Please answer the following questions.
(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.
This posting contains the solution to the given problems.
Electrical Engineering: Op-Amp
1. Show that gain rolls-off at -6 dB/octave for a passive LP filter.
2. (a) Write down the expression for the frequency-dependent open-loop gain of an operational amplifier. Sketch the magnitude of the open-loop gain of an operational amplifier as a function of frequency. Explain what is meant by a `single-lag' response of an op-amp.
(b) Using the example of a simple RC high-pass filter circuit, show how the inclusion of a coupling capacitor will limit the low frequency of any amplifier circuit.
(c) Derive the expression for the high-frequency closed-loop gain of a basic non-inverting amplifier (the feedback equation). Sketch the circuit of the amplifier to illustrate your derivation. What is the feedback fraction β for this circuit?