A message signal of frequency 20 KHz. and peak voltage of 3 volts is used to modulation a carrier of frequency 1 MHz . and peak voltage 30 volt .Determine the modulation index and the side bands.

To determine the modulation index and the sidebands for the given message signal and carrier signal, we need to understand a few key concepts in amplitude modulation (AM). The modulation index is a measure of the extent of modulation applied to the carrier wave, while the sidebands are the frequencies generated as a result of this modulation.

Understanding the Modulation Index

The modulation index (m) in amplitude modulation is defined as the ratio of the peak voltage of the message signal (Vm) to the peak voltage of the carrier signal (Vc). The formula for the modulation index is:

m = Vm / Vc

Given Values

• Peak voltage of the message signal (Vm) = 3 volts
• Peak voltage of the carrier signal (Vc) = 30 volts

Calculating the Modulation Index

Now, substituting the values into the formula:

m = 3 V / 30 V = 0.1

This means the modulation index is 0.1, indicating that the carrier wave is modulated to a relatively small extent by the message signal.

Identifying the Sidebands

In amplitude modulation, the modulation creates sidebands around the carrier frequency. The sidebands are located at frequencies that are the sum and difference of the carrier frequency and the message frequency. The formula for the sideband frequencies is:

Upper Sideband (USB) = fc + fm

Lower Sideband (LSB) = fc - fm

Given Frequencies

• Frequency of the message signal (fm) = 20 kHz = 20,000 Hz
• Frequency of the carrier signal (fc) = 1 MHz = 1,000,000 Hz

Calculating the Sidebands

Now, we can calculate the upper and lower sidebands:

USB = 1,000,000 Hz + 20,000 Hz = 1,020,000 Hz (or 1.02 MHz)

LSB = 1,000,000 Hz - 20,000 Hz = 980,000 Hz (or 0.98 MHz)

Summary of Results

To summarize, we have:

• Modulation Index (m) = 0.1
• Upper Sideband (USB) = 1.02 MHz
• Lower Sideband (LSB) = 0.98 MHz

This analysis shows how the modulation process works and how the sidebands are generated around the carrier frequency. Understanding these concepts is crucial for grasping the principles of amplitude modulation in communication systems.