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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
Acoustics II:loudspeakers
Kurt Heutschi2013-01-18
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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 × `
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
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
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%
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)
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
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
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
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
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
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)
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
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
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
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
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
I two perforated stationary electrodes (acousticallytransparent)
I lightweight stretched membrane in between (0.2g/dm2)
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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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
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
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
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
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
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
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
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
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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Loudspeaker systems
continuous power testing with standard third-octavespectrum according to IEC 268:
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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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!
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
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
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
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)
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
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:
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:
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
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
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
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)
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
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:
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]:
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)
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
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
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
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