Final answer:
When an AM signal is passed through a filter that removes the lower sideband, the envelope detector output voltage can be represented as Vout = Aμ/2 + Aμ/4 cos(2ωmt) - Aμ/4 cos((2ωc + 2ωm)t). The ratio of the fundamental to the second harmonic in the output voltage is 1:1.
Step-by-step explanation:
When an AM signal is passed through a filter that removes the lower sideband, the resulting signal can be analyzed using an envelope detector. (a) The expression for the detector output voltage can be found by multiplying the original AM signal by the carrier wave and applying an envelope detector. The output voltage can be represented as Vout = Aμ/2 + Aμ/4 cos(2ωmt) - Aμ/4 cos((2ωc + 2ωm)t), where A is the amplitude of the carrier wave, μ is the modulation index, ωm is the angular frequency of the audio signal, and ωc is the angular frequency of the carrier wave.
(b) To determine the ratio of the fundamental to the second harmonic in the output voltage, we can examine the cosine terms in the expression for Vout. The fundamental frequency corresponds to the term Aμ/4 cos(2ωmt), while the second harmonic corresponds to the term Aμ/4 cos((2ωc + 2ωm)t). Therefore, the ratio of the fundamental to the second harmonic is Aμ/4 : Aμ/4 = 1 : 1.