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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       
                                   vx 0              1
                                      X 0 1  jRsQ0    
                                          
                                                 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              
                              2rSD 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:
                       BL2
                             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  jLL                               v in 1 
                           RL                                           jRHCH

              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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