A modulating wave has a peak value of 2 volts while the carrier wave equation for the voltage is 1.2 sin (20t + 15°).Determine the modulating index.
To determine the modulating index, we need to first find the peak value of the modulating wave.
The peak value of the modulating wave is given as 2 volts.
The formula for the modulating index is the ratio of the peak value of the modulating wave to the peak value of the carrier wave.
So, the modulating index (m) can be calculated as follows:
m = (Peak value of modulating wave) / (Peak value of carrier wave)
Since the peak value of the modulating wave is 2 volts, and the peak value of the carrier wave can be obtained from the given equation as 1.2, we can calculate the modulating index as:
m = 2 volts / 1.2 = 1.667
Therefore, the modulating index is 1.667.
To determine the modulating index, we need to compare the peak value of the modulating wave to the peak value of the carrier wave. The modulating index is calculated as the ratio of the peak value of the modulating wave to the peak value of the carrier wave.
Step 1: Find the peak value of the modulating wave.
The peak value of the modulating wave is given as 2 volts.
Step 2: Find the peak value of the carrier wave.
The peak value of a sin wave is simply the absolute value of the coefficient multiplying the sin function, which in this case is 1.2.
Step 3: Calculate the modulating index.
The modulating index (m) is given by the formula:
m = (peak value of modulating wave) / (peak value of carrier wave)
Using the values we found in steps 1 and 2, we can substitute them into the formula:
m = 2 / 1.2
By performing the calculation, we find that the modulating index is approximately 1.67.
Therefore, the modulating index for this scenario is 1.67.