# Figure of merit of FM

The block diagram of FM Receiver in the presence of noise is as follows The incoming signal at the front end of the receiver is an FM signal  got interfered by Additive noise , since the FM signal has a transmission band width ,the Band Pass filter characteristics are also considered over the band of interest i.e from to .

The output of Band Pass Filter is  is passed through a Discriminator for simplicity simple slope detector (discriminator followed by envelope detector) is used, the output of discriminator is  this signal is considered over a band of  by using a LPF .

The input noise to the BPF is n(t),  the  resultant output noise is band pass noise

phasor representation of Band pass noise is  where  and .

are orthogonal, independent and are Gaussian.

– follows a Rayleigh’s distribution and  is uniformly distributed over  are separate random processes.

substituting Equations (1), (3) in (2)

where .

now the analysis is being done from it’s phasor diagram/Noise triangle as follows is the resultant of two phasors  and .

since

because .

is the phase of the resultant signal  and when this signal is given to a discriminator results  an output.

i.e,

i.e,

As

the second term in the Equation  where  – denotes noise after demodulation.

this can be approximated to , which is a valid approximation. In this approximation  is Quadrature-phase noise with power spectral density  over

the power spectral density of  will be obtained from Equation (6) using Fourier transform property

,

elsewhere.

the power spectral density functions are drawn in the following figure , from Carson’s rule

the band width of v(t) has been restricted by passing it through a LPF. Now,

.

To calculate Figure of Merit

Calculation of :-

output Noise power

The output signal power is calculated from  tha is

From Equations(I) and (II)

Calculation of :-

input signal power

noise signal power

from Equations (III) and (IV)

Now the Figure of Merit of FM is

to match this with AM tone(single-tone) modulation is used i.e,  then the signal power   and

since for tone(single-tone) modulation .

when you compare single-tone FM with AM

.

the modulation index  will be beneficial in terms of noise cancellation, this is one of the reasons why we prefer WBFM over NBFM.     (3 votes, average: 4.00 out of 5) Loading... ## Author: vikramarka

Completed M.Tech in Digital Electronics and Communication Systems and currently working as a faculty.

Posted on Categories Analog Communications