# Analog Communication SNR Calculations - Analog Communication

## Find out the calculations of Signal to Noise Ratios?

In this chapter, let us calculate Signal to Noise Ratios and Figure of Merits of various modulated waves, which are demodulated at the receiver.

## Signal to Noise Ratio

Signal-to-Noise Ratio (SNR) is the ratio of the signal power to noise power. The ratio is usually measured in decibels used to calculate the ratio formulas. When the value of SNR becomes higher, then the quality of the output received will be greater.

## Figure of Merit

It is so because for a receiver, the channel is the input.

## SNR Calculations in AM System

Consider the following receiver model of AM system to analyze noise.
Where,

Assume the band pass noise is mixed with AM wave in the channel as shown in the above figure. This combination is applied at the input of AM demodulator. Hence, the input of AM demodulator is.

Where nI(t)nI(t) and nQ(t)nQ(t) are in phase and quadrature phase components of noise.
The output of AM demodulator is nothing but the envelope of the above signal.
Therefore, the Figure of merit of AM receiver is less than one.

## SNR Calculations in DSBSC System

Consider the following receiver model of DSBSC system to analyze noise.
We know that the DSBSC modulated wave is
Average power of DSBSC modulated wave is
Average power of noise in the message bandwidth is
Substitute, these values in channel SNR formula.
Assume the band pass noise is mixed with DSBSC modulated wave in the channel as shown in the above figure. This combination is applied as one of the input to the product modulator. Hence, the resultant input of this product modulator is
Average power of noise at the output is

## SNR Calculations in SSBSC System

Consider the following receiver model of SSBSC system to analyze noise.
We know that the SSBSC modulated wave having lower sideband is
Average power of SSBSC modulated wave is
Average power of noise in the message bandwidth is
Substitute, these values in channel SNR formula.
Assume the band pass noise is mixed with SSBSC modulated wave in the channel as shown in the above figure. This combination is applied as one of the input to the product modulator. Hence, the input of this product modulator is
The local oscillator generates the carrier signal c(t)=cos(2πfct)c(t)=cos⁡(2πfct). This signal is applied as another input to the product modulator. Therefore, the product modulator produces an output, which is the product of v1(t)v1(t) and c(t)c(t).
When the above signal is applied as an input to low pass filter, we will get the output of low pass filter as
Average power of the demodulated signal is
Average power of noise at the output is
When the above signal is applied as an input to low pass filter, we will get the output of low pass filter as
Average power of the demodulated signal is
Average power of noise at the output is
Substitute, these values in output SNR formula
Substitute, the values in Figure of merit of SSBSC receiver formula
Therefore, the Figure of merit of SSBSC receiver is 1.