Power of an AM Signal

Power of an AM (Amplitude Modulated) Signal

1. Standard AM Signal Form

An AM signal is written as:

s(t) = A_c [1 + m cos(ω_m t)] cos(ω_c t)

Where:

• A_c = carrier amplitude
• m = modulation index (0 to 1)
• ω_c, ω_m = carrier and message frequencies

2. Total Power in AM Signal

The total transmitted power is:

P_total = P_c (1 + m²/2)

Where:

• P_c = A_c² / (2R)
• R = load resistance

3. Sideband Power

Total sideband power:

P_SB = P_c × (m² / 2)

Each sideband has:

P_USB = P_LSB = (P_c × m²) / 4

4. Key Observations

• Carrier consumes most power
• Efficiency depends on modulation index (m)
• Maximum efficiency at m = 1

5. Efficiency of AM

η = m² / (2 + m²)

Maximum efficiency = 33.33% at m = 1

6. Example

If P_c = 100 W and m = 0.8:

P_total = 100 (1 + 0.8² / 2) = 132 W

Summary

• Total power = Carrier + Sidebands
• P_total = P_c (1 + m²/2)
• Sidebands carry information
• Efficiency is low in standard AM