Final answer:
In SSB+C, a much higher carrier amplitude is required compared to AM, resulting in higher transmitted power and consequently higher power loss due to the increased voltage, leading to lower power efficiency.
Step-by-step explanation:
To prove that the required carrier amplitude in Single Sideband with Carrier (SSB+C) is much larger than in Amplitude Modulation (AM), and consequently, the power efficiency of SSB+C is very low, we can consider the relationship between transmitted power and the efficiency of transmission.
In AM, the power used to transmit the signal (Ptransmitted) is a function of the current through the transmission wire (Itransmitted) squared multiplied by the resistance of the wire (Rwire) as shown by Ptransmitted = Itransmitted² Rwire. The power lost during transmission (Plost) is the product of the transmitted current and the transmitted voltage (Vtransmitted): Plost = Itransmitted Vtransmitted.
In SSB+C, the carrier amplitude must be high to enable the receiver to reconstruct the original signal accurately. A higher carrier amplitude means higher transmission power, which leads to a higher power lost during transmission because of the increased voltage. This, combined with a relatively fixed resistance of the wire, results in reduced power efficiency compared to traditional AM, which does not require as high of a carrier amplitude.