A carrier is amplitude modulated with modulation index of 60% yielding transmitted power of 472 W. How much power can be saved by suppressing carrier and one sideband of the modulated signal?

Amplitude Modulation and Power Calculation

Problem Statement: A carrier signal is amplitude modulated with a modulation index of 60%, resulting in a transmitted power of 472 W. We are tasked with determining how much power can be saved by suppressing the carrier and one sideband of the modulated signal.

Solution:

To solve this problem, let us analyze the power distribution in an amplitude-modulated signal.

Step 1: Power Components in an Amplitude-Modulated Signal

In amplitude modulation (AM), the total transmitted power (P_t) consists of:

• Carrier power (P_c).
• Power in the two sidebands (P_USB and P_LSB), which are equal in magnitude.

The total transmitted power is given by:

P_t = P_c + P_USB + P_LSB

The power in each sideband is determined by the modulation index (m), and is given as:

P_USB = P_LSB = (m²/4) × P_c

Thus, the total transmitted power can be expressed as:

P_t = P_c (1 + m²/2)

Step 2: Calculate the Carrier Power (P_c)

From the problem, the modulation index (m) is 60%, or m = 0.6. The total transmitted power (P_t) is 472 W. Substituting these values into the formula for total transmitted power:

472 = P_c (1 + (0.6)²/2)

First, calculate (0.6)²/2:

(0.6)²/2 = 0.36/2 = 0.18

Now substitute this value into the equation:

472 = P_c (1 + 0.18)

472 = P_c × 1.18

P_c = 472 / 1.18

P_c ≈ 400 W

Thus, the carrier power is 400 W.

Step 3: Calculate the Sideband Power

The power in the sidebands is given by:

P_sidebands = P_USB + P_LSB = (m²/2) × P_c

Substitute m = 0.6 and P_c = 400 W:

P_sidebands = (0.6)²/2 × 400

P_sidebands = 0.36/2 × 400

P_sidebands = 0.18 × 400

P_sidebands = 72 W

The total power in the sidebands is 72 W, with each sideband contributing 36 W.

Step 4: Power Saved by Suppressing the Carrier and One Sideband

When the carrier and one sideband are suppressed, the remaining power is the power in the other sideband. Thus, the power saved is:

Power saved = P_t - P_remaining

The remaining power is the power in one sideband:

P_remaining = P_LSB or P_USB = 36 W

Substitute the values:

Power saved = 472 - 36

Power saved = 436 W

Final Answer: The power saved by suppressing the carrier and one sideband is 436 W.