Analog Feedback Active Noise Control
0) Introduction to single channel feedback noise control
The system consists of a microphone sensor, a loudspeaker actuator, and an equalizer to correct for the delay from the speaker to the microphone and for the transfer function of the speaker itself. The microphone is usually placed close to the speaker. The system transfer function is increasingly difficult to equalize as the mic moves away from the speaker (the phase change goes from gradual over the bandwidth of interest to very rapid). A disturbance input at the sensor (low frequency acoustic noise) can be attenuated by the proper choice of equalization. The zone of silence around the sensor is approximately 1/10 th of the wavelength of the noise to be attenuated.
see Sections 7.3, 7.4 and 7.7 from Active Control of Sound, Nelson and Elliott and Section 6.2 from Active Noise Control Systems, Kuo and Morgan
1) Pick the problem
For example, reduce a 100 Hz tone by at least 10 dB in the vicinity of an error microphone
2) Assemble the HW needed
Noise generator to measure the system transfer function - use an analyzer with a built in source, buy, or build your own
Audio generator for acoustic disturbance noise source B&K Precision, $89
Electret microphone
Microphone preamp with single pole Butterworth high pass filter
Power amplifier, e.g. 12VDC, 50 W, low level input car amp, adjustable output
Actuator (loudspeaker) sized for application - e.g. 8 inch Radio Shack
Find freeware/shareware enclosure design SW on internet - e.g. for 100 Hz use enclosure with 35x17x4.5 inches ID, ¾ inch plywood, filled interior with glass wool
Data recording can be direct to sound card (watch out for DC offsets, remove these by subtracting the mean from each data vector) and PC OR to Teac Tascam DA-P1, two channel DAT recorder
2) Measure the plant
Send pink noise through power amp (gain set low) and loudspeaker
Record pink noise source and noise from mic preamp simultaneously
Use MATLAB or equivalent to get complex representation of system transfer function - must be complex to get phase info
Note that Nyquist plot of transfer function will show system instability
3) Equalize the plant
Chose biquad filter topology that will give you poles and zeros in LHP
Determine equalization needed for frequency of interest, i.e. phase shift is either around 0 degrees or 180 degrees
Poles need to placed at frequency of interest near vertical axis, closer gives higher gain at frequency of interest
Adjust zero locations to give desired minimum phase response
I used MATLAB zp2tf to obtain s domain coefficients
I then checked response with filter design equations
NOTE: Final circuit could utilize positive or negative feedback! Keep Nyquist response from circling 1 or -1 point on real axis
Chose R’s and C’s from filter design equations, i.e. match filter design equation coefficients with s domain coefficients
4) Close the loop
Remove noise source from circuit
Put equalizer after mic preamp and before power amp
Increase gain of power amp until instability is heard (low level, high frequency noise)
Measure zone of silence around residual error microphone with sound level meter