Your Federal Quarterly Tax Payments are due April 15th Get Help Now >>

Electro-Mechano-Acoustical_20Circutis_3_ by xiangpeng

VIEWS: 41 PAGES: 29

									         Electro - Mechano - Acoustical
1) Mechanical Circuits
   - Physical and Mechanical Meaning of Circuit Elements
   - Mechanical Circuits
2) Acoustical Circuits
   - Acoustical Elements
3) Transducer
   - Transformation Type Element
   - Gyration Type Element
4) Circuit Theorems and Energy and Power
   - Conversion from Mobility-Type Analogies to Impedance-Type Analogies
   - Thevenin’s Theorem
   - Energy and Power Relations
   - Transducer Impedances
   - Combinations of Electrostatic and Electromagnetic Transducer
1) Mechanical Circuits
  Physical and Mechanical Meaning of Circuit Elements


- Generators of Two Type

- Circuit Elements of Four Type




                           Acoustics Chap 3 (Leo L. Beranek)   2
- a  e(Voltage, f(Force), u(Velocity), p(Pressure), U(Volume Velocity)
- b  i(Current), u(Velocity), f(Force), U(Volume Velocity), p(Pressure)
- c  Mass, Compliance, Inductance, Resistance……
       ( 여기서 c 는 a,b가 선택된 의미에 따라 결정된다. )




                      Acoustics Chap 3 (Leo L. Beranek)                    3
   Mechanical Circuits

- Velocity is an
Analog to Voltage in
that it can be
Measured without
Interrupting the
Flow Quantity. (Not
Force and Current)




                       Acoustics Chap 3 (Leo L. Beranek)   4
                                                             Force : Voltage
  Direct(Impedance) Analogy
                                                            Velocity : Current

                                                        Velocity : Voltage
  Inverse(Mobility) Analogy
                                                             Force : Current

a) Mechanical Impedance ZM, and Mechanical Mobility zM
  - Mechanical Impedance, ZM si Complex Ratio of Force to Velocity
        N  sec 
                 SI   mech.ohm.
        m 
 - Mechanical Mobility, zM si Complex Ratio of Velocity to Force
        m 
                 SI   mech.mohm.
        N  sec 

                        Acoustics Chap 3 (Leo L. Beranek)                        5
b) Mass MM
  - Newton’ Second Law
                       du(t )
        f (t )  M M
                        dt

  - 전제조건 : 주기적인 성질을 갖는 시스템을 고찰 u  u0 e jt                   
           Steady State (  2 )




     f  jM M u           (Impedance Type)


         f
    u                    (Mobility Type)
       jM M

                       Acoustics Chap 3 (Leo L. Beranek)           6
c) Mechanical Compliance CM

                      1
     f (t )  kx 
                     CM  u (t )dt
         Where    u (t )  u1  u2



     이전과 동일한 전제조건 하에서

            u
   f                     (Impedance Type)
         j C M


   u  jCM f            (Mobility Type)

                          Acoustics Chap 3 (Leo L. Beranek)   7
d) Mechanical Resistance RM, and Mechanical Responsiveness rM

        f  RM u

               1    m 
       rM                   SI       mech.mohm.
              RM    N  sec 



     f  RM u      (Impedance Type)



     u  rM f      (Mobility Type)


                      Acoustics Chap 3 (Leo L. Beranek)         8
e) Mechanical Generators

        Constant Velocity                             Constant Force
 Very Strong Motor Attached to a           Electromagnetic Transducer
 Shuttle Mechanism                         (e.g. Moving-Coil Loudspeaker)




                      Acoustics Chap 3 (Leo L. Beranek)                     9
e) Levers (Transformer)
     f1l1  f 2l2

    u1l1  u2l2     (Assuming Small Displacement)
                      2
          u1  l1                                             l1 
    zM 1     zM 2                                           :1
          f1  l2                                            l 
                                   (Mobility Type)
                                                             2
                                                               l2 
                      2
         f1  l2 
    ZM1     ZM 2               (Impedance Type)             :1
                                                              l 
         u1  l1 
                                                             1




                          Acoustics Chap 3 (Leo L. Beranek)            10
f) Mechanical Impedance and Mobility

        Mechanical Impedance in Series           Mechanical Impedance in Parallel
                 ( u=Const )                               ( f=Const )

+                                               +
                                     +                      u            u1        u2
                             Z1      f1
                                      -
    f        u                                      f               Z1        Z2
                                     +
                             Z2      f2
                                      -
-                                               -

f1  uZ1 , f 2  uZ 2                               f  u1Z1  u2 Z 2
f  f1  f 2                                     u  u1  u2
               f1  f 2                                 1    u u1  u2 1  1
ZTotal
            f
                       Z1  Z 2                                   
            u     u                              ZTotal      f    f    Z1 Z 2
                           Acoustics Chap 3 (Leo L. Beranek)                            11
        Mechanical Mobility in Series               Mechanical Mobility in Parallel
                ( f=Const )                                  ( u=Const )

+                                               +
                                     +                       f                f1        f2
                             z1      u1
                                      -
    u         f                                     u                    z1        z2
                                    +
                             z2     u2
                                     -
-                                               -
u1  fz1 , u2  fz2                                 u  f1 z1  f 2 z2
u  u1  u2                                         f  f1  f 2
              u u1  u2                                 1     f  f1  f 2 1 1
    zTotal             z1  z2                                       
              f    f                                zTotal    u     u     z1 z2


                           Acoustics Chap 3 (Leo L. Beranek)                                 12
2) Acoustical Circuits
   Acoustical Elements
 - Sound Pressure p(N/m2=Pa) is Measured without Modifying the Device.
  It is Desirable to make Pressure Analogous to Voltage.
 - Acoustical Impedance, ZA is the Complex Ratio of Pressure to Volume
  Velocity, v(Nsec/m5) or SI Acoustic ohm.
 - Acoustic Mobility zA, is Complex Ratio of Velocity to Pressure.

              p ( N / m2 )                                   v
          ZA   3                                      zA 
              v (m / sec)                                    p

        * The Flow Quantity : v   u ds     ( U= 입자의 속도 )


                         Acoustics Chap 3 (Leo L. Beranek)               13
a) Basic Acoustical Elements Can be Realized by Considering the
                       Following Device

                      x0                               x l
          Piston
                             Cross Section Area = S


                   u  u0j t

  - Simple Plane Wave Propagating to and fro in X-Direction.
  - Constant Velocity Source.
  - 피스톤 부분의 공기 입자는 피스톤과 함께 움직인다.

                                      d2p
       * Helmholtz Eq is                    k2 p  0
                                      dx 2
                    Acoustics Chap 3 (Leo L. Beranek)             14
* Euler’s Eq is
                           1 p        u        
              u ( x)                   0   p 
                         j  0 x      t        
                  dp                    p 1 D dp 
                       j  0u             
                                         
                  dx                    x      dx 

   Let        p( x)  A sin kx  B cos kx
             dp
                  k ( A cos kx  B sin kx)
             dx
                          j
              u ( x)      ( A cos kx  B sin kx)
                        0c
   From Boundary Condition
                                  jA
              u ( x  0)  u 0           or     A   j (  0 cu0 )
                                 0c
                         Acoustics Chap 3 (Leo L. Beranek)             15
i) Close End Problem
                               jB
     u (l )  0  u0 cos kl      sin kl
                              0c
      B   j 0 cu0 cot kl , u ( x)  u0 (coskx  cot kl  sin kx)
     p( x)   j 0 cu0 (sin kx  cos kx  cot kl)
“Input” Acoustic Impedance Z A @ x  0
          p        p x 0  j 0 cu0 cot kl  j 0 c cot kl
    ZA                                  
          v x 0 u0 S            u0 S              S
               c
         j  0  cot kl
              S 
 For Small kl(i.e. kl  1 , l   / 8) and cot kl  1  kl  A
                                                    kl       3

                0 c   1 kl   j 0 c     j 0l
                                          2
     Z A   j                        
               S   kl 3       Sl          3S
                                           A         B
                         Acoustics Chap 3 (Leo L. Beranek)             16
  0c 2                      1        1
        if l                      
  jSI         16            SI  jC A
                           j 
                                c2 
                                     
                               0 
      Volume
CA                                  Acoustic Compliance
       0c

  Again, we Write

            c                1          l
Z A   j  0  cot kl                 j 0           (kl  1)
           S                 V         3S
                           j 
                                c2 
                                     
                               0 
       1        MA                             0l
           j            where M A 
     jC A      3                              S

                    Acoustics Chap 3 (Leo L. Beranek)               17
 ii) Open End Problem
   Assume that Negligible Sound Radiates from that End (i.e. p=0 @ x=)
       p( x  l )   j 0 cu0 sin kl  B cos kl  0
       B  j 0 cu0 tan kl
       p( x)  j 0 cu0  sin kl  cos kx  tan kl
  “Input” Acoustic Impedance Z A @ x  0
             p       p x 0     0c 
      ZA                   j      tan kl
            v x  0 u0 S        S 
    For k <<1
                 l                               tan kl  (kl) 
                                                                    (kl)3
                                                                           kl
      Z A  j   0   jM A              Where
                                                                      3
                 S 
                                                             1        MA
 ZA that Open End and Close End is          jM A  Z A         j
                                                           jC A      3

                          Acoustics Chap 3 (Leo L. Beranek)                      18
b) Acoustic Mass, MA (kg/m4)

  - Associated with an Open Tube of Fluid, the Entrained Fluid will be
   Accelerated with Negligible Compression.
  - Effective Length “” is Longer than  Because
    Particle of Fluid in the Neighborhood of either
    End are also Accelerated.
  - “p” is the Pressure Difference from End to End.
  - “U” is Volume Velocity Owing through the Tube.


                        0l
   p  jM AU  j            U
                        S


                        Acoustics Chap 3 (Leo L. Beranek)                19
c) Acoustic Compliance, CA (m5/N)

 - Associated with a Closed Rigid-Wall Container
  of Fluid all of whose Dimensions are Small
  Compared to “” , the Enclosed Fluid is Compressed
  with Negligible Acceleration.
 - “p” is the Pressure Only to Compress the Volume “V”
 - “U” is the Instantaneous Volume Velocity Flowing
   into “V”


            U                          V
      p               Where C A 
           jC A                      0c 2



                        Acoustics Chap 3 (Leo L. Beranek)   20
d) Acoustic Compliance, RA (Nsec/m5)
 - Losses Due to the Viscous Flow of a Fluid through some Materials.

 - Acoustic Responsiveness
                1
         rA 
                RA
   p  RAU           (Impedance Type)
   U  rA p          (Mobility Type)

e) Acoustic Generator
         Constant Pressure                     Constant Volume Velocity




                        Acoustics Chap 3 (Leo L. Beranek)                 21
2) Transducer
   Transformation Type Element


                                                         Lorent Force
                                                         f  Bli
                                                         Faraday' s Law
                                                         e  Blv


                                                        a
                                                          b
                b   C:1       d                         c
                               +                        bc  d
            +
            a                  b                        a    2 g
            -                  -                          c
                                                        b      d
                    Acoustics Chap 3 (Leo L. Beranek)                     22
Acoustics Chap 3 (Leo L. Beranek)   23
Acoustics Chap 3 (Leo L. Beranek)   24
Acoustics Chap 3 (Leo L. Beranek)   25
Acoustics Chap 3 (Leo L. Beranek)   26
Acoustics Chap 3 (Leo L. Beranek)   27
Acoustics Chap 3 (Leo L. Beranek)   28
Acoustics Chap 3 (Leo L. Beranek)   29

								
To top