The equations governing the motion of a moving coil loudspeaker/microphone can be expressed as
F+Bil = m(d2x/dt2) + r(dx/dt) + (x/s)
F = PA
V - Bi(dx/dt) = L(di/dt) + Ri + e
x is the displacement of the microphone cone m
V is the applied voltage V
i is the current through the coil A
F is the external force N
P is Pressure Pa
m is the mass of the cone 10-4 kg
r is the resistance to motion 5 Nsm-1
s is the compliance of the cone 10-6 mN-1
is the length of the wire on the coil 10 m
L is the inductance of the coil 1 mH
B is the magnetic field 0.1 T
R is the electrical resistance of the coil 5 k
A is the area of the cone 10-4m2
e is the pickup noise V
a) The microphone is connected to an instrumentation amplifier with an input impedance of 5 k and a gain of 100dB. Given that the inputs are pressure and pickup noise and the output is the amplifier voltage derive either a pair of transfer functions OR a state space representation of the system.
b) Using Matlab determine the bode response if the system to both Pressure and electrical pickup noise. Comment critically on your results, explaining the major features of the plot.
c) Convert the system to a Simulink block and determine the rms amplitude of response to a sound wave of pressure 10-2 Pa at 200Hz. Compare the resultant with part b).
2) The microphone is used to measure the acoustic noise from an induction motor in an area of high electrical interference (50 Hz) and broadband white noise. The motor is running at 2400rpm and produces noise both at this frequency (fundamental) and at harmonics up to 600 Hz and is analysed using a PC.
a) Determine a suitable sampling frequency. Design a notch filter to remove the 50Hz component, paying particular attention to any assumptions you have made in the design.
b) Implement the filter in Matlab and determine the bode response of the system and comment on your results, particularly the width of the notch.
c) Implement the filter in Simulink and using a signal source containing both 50Hz and 55Hz of rms amplitudes 1 and 0.1 respectively. Determine the output of the filter and comment critically on your results.
3) The dataset en311_03.mat (available in the unit box) contains information on the pressure, noise level of the workshop in which the induction motor/microphone is placed.
a) Using both the microphone model and filter model implement a instrumentation system in Simulink to measure the rms voltage.
b) Modify the system such that an alarm is triggered if the rms voltage level from the microphone is twice that of the value in part a).
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