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Electrical Signal Feedback

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(a) It is found that if a microphone is brought into the proximity of a loudspeaker on a public address (P.A.) system, the system will `howl'. Carefully explain, making reference to feedback theory, why this is so.
(b) Suggest two actions that could be adopted to remedy the howling.
(c) Represent the howling system by a block diagram.
(d) Measurements show that for a particular arrangement of the equipment and at a particular amplifier setting, the system will howl if 1% of the output power is fed back to the microphone. Estimate the power gain of the P.A. amplifier in decibels.
(e) Analysis shows that the frequency at which the system howls; is 16 kHz and it is proposed to use a filter to attenuate all frequencies above 14 kHz. This is to be done using a simple RC filter. If the resistor in the filter has a value of 10 k, calculate a suitable value for the capacitor.