Message frequency 20KHz,the peak voltage 20V is used to modulate a carrier signal of frequency 2MHz and peek voltage 40V.determine modulationindex and sideband produced?

To determine the modulation index, we first need to calculate the modulation depth, which is given by the formula:

Modulation Depth = (Peak Voltage of Message Signal) / (Peak Voltage of Carrier Signal)
Modulation Depth = 20V / 40V
Modulation Depth = 0.5

The modulation index is then given by the formula:

Modulation Index = Modulation Depth / 2
Modulation Index = 0.5 / 2
Modulation Index = 0.25

Next, we need to determine the sidebands produced. The sidebands are located at frequencies that are the sum and difference of the carrier frequency and the message frequency. In this case, the carrier frequency is 2MHz and the message frequency is 20KHz.

The sidebands are therefore located at frequencies of:

2MHz + 20KHz = 2.02MHz
2MHz - 20KHz = 1.98MHz

Therefore, the sidebands produced are at frequencies of 1.98MHz and 2.02MHz.

Modulation Index (m):

The modulation index is given by the ratio of peak modulating voltage to peak carrier voltage:

```
m = (20V) / (40V) = 0.5
```

Sidebands Produced:

Amplitude modulation (AM) produces two sidebands, one above and one below the carrier frequency. The frequencies of these sidebands are given by:

```
f_USB = f_c + f_m
f_LSB = f_c - f_m
```

where:

- f_USB is the frequency of the upper sideband
- f_LSB is the frequency of the lower sideband
- f_c is the carrier frequency
- f_m is the modulating frequency

In this case, the carrier frequency is 2MHz and the modulating frequency is 20KHz. Therefore, the sideband frequencies are:

```
f_USB = 2MHz + 20KHz = 2.02MHz
f_LSB = 2MHz - 20KHz = 1.98MHz
```