Historic transducers: Balanced armature receiver (BAR)

Transcription

1 4aEA, Acoustic Transduction: Theory and Practice I Historic transducers: Balanced armature receiver (BAR) oori Kim and Jont B. Allen University of Illinois, Urbana-Champaign Electrical & Computer Engineering Dept.

2 Table of contents 1. Balanced Armature Receiver (BAR) 2. Overview: operational principle of the BAR 3. Illustrative case studies of the BAR I=0 and I 0 (Eddy-currents) 4. Force on the armature (F m ) with Hysteresis effect 5. Conclusions 2

3 Balanced Armature Receiver (BAR) The oldest telephone receiver is invented by A. G. Bell in 1876 A. G. Bell, U.. paent in 1876 Attraction and release of the armature are controlled by the current from the coils, which generates electromagnetic fields Has evolved into the modern hearing-aid devices

4 An example of the modern style BAR, Knowles ED7045 Cross section of Knowles ED receiver Inside of the BAR without case and diaphragm

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6 Overview of the BAR s operation

7 diaphragm μ 0 << μ a μ 0 H The AC magnetic (solenoid) field s direction is perpendicular to the current. μ a I>0 + -

8 diaphragm μ 0 << μ a μ 0 H Hysteresis loss (the energy required to rotate the domains of magnetic dipoles) will occur when the induced magnetic field affects the armature. μ a I>0 + -

9 diaphragm μ 0 << μ a μ 0 H An eddy current is generated in the opposite direction of the conducting current. This phenomenon is independent of the permanent magnet. μ a I>0 + -

10 diaphragm μ 0 << μ a μ 0 H μ a Due to the polarity between the permanent (DC) magnetic field and the generated AC magnetic field, the armature feels a force. I>0 + -

11 diaphragm Magnetic force, F m : Force between two nearby magnetized surfaces to create a magnetic image Due to the polarity between the permanent (DC) magnetic field and the generated AC magnetic field, the armature feels a force.

12 Illustrative case studies of the BAR: I = 0 and I 0 (Eddy-currents)

13 I=0 diaphragm Magnetic poles always come in pairs ( and ) Polarity of magnetic dipoles, net magnetic density B=0 Ψ 0up Ψ 0down

14 I=0 diaphragm Polarity of magnetic dipoles, net magnetic density B=0 The magnetic dipoles are lined up from to. Ψ 0up Ψ 0down

15 I=0 diaphragm The armature behaves as a magnet with magnetic flux density B 0 (Tesla=Wb/m 2 ) Polarity of magnetic dipoles, net magnetic density B=0 Ψ 0up Ψ 0down B 0

16 I=0 diaphragm Polarity of magnetic dipoles, net magnetic density B=0 Ψ UPgap Ψ Ψ DC_upper 0up Ψ DC_lower Ψ 0down B 0 Ψ LOWgap

17 I=0 diaphragm Polarity of magnetic dipoles, net magnetic density B=0 The armature is balanced Ψ DC_upper + Ψ DC_lower = 0 (the net flux) Ψ Ψ DC_upper 0up Ψ DC_lower Ψ 0down F UPgap Ψ UPgap B 0 F LOWgap Ψ LOWgap

18 I>0 H + -

19 I>0 H Ψ AC Ψ up > Ψ low Ψ UPgap Ψ up =Ψ DC_upper +Ψ AC Ψ low =Ψ DC_lower -Ψ AC Ψ AC Ψ LOWgap

20 I>0 Going up H F UPgap >F LOWgap, so the armature goes up Ψ AC Ψ UPgap = (Ψ up Ψ low )+Ψ LOWgap F UPgap Ψ up Ψ low Ψ UPgap >Ψ LOWgap F LOWgap Ψ AC Ψ LOWgap

21 Eddy current μ 0 << μ a z ρ H -H z (Vanderkooy 1989) H z = J cφ + D J cφ = σe φ (1. Ampere s law) E φ = B z (2. Faraday s law) H = ( H) 2 H (3. Vector identity) 0 μ 0 μ a I>0 + - H z H z = 2 H z ( 3) σe φ = 2 H z ( 1) σ E φ = σb z ( 2) Finally, 2 dh H z = σμ z a dt In the frequency domain (jk) 2 =σμ a jω k ρ = ± σμ a ω e 45 (diffusion) 2H z (ρ, t)=2h 0 e jωt kρ

22 Force on the armature and hysteresis

23 Force on the armature F m exists for two opposing poles across an air gap Opposite poles attract and like poles repel

24 Hysteresis can be explained by describing the F m, Assumption: Core is initially not magnetized 1. Electrical energy: W = v t i t dt [J = m] 2. W d = HlAdB la 3. Therefore F m = W d A = HdB = 1 μ B2 Faraday: BdB A d Ampere: = B [ Hl/ J dt 2μ F m = AB2 2μ = A gb g = Ψ g [] 2μ 0 2μ 0 A g 2 2 m 3 = m 2]

25 W d = HlAdB la = HdB = 1 μ BdB = B2 2μ [ J m 3 = m 2] The green formula can be related to the famous hysteresis loop graph x-axis and y-axis represent H and B Hysteresis loss: subtraction of two regions A typical hysteresis phenomenon of Ferro-magnetic material B H ( We are interested in BAR s operational region

26 Hunt 1954, Ch. 7, Moving armature transducer systems BAR type receivers are operating in a lens shaped region The region can be linearly approximated Centered at φ 0 (due to the permanent magnet) Alternating φ i F m = Ψ g 2 = (Ψ 0+Ψ i ) 2 2μ 0 A g 2μ 0 A g = Ψ Ψ 0 Ψ i +Ψ i on-linear part 2μ 0 A econd harmonic g distortion

27 Conclusions Principles of the BAR's operation include the Eddy-current effect, hysteresis loss, and force on the two magnets Current I Eddy Hysteresis Moving the mass mass Force F Induced H Coupled to B 0 Kim,., Allen, J.B., Two-port network analysis and modeling of a balanced armature receiver. Hearing Research 301, This work will provide a fundamental, clearer insight into this type of BAR system

28 References 1. Members of the taff of the Department of Electrical Engineering, Massachusetts Institute of Technology., Magnetic Circuits and Transformers: A First Course for Power and Communication Engineers, volume 2 of Principles of Electrical Engineering eries. Wiley, ew York. 2. Hunt, F.V., Electroacoustics: The analysis of transduction and its historical background. Harvard University Press. Harvard University, Massachusetts. 3. Mott, E.E., Miner, R.C., The ring armature telephone receiver. The Bell ystem Technical Journal, Jensen, J., Agerkvist, F.T., Harte, J.M., onlinear time-domain modeling of balanced armature receivers. J. Audio Eng. oc 59, Kim,., Allen, J.B., Two-port network analysis and modeling of a balanced armature receiver. Hearing Research 301, Lewin, W., 2002a. Lecture 16: on-conservative fields - do not trust your intuition. UniversityLecture, Electricity and Magnetism (Physics 8.02). 7. Lewin, W., 2002b. Lecture 20: Faraday s law - most physics college books have it wrong! University Lecture, Electricity and Magnetism (Physics 8.02). 8. Vanderkooy, J., A model of loudspeaker driver impedance incorporating eddy currents in the pole structure. J. Audio Eng. oc. 37(3),

29 Thanks