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UNIVERSITY OF SALFORD CRN: 23461 SCHOOL OF COMPUTING, SCIENCE & ENGINEERING SEMESTER TWO EXAMINATION PROGRAMMES: BSc (Hons) Acoustics BSc (Hons) Audio Technology BLOCK CODES: S/AT/F2 S/AU/F2 S/AU/S3 ELECTROACOUSTICS Friday 22 May 2009 14:00 – 17:00 Instructions to Candidates Time allowed 3 hours Answer 4 questions Speed of sound in air at STP c = 343ms-1 Density of air at STP ρ0 = 1.21kgm-3 Electric permittivity of air ε0 = 8.85*10-12Fm-1 Vented cabinet design chart provided 1 1. (a) Sketch a simple equivalent circuit for a microphone and briefly describe what physical aspect each component represents. (3 Marks) (b) Describe the three main control regimes for a simple microphone and discuss their application, with sketches of appropriate frequency dependencies, to both electrodynamic and condenser microphones. Your answer should include the necessary strategies to widen the frequency response. (9 Marks) (c) For a condenser microphone the relationship between AC voltage v and displacement x is given by V 1 vx 0 1 X 0 1 jRsQ0 V0 Where v = output voltage x = displacement V0 = DC voltage drop over capacitor X0 = plate separation distance Rs = resistor Q0 = DC backplate charge By analysing your circuit diagram from a) show that the open circuit sensitivity is given by v 2V0S P X 0k Where |v| = output voltage amplitude |P| = pressure amplitude S = diaphragm area k = stiffness (5 marks) (d) A condenser capsule is designed with a resonant frequency of 23kHz. The diaphragm is 1/2in (1.27cm) in diameter, the polarisation voltage is 48V and the plate gap is 15μm. If the nickel diaphragm is 3μm thick, and the density of nickel is 8.8x103 kgm-3, find the mass of the diaphragm and estimate the required stiffness and DC charge. (6 Marks) (e) Calculate the sensitivity of the capsule in its normal operating region in dB relative to 1VPa-1 (2 Marks) 2 2. (a) Draw a schematic diagram of an electret microphone and label the parts. (4 marks) (b) Describe, in words, the function of each part of the microphone, the location at which a sound wave is incident, and its effect on the microphone components. (4 marks) (c) How is the output voltage, V, related to the surface charge density and microphone capacitance C? (1 mark) S (d) The capacitance of a pair of plates of area S and separation X is C where X is the permittivity constant for the material between the plates. Show that Xd V 0 d X for the electret microphone, where 0 is the permittivity of a vacuum or air, X is the total spacing of the air-gap at any time and is the permittivity of the dielectric used. (4 marks) (e) The frequency dependence of the small voltage fluctuation amplitude, |v|, can be expressed by the following equation: f0 v f v max V 2 V 2 f f0 1 Q f 0 f Using words and equations describe, in terms of Q and f0, how the small fluctuating voltage, v, will vary with frequency f. What voltage amplitude is obtained at (i) f << f0 (ii) f = f0 (iii) f >> f0 (6 marks) (f) If the electret charge decays exponentially with a half-life of 80 years, what is the annual change in sensitivity? (6 marks) 3 3. A single-diaphragm condenser microphone is constructed as shown in the diagram below ZAD Pf C2 M1 Pb R2 R1 where symbols have their usual meaning (a) Describe the function of each part of the single-diaphragm microphone given in the diagram above. Describe, in words, the main advantage of a double- diaphragm microphone as opposed to a single diaphragm microphone. (3 Marks) (b) Draw the equivalent circuit for the single diaphragm microphone in the diagram above. (3 Marks) (c) Analysing the simplified T-network shown below, derive the following expression for microphone sensitivity: U Z0 p2 Z1 U1 pf Z2 pb U Z1 jkd cos Z 2 pf Z 0 Z1 Z1Z 2 Z 2 Z 0 (7 marks) (d) If the microphone is placed close to a sound source, the proximity effect will change the response. Explain how and why the response is changed and include a diagram of the signal to noise ratio. (3 Marks) (e) A double diaphragm microphone has a front diaphragm response of KVf 1 cos and a back diaphragm response of b KVb 1 cos . vf v Pf Pf Combine the responses and suggest appropriate polarisation schemes to give omnidirectional, bi-directional, cardioid, and supercardioid responses. Draw the respective directivity patterns. (9 Marks) 4 4. A moving-coil driver can be represented at low frequencies by an electrical circuit consisting of a voltage source v in series with a resistor RE, and in parallel with a capacitor MMS/(BL)2, an inductor CMS(BL)2 and a resistor (BL)2/RMS. (a) Draw the analogue circuit for the drive unit in Mobility form. Which additional impedance would affect the driver at medium to high frequencies? How would you represent this impedance in the circuit? (4 marks) (b) Describe the characteristics of a real moving coil driver which are represented by each parameter of the model. Describe how the presence of an ‘air-load’ would affect each parameter if the driver were placed in a sealed cabinet. (4 marks) (c) Show that the total impedance of the electro-mechanical analogue can be written as ( j / s ) / Q MS Z E R E R ES 2 j 1 j 1 s Q MS s (BL ) 2 1 1 Where R ES s 2 Q MS R Ms C MS M MS s C MS R MS and symbols have their usual meaning (4 marks) (d) The acoustic pressure from a driver mounted in an infinite baffle can be modelled using the piston assumption, where vBL 0 2J (ka sin( )) | p | E( j ) 1 2rSD R E M AT ka sin( ) A mid-range driver has the following characteristics: SD = 0.021 m2 BL = 10.3 Tm MMS = 24.5 g RE = 8Ω QTS = 0.24 fs = 28 Hz For the reference region calculate i) the on-axis sensitivity at 1 m distance re 1 W input power, ii) the efficiency and iii) the acoustic output power. (7 marks) /Contd… 5 (e) A sealed box is designed for the driver in part (d) with the aim of achieving a Butterworth alignment. Find the required box volume, and sketch the resulting low frequency response. What happens to the response as an increasing volume of damping material is inserted into the cabinet? Sketch the result on your graph. (6 Marks) The compliance of an enclosed volume of air is given by: V C AB 0c 2 All symbols have their usual meaning. 6 5. (a) A vented loudspeaker can be represented by the following lumped parameter model: BL2 2 RESD M AD C AD R AD M AF R AF M AV R AV U Uv C AB M AF ,V vBL S D RE R AB R AF ,V (i) Draw a sketch of the loudspeaker and label the impedances/reactances onto their respective mechanical parts. Explain in words why CAB and RAB are in parallel to MAV, RAV, MAF,V, RAF,V in the circuit diagram. (4 marks) (ii) Sketch a graph of the rear acoustic load ZAB and driver volume velocity UD against frequency. Mark on the Helmholtz frequency fB and give a formula used for its calculation. Explain the relationship between ZAB and UD - does the port or the driver contribute most radiated pressure in the vicinity of fB ? (4 marks) (iii) The pressure radiated by a vented loudspeaker system can be considered in terms of three important resonances fB, fL and fH. The sketch below is a simplification of the mechanical system involved – copy it and annotate the component names of the masses and springs. Use it to illustrate the relative motion of each component at the three resonant frequencies. u=0 Why, when the two masses oscillate in antiphase, are the pressure contributions which they radiate in-phase? Over what bandwidth does this occur? (9 Marks) (b) Using the design chart provided (on page 9), suggest a design for a vented cabinet including volume and vent properties when supplied with a driver having the following small-signal parameters: SD = 210 cm2 QTS = 0.24 Bl = 10.3 Tm MMS = 24.5 g RE = 8 fs = 28 Hz (8 marks) 7 6. (a) Explain the difference between active and passive loudspeakers and discuss why one might be chosen over the other. (3 marks) (b) Sketch the circuit diagram for a passive first-order 2-way cross-over network, and state the major assumption which is normally made when calculating component values. (3 marks) (c) Adopting this assumption, show that the voltage across the low- and high- frequency units can be described respectively by: vH 1 vL 1 1 v in 1 jLL v in 1 RL jRHCH where symbols have their usual meaning. (3 marks) (d) Show that the Butterworth design gives the following values for the low frequency inductor and high frequency capacitor: RL 1 LL CH x RH x (3 marks) (e) Show that the Butterworth filter design puts 90° of phase between the low- and high- frequency drivers at the cross-over frequency. What does this imply regarding the dB-cut for this driver at crossover for a flat response? Use equations and an Argand diagram in your answer. (3 marks) (f) The 2nd order Linkwitz-Riley design uses the following component values: 2RL 1 2RH 1 LL CL LH CH x 2RL x x 2RH x Find these values to 2 dp for a nominal 4Ω system, with cross-over frequency at 3.7 kHz. Sketch the expected magnitude response. Why might the actual performance differ from that expected? (5 marks) (g) Describe in words what steps need to be taken to derive from first principles an appropriate circuit which might be used to correct for the voice coil inductance. Would this circuit be used with a woofer or a tweeter – explain your answer. Include a diagram of the final compensation circuit. (5 marks) 8 Vented Cabinet Design Chart fs = free air resonance QTS = Q-factor of driver = CAS/CAB H = fB/fS, 9

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posted: | 2/23/2010 |

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