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.
Signal to Noise Ratio

Figure of Merit

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.
SNR Calculations in AM System
Amplitude modulated wave
Where,
ang 5(2)

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.

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.
output of AM demodulator
 Figure of merit of AM receiver
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.
SNR Calculations in DSBSC System
We know that the DSBSC modulated wave is
DSBSC modulated wave
Average power of DSBSC modulated wave is
Average power of DSBSC modulated wave
Average power of noise in the message bandwidth is
power of noise in the message bandwidth
Substitute, these values in channel SNR formula.
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
resultant input of this product modulator
ang 6(1)
Average power of demodulated signal
Average power of noise at the output is
Average power of noise at the output

SNR Calculations in SSBSC System

Consider the following receiver model of SSBSC system to analyze noise.
SNR Calculations in SSBSC System
We know that the SSBSC modulated wave having lower sideband is
SSBSC modulated wave having lower sideband
Average power of SSBSC modulated wave is
Average power of SSBSC modulated wave
Average power of noise in the message bandwidth is
Average power of noise in the message bandwidth
Substitute, these values in channel SNR formula.
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
 input of this product modulator
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).
product modulator produces an output,
When the above signal is applied as an input to low pass filter, we will get the output of low pass filter as
output of low pass filter
Average power of the demodulated signal is
Average power of the demodulated signal
Average power of noise at the output is
Average power of noise at the output
When the above signal is applied as an input to low pass filter, we will get the output of low pass filter as
d1(2)
Average power of the demodulated signal is
Average power of the demodulated signal
Average power of noise at the output is
Average power of noise at the output
Substitute, these values in output SNR formula
output SNR formula
Substitute, the values in Figure of merit of SSBSC receiver formula
Figure of merit of SSBSC receiver formula
Therefore, the Figure of merit of SSBSC receiver is 1.

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