![Page 1: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/1.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Acoustics II:loudspeakers
Kurt Heutschi2013-01-18
![Page 2: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/2.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
loudspeakers: transducerprinciples
![Page 3: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/3.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
transducer principles
membrane driver principles:
I electrodynamic
I electrostatic
![Page 4: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/4.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
electrodynamic transducer
![Page 5: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/5.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
electrodynamic transducer
drive mechanism: force F acting on a wire of length `carrying current I and located in a magnetic field B :
F = B × ` · I
the other way round, a voltage U is induced for a wiremoving with velocity u:
U = B × ` · u
![Page 6: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/6.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
electrostatic transducer
![Page 7: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/7.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
electrostatic transducer
drive mechanism: electrostatic force F acting on a platecondenser of area S and distance x and for a voltage U :
F =ε0SU
2
2x2
with: ε0: electric field constant = 8.85×10−12 AsV−1m−1
I non-linear relation between force and voltage makesbiasing necessary!
I ≈ linear behavior for small variations
![Page 8: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/8.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
sound radiation by a movingmembrane
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loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
sound radiation by a moving membrane
diffraction of plane wave at a circular opening (assumingKirchhoff approximation):
movie: diffraction at circular opening
![Page 10: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/10.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
directivity
![Page 11: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/11.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
directivity
Calculation of sound pressure p̌ for a piston
I of area S
I with velocity v̌nI in an ∞ wall
with help of the Rayleigh-Integral:
p̌ =jωρ
2π
∫S
v̌n1
re−jkrdS
![Page 12: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/12.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Far field directivity for circular piston
in larger distances: 1/r term can be assumed constant(= r0)
p̌(φ) ≈ v̌nr0jka2ρc
J1(ka sin θ)
ka sin θ
wherev̌n: velocity of the pistonr0: reference distancek : wave number = 2π/λa: radius of pistonJ1: Bessel functionθ: angle to the receiver position
![Page 13: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/13.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Directivity
Directivity of the piston radiator in the ∞-wall:
ka = 1 ka = 2 ka = 5 ka = 10
![Page 14: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/14.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
radiated power
![Page 15: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/15.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
radiated power
Radiation of a membrane depends on:
I membrane velocity (usually piston movement isassumed)
I membrane area
I surrounding of the membrane
I medium
![Page 16: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/16.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Radiated power
radiation impedance ZRo :
ZRo =p
v
wherep: average sound pressure at the surface of themembranev : velocity of the membrane (normal component)
I describes loading of the membrane
I calculation with wave theoretical methods
I often alternative definition with volume flow is used:ZR = p
Q
I radiation impedance is complex quantity → activeand reactive component
![Page 17: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/17.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Radiated power
effectively radiated power W by moving membrane is
W = Q2Re[ZR ]
withQ: volume flow (product of velocity and membrane area)Re[ZR ]: real (active) part of radiation impedance
![Page 18: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/18.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Radiated power
examples of radiation impedances (rel. to ρc):
piston in ∞-wall free piston
![Page 19: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/19.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Radiated power
simulation of radiation impedances in equivalentnetworks (frequency range with f 2 dependency):
I often series arrangement of frequency dependentresistance (real part) and inductance (imaginarypart)
I approximation of the load in networks: parallelarrangement
I resistance R = ρc (dominates above ka = 1)I inductance L = ρa/
√2 (dominates below ka = 1)
![Page 20: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/20.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
velocity distribution on amembrane
![Page 21: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/21.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
velocity distribution on a membraneI investigation of the membrane movement of a 20
cm woofer
I measurement method: Laser vibrometer (Doppler)
![Page 22: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/22.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
velocity distribution on a membrane
frequency: 218 Hzmovie: frequency: 218 Hz
![Page 23: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/23.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Velocity distribution on a membrane
frequency: 656 Hzmovie: frequency: 656 Hz
![Page 24: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/24.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Velocity distribution on a membrane
frequency: 2000 Hzmovie: frequency: 2000 Hz
![Page 25: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/25.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
electrodynamic loudspeaker
![Page 26: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/26.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
electrodynamic loudspeaker:principle of operation
![Page 27: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/27.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
principle of operation
![Page 28: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/28.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Electrodynamic loudspeaker:Equivalent network
![Page 29: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/29.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Equivalent networkelements to consider:
MAR ,RAR acoustical mass and resistance of the air atthe rear side of the membranecorresponding to real and imaginary part ofthe radiation impedance
m, s mass of the membrane and the coil,stiffness of the membrane
Rm mechanical friction (suspension of themembrane)
MAV ,RAV acoustical mass and resistance of the air atthe front side of the membranecorresponding to real and imaginary part ofthe radiation impedance
RE , LE electrical resistance and inductance of thecoil
![Page 30: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/30.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Equivalent network
I B × `: force factor
I electrical interface:I source current → force FI membrane velocity → induced voltage
![Page 31: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/31.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Equivalent network
elimination of the gyrators by dual conversion withr = 1/A, omit the 1:1 transformers
![Page 32: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/32.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Equivalent network
behavior of volume flow Q:
I low frequencies: capacitor dominates → Q ∼ ω
I resonance frequency: Q limited by resistances
I high frequencies: inductances dominate → Q ∼ 1/ω
![Page 33: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/33.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Equivalent network
I radiated sound power W = Q2 · Re[ZR ]
I independent of frequency for Q ∼ 1/ω andRe[ZR ] ∼ ω2
I → operation above resonance
I → piston mounted in ∞-wall
I → upper limiting frequency: ka < 1
![Page 34: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/34.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Electrodynamic loudspeaker:Nonlinearities
![Page 35: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/35.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Nonlinearities
I for large amplitudes, the element values will varyaccording to the membrane position
I → nonlinear behavior
I critical:I stiffness of the outer and inner suspensionI inductance of the moving coil LEI force factor B × `
![Page 36: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/36.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
electrodynamic loudspeaker:mounting in a cabinet
![Page 37: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/37.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
mounting in a cabinetI Chassis in ∞-wall realized by mounting in a cabinetI alterations:
I no radiation impedance at rear sideI increasing stiffness due to enclosed air in the
cabinet → acoustical compliance CA
![Page 38: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/38.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Mounting in a cabinet
consequences:
I total capacitance of series resonance circuit islowered
I increased resonance frequency
I the smaller the volume, the higher the resonancefrequency
I → cabinet volume not too small and:I filling with porous material → isothermal
behaviour → effective volume increased by 15%
![Page 39: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/39.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Mounting in a cabinetequivalent network so far:
further steps:
I combination of elements of the same type
I dual conversion of the complete network withr = 1/A
I ignore real part of the radiation impedance (o.k. forlow frequencies)
![Page 40: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/40.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Mounting in a cabinet
quantity of interest: volume flow Q appears as voltageU ′S :
U ′S =Q
A
![Page 41: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/41.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Mounting in a cabinet
elimination of transformer by impedance scaling with(B × `)2
quantity of interest: volume flow Q is transformed intovoltage US :
US = (B × `)U ′S = (B × `)QA
![Page 42: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/42.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Mounting in a cabinet
I potential problems introduced by the cabinet(compared to the ∞-wall):
I mechanical vibrations of the cabinet → boomingI diffraction at the edgesI standing waves (resonances) in the cabinet
![Page 43: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/43.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
electrodynamic loudspeaker:electrical impedance
![Page 44: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/44.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
electrical impedance
![Page 45: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/45.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Electrical impedance
?
I characteristic impedance (typical values: 4 or 8Ohm)
![Page 46: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/46.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
electrodynamic loudspeaker:sound pressure frequency
response
![Page 47: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/47.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
sound pressure frequency response
I restriction to low frequenciesI → omnidirectional radiation
p(d) =
√W ρ0c
4πd2=
Q√
Re[ZR ]ρ0c√4πd
wherep(d): sound pressure in distance dW : radiated sound powerQ: volume flow of the membrane (velocity times area)Re[ZR ]: Real part of the radiation impedance
![Page 48: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/48.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Sound pressure frequency response
radiation impedance (approximation for low frequencies,mounted in a cabinet):
Re[ZR ] =ρ0c
2(ka)2
1
a2π=ρ0ω
2
2πc
withk : wave numbera: radius of the membraneω: angular frequency
![Page 49: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/49.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Sound pressure frequency response
determination of Q: US = (B × `)QA
neglecting LE :
US
U≈ jωLRRR
−ω2LRRRCRRE + jω(LRRR + LRRE ) + RRRE
![Page 50: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/50.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Sound pressure frequency response
p(d)
U=
ρ0a2
d√
8B`
1
j
1
RECR
−ω2LRCR
−ω2LRCR + jω LRRR+LRRE
RRRE+ 1
frequency dependency → high-pass function 2. order:
G (jω) =−ω2T 2
c
−ω2T 2c + jω Tc
QTC+ 1
withTc = 1
ωc
ωc : lower limiting frequency of the high-pass filterQTC : quality factor of the high-pass filter
![Page 51: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/51.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Sound pressure frequency response
p(d)/U for different values of QTC :
![Page 52: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/52.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
electrodynamic loudspeaker:Thiele-Small parameters
![Page 53: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/53.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Thiele-Small parameters
Thiele-Small parameters for the characterization of afree chassis:
resonance frequency fs in Hz : lower frequency end ofthe range of usage
compliance equivalent volume VAS in l stiffness of themembrane and suspension, expressed asequivalent air volume of equal stiffness
![Page 54: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/54.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Thiele-Small-Parameters
mechanical Q factor QMS mechanical damping of theresonance (by RR)
electrical Q factor QES : electrical damping of theresonance (by RE and possible outputresistance of voltage source)
total Q factor QTS QTS = QMSQES
QMS+QES
membrane area A in m2
DC-resistance RE in Ohm
force factor B × ` in T×m
![Page 55: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/55.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Thiele-Small-Parameters
I determination by two electrical impedancemeasurements
I case a): chassis free
I case b): chassis mounted in a cabinet oralternatively loaded with additional mass put on themembrane
![Page 56: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/56.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Thiele-Small-Parameters: mounted in a
cabinet
free chassis specified by fS , QTS , VAS
behavior of chassis mounted in a cabinet of volume VB :
fc = fs
√VAS
VB+ 1
QTC = QTS
√VAS
VB+ 1
![Page 57: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/57.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Thiele-Small-Parameters: mounted in a
cabinetexample → amplitude responses for different cabinetvolumes:
![Page 58: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/58.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Electrodynamic loudspeaker:velocity and displacement of
the membrane
![Page 59: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/59.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Velocity and displacement of the
membrane
I in the range of operation: membrane velocity v ∼ 1f
I → membrane displacement: x ∼ 1f 2
I → maximal excursion at lower frequency end ofrange of operation
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loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
electrodynamic loudspeaker:bass reflex cabinet
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loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
bass reflex cabinetI extension of frequency range of operation to lower
frequenciesI strategy: introduction of additional resonance:
I acoustical compliance: air volume in cabinet: CA
I acoustical mass: cylinder of air in tube: Mp
I around resonance strongest oscillations of aircolumn
I → relevant sound radiation
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loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Bass reflex cabinet
Spice simulation:chassis: fs = 31 Hz; QTS = 0.3; VAS = 118 l
![Page 63: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/63.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Bass reflex cabinet
![Page 64: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/64.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Bass reflex cabinet
![Page 65: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/65.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Bass reflex cabinet
possible problems:
I not satisfying transient behavior
I possible flow noise at end of tubeI overcome by passive membrane systemsI realization of mass by mechanical means
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loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Electrodynamic loudspeaker:Bandpass cabinet
![Page 67: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/67.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Bandpass cabinet
I sub-woofer with acoustical low-pass filtering
I bandpass cabinet with chassis mounted in theinterior of the cabinet
![Page 68: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/68.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
electrodynamic loudspeaker:feed-back
![Page 69: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/69.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
feed-back
I aim of feed-back systems:I controlling oscillation at resonanceI lowering of non-linearities (large membrane
excursions)
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loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Feed-back
I observation of membrane condition:I measurement of membrane velocity by additional
moving coilI measurement of membrane position by capacitive
sensorI measurement of membrane position by optical
means
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loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Electrodynamic loudspeaker:Control of membrane
velocity
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loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Control of membrane velocity
I neutralization of driving coil DC resistanceI powering by amplifier with negative output
resistance
I → direct control of membrane velocity US ≈ U
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loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Control of membrane velocity
I excellent transient behavior
I electrical 1/f -correction necessary to fulfill Q ∼ 1/f
I control effect gets lower for high frequencies as LEbecomes important
I caution: RE − RA > 0 → stability condition!
I |RE | ≈ |RA| is very delicate (temperaturedependency of RE )
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loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Control of membrane velocityrealization example: Studer A723
I negative output resistance:I increase in output current → increase in output
voltage
![Page 75: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/75.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Electrodynamic loudspeaker:Digital Equalizing
![Page 76: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/76.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Digital Equalizing
I impulse response of loudspeaker: h(t)
I inverse filter g(t) where g(t) ∗ h(t) = δ(t)
I pre-filtering of audio signal with g(t)
I but:I physical limitations (1/0→∞)I h(t) depends on radiation angleI h(t) depends on membrane excursion
(nonlinearities)
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loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
horn loudspeaker
![Page 78: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/78.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
horn loudspeakerI improved impedance matching (membrane
movement → air)I significantly higher efficiencyI more pronounced directivity
![Page 79: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/79.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
horn loudspeaker
common horn shape: exponential function:
S(x) = STemx
whereS(x): cross sectional area at xST : cross sectional area at the throat (x = 0)m: geometrical constant
![Page 80: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/80.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
horn loudspeaker
wave equation for the exponential horn:
∂2p
∂t2−c2m∂p
∂x− c2
∂2p
∂x2= 0
guess for p(t):
p(t) = p̂eaxe jωt
with coefficient a:
a = −
(m
2+ j
√4(ω/c)2 −m2
2
)
![Page 81: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/81.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Horn loudspeaker
determination of sound particle velocity:relation between p and v :
∂p
∂x= −ρ∂vx
∂t
in complex writing:
v = − 1
jωρ
∂p
∂x
with p inserted:
v =1
jωρ
(m
2+ j
√4(ω/c)2 −m2
2
)p
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loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Horn loudspeaker
radiation impedance:
ZRo =p
v=
2jωρ
m + j√
4(ω/c)2 −m2
discussion of ZRo :
2(ω/c) < m ZRo is purely imaginary
2(ω/c) ≥ m ZRo has a real and imaginary part with
Re[ ZRo ] = ρc√
1− m2
4(ω/c)2
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loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Horn loudspeakerexemplarily radiation impedance for m = 3.7:
I region of usage: constant impedanceI → volume flow Q has to be constant (operation at
resonance with strong damping)I caution: non-linear distortions due to high flow
amplitudes in the throat
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loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Horn loudspeaker
I practical design rules (reflections at the end can beignored):
I length of the horn > 3λI circumference at the end > λ
![Page 85: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/85.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Horn loudspeaker
compression driver (principle):
I acoustical transformer:I low velocity of large membrane → high velocity in
small throat
![Page 86: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/86.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Horn loudspeakercompression driver (practical design):
I phase plugs:I suppression of cavity resonancesI guarantee in-phase superposition of velocities in
throat cross section
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loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
electrostatic loudspeaker
![Page 88: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/88.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
electrostatic loudspeakerI push-pull principle → sandwich structure:
I two perforated stationary electrodes (acousticallytransparent)
I lightweight stretched membrane in between (0.2g/dm2)
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loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
electrostatic loudspeaker
I bias voltage needed
I excellent transient behavior (lightweight andhomogeneously driven)
I only small excursions possible → large membraneareas needed
I in tendency weak for bass frequencies
I focusing of high frequencies
I reflectors at rear side of speaker may cause problems
![Page 90: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/90.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
magnetostatic loudspeaker
![Page 91: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/91.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
magnetostatic loudspeaker
![Page 92: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/92.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
loudspeaker systems
![Page 93: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/93.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
loudspeaker systems
I radiation of the whole audio frequency range (20 Hz. . . 20 kHz) with one chassis is problematic as
I radiation at low frequencies requires largemembrane excursion or large membrane areas →low upper limiting frequency (kr = 2)
I Doppler distortions (frequency modulations of highfrequency signal components by low frequencies
![Page 94: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/94.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Loudspeaker systems
I solution:I subdivision of whole frequency range into several
bands by frequency dividing network and radiationby different specialized chassis
I typical 2 and 3 way systems
![Page 95: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/95.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Loudspeaker systems
potential difficulties:
I destructive interferences in the transition region dueto:
I differences in phase response of the chassisI differences in path length: chassis → listener
solutions:
I adjustment of phase response
I adjustment for equal path lengths by geometricalmeans
I optimal: concentric dual chassis
![Page 96: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/96.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Loudspeaker systems
power handling:
I defined by:I max. membrane excursion → specified by peak
powerI heating → specified by average power
![Page 97: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/97.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Loudspeaker systems
continuous power testing with standard third-octavespectrum according to IEC 268:
![Page 98: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/98.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Loudspeaker systems
cumulated power for the spectrum according to IEC 268:
caution: maximum power handling of a chassis isspecified as power of the whole system!
![Page 99: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/99.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
loudspeaker measurements
![Page 100: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/100.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
loudspeaker measurements
I frequency response of the electrical impedance atthe terminals
I frequency response of sound pressure on axis
I impulse response of sound pressure on axis
I cumulative decay spectrum of sound pressure onaxis
I directivity of sound pressure for various discretefrequencies
![Page 101: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/101.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
cumulative decay spectrum of sound
pressure
I description of the transient behavior as a functionof frequency
I experiment: excitation with tone burst signal
![Page 102: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/102.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
cumulative decay spectrum
I post-oscillation of the membrane produces soundpressure signal sω(t)
sω(t) = Hω(t) sin(ωt)
withHω(t): modulation of amplitudeω: angular frequency of the excitation signal
→ waterfall diagram of Hω(t)
![Page 103: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/103.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
cumulative decay spectrum
![Page 104: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/104.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
cumulative decay spectrum
efficient generation by taking FFT of time-windowedimpulse response:
![Page 105: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/105.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
cumulative decay spectrumexample of a measurement of a mid-range speaker:
![Page 106: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/106.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
exotic transducers
![Page 107: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/107.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
NXT - distributed mode -loudspeaker
![Page 108: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/108.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Distributed mode - loudspeaker
history:
I 1991 first patent by Ken Heron of Britain’s DefenceEvaluation and Research Agency (DERA)
I British company NXT gets a licence on the principleof operation.
I further investigation of the concept anddevelopment of the corresponding technology
I today, NXT sells licences to other manufacturers
![Page 109: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/109.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Distributed mode - loudspeaker: principle
I NXT speakers consists of large panels
I drivers excite as many partial oscillations as possible(bending waves) → panel oscillates with ’arbitrary’local velocity distribution
I local oscillation pattern leads to energeticsummation at a receiver → omnidirectionalradiation characteristics (figure-of-eight in case ofmounting in free space)
![Page 110: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/110.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Distributed mode - loudspeaker
construction:
I large panels z.B. 60x60 cm
I excitation by one or several drivers
![Page 111: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/111.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Distributed mode - loudspeaker
typical amplitude response:
![Page 112: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/112.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Distributed mode - loudspeaker
typical impulse response [ms units]:
![Page 113: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/113.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Distributed mode - loudspeaker
applications:
I invisible P.A. systems (e.g. speaker arrays mountedin a ceiling)
I in case of special requirements (fire retardant,cleanable)
I optical-acoustical double-usage (e.g. surface foroptical projection acts as speaker as well)
![Page 114: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/114.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Air motion transformer
![Page 115: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/115.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Air motion transformer
history:
I Oskar Heil, USA
![Page 116: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/116.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
Air motion transformer: principle
I folded plastic foil between permanent magnet (largeair gap → strong magnet required
I conductors along the folds (up and down)
I force across the membrane surface → folds areopened and closed
![Page 117: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/117.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
air motion transformer
advantages:
I small membrane movement → efficient volumevariation → high volume flow
I typical transformation ratio: 1:5
I excellent transient behavior
![Page 118: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/118.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
back
air motion transformer
impulse response eton:
![Page 119: Acoustics II: loudspeakers - ISI · PDF fileloudspeakers transducer principles ... electrodynamic transducer drive mechanism: ... moving with velocity u: U = B ‘u. loudspeakers](https://reader031.vdocuments.us/reader031/viewer/2022021818/5aa9dc697f8b9a8b188d622a/html5/thumbnails/119.jpg)
loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
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air motion transformer
impulse response visaton tweeter:
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loudspeakers
transducerprinciples
electrodynamic
electrostatic
radiation
directivity
radiated power
velocity distribution on amembrane
electrodynamicloudspeaker
equivalent network
cabinets
electrical impedance
sound pressure frequencyresponse
Thiele-Small parameters
cabinet types
optimizations
horn loudspeaker
electrostaticloudspeaker
magnetostaticloudspeaker
loudspeakersystems
measurements
exotic transducers
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eth-acoustics-2