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Why the Synchronous detection of AM signals is considered as a disadvantage?

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Why the Synchronous detection of AM signals is considered as a disadvantage?

(a) Needs additional system for synchronization of carrier

(b) Receiver is available at cheap prices

(c) Needs less number of system as estimated for generation of carrier

(d) Receiver is not complex

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Query is from Frequency Domain Description in section Amplitude Modulation of Analog Communications

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Right answer is (a) Needs additional system for synchronization of carrier

The best explanation: Disadvantage of synchronous detection of AM signal are that it needs an additional system for generation of carrier. It also needs additional system for synchronization of carrier. Moreover receiver is complex and costly.

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