US2094062A - Electromechanical impedance - Google Patents

Electromechanical impedance Download PDF

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Publication number
US2094062A
US2094062A US43154A US4315435A US2094062A US 2094062 A US2094062 A US 2094062A US 43154 A US43154 A US 43154A US 4315435 A US4315435 A US 4315435A US 2094062 A US2094062 A US 2094062A
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United States
Prior art keywords
wire
field
vibration
mechanical
length
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Expired - Lifetime
Application number
US43154A
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English (en)
Inventor
Darlington Sidney
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AT&T Corp
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Bell Telephone Laboratories Inc
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Publication date
Priority to NL47516D priority Critical patent/NL47516C/xx
Application filed by Bell Telephone Laboratories Inc filed Critical Bell Telephone Laboratories Inc
Priority to US43154A priority patent/US2094062A/en
Priority to GB24812/36A priority patent/GB462888A/en
Priority to DEI55993D priority patent/DE745757C/de
Priority to FR816361D priority patent/FR816361A/fr
Application granted granted Critical
Publication of US2094062A publication Critical patent/US2094062A/en
Anticipated expiration legal-status Critical
Expired - Lifetime legal-status Critical Current

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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H9/00—Networks comprising electromechanical or electro-acoustic devices; Electromechanical resonators
    • H03H9/0023—Balance-unbalance or balance-balance networks
    • H03H9/0095—Balance-unbalance or balance-balance networks using bulk acoustic wave devices
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H9/00—Networks comprising electromechanical or electro-acoustic devices; Electromechanical resonators
    • H03H9/24—Constructional features of resonators of material which is not piezoelectric, electrostrictive, or magnetostrictive
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H9/00—Networks comprising electromechanical or electro-acoustic devices; Electromechanical resonators
    • H03H9/46—Filters
    • H03H9/54—Filters comprising resonators of piezoelectric or electrostrictive material
    • H03H9/542—Filters comprising resonators of piezoelectric or electrostrictive material including passive elements

Definitions

  • This invention relates to electromechanical impedances and more particularly to impedance devices which exhibit resonance characteristics due to the resonant vibration of a mechanical element.
  • an electromechanical impedance comprises an electric circuit to which a mechani-' r is the type of electromechanical coupling employed, this being so arranged that the driving forces applied to the vibrator are distributed along its length and are so graduated from point to point as to prevent vibrations in any other than the fundamental mode of the vibrator.
  • Fig. 3 is a diagram explanatory of the operation of the device of Fig. 1;
  • FIG. 4 and 5 illustrate an alternative form of the invention
  • Fig. 6 is a schematic representation of the device of Fig. 4.
  • Fig. 7 illustrates'the application of the invention to wave filters
  • Fig. 8 shows a modified form of the invention.
  • l is a stretched wire extending between points A and B at which it is anchored to rigid supports, not shown, 2 and 3 are the poles of a magnet, in the space between which the wire I is located, 4 and 5 are conductors leading to electrical terminals T1 and T2.
  • the magnet poles are tapered towards the airgap, as shown in the end elevation in Fig. 2; to provide a concentrated magnetic field in the neighborhood of the wire.
  • the pole faces instead of being parallel as is usual in devices of this type are closest together at the center and diverge symmetrically towards the ends.
  • This shaping of the pole faces is toprovide a magnetic flux which varies in intensity along the wire in accordance with a sine law, the flux density having a maximum value at the midpoint of the wire and diminishing sinusoidally to a negligibly small value at the ends of thewire.
  • the device of the invention Because of the -slnusoldal distribution of the flux density in the device of the invention, energy is supplied to the wire only in its fundamental mode of motion and hence vibrations in the other possible modes are suppressed.
  • the device thus exhibits a single resonance on the mechanical side which appears as a single anti-resonance in the electrical circuit.
  • Fig. 3 The explanation of the suppression of the higher resonances will appear from a consideration of Fig. 3.
  • the horizontal line AB represents the wire in its position at rest.
  • the ordinates of curve 4 measured from AB represent the flux density at the difierent points along the wire, the curve being sinusoidal.
  • Dotted curve 5 outlines the form of the wire in its third harmonic mode of vibration, the displacements from the line AB likewise following a sinusoidal variation but of triple frequency.
  • the velocity of vibration varies sinusoidally along the wire in the same manner as the displacement and its value V at the point a: is given by where 'V@ denotes the velocity at the mid-point for the assumed mode of vibration.
  • the character of the impedance of the vibrating wire as measured in the electric circuit may be. ascertained from the differential equation for the motion of the .wire.
  • the driving force on an element of the wire da: at a point distant :r from the center is equal to gxdx where i denotes the instantaneous value of the current in the wire. This is opposed by two reactions; one due to the transverse elasticity of the wire contributed by the tension, and one due to the mass acceleration reaction of the elemental length dx.
  • the first component has the value transverse displacement of the wire at the point :11.
  • the second component has the value where p is the linear density of the wire.
  • Equation 8 indicates a single resonance at a frequency corresponding to The back electromotive force generated by the motion of the wire is given by Except for a component equal to the resistance of the wire, which is simply added in series, the impedance is given by the ratio of the back electromotive force to the current and has the value which corresponds to the impedance of a capacity When the several quantities are measured in c. g. s. units Formulae 12 and 13 give'the capacity and inductance in absolute electrical units.
  • the sinusoidal distribution of the flux density may be closely approximated by so shaping the pole faces that theirseparation is equal to see x :12, as before, being measured from the mid-point of the wire or the air-gap. Due to the fringing of the magnetic field the flux density will not fall quite to zero at the ends of the air-gap, but by extending the wire at each end slightly beyond the magnet poles the fringing effect may be largely compensated and the flux density at the ends will be small enough to have negligible effect.
  • FIG. 4 Another form of the invention, in which the electro-mechanical coupling is electrostatic instead of electromagnetic, is illustrated in Figs. 4 and 5, the former being a longitudinal section of the device and the latter a transverse section at the line XX in Fig. 4.
  • the vibrating element is a thin metallic strip 8 which is held stretched in an air-gap between conducting electrodes 6 and I.
  • the strip 8 is clamped at its ends by insulating blocks 9, 9' and l0, l0 which also serve to support the electrodes and to maintain their proper separation at the air-gap.
  • the details of the assembly are omitted for the sake of clarity, but these may be in accordance with familiar practice.
  • Electrodes 6 and 1 are polarized with respect to the vibrator 8 by battery ll one terminal of which is connected directly to 8 and the other to electrodes 6 and I through protective high resistances R and R.
  • the operating terminals of the system T1 and T2 are connected to electrodes 6 and 1 respectively.
  • the device operates in the same manner as a balanced electrostatic telephone.
  • Battery ll establishes equal steady electric fields between vibrator 8 and electrodes 6 and 1 respectively, upon which are superimposed oppositely directed fields from alternating voltages applied to terminals T1 and T2. These superimposed voltages interacting with the steady polarizing fields produce synchronous vibrations of the strip 8 which in turn generate synchronous back electromotive forces in the electric circuit.
  • the strip 8 Because of its uniformly distributed mass and transverse elasticity the strip 8 has a series of natural resonances at harmonically related frequencies just as in the case of the stretched wire of the device of Fig. 1.
  • the higher frequency modes of vibration are prevented in this case also by so graduating the driving force along the length of the strip that energy is supplied thereto only in the fundamental mode of vibration.
  • the driving force at any point on the strip is proportional to the square of the electric field intensity at that point, the field being made up of two components, one due to the polarizing voltage and one due to the superimposed alternating voltage, both of which are distributed in the same manner.
  • the forces on the two surfaces of the vibrator, due to each component separately, balance each other and the only forces tending to produce motion are those represented by the product of the two components. Since the polarizing voltage is steady the forces represented by the products are synchronous with the superimposed forces.
  • the driving force be distributed sinusoidally along the strip as in the case of the electromagnetic device of Fig. 1.
  • the graduation of the air-gaps in this case affects the distribution of the polarizing field intensity and the alternating field intensity equally, it is necessary to give the air-gaps a modified shape such that the separation of the electrodes from the vibrator is proportional to :1: being the distance from the middle of the vibrator and I being the length of the electrodes. Since each air-gap acts as a separate source of driving force the two should be symmetrical.
  • the air-gaps field at the ends of the electrode may be largely compensated by extending the vibrator slightly beyond the electrodes as illustrated in Fig. 4.
  • the device is equivalent to an electrical impedance of the type shown in Fig. 6 which comprises a capacity Co shunted by an inductance L1 and capacity C1 connected in series.
  • the capacity Co is that between electrodes 6 and I with the vibrator at rest and at the mean potential of the two electrodes.
  • Inductance L1 and capacity C1 are contributed by the motion of the vibrator and their resonance frequency is that of the fundamental mechanical resonance of the vibrator.
  • the impedance Z of the device is given by where f denotes frequency, fl is the fundamental resonance frequency of the vibrator, and f2 is a higher frequency at which the combination is anti-resonant.
  • the value of I2 is given by where E is the polarizing voltage in absolute units, p is the surface density of the vibrating strip in grams per square centimeter, and Do is the minimum air-gap between the vibrator and the electrodes.
  • the resonant impedance characteristics of the devices. of the invention make them useful as impedance elements for the construction of broad band wave filters in which they may be connected in substantially the same manner as other twoterminal impedances.
  • due regard must be given to the proportioning of the elements so that the resonances and the absolute magnitudes of the several elements cooperate to provide the desired selective characteristics. The principles of such cooperation are well-known and are explained,
  • FIG. 7 An example of the application of the electrostatic device of the invention in a lattice type wave filter is shown in Fig. 7.
  • the line branches of the network include similar balanced electrostatic elements l3 and I3 of the type shown in Fig. 5 and the lattice branches include elements I and I I, also similar to each other, but resonant at frequencies different from the resonances of the line elements.
  • Inductances L included in each of the four line conductors external to the lattice cooperate with the network impedances in controlling the width of the transmission band in a manner explained in an article by W. P. Mason entitled Electrical wave filters employing quartz crystals as elements, Bell System Technical Journal vol. XIII No. 3, July 1934, pages 416 to 425.
  • a network of high resistances R1 to Rs connects a polarizing battery ii to the electrodes of the electromechanical ele- V ments, the resistances being so balanced as not to disturb the distribution of currents in the filter branches and being of sufficiently high values to avoid excessive energy dissipation of the transmitted currents.
  • FIG. 8 A further modified form of the invention, in which one particular harmonic mode of vibration is suppressed, is illustrated in Fig. 8.
  • the device shown there is a modification of the electro-magnetic device of Fig. l, the curved polepieces 2 and 3 being replaced by pole-pieces having parallel opposed faces but extending only over approximately two thirds of. the length of the wire on each side of the mid-point.
  • the third harmonic mode is suppressed.
  • the reason for the suppression is readily seen from the dotted curve l6 which shows the Wire in its third harmonic mode.
  • the motion of the central loop of the wire generates a back electromotive force in one direction and the motion of the wire in its two outer loops generates back electromotive forces in the opposite direction. Since the field is of uniform intensity from the center of the one outer loop to the center of the other and substantially zero elsewhere, the sum of the back electromotive forces, is zero and the resultant electromagnetic 'coupling for this mode of motion is also zero.
  • An impedance element comprising a uniform stretched conducting wire, means providing a magnetic field perpendicular to said wire, a pair of electrical terminals, and an electrical path between said terminals including said Wire, said field producing means being so proportioned as to provide a field of maximum intensity at the mid-point of said wire and diminishing sinusoidally to substantially zero at the ends of said wire.
  • the field producing means is a magnet having opposed pole faces forming an air-gap in which the wire is free to vibrate, the separation of the pole faces being a minimum at the mid-point of the wire and increasing towards the ends of. the wire substantially in accordance with the law electrode and said foil, the separation between said electrode and said foil being a minimum at the mid-point of the foil and. increasing towards the ends of the foil substantially in accordance with the law If ww 86C 1 where w is the separation at a point distant :r from the mid-point of the foil, wo is the separation-at the mid-point, and l is the length of the foil.
  • An electrical circuit element comprising an electrical path extending between a pair of terminals, a mechanical vibratory element included in said path, said vibratory element comprising an extended longitudinal member having distributed mass and elasticity whereby it is inherently capable of transverse vibration in a fundamental mode and also in different secondary modes at different frequencies, means establishing a steady field normal to the longitudinal axis of said member which coacts with the vibratory motion thereof.
  • said field establishing means including polar members shaped to distribute the field'along the length of said vibratory member and to provide different field intensities at different points along the length thereof, the gradation of the field intensity thereby produced being proportioned to make the net resultant electromotive force generated in said electrical path substantially zero for vibration of said vibratory member in at least the two secondary modes adjacent the fundamental mode.
  • An electrical circuit element comprising an electrical path extending between a pair of terminals, a mechanical vibratory element included in said path, said vibratory element comprising an extended longitudinal member having distributed mass and elasticity whereby it is inherently capable of transverse vibration in a fundamental mode and also in different secondary modes at different frequencies, means establishing a steady field normal to the longitudinal axis of said member which coacts with electrical oscillations in said path to produce oscillatory.
  • said field producing means including polar members shaped to distribute the field along the length of said vibratory member and to provide different field intensities at diiferent points along the length thereof, the gradation of the field intensity thereby produced being proportioned to make the net oscillatory mechanical force tending to set the vibratory member into motion in its secondary modes substantially zero for at least the two secondary modes adjacent the fundamental mode.
  • An electrical circuit element comprising an electrical path extending between a pair of terminals, a mechanical vibratory element included in said path, said vibratory element'comprising a longitudinally extended member having uniform longitudinal distribution of mass and elasticity whereby it is inherently capable of transverse vibration in a fundamental mode and in different secondary modes at harmonically related frequencies, means establishing a steady field normal to the longitudinal axis of said member which coacts with electrical oscillations in said path to produce oscillatory mechanical forces upon said member, said field producing means including polar members shaped to distribute the field along the length of said vibratory element and to provide different field intensities at difirent points along the length thereof, the gradation of the field intensity thereby produced being proportioned to make the resultant oscillatory mechanical force tending to set the vibratory element into motion in its secondary modes sub-' stantially zero for at least the two secondary modes adjacent the fundamental mode.
  • An electrical circuit element comprising an electrical pathextending between two terminals, a mechanical vibratory element included in said path, said vibratory element comprising a stretched longitudinal member having uniform mass per unit length, means establishing a steady field normal to the longitudinal axis of said member which coacts with electrical oscillations in said path to produce mechanical forces upon said member, said field establishing means including polar members shaped to distribute the field along the length of said vibratory member and to provide different field intensities at different points along the length thereof, the gradation of the field intensity thereby produced being proportioned to make the resultant oscillatory mechanical force tending to set the vibratory element in motion in its inherent harmonic modes of vibration substantially zero for at least the first two said harmonic modes.
  • An electrical circuit element comprising an electrical path extending betwen two terminals, a mechanical vibratory element included in said path, said vibratory element comprising a longitudinal member having uniform mass per unit length and uniformly distributed transverse elasticity, whereby it is inherently capable of trans-' verse vibration in a fundamental mode and in different secondary modes at harmonically related frequencies, means establishing a steady field normal to the longitudinal axis of said member which coacts with oscillations in said electrical path to produce oscillatory mechanical forces acting upon said member, said field producing means including polar members shaped to distribute the field along the length of said vibratory element and to provide different field intensities at different points along the length thereof, the gradation of the field intensity thereby produced being proportioned to provide a mechanical force on 'said vibratory member which is a maximum at the midpoint thereof and diminishes sinusoidally to substantially zero at the ends thereof.
  • An electrical circuit element comprising an electrical path extending between two terminals, a mechanical vibratory element included in said path, said vibratory element comprising a stretched longitudinal member having uniform mass per unit length, means establishing a steady field normal to the longitudinal axis of said member and extending along the length thereof which coacts with electrical oscillations in said path to produce mechanical forces acting upon said member, said field producing means including polar members shaped to provide a continuous gradation of the field intensity along the length of said vibratory member such that the mechanical force on said vibratory member is a maximum at the midpoint thereof and diminishes sinusoidally to substantially zero at the ends thereof.

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  • Physics & Mathematics (AREA)
  • Acoustics & Sound (AREA)
  • Piezo-Electric Or Mechanical Vibrators, Or Delay Or Filter Circuits (AREA)
  • Apparatuses For Generation Of Mechanical Vibrations (AREA)
US43154A 1935-10-02 1935-10-02 Electromechanical impedance Expired - Lifetime US2094062A (en)

Priority Applications (5)

Application Number Priority Date Filing Date Title
NL47516D NL47516C (de) 1935-10-02
US43154A US2094062A (en) 1935-10-02 1935-10-02 Electromechanical impedance
GB24812/36A GB462888A (en) 1935-10-02 1936-09-11 Improvements in or relating to electro-mechanical impedances
DEI55993D DE745757C (de) 1935-10-02 1936-09-23 Elektromechanisches Impedanzelement mit einem sich im wesentlichen in einer Richtung erstreckenden und gespannten Schwingungsglied, welches aus einem Stromkreis elektrisch erregt wird
FR816361D FR816361A (fr) 1935-10-02 1936-09-23 Impédances électromécaniques

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
US43154A US2094062A (en) 1935-10-02 1935-10-02 Electromechanical impedance

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US2094062A true US2094062A (en) 1937-09-28

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US43154A Expired - Lifetime US2094062A (en) 1935-10-02 1935-10-02 Electromechanical impedance

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DE (1) DE745757C (de)
FR (1) FR816361A (de)
GB (1) GB462888A (de)
NL (1) NL47516C (de)

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2958040A (en) * 1958-02-10 1960-10-25 J B T Instr Inc Electrical frequency responsive device
US3164987A (en) * 1961-03-28 1965-01-12 Bosch Arma Corp Electrostatic vibration transducer
US3190129A (en) * 1961-07-10 1965-06-22 Bosch Arma Corp Accelerometer and parts therefor
US3218846A (en) * 1960-10-26 1965-11-23 Chemetron Corp Ultrasonic flaw testing apparatus
US3465597A (en) * 1965-05-25 1969-09-09 Singer General Precision Vibrating-column accelerometer
US20150042197A1 (en) * 2011-12-23 2015-02-12 Roland Hagenlocher Permanent magnet excited electric machine

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE494716C (de) * 1927-07-08 1930-04-29 Elektrotechnischer Trust Der S Piezoelektrischer Schwingungserzeuger
GB344034A (en) * 1929-11-28 1931-03-02 James Robinson Improvements in or relating to wireless receiving systems
US1906250A (en) * 1931-11-18 1933-05-02 Union Switch & Signal Co Electric filtering apparatus

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2958040A (en) * 1958-02-10 1960-10-25 J B T Instr Inc Electrical frequency responsive device
US3218846A (en) * 1960-10-26 1965-11-23 Chemetron Corp Ultrasonic flaw testing apparatus
US3164987A (en) * 1961-03-28 1965-01-12 Bosch Arma Corp Electrostatic vibration transducer
US3190129A (en) * 1961-07-10 1965-06-22 Bosch Arma Corp Accelerometer and parts therefor
US3465597A (en) * 1965-05-25 1969-09-09 Singer General Precision Vibrating-column accelerometer
US20150042197A1 (en) * 2011-12-23 2015-02-12 Roland Hagenlocher Permanent magnet excited electric machine
US9806574B2 (en) * 2011-12-23 2017-10-31 L-3 Communications Magnet-Motor Gmbh Low loss permanent magnet excited electric machine

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Publication number Publication date
NL47516C (de)
DE745757C (de) 1944-05-22
GB462888A (en) 1937-03-17
FR816361A (fr) 1937-08-06

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