Envelope detection of amplitude-modulated (AM) signals For a simple diode (envelope) detector to recover the message correctly from an AM waveform, which spectral components must be present?

Introduction / Context:
An envelope detector tracks the amplitude of a passband signal to recover the baseband message. For the envelope to mirror the original modulation, the transmitted AM spectrum must include sufficient carrier amplitude and at least one sideband component.

Given Data / Assumptions:

• Simple diode detector followed by RC smoothing (no synchronous carrier recovery).
• Conventional full-carrier AM (DSB-LC) or single-sideband with carrier (SSB+C) can be envelope-detected if the carrier is strong enough.
• Suppressed-carrier systems require coherent detection instead.

Concept / Approach:

In DSB-LC, the transmitted waveform’s envelope equals the message (scaled) provided the modulation index is within limits and carrier is large relative to sidebands. Even SSB+C can be envelope detected because the residual carrier restores a detectable envelope. However, if the carrier is suppressed (as in SSB-SC or DSB-SC), an envelope detector fails because there is no stable amplitude reference.

Step-by-Step Solution:

Verification / Alternative check:

AM broadcast uses DSB-LC specifically to enable cheap envelope detectors in receivers.

Why Other Options Are Wrong:

(b) While both sidebands are used in DSB-LC, strictly one sideband is enough if the carrier is full—thus (a) is the minimum sufficient condition; (c) with suppressed carrier cannot be envelope detected; (d) a small fraction of carrier may fail under fading; (e) SSB-SC needs synchronous detection.

Common Pitfalls:

Assuming both sidebands are mandatory; forgetting that the carrier amplitude must be adequate to prevent envelope distortion.

Final Answer:

One sideband and a full-amplitude carrier