection of some of these is shown in the diagrams. Figure 6 shows a filter using disc flexural resonators and magnetostrictive transducers. The transducer drives the centre of the first resonator, causing it to vibrate. The edges of the disc move in antiphase to the centre when the driving signal is at, or close to, resonance, and the signal is transmitted through the connecting rods to the next resonator. When the driving signal is not close to resonance, there is little movement at the edges, and the filter rejects (does not pass) the signal. Figure 7 shows a similar idea involving longitudinal resonators connected together in a chain by connecting rods. In this diagram, the filter is driven by piezoelectric transducers. It could equally well have used magnetostrictive transducers. Figure 8 shows a filter using torsional resonators. In this diagram, the input has a torsional piezoelectric transducer and the output has a magnetostrictive transducer. This would be quite unusual in a real design, as both input and output usually have the same type of transducer. The magnetostrictive transducer is only shown here to demonstrate how longitudinal vibrations may be converted to torsional vibrations and vice versa. Figure 9 shows a filter using drumhead mode resonators. The edges of the discs are fixed to the casing of the filter (not shown in the diagram) so the vibration of the disc is in the same modes as the membrane of a drum. Collins calls this type of filter a disc wire filter.The various types of resonator are all particularly suited to different frequency bands. Overall, mechanical filters with lumped elements of all kinds can cover frequencies from about 5 to 700 kHz although mechanical filters down as low as a few kilohertz (kHz) are rare. The lower part of this range, below 100 kHz, is best covered with bar flexural resonators. The upper part is better done with torsional resonators. Drumhead disc resonators are in the middle, covering the range from around 100 to 300 kHz.
The frequency response behaviour of all mechanical filters can be expressed as an equivalent electrical circuit using the impedance analogy described above. An example of this is shown in figure 8b which is the equivalent circuit of the mechanical filter of figure 8a. Elements on the electrical side, such as the inductance of the magnetostrictive transducer, are omitted but would be taken into account in a complete design. The series resonant circuits on the circuit diagram represent the torsional resonators, and the shunt capacitors represent the coupling wires. The component values of the electrical equivalent circuit can be adjusted, more or less at will, by modifying the dimensions of the mechanical components. In this way, all the theoretical tools of electrical analysis and filter design can be brought to bear on the mechanical design. Any filter realisable in electrical theory can, in principle, also be realised as a mechanical filter. In particular, the popular finite element approximations to an ideal filter response of the Butterworth
Butterworth filter
The Butterworth filter is a type of signal processing filter designed to have as flat a frequency response as possible in the passband so that it is also termed a maximally flat magnitude filter...
and Chebyshev filter
Chebyshev filter
Chebyshev filters are analog or digital filters having a steeper roll-off and more passband ripple or stopband ripple than Butterworth filters...
s can both readily be realised. As with the electrical counterpart, the more elements that are used, the closer the approximation approaches the ideal, however, for practical reasons the number of resonators does not normally exceed eight.
Semi-lumped designs
Frequencies of the order of megahertz (MHz) are above the usual range for mechanical filters. The components start to become very small, or alternatively the components are large compared to the signal wavelength. The lumped element modelLumped element model
The lumped element model simplifies the description of the behaviour of spatially distributed physical systems into a topology consisting of discrete entities that approximate the behaviour of the distributed system under certain assumptions...
described above starts to break down and the components must be considered as distributed elements
Distributed element model
In electrical engineering, the distributed element model or transmission line model of electrical circuits assumes that the attributes of the circuit are distributed continuously throughout the material of the circuit...
. The frequency at which the transition from lumped to distributed models takes place is much lower for mechanical filters than it is for their electrical counterparts. This is because mechanical vibrations travel at the speed of sound for the material the component is composed of. For solid components, this is many times (x15 for nickel-iron) the speed of sound in air but still considerably less than the speed of electromagnetic waves (approx. in vacuum). Consequently, mechanical wavelengths are much shorter than electrical wavelengths for the same frequency. Advantage can be taken of these effects by deliberately designing components to be distributed elements, and the components and methods used in electrical distributed element filter
Distributed element filter
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...
s can be brought to bear. The equivalents of stubs and impedance transformers
Quarter wave impedance transformer
A quarter-wave impedance transformer, often written as λ/4 impedance transformer, is a component used in electrical engineering consisting of a length of transmission line or waveguide exactly one-quarter of a wavelength long and terminated in some known impedance. The device presents at its...
are both achievable. Designs which use a mixture of lumped and distributed elements are referred to as semi-lumped.
An example of such a design is shown in figure 10a. The resonators are disc flexural resonators similar to those shown in figure 6, except that these are energised from an edge, leading to vibration in the fundamental flexural mode with a node in the centre, whereas the figure 6 design is energised in the centre leading to vibration in the second flexural mode at resonance. The resonators are mechanically attached to the housing by pivots at right angles to the coupling wires. The pivots are to ensure free turning of the resonator and minimise losses. The resonators are treated as lumped elements; however, the coupling wires are made exactly one half-wavelength (λ/2) long and are equivalent to a λ/2 open circuit stub in the electrical equivalent circuit. For a narrow-band filter, a stub of this sort has the approximate equivalent circuit of a parallel shunt tuned circuit as shown in figure 10b. Consequently, the connecting wires are being used in this design to add additional resonators into the circuit and will have a better response than one with just the lumped resonators and short couplings. For even higher frequencies, microelectromechanical methods can be used as described below.
Bridging wires
Bridging wires are rods that couple together resonators that are not adjacent. They can be used to produce poles of attenuation in the stopbandStopband
A stopband is a band of frequencies, between specified limits, through which a circuit, such as a filter or telephone circuit, does not allow signals to pass, or the attenuation is above the required stopband attenuation level...
. This has the benefit of increasing the stopband rejection. When the pole is placed near the passband
Passband
A passband is the range of frequencies or wavelengths that can pass through a filter without being attenuated.A bandpass filtered signal , is known as a bandpass signal, as opposed to a baseband signal....
edge, it also has the benefit of increasing roll-off
Roll-off
Roll-off is a term commonly used to describe the steepness of a transmission function with frequency, particularly in electrical network analysis, and most especially in connection with filter circuits in the transition between a passband and a stopband...
and narrowing the transition band
Transition band
The transition band is a range of frequencies, that allows a transition between a passband and a stopband of a signal processing filter. The transition band is defined by a passband and a stopband cutoff frequency or corner frequency....
. The typical effects of some of these on filter frequency response are shown in figure 11. Bridging across a single resonator (figure 11b) can produce a pole of attenuation in the high stopband. Bridging across two resonators (figure 11c) can produce a pole of attenuation in both the high and the low stopband. Using multiple bridges (figure 11d) will result in multiple poles of attenuation. In this way, the attenuation of the stopbands can be deepened over a broad frequency range.
The method of coupling between non-adjacent resonators is not limited to mechanical filters. It can be applied to other filter formats. For instance, channels can be cut between cavity resonators, mutual inductance can be used with discrete component filters, and feedback paths can be used with active analogue or digital filter
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...
s. Nor was the method first discovered in the field of mechanical filters; the earliest description is in a 1948 patent for filters using 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...
cavity resonators. However, mechanical filter designers were the first (1960s) to develop practical filters of this kind and the method became a particular feature of mechanical filters.
Microelectromechanical filters
Microelectromechanical systems
Microelectromechanical systems is the technology of very small mechanical devices driven by electricity; it merges at the nano-scale into nanoelectromechanical systems and nanotechnology...
(MEMS). MEMS are very small micromachines with component sizes measured in micrometre
Micrometre
A micrometer , is by definition 1×10-6 of a meter .In plain English, it means one-millionth of a meter . Its unit symbol in the International System of Units is μm...
s (μm), but not as small as nanomachines
Nanotechnology
Nanotechnology is the study of manipulating matter on an atomic and molecular scale. Generally, nanotechnology deals with developing materials, devices, or other structures possessing at least one dimension sized from 1 to 100 nanometres...
. These systems are mostly fabricated from silicon
Silicon
Silicon is a chemical element with the symbol Si and atomic number 14. A tetravalent metalloid, it is less reactive than its chemical analog carbon, the nonmetal directly above it in the periodic table, but more reactive than germanium, the metalloid directly below it in the table...
(Si), silicon nitride
Silicon nitride
Silicon nitride is a chemical compound of silicon and nitrogen. If powdered silicon is heated between 1300° and 1400°C in an atmosphere of nitrogen, trisilicon tetranitride, Si3N4, is formed. The silicon sample weight increases progressively due to the chemical combination of silicon and nitrogen...
(Si3N4), or polymer
Polymer
A polymer is a large molecule composed of repeating structural units. These subunits are typically connected by covalent chemical bonds...
s. A common component used for 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...
filtering (and MEMS applications generally), is the cantilever
Cantilever
A cantilever is a beam anchored at only one end. The beam carries the load to the support where it is resisted by moment and shear stress. Cantilever construction allows for overhanging structures without external bracing. Cantilevers can also be constructed with trusses or slabs.This is in...
resonator. Cantilevers are simple mechanical components to manufacture by much the same methods used by the semiconductor industry; masking, photolithography
Photolithography
Photolithography is a process used in microfabrication to selectively remove parts of a thin film or the bulk of a substrate. It uses light to transfer a geometric pattern from a photomask to a light-sensitive chemical "photoresist", or simply "resist," on the substrate...
and etching, with a final undercutting etch to separate the cantilever from the substrate. The technology has great promise since cantilevers can be produced in large numbers on a single substrate—much as large numbers of transistors are currently contained on a single silicon chip.
The resonator shown in figure 12 is around 120 μm in length. Experimental complete filters with an operating frequency of 30 GHz have been produced using cantilever varactors as the resonator elements. The size of this filter is around 4×3.5 mm. Cantilever resonators are typically applied at frequencies below 200 MHz, but other structures, such as micro-machined cavities, can be used in the microwave bands. Extremely high Q resonators can be made with this technology; flexural mode resonators with a Q in excess of 80,000 at 8 MHz are reported.
Adjustment
The precision applications in which mechanical filters are used require that the resonators are accurately adjusted to the specified resonance frequency. This is known as trimming and usually involves a mechanical machining process. In most filter designs, this can be difficult to do once the resonators have been assembled into the complete filter so the resonators are trimmed before assembly. Trimming is done in at least two stages; coarse and fine, with each stage bringing the resonance frequency closer to the specified value. Most trimming methods involve removing material from the resonator which will increase the resonance frequency. The target frequency for a coarse trimming stage consequently needs to be set below the final frequency since the tolerances of the process could otherwise result in a frequency higher than the following fine trimming stage could adjust for.The coarsest method of trimming is grinding
Grinding (abrasive cutting)
Grinding is an abrasive machining process that uses a grinding wheel as the cutting tool.A wide variety of machines are used for grinding:* Hand-cranked knife-sharpening stones * Handheld power tools such as angle grinders and die grinders...
of the main resonating surface of the resonator; this process has an accuracy of around . Better control can be achieved by grinding the edge of the resonator instead of the main surface. This has a less dramatic effect and consequently better accuracy. Processes that can be used for fine trimming, in order of increasing accuracy, are sandblasting
Abrasive blasting
Abrasive blasting is the operation of forcibly propelling a stream of abrasive material against a surface under high pressure to smooth a rough surface, roughen a smooth surface, shape a surface, or remove surface contaminants. A pressurized fluid, typically air, or a centrifugal wheel is used to...
, drilling, and laser ablation
Laser ablation
Laser ablation is the process of removing material from a solid surface by irradiating it with a laser beam. At low laser flux, the material is heated by the absorbed laser energy and evaporates or sublimates. At high laser flux, the material is typically converted to a plasma...
. Laser trimming is capable of achieving an accuracy of .
Trimming by hand, rather than machine, was used on some early production components but would now normally only be encountered during product development. Methods available include sanding and filing
File (tool)
A file is a metalworking and woodworking tool used to cut fine amounts of material from a workpiece. It most commonly refers to the hand tool style, which takes the form of a steel bar with a case hardened surface and a series of sharp, parallel teeth. Most files have a narrow, pointed tang at one...
. It is also possible to add material to the resonator by hand, thus reducing the resonance frequency. One such method is to add solder
Solder
Solder is a fusible metal alloy used to join together metal workpieces and having a melting point below that of the workpiece.Soft solder is what is most often thought of when solder or soldering are mentioned and it typically has a melting range of . It is commonly used in electronics and...
, but this is not suitable for production use since the solder will tend to reduce the high Q of the resonator.
In the case of MEMS filters, it is not possible to trim the resonators outside of the filter because of the integrated nature of the device construction. However, trimming is still a requirement in many MEMS applications. Laser ablation can be used for this but material deposition methods are available as well as material removal. These methods include laser
Pulsed laser deposition
Pulsed laser deposition is a thin film deposition technique where a high power pulsed laser beam is focused inside a vacuum chamber to strike a target of the material that is to be deposited...
or ion-beam induced deposition
Ion beam deposition
Ion Beam Deposition is a process of applying materials to a target through the application of an ion beam.thumb|Ion beam deposition setup with mass separator...
.
See also
- Ceramic resonatorCeramic resonatorA ceramic resonator is an electronic component that when combined with other appropriate components, can produce oscillations at a specific frequency...
- Surface acoustic waveSurface 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:...
- Crystal oscillatorCrystal oscillatorA 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...
- Crystal filterCrystal filterA crystal filter is a special form of quartz crystal used in electronics systems, in particular communications devices. It provides a very precisely defined centre frequency and very steep bandpass characteristics, that is a very high Q factor—far higher than can be obtained with conventional...