Transcript
Electroacoustic Transducers with Magnetic Field
Electroacoustic and electromechanical transducers Systems for conversion of the energy of the electromagnetic field to the energy of the acoustic field (mechanical energy) or vice versa (reciprocity) transmitter u, i
electromechanical transducer
F, v
mechanical acoustic transducer
receiver Electroacoustic transducer
p, w
Cascade equation of an electromechanical transducer
F = f (u , i ) v = g (u , i ) Total differential of all variables
∂F ∂F dF = du + di ∂u ∂i ∂v ∂v dv = du + di ∂u ∂i
∂F ∂u ∂F ∂i ∂v ∂u ∂v ∂i
= a11 = a12 = a21 = a22
Linearization of a transducer (realistically), inverse matrix describes the backward conversion
which are elements of the matrix A:
F u v = A i inverse matrix describes behaviour of a receiver
u −1 F i = A v
In case of description of electroacoustic transducers voltage/current to acoustic pressure/volume velocity (and vice versa) conversion is modelled. The principle is the same as above, only constants are different
p u w = α i u i = α
−1
p w
We will now try to find elements of the matrice A or α based on the physical nature of the electro-mechanical or electroacoustic conversion. Basic equations from the electromagnetic field will be used. Principle of derivation: force action of magnetic or electric field are described as functions of variables. They have a constant (polarizing) component and a variable (superposed, much smaller) component. After linearization a set of two equation is derived, which serves as a description of a two-port network we are searching.
Classification of Electroacoustic Transducers - with magnetic field (electrodynamic, electromagnetic, magnetistrictive) - with electric field (electrostatic, piezoelectric, piezoplastic) - other principles (ionic, carbonic, thermoacoustic, optic…)
Reciprocal transducers X Non-reciprocal transducers
transducers described with circuits with lumped x distributed elements
Transducers with Magnetic Field Electromagnetic transducer
1 B2 w = HB = 2 2µ 0
Situation in the gap (3) the armature exerts power:
Fdη = wSdη
SB 2 F= 2µ 0 magnetic flux:
SB = Φ Φ 2 F= 2µ 0 S
Fm n( I 0 + i ) Φ = = d−η Rm µ 0S
F=
µ 0 Sn ( I 0 + i ) 2
2( d − η
)
2
2
total differential (variable i and η): 2 I + i ( I + i ) dF = n 2 µ 0 S 0 2 di − n 2 µ 0 S 0 dη 3 (d − η ) (d − η )
because i << I0 and η << d, we can simplify and integrate:
2
I0 I0 2 F = n µ 0S 2 i − n µ 0S 3 η d d 2
Harmonic phenomena:
Using:
v η = jω
nI 0 µ 0 S = Φ d nΦ 0 = L0 I0 nΦ 0 = ka d
0
k a2 F = kai − v jω L0 1 F = kai − v jω c n L0 where c n = 2 ka
is the negative compliance
Negative compliance is related to stability. There must be some force acting against the force of the magnetic fied so that the armature is not attracted to the magnetic circuit. In this way a steady point is assured.
voltage induced in the coil:
∂Φ u= n ∂t
using the relation for magnetic flux:
∂ I0 + i u = n µ 0S ∂t d − η 2
u = n2µ 0S
I + i ∂η 1 ∂i − n2µ 0S 0 d − η ∂t (d − η ) 2 ∂ t
again i << I0 and η << d, using above mentioned substitutions:
u = L0
∂i ∂η − ka ∂t ∂t
for harmonic signal:
u = jω L0i − k a v
1 F = kai − v jω c n We have two circuit equations, from which an equivalent circuit can be derived: -cn
using gyrator with the cascade matrix:
F 0 v = −1 ka
ka 0
u i
gyrator is a two-port network changing character of impedances in electroacoustics – transformation: i – F, u – v, L – c, C – m, R – 1/r longitudinal elements change to transversal and vice versa
equivalent circuit of an electromagnetic transducer
electric part
mechanical part
acoustic part
Quasistatic Stability of the Electromagnetic Transducer
a… static distance without magnetic field l… static distance with magnetic field
Retroactive force of the elastor FS = s(a-l) Force due to magnetic field µ 0 Sn 2 ( I 0 ) F= 2 2( l )
• • •
2
System stable between l2 a l1 System stable at one point, small deviation – instability System unstable, l12 = 2a/3
µ 0 Sn 2 I 02 1 = s( a − l ) 2 2 l 2 2 µ Sn I0 3 2 0 l − al + = 0 2s
l1, 2
2 = a 3
s1, 2 =
s > s1.2
µ 0 Sn 2 I 02 2 a 3
3
Electrodynamic Transducer membrane pole pieces voice coil
force acting on a conductor in magnetic field
dF = Bxi d since the vectors are perpendicular:
F = Bi
voltage on a coil invariable magnetic field
∂i ∂Φ u = L0 + ∂t ∂t
Φ = B η
∂Φ ∂η = B = Bv = k a v ∂t ∂t
transduction factor ka =Bl , B is magnetic induction in the gap, l the length of the conductor in the voice coil
for the case of harmonic signal:
u = j ω L0 i + k a v The same description as in case of the electromagnetic transducer BUT negative compliance is infinity (stability ensured)
Electroacoustic transducers with magnetic field
equivalent circuit comprises the ideal transformer, which models mecanical-acoustic transduction in some cases the mechanical part is transformed to the acoustic part
Equivalent circuit of electroacoustic transducers
with magnetic field
ribbon microphone
(tonmeister.ca)
Pressure loudspeaker – velocity transformation
Electrodynamic Loudspeaker • • • •
comercially most successful patented in 1924 (1877 started) design has not changed over the years improvement of parameters by using new materials or membrane shapes
Parts of the Electrodynamic Loudspeaker
Terminology • acoustic axis – usually the same as geometric axis. direction in which the directional characteristics is maximal • reference point – cross-section of the acoustic axis and the plane comprising edges of the membrane
Equivalent circuit of the electrodynamic loudspeaker
u
p
Electrical part of the scheme • Inductance of the voice coil • Resistance of the voice coil
Mechanical part of the scheme • • • • • • •
mass of the voice coil friction of the voice coil mass of the membrane compliance of the membrane damping of the membrane compliance of the spider and suspension damping of the spidet and suspension
Acoustic part of the scheme
• Radiation impedance • Acoustic impedance of acoustic system at the rear (baffle)
Transformation of the electric part to the mechanical one Ideal gyrator F = (Bl) i
u = (Bl) v
Transformation of the mechanical part to the acoustical one Ideal transformer p = F/S w = v.S
Input electric impedance of the electrodynamic loudspeaker
• resonant frequency • nominal impedance (4, 6, 8, 16, 32… Ω)
Directional Characteristics Dependency of the acoustic sound pressure level on the angle between the acoustic axis and the measurement pointreference point link
at low frequencies it is close to omnidirectional characteristics
Design of the electrodynamic loudspeaker • voice coil – longer than the air gap
– shorter than the air gap
to ensure linearity
Materials for membranes • Paper • Plastic – Kevlar (Du Pont)
• Metal each has advantages and disadvantages, their usage is a compromise, differ in mass and stiffness
Membrane shape • Conical • Parabolic (rotational) • Exponential (rotational)
influences radiation characteristics, turbulences
Arrangement of the magnetic circuit • ring magnet • cylindric magnet
Pole pieces must ensure mutual perpendicularity of the magnetic field, displacement of the coil and the conductor for maximum efficiency
Magnetic Induction Values in the Gap in the past – fractions of 1 Tesla now – 1 Tesla present technological limit 10 – 15 T
Loudspeaker Basket • open (with openings) • closing the membrane from the back
Division of Loudspeakers by the Frequency Band
• • • • •
low frequency (20 – 1000 Hz) subwoofers (20 – 100 Hz) squawkers (200 – 5000 Hz) tweeters (1000 – 20000 Hz) wide band (50 – 20000 Hz)
Why produce loudspeakers for various frequency bands?
sensitivity depends on frequency (loudspeaker parameters) parameters depend on the design optimization
Low Frequency Loudspeaker incl. sub-woofer very compliant suspension membrane can perform piston-like displacements
Squawkers Mid-range loudspeakers (300-5000 Hz) (squawker). Membrane takes form of¨a spherical cap (suspension and voice coil are at the periphery) or short and very outspread cone (voice coil at its smaller diameter, suspension at the greater diameter)
Tweeters membrane and a voice coil are very light to enable fast movement suspension and spider are stiff so that to suppress low frequencies spherical tweeter (impregnated textile, thin metal…) ribbon tweeter (thin aluminium foil in magnetic field) other principles – piezo, condenser,.. often with a waveguide (impedance matching)
Division of Loudspeakers by the Shape of the Membrane • • • •
Circular Eliptical Square (it was a fashion for a short time ) other shapes (car audio)
Thielle – Small Parameters - above mentioned parameters of the equivalent circuit - small signal parameters - large signal parameters - other parameters
Small signal parameters Fs … resonnt frequency Qes .. electric quality factor Qms … mechanical quality factor Qts … total quality factor V equivalent volume Large signal parameters Xmax … maximum linear displacement Xmech … maximum physical displacement before break up Pe … heat capacity in Watts Vd … maximum volume displacement = Xmax x S
other parameters Zmax … loudspeaker impedance at Fs, used for Q measurement EBP …. (Efficiency bandwidth product) Zj … nominal impedance reference efficiency
Loudspeaker production concentrated in a few places around the world which supply all companies producing audio equipment not fully automated, great propotion of human labour
Loudspeaker testing production purposes – quality control finding/check up of parameters
KLIPPEL - a new generation of diagnostics tools dedicated to Quality Control. The Klippel QC System provides a comprehensive hardware and software solution for a fast testing all kinds of electro-acoustical devices. □ SPL □ THD □ Polarity □ Rub& Buzz □ Impedance □ Parameters □ Classification □ Grading
Loudspeaker non-linearities
Wolfgang Klippel, Dresden
Enclosures main task: preventing the acoustic short-circuit at lf improving the sensitivity – frequency „shaping“ ideal baffle – infinite plane
Closed box its inner space is modelled (at low frequencies only!!) by the acoustic compliance, sometimes also by acoustic resistance (when damped by absorbing material) by incorporating the compliance (volume) into the system the resonant frequency changes
Bass-reflex enclosure making use of energy radiated to the enclosure tuning the bassrefle by the mass and compliance widening the frequency band to low frequencies steeper fall of sensitivity at low frequencies
Passive radiator bass-reflex principle, mass and resistance of the air are substituted by the mass and resistance of the membrane the design of the passive radiator is the same as that of a loudspeaker, only magnet and voice coil are missing. The system is tuned by the mas attached to the center of the membrane
Crossovers • Loudspeakers are optimized for given frequency bands • For transmitting the whole audio frequency band correctly we need to divide appropriate FB for respective loudspeaker • Crossover networks – electric filters, active or passive
Evolution of Loudspeakers Patent Selection
ceiling loudspeaker
possibility of making the magnetic field more homogeneous
Loudspeaker with the underhung membrane
Derivation of the transfer function of the electrodynamic loudspeaker Equivalent circuit of the electrodynamic loudspeaker in the closed box:
Radiation impedance
/
Equivalent circuits of electroacoustic transducers
with magnetic field
with electric field
