 Learning Objectives



Learning Objectives : After reading this chapter you should be able to :  define white noise and noise bandwidth  explain performance of amplitude modulation in presence of noise  define signal to noise ratio, noise figure and figure of merit.  explain performance of frequency and phase modulation in presence of noise  compare AM and FM in presence of noise  describe pre-emphasis and de-emphasis circuits

Table of Contents 1.

Mixing of Noise with Sinusoid

2.

White Noise

3.

Linear Filtering of Noise

4.

Noise Bandwidth

5.

Quadrature components of Noise

6.

Noise in Double sideband suppressed Carrier (DSB-SC) System

7.

Noise in Single sideband suppressed Carrier (SSB-SC) System

8.

Amplitude-Modulation System (Envelope Detector Method)

9.

Noise in FM Receivers

10.

Noise in FM System

11.

Pre-emphasis & De-emphasis circuit

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Analog Communication

1.

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Mixing of Noise with Sinusoid : In communication systems, noise may be mixed with (i.e., multiplied by) a deterministic sinusoidal waveform be 2f 0t . Then the product of this waveform with a spectral noise component is given by, a b nk (t ) cos 2f 0t  k cos 2 (k f  f 0 ) t  k sin 2 (k f  f 0 ) t 2 2 ak b  cos 2 (k f  f 0 ) t  k sin 2 (k f  f 0 ) t …… (i) 2 2 Thus the mixing gives rise to two noise spectral components, one at the sum frequency f 0  k f and one at the difference frequency f 0  k f . In addition, the amplitudes of each of the two noise spectral components generated by mixing has been reduced by a factor of 2 with respect to the original noise spectral component. Hence the variances (normalized power) of the two new noise components are smaller by a factor of 4. Accordingly, if the power spectral density of the original noise component at frequency k f is Gn (k f ) , then, from equation (i), the new components have spectral densities G (k f ) Gn (k f  f 0 )  Gn (k f  f 0 )  n ….. (ii) 4 In the limit as f  0 , we replace k f by the continuous variable f, and equation (ii) becomes G (f) Gn ( f  f 0 )  Gn ( f  f 0 )  n ….. (iii) 4 Given the power spectral density plot Gn ( f ) of a noise waveform n(t ) ,the power spectral density of

n(t ) cos 2f 0t is arrived at as follows : divide Gn ( f ) by 4, shift the divided plot to the left by amount f 0 , to the right by amount f 0 , and add the two shifted plots. 2.

White Noise : (i) Noise in an idealized form is known as white noise. The white noise contains all the frequency components in equal proportion. This is analogous with white light which is a superposition of all visible spectral components. (ii) The white noise has Gaussian distribution that means the probability distribution function (PDF) of white noise has the shape of Gaussian PDF. Therefore, it is also called as Gaussian noise.  (iii)The power spectral density (PSD) of a white noise is given by, S n ( f )  2

Fig. Power spectral density of white noise (iv) This equation shows that the PSD of white noise is independent of frequency. As  is constant, the PSD is uniform over the entire frequency range including the positive as well as the negative frequencies. (v) The best example of white noise is the Thermal noise or Johnson noise. (vi) Since the PSD of thermal and shot noise is independent of the operating frequencies, therefore, shot noise and thermal noise can be treated as white Gaussian noise for all practical purposes. (vii) The power spectral density and the auto correlation function form a Fourier transform pair i.e. FT R()  S( f )  GATE ACAD EMY PUB L ICATIONS  GATE ACAD EMY PUBL ICATIONS  GATE ACAD EMY PUBL ICATIONS  GATE ACAD EMY PUBL ICATIONS  Copyrights © All rights reserved by GATE ACADEMY PUBLICATIONS. No part of this booklet may be reproduced or utilized in any form without the written permission.

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Noise in AM & FM

  R()  F 1  S ( f )   F 1    () 2 2  () 2 (viii) The auto correlation function of the white noise contains a delta function scaled by a factor  / 2 and situated at   0 .

The auto correlation function for white noise is R() 

3.

Fig. Auto correlation function of white noise Linear Filtering of Noise : Filters are connected in order to reduce the noise power. Generally, these filters are narrowband filters which are designed to pass a specific range of frequencies. In order to minimize the noise power that is presented to the demodulator of a receiver, we introduce a filter before the demodulator as shown in figure. Thus, a filter is connected before a demodulator to reduce the noise power input. The bandwidth of the filter is made as narrow as possible so as to avoid transmitting any unnecessary noise to the demodulator.

Assumptions : (i) The input noise signal ni (t ) and the output noise signal be n0 (t ). (ii) The power spectral density of input noise signal be Si ( f ) and the power spectral density of the output noise signal be S0 ( f ) such that S0 ( f )  H ( f ) Si ( f ) . 2

(iii)The input noise is AWGN (Additive White Gaussian Noise), then the power spectral density at the filter input is given by Si ( f )   / 2 . R-C Low Pass Filter (LPF) : The RC low pass filter and variation of its transfer function with frequency are as shown in figure (a) and (b) respectively.

H ( f ) is the transfer function of the filter and f c is its cut-off frequency. The transfer function of the RC low pass filter (LPF) is given by, 1 H( f )  1  j( f / fc )

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Then,

 1   1 S0 ( f )  H ( f ) Si ( f )     2 1  j( f / fc ) 2 2 1  ( f / f c )  2

The noise power at the filter output Pn is 

Pn 







Sno ( f ) df 



f c2  1  df   1  ( f / fc )2  fc2  f 2 df 2  2  

  f    Pn   f c  tan 1      f 2  f c    2  With white noise input of power spectral density

     2  2 

a

2

1 1 x  tan 1   2 x a a

 / 2 , the noise output of the filter is

 f c 2 The above expression illustrates that the output noise power can be reduced by reducing the value of the cut-off frequency f c . Pn 

4.

Noise Bandwidth : Consider that white noise is present at the input to a receiver and a filter with transfer function H ( f ) centered at f 0 such as indicated by the solid plot of below figure, is being used to restrict the noise power actually passed on to the receiver. Now contemplate a rectangular filter as shown by the dotted plot in below figure. This filter is also centered at f 0 . Let the rectangular filter bandwidth Bn be adjusted so that the real filter and the rectangular filter transmit the same noise power. Then the bandwidth Bn is called the noise bandwidth of the real filter. The noise bandwidth is the bandwidth of an idealized (rectangular) filter which passes the same noise power as does the real filter.

Equivalent noise bandwidth may be defined as the bandwidth of an ideal band pass system which produces the same noise power as the actual system does. We illustrate the concept of noise bandwidth by considering the case of the low-pass RC filter with transfer 1 1 function H ( f )  , where the 3-dB bandwidth f c  . For this filter, H ( f ) attains its 2RC 1  j( f / fc ) maximum at f  0 . The noise equivalent bandwidth may be obtained by replacing the arbitrary low pass filter of transfer function H ( f ) by an equivalent ideal low pass filter having zero-frequency response H (0) and bandwidth BN .

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Noise in AM & FM

If the input white noise to the filter has power spectral density Sni ( f )   / 2 and the power spectral density of the output noise is Sno ( f ) , then Sno ( f )  | H ( f ) |2 S ni ( f ) 

 | H ( f ) |2 2

The noise power at the filter output Pn is 







  Pn   Sno ( f ) df   | H ( f ) |2 df   2 | H ( f ) |2 df    | H ( f ) |2 df 2  2 0  0

…..(i)

The same white noise source is connected to the input of an ideal low-pass filter (LPF). This ideal lowpass filter (LPF) has zero frequency response H (0) and bandwidth BN . Pn  BN H (0)

2

…..(ii)

The filtered noise power Pn is a finite value. It is also proportional to the bandwidth BN . From (i) and (ii), the noise-equivalent bandwidth for a low-pass filter (LPF) is given by 

Noise equivalent bandwidth, BN  5.

 H( f )

2

0

H (0)

2

df 



1 2 H (0)

2

 H ( )

2

d

0

Quadrature components of Noise : (i) After modulation, a baseband signal is converted to a modulated signal with a bandpass spectrum. During transmission through the channel, the modulated (bandpass) signal gets corrupt by wideband noise. The noise is often assume to be additive with a flat PSD (Additive White Gaussian Noise). (ii) At the receiver, the signal is first filtered to remove the out-of-band noise. Hence, the output of the bandpass filter is the (useful) modulated signal contaminated by bandpass noise. (iii)We assume that the centre frequency to the filter is equal to the carrier frequency f c and the bandwidth of the filter is equal to the signal bandwidth. (iv) As seen from figure, the modulated signal gets through (ideal) bandpass filter unaltered, while the wideband noise at the filter input results in bandpass noise.

(v) The bandpass noise is modelled as a sinusoid with random time-varying amplitude and phase. n(t )  A(t ) cos[2f ct  (t )] Where A(t ) and (t ) are the randomly-varying envelope and phase of the bandpass noise n(t ) , therefore, the bandpass noise, has the characteristics of both amplitude and angle modulation.  GATE ACAD EMY PUB L ICATIONS  GATE ACAD EMY PUBL ICATIONS  GATE ACAD EMY PUBL ICATIONS  GATE ACAD EMY PUBL ICATIONS  Copyrights © All rights reserved by GATE ACADEMY PUBLICATIONS. No part of this booklet may be reproduced or utilized in any form without the written permission.

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n(t )  A(t ) cos (t ) cos 2f ct  A(t )sin (t )sin 2f ct

n(t )  nc ( t )cos 2f c t  ns (t )sin 2f c t Where,

…..(i)

nc (t )  A(t ) cos (t )  nI (t ) is the in-phase or I-component ns (t )  A(t ) sin (t )  nQ (t ) is the quadrature-phase or Q-component

(vi) This equation is called as quadrature component representation due to the presence of sine and cosine terms which are in quadrature (90°) relation with each other. (vii) Both nc (t ) and ns (t ) are low pass signals, each bandlimited to f m Hz, and the powers (mean-square values) of n(t ), nc (t ) and ns (t ) are identical.

n2 ( t )  nc2 ( t )  ns2 ( t ) (viii) Furthermore, both nc (t ) and ns (t ) have the same power spectrum density, which is related to the power spectrum density, S0 ( f ) of the bandpass noise as :

Snc ( f )  Sns ( f )  S0 ( f  f c )  S0 ( f  f c ) (ix) Another important property of nc (t ) and ns (t ) is that they are uncorrelated with each other.

E nc (t ) ns (t )  0 Phasor Diagram of the Quadrature Representation of Noise The quadrature representation of noise expressed by equation (i) i.e. n(t )  nc (t ) cos 2f ct  ns (t )sin 2f ct can be represented using the phasor diagram representation as shown in figure. The amplitude of the in phase (cosine) component is nc (t ) and that of the quadrature (sine) component is

ns (t ) . The resultant of the two phasors is expressed as, r (t )  nc2 (t )  ns2 (t )

 n (t )  And the angle  (t ) is given by, (t )  tan 1  s   nc (t ) 

6.

Fig. Phasor diagram of the quadrature representation of noise The quadrature representation is generally useful in the analysis of noise and the phasor interpretation is useful in the discussion of the angle modulation communication systems. Noise in Double sideband suppressed Carrier (DSB-SC) System : The DSB-SC system uses coherent or synchronous detection scheme at the receiver. Figure shows the block diagram of DSB-SC system from noise point of view.

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Noise in AM & FM

The performance of a DSB-SC system is judged by its figure of merit  . S /N  0 0 S i /N i Where,

S0  Output signal power, N 0  Output noise power

Si  Input signal power at the detector, N i  Input noise power at the detector 6.1 Input Signal Power : The modulated (DSB-SC) signal at the input of the demodulator is given as s(t )  m(t ) cos ct , where m(t ) is the modulating signal and cos ct is the carrier signal. Thus, the input signal power Si is given as the mean square value of signal s(t )  m(t ) cos ct . Hence, 1 2 …..(i) Si   m(t ) cos c t   m 2 (t ) 2 6.2 Output Signal Power : In synchronous detection method, the incoming DSB-SC signal at the detector input is multiplied by a synchronous carrier cos ct . Thus, the signal at the multiplier output is 1 1 1 e(t )  m(t ) cos ct  cos ct  m(t ) cos 2 ct  m(t ) 1  cos 2ct   m(t )  m(t ) cos 2ct 2 2 2 This signal is finally passed through the low pass filter (LPF). Thus the signal at the demodulator output is s0 (t ) 

1 m(t ) 2

Therefore, the output signal power at the demodulator is given as 2

1 1  S0   m(t )   m2 (t ) 2 4  

From (i) and (ii),

…..(ii)

S0 m2 (t ) / 4 1   Si m2 (t ) / 2 2

6.3 Input Noise Power : The noise at the input of the receiver is white and Gaussian in nature. This noise after passing through the band-pass filter (BPF) is converted into a band-pass noise.

Fig. Input noise spectral density

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Analog Communication

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Above figure represents power spectrum density of the band-pass white noise at the input of demodulator. Therefore, the input noise power N i at the input of demodulator is given as  …..(iii) N i   2 f m  f m 2 From (i) and (iii), the input signal to noise ratio is given by,

Si m2 (t ) …..(iv)  Ni 2f m 6.4 Output Noise Power : The input noise n(t ) is applied to the band pass filter which produces spectral density S1 ( f ) having bandwidth 2 f m same as Sni ( f ) . The signal is then multiplied by synchronous carrier signal cos ct in synchronous demodulator and produces spectral density S 2 ( f ) . When a noise spectral density S1 ( f ) at frequency f is multiplied by cos 2f ct , the original noise component is replaced by two components, one at a frequency f  f c and one at frequency f  f c .

Fig. Noise spectral density at the input of the multiplier

Therefore, spectral density is, S2 ( f ) 

S1 ( f  f c )  S1 ( f  f c ) 4

Fig. Noise spectral density at the output of the multiplier This signal is then applied to a baseband low pass filter. Finally, the noise transmitted has the spectral density Sno ( f ) .

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Fig. Noise spectral density at the output of low pass filter Total noise power N = White noise power spectrum density  Bandwidth f  N 0   2f m  m 4 2 From (iv) and (v), the output signal to noise ratio is given by,

S0 m2 (t ) / 4 m2 (t )   N0 f m / 2 2f m N f / 2 1 From (iii) and (iv), 0  m  Ni f m 2 From equations (iv) and (vi), the figure of merit  for DSB-SC system is 

…..(v)

…..(vi)

S0 /N 0 m 2 (t ) 2f m   S i /N i 2f m m 2 (t )

S0 S S  i  i N 0 N i f m Noise in Single sideband suppressed Carrier (SSB-SC) System : The receiver of an SSB-SC system is similar to that for DSB-SC system for synchronous detection except for the fact that the bandwidth of the band-pass filter of SSB-SC receiver is one half of that required for DSB-SC. 

7.

Noise in AM & FM

FOM DSB  SC   DSB  SC  1 or

Fig. Noise performance of SSB The performance of a SSB-SC system is judged by its figure of merit  . S /N  0 0 S i /N i S0  Output signal power, N 0  Output noise power Where,

Si  Input signal power at the detector, N i  Input noise power at the detector 7.1 Input Signal Power : The incoming signal to the SSB-SC receiver may be expressed as s(t ) SSB  m(t ) cos ct  mh (t )sin ct . Here the plus sign is for upper sideband and minus sign is for lower sideband, m(t ) is the message signal and mh (t ) is its Hilbert transform. The signal power available at the input of the demodulator is 1 1 Si  m2 (t )  m 2 h (t )  m 2 (t ) …..(i) 2 2 At this point, it may be noted that the average power of the baseband signal m(t ) is same as that of its Hilbert transform. This is due to the fact that mh (t ) is basically the signal m(t ) in which all the frequency components undergo a phase shift of  /2 . Hence, m(t ) and mh (t ) occupy the same spectral range i.e., m . Moreover, the power spectrum density of m(t ) and mh (t ) are the same. This means that the average power of the message or baseband signal and its Hilbert transform are the same. 7.2 Output Signal Power :

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Since, the incoming signal is multiplied by a synchronous local carrier cos wct , therefor the output will be e(t )  m(t )cos ct  mh (t )sin ct  cos ct  m(t )cos2 ct  mh (t )sin ct cos ct 1 1 m(t ) 1  cos 2ct   mh (t ) sin 2ct  2 2 This signal is finally passed through the low-pass filter (LPF) which rejects all the terms excepting the 1 term which occupies a bandwidth m . Hence, the final demodulated output signal is s0 (t )  m(t ) . 2 Therefore, the output signal power of the demodulator is 1 …..(ii) S0  m 2 (t ) 4 From (i) and (ii), e(t ) 

S0 m 2 (t ) / 4 1   Si 4 m 2 (t )

7.3 Input Noise Power : The noise at the input of the receiver is white and Gaussian in nature. This noise after passing through the band-pass filter (BPF) is converted into a band-pass noise.

Fig. Input noise spectral density Above figure represents power spectrum density of the band-pass white noise at the input of demodulator. Therefore, the input noise power Ni at the input of demodulator is given as  N i   2 f m  f m …..(iii) 2 From (i) and (iii), the input signal to noise ratio is given by,

Si S m2 (t ) …..(iv)  i  Ni f m f m 7.4 Output Noise Power : The input noise n(t ) is applied to the band pass filter which produces spectral density S1 ( f ) having bandwidth f m for SSB-SC (upper sideband). The signal is then multiplied by synchronous carrier signal cos ct in synchronous demodulator and produces spectral density S 2 ( f ) . When a noise spectral density S1 ( f ) at frequency f is multiplied by cos 2fc t , the original noise component is replaced by two components, one at a frequency f  f c and one at frequency f  f c .

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Noise in AM & FM

Fig. Noise spectral density at the input of the multiplier

Therefore, spectral density is, S ( f  f c )  S1 ( f  f c ) S2 ( f )  1 4

Fig. Noise spectral density at the output of the multiplier This signal is then applied to a baseband low pass filter. Finally, the noise transmitted has the spectral density Sno ( f ) .

Fig. Noise spectral density at the output of low pass filter Total noise power N = White noise power spectrum density  Bandwidth f  N 0   2f m  m 8 4 N 0 f m / 4 1   From (iii) and (v), Ni f m 4 From (ii) and (v), the output signal to noise ratio is given by,

S0 m2 (t ) / 4 m2 (t )   N0 f m / 4 f m From equations (iv) and (vi), the figure of merit  for SSB-SC system is

…..(v)

…..(vi)

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Analog Communication



S0 /N 0 m 2 (t ) f m   S i /N i f m m 2 (t )

S0 S S  i  i N 0 N i f m Amplitude-Modulation System (Envelope Detector Method) : 

8.

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FOM SSB  SC   SSB  SC  1 or

The performance of a AM system is judged by its figure of merit  . S /N  0 0 S i /N i Where, S0  Output signal power, N 0  Output noise power

Si  Input signal power at the detector, N i  Input noise power at the detector 8.1 Input Signal Power : In amplitude modulation system, a large carrier is accompanied with the two upper and lower sidebands. Now, if ni (t ) is the additive noise signal, then the input to the detector is expressed as

s(t ) AM   Ac  m(t ) cos ct  ni (t )

The input signal power Si is given as, Si 

1 2 Ac  m 2 (t )    2

…..(i) …..(ii)

8.2 Output Power : The output of the envelope detector (popularly used in AM receivers) will be the envelope of the AM signal s(t ) AM . Thus, to find the detected output we are required to find the envelope of s(t ) AM . Substituting band pass noise model for ni (t ) in equation (i), we get

s(t ) AM   Ac  m(t ) cos ct  nc (t )cos ct  ns (t )sin ct

s(t ) AM   Ac  m(t )  nc (t ) cos ct  ns (t )sin ct s(t ) AM  A(t )cos ct  (t )

where A(t ) and (t ) respectively, are randomly time varying amplitude and phase angle of s(t ) AM . These are given as   ns (t ) 2 (t )  tan 1  A(t )   Ac  m(t )  nc (t )  ns2 (t )   Ac  m(t )  nc (t )  The time varying amplitude A(t ) is the envelope of s(t ) AM and therefore, the output of the envelope detector will be envelope A(t ) . The envelope A(t ) has both, signal and noise components. The noise performance depends on the relative magnitudes of the signal and noise. In small noise case, noise is taken to be much smaller than signal, i.e. ni (t )   A  m(t ) A phasor-representation of envelope A(t ) is shown in below figure. The noise component nc (t ) is shown to be in phase with signal  A  m(t ) , whereas, ns (t ) is in phase quadrature. Now, since

ni (t )   A  m(t ) , the noise component ns (t ) is also much smaller than  A  m(t ) .

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Noise in AM & FM

Fig. Phasor diagram of the envelope A(t) It is clear from the phasor diagram that if ns (t ) is much smaller, then (t ) is also much smaller and may be assumed to be zero, When ns (t )  0 , the envelope A(t ) becomes, A(t )  A  m(t )  nc (t ) Therefore, the output of the envelope detector contains a useful (modulating) signal x(t ) and a noise component nc (t ) . The carrier amplitude carries no useful information. The signal power S 0 and the noise power N 0 , at the output of the detector, may be as follows : Output Signal Power : It is the mean square value of useful signal m(t ) .

S0  m2 (t ) …..(iii) Output Noise Power : As the noise signal n0 (t ) at the output of the detector is nc (t ) with the power spectrum density given as Sn 0 ( f )  Snc ( f ) The AM system contains both sidebands. Thus, Sn 0 ( f )  Snc ( f )   The output noise power is given by, N0  Sn 0 ( f )  BW   2 f m  2f m …..(iv) The figure of merit  is obtained as S0 /N0 m2 (t ) / (2f m ) m2 (t )   Si /Ni 1  A 2  m2 (t )  / (f ) Ac2  m2 (t ) c m  2 For single tone sinusoidal modulation : Am2 2  m (t )   m(t )  Am cos mt 2 A Modulation index in AM, ma  m   Ac 

SNRo ma2 2   SNRi 2  ma2 2   2 Threshold Effect in AM Detection 

9.

Am2 / 2  2 Ac  Am2 / 2

 AM 

Definition : Threshold is defined as the value of the signal-to-noise ratio at the input of the detector below which the output signal-to-noise ratio deteriorates much more rapidly than the input signal-to-noise ratio. As a result, the loss of information signal contents in an AM detector due to the presence of the large noise is referred to as the threshold effect. (i) When the input noise increases beyond threshold level, the signal quality at the output deteriorates quite rapidly. (ii) Whenever the carrier signal power to noise power ratio approaches unity or less than unity in an AM detector, the threshold effect starts. (iii)For example, when output S/N is on the order of 10 dB or less, threshold effect occurs (iv) When the noise is small compared to the signal, the output S/N performance of the AM envelope detector is identical to that of synchronous detector.

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For a signal with reasonable quality in the presence of large noise, output S/N should be on the order of 30 dB. In practical AM communication systems, threshold is not a limiting condition for satisfactory operation. 10.

Noise in FM Receivers : (i) The receiver model of an FM receiver is shown in below figure.

(ii) The noise (t ) is a white Gaussian noise with zero mean value. Its power spectral density is /2 . (iii) s (t ) represents the received FM signal having a carrier frequency f c and transmission bandwidth BT . We assume that almost all the transmitted power lies inside the frequency band f c  ( BT / 2) .

11.

(iv) Band-pass filter : The band-pass filter has a mid-frequency f c and bandwidth BT . This is necessary in order to pass the FM signal without any distortion. (v) Noise : Since BT is small as compared to f c , it is possible for us to use the narrowband representation for n(t ) . Note that n(t ) represents the filtered version of the received noise to (t ) . We can represent n(t ) in the form of in-phase and quadrature components nI (t ) and nQ (t ) respectively. (vi) Limiter : In FM, only the carrier frequency is changed and the amplitude of the FM wave is supposed to remain constant. But due to noise added to the FM wave, its amplitude changes. To avoid this from happening, an amplitude limiter is connected after the band-pass filter. (vii) Discriminator : The FM discriminator consists of two parts namely a slope network having a purely reactive transfer function and an envelope detector. Both these parts are implemented as integral parts of a single unit. (viii) Post detection low pass filter : A post detection low pass filter is connected after the discriminator. It is named as baseband low pass filter. The bandwidth of this filter is just large enough to pass the highest frequency component of the message signal. This filter will remove all the out of band frequency components and noise, present in the discriminator output. This is necessary to minimize the effects of noise on the output. Noise in FM System : The output of the band-pass filter of FM receiver consists of the filtered component n(t ) of the input noise (t ) .

Fig. Noise model of FM receiver drawn partially The filtered noise n(t ) can be expressed in terms of the in phase and quadrature component as n(t )  nI (t ) cos(2f ct )  nQ (t )sin(2f ct ) It is possible to express n(t ) in terms of its envelope and phase as follows : n(t )  r (t ) cos[2f ct  (t )] where the envelope and the phase are given by,

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Noise in AM & FM 1/2

1/2

r (t )  n (t )  n (t )  2 I

2 Q

 nQ (t )  and  (t )  tan    nI (t )  1

The FM wave at the input is given by, t   s(t )  Ac cos  2f ct  2k f  m(t ) dt   Ac cos  2f ct  (t ) 0   The noisy signal at the band-pass filter output is given by, x(t )  s(t )  n(t )  Ac cos 2fct  (t )  r (t )cos 2fct  (t )

x(t )  Ac cos  2fct  (t )  r (t )cos 2f ct  (t )  (t )  (t )

x(t )  Ac cos  2fct  (t )  r (t )cos 2fct  (t ) cos (t )  (t )  r (t )sin 2f ct  (t ) sin (t )  (t )

x(t )   Ac  r (t ) cos  (t )  (t )  cos  2f ct  (t )   r (t )sin (t )  (t )  sin  2f ct  (t ) 



Where,

  B  A cos  2f ct  (t )  B sin  2f ct  (t )  A2  B 2 cos 2f ct  (t )  tan 1     A     r (t )sin  (t )  (t )   x(t )  M cos  2f ct  (t )  tan 1    M cos  2f ct  (t )   Ac  r (t ) cos (t )  (t )   M

A

c

 r (t ) cos  (t )  (t )   r (t ) sin (t )  (t )   2

 oa  ab 

2

 (bc) 2

x(t ) can be represented by a phasor diagram as shown in below figure.

Note that the signal term Ac is being used as a reference. The resultant phasor x(t ) has a phase (t ) . It can be obtained from the phasor diagram of as,  r (t ) sin  (t )  (t )   (t )  (t )  tan 1     Ac  r (t ) cos  (t )  (t )   Expression for Noise in the Detector Output : If the discriminator is ideal, then it acts as a pure differentiator. Hence, its output is proportional to  '(t ) / 2 where  '(t ) is the time derivative of input (t ) . To simplify the analysis assume that the carrier to noise ratio at the discriminator input is large, compared to unity. Also assume that the expression for (t ) can be simplified as follows : r (t ) (t )  (t )  sin  (t )  (t )  Ac t



r (t ) (t )  2k f  m() d   sin  (t )  (t )  Ac 0

The output of an ideal discriminator is given by, v(t ) 

v(t )  

t

(t )  2k f  m() d  0

1 d (t ) 2 dt

t  1 d  r (t ) 2  k sin (t )  (t )  f  m() d   2 dt  Ac 0 

v(t )  k f m(t )  nd (t )

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Where nd (t ) represents the noise term and it is given by, 1 d nd (t )  r (t ) sin (t )  (t ) 2Ac dt If the carrier to noise ratio is high, the expression for nd (t ) can be simplified as follows nd (t ) 

1 d r (t ) sin (t ) 2Ac dt

But r (t )sin (t )  nQ (t ) i.e. the quadrature component of the filtered noise n(t ) . 

nd (t ) 

1 d nQ (t ) 2Ac dt

This expression shows that the additive noise nd (t ) which appears in the discriminator output is dependent only on carrier amplitude Ac and the quadrature component nQ (t ) of the narrow band noise n(t ) . Output Signal to Noise Ratio : It is the ratio of average output signal power to the average output noise power. The discriminator output is given by, v(t )  k f m(t )  nd (t ) . Hence the message component in the output of the discriminator output and hence in the low pass filter output is equal to k f m(t ) . So the average signal power is equal to k 2f P , where P represents the average power of message signal m(t ) .  Average signal power  k 2f P

New let us obtain the average noise power at the output of the discriminator.  d nQ (t )  j 2f 1 d nQ (t ) 1 nd (t )   FT  nd (t )  FT  FT nQ (t )   2Ac dt 2Ac  dt  2Ac Therefore the relation between the power spectral density of nd (t ) i.e. S Nd ( f ) and the power spectral density of the quadrature component nQ (t ) i.e. S NQ ( f ) is

S Nd ( f ) 

f2 S NQ ( f ) Ac2

Assume that the band-pass filter in the FM receiver model has an ideal frequency response, with mid-band frequency f c and the bandwidth BT . Therefore, the quadrature component nQ (t ) or n(t ) exhibits the ideal low pass characteristics as shown in figure (a). The power spectral density of nd (t ) is shown in figure (b) and given mathematically as, BT   2  0 elsewhere   In the noisy FM receiver model a low pass filter is connected at the output of the frequency discriminator. The bandwidth of this filter is equal to the message bandwidth W. If the type of FM is wideband FM, then W  BT / 2 , where BT is the transmission bandwidth of FM signal. This filter will reject all the out of S Nd ( f ) 

f 2 Ac2

f 

band components (components outside the band W  f  W ) of nd (t ) . Hence the power spectral density of the output noise n0 (t ) appearing at the receiver output is given by,

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f 2 Ac2

0

Noise in AM & FM

 f  fm   otherwhere 

The power spectral density S N 0 ( f ) has been shown in figure (c).

The average noise power in the output is obtained by integrating the power spectral density from  f m to

f m as follows :  Average output noise power   S N 0 ( f ) df  2 Ac  fm fm

fm



 fm

fm

  f3 2 3 fm f df  2    3 Ac2 Ac  3   f m 2

The average output noise power is inversely proportional to average carrier power Ac2 / 2 . Therefore with increase in carrier power the output noise will reduce. The output signal to noise ratio is given by, k 2f P Average output signal power SNR0   Average output noise power 2f m3 / 3 Ac2 

SNR0 

3 Ac2 k 2f P 2f m3

Channel Signal to Noise Ratio ( SNRi ) : The average power in the FM wave s (t ) is Ac2 / 2 . The average noise power in the message bandwidth is

f m . Hence the channel signal to noise ratio is given by, Ac2 SNRi  SNR0  2f m 2 2 SNR0 3 Ac k f P 2 f m   2 Figure of Merit :   SNRi 2f m3 Ac

2

SNR0 3 k f P FOM FM   FM    SNRi f m2 Noise Performance of a Single Tone FM : The modulating signal is sinusoidal for the single tone FM, The frequency modulated wave with single tone FM is as follow :

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t     f s(t )  Ac cos 2f ct  sin(2f mt )   Ac cos 2f ct  2k f  m() d   fm   0   f  2f m cos(2f mt )  2k f m(t ) On equating and differentiating, fm f  m(t )  cos(2f mt ) kf

This shows that the amplitude of message signal m(t ) is Am 

f . So the average power of the message kf

Am2 (f ) 2  signal-developed across a 1  resistor is, P  2 2 k 2f The output signal to noise ratio for the output signal to noise ratio is given by, 3 A2 k 2 P 3 A2 (f ) 2 3 A2 (m ) 2 SNR0  c f 3  c 3  c f 2f m 4f m 4f m f Where m f  is the modulation index. W Figure of merit : 2 2 SNR0 3 Ac (m f ) 2f m    2 SNRi 4f m Ac

12.

3 3 FOM FM   FM  (m f )2  ()2 2 2 Thus the figure of merit is directly proportional to the square of modulation index. Threshold Effect in Angle Modulation Definition : In FM receiver, with the increase of the input noise power (decrease of carrier S/N ratio), initially some sound clicks are heard in the receiver output. As the carrier S/N ratio is further decreased, the clicks rapidly merge into a crackling or sputtering sound. This phenomenon is known as the threshold effect. (i) Threshold effect is of grave concern in angle-modulation systems. (ii) Experimentally it has been observed that occasional clicks are heard in the receiver output at a carrier S/N ratio of about 13 dB. (iii)An increase in the average number of clicks per second tends to decrease the output S/N more rapidly just below the threshold value. Definition of Threshold Value The threshold value is defined as the minimum carrier S/N ratio which yields an improvement in the performance of FM system from that of small noise power. (i) The threshold value depends on the modulation index. (ii) Larger value of mf or mp (For FM or PM) results in impoved performance above the threshold. (iii)Higher signal power will be required if the system is to operate above the threshold. Note : Bandwidth and S/N cannot be traded for improved performance indefinitely. System performance may even deteriorate with larger values of modulation index if transmitted power is not appropriately increased.

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Noise in AM & FM

In low-power applications, it is possible to lower the value of predetection S/N at which threshold occurs in FM systems. For example, by using PLL technique of FM demodulation, threshold can be lowered by about 2 dB (particularly important in low-power digital applications such as satellite communications). By using feedback demodulation technique, threshold level can be lowered by as much as 7 dB. 13.

Nonlinear Effects in FM Systems : (i) When a FM signal is transmitted through a nonlinear channel, the output consists of a dc component plus multiple frequency-modulated signals n/c, where n is 1, 2, 3.... (ii) Thus, an FM signal is affected by a communications channel with amplitude nonlinearities. (iii)Another nonlinear effect which is dominant in FM systems is due to the presence of phase nonlinearities. (iv) An FM signal may pick up spurious amplitude variations due to external noise and interference during transmission. (v) When such an FM signal is passed through a repeater or amplifier, the output may contain undesired phase modulation. (vi) This results into considerable distortion.

The distortion must be kept low by designing the value of AM-to-PM conversion constant which may be interpreted as the peak phase change at the output for a 1 dB change in envelope at the input below 2 degrees per dB. 14.

Effect of Noise : (i) When the signal level at the FM/PM demodulator input decreases, the phase of the demodulator input indicates that the information signal contains a lot of noise. (ii) When the signal power and noise power at the input of the demodulator are of the same order of magnitude, then the variations of the noise phase cause comparable variations of the resultant signal. (iii)If the noise spike is present, then the demodulation of FM signal becomes difficult. (iv) If the duration of the noise spike or spacing between two adjacent noise spikes is of significant value, then the demodulation of FM signal becomes extremely difficult. (v) These noise spikes can be heard as clicking or crackling sound in voice communication using FM or PM. (vi) When the carrier S/N is high, an increase in the transmission bandwidth provides a corresponding increase in the output S/N, also called figure of merit of the FM system. (vii)The FM does provide a practical trade-off between the transmission bandwidth and the noise performance.

15.

Noise Reduction (i) When white noise is present at the input to the FM demodulator, the spectral density of the noise output is quite high.

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(ii) A uniform noise spectral density at the input gives rise to a uniform output-noise spectral density. (iii)The spectral density of the noise at the output of an FM demodulator increases with the square of the frequency. (iv) To keep the signal level above the noise at low frequencies, a pre-emphasis circuit is necessary prior to the frequency modulator. (v) The improvement in S/N which results from pre-emphasis depends on the frequency dependence of the power spectral density of the modulating signal. (vi) A de-emphasis circuit at the FM receiver is the most effective in suppressing noise if its response falls with increasing frequency. (vii)Since the spectral density of the audio signal is smallest precisely where the spectral density of the noise is greatest. (viii)An audio signal usually has the characteristics that its power spectral density is relatively high in the low-frequency range and falls off rapidly at the higher frequency. Experimentally it is established that the FM system exhibits a threshold. For larger  f threshold S/N is also higher. The output S/N can be improved by reducing transmission bandwidth. (ix) In angle-modulation systems, S/N can be increased by increasing the modulator sensitivity ( k f for FM and k p for PM) without the necessity of increasing the transmitter power. (x) However, this will also increase the transmission bandwidth. (xi) Thus, it is possible to trade off bandwidth for S/N in angle-modulation systems.

Wideband frequency modulation (WBFM) systems are used in most of the low-power applications such as in space communications.

16.

Capture Effect in FM Receivers (i) FM receivers have the ability to differentiate between two signals received at the same frequency. (ii) If two FM radio stations are received simultaneously at the same frequency, the receiver locks onto the stronger FM radio station while suppressing the weaker FM radio station. (iii)If the received signal levels of both FM radio stations are approximately same, the receiver cannot sufficiently differentiate between them and may switch back and forth. (iv) The capture effect is also observed when mobile FM receivers are moving from one FM transmitter to another one. (v) There is no interference until the signal from the second FM transmitter is less than about half of the signal from the first one. (vi) But as the signal from the second FM transmitter becomes stronger than the first one, it becomes quite audible at the background of the first one. (vii)As the mobile FM receiver travels closer and closer to the second FM transmitter, the signal from the second transmitter becomes stronger.

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Noise in AM & FM

(viii)Ultimately it may predominate the signal from the first transmitter, eventually being captured by the second FM transmitter. (ix) If FM mobile receiver is approximately at the center of two FM transmitters, then received signals would be alternating from two transmitters. (x) Due to this the FM receiver will be captured alternately by two FM transmitters. Definition : The capture ratio of an FM receiver is the minimum difference in received signal strength, measured in dB, between the two received signals necessary for the capture effect to suppress the weaker signal.

Capture ratio of 1 dB are typical for high-quality FM receiver. 17.

Noise Figure Comparison of FM and AM The noise performance of FM and AM ( ma  1 ) for frequency or amplitude modulation of the carrier signal can be compared in terms of figure of merit or noise figure. Assuming that the input noise power  spectral density , baseband bandwidth f m , and input signal power Si are equal in both FM and AM, 2 then the ratio 3 2  NFFM 2 f 9 2   f 1 NFAM 2 3 Total transmitted powers in FM and AM are unequal even when the unmodulated carrier powers are the same. FM offers the possibility of improved signal-to-noise ratio over AM when

9 2 2  f  1, or  f  , 2 3

 f  0.47 .

As  f increases, the improvement becomes more significant. However, improvement in FM is achieved at the expense of requiring greater bandwidth [ BFM  2( f  1) f m ]. When  f  1 (wideband FM), then BFM  2 f f m , therefore,

BFM 2 f f m   f BAM 2 fm NFFM 9  BFM     NFAM 2  BAM 

2

This implies that an increase in bandwidth by a factor of 2 results in improvement in FM by a factor of 4 or 6 dB. Thus, an improvement in signal-to-noise ratio is a prominent feature of wideband FM. 18.

Pre-emphasis & De-emphasis circuit :

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(i) PSD of noise at the receiver output Sno ( f ) shows that the noise power density at the demodulator output increase parabolically with frequency.

(ii) This means the effect of noise increases with increase in frequency. This is unfortunate because noise is strongest in the frequency range in which the signal is the weakest. (iii)The signal to noise ratio therefore becomes poor at higher frequencies and the quality of FM reception degrades. The high frequency component of the message is badly affected by the noise. (iv) This problem can be solved by using circuits called pre-emphasis and de-emphasis. In the preemphasis and de-emphasis methods simple RC circuits are used to improve threshold. 18.1 Pre-emphasis : (i) Signal to noise ratio at the output ( S0 / N0 ) of the detector becomes very low towards the higher edge of the message band and may cause threshold effect, in spite of the fact that S0 / N0 is large enough at lower edge of message band. (ii) The threshold effect may be avoided by improving S0 / N0 at the higher edge of the message band. In FM, the noise has a greater effect on the higher modulating frequencies. This effect can be reduced by increasing the value of modulation index ( m f ) for higher modulating frequencies ( f m ) . (iii)This can be done by increasing the deviation  f and  f can be increased by increasing the amplitude of modulating signal at higher modulating frequencies. (iv) This is done by a simple RC network known as pre-emphasis circuit which boosts the signal amplitude of higher frequencies in the message band before they modulate the carrier.

Fig. Pre-emphasis circuit (v) The boosted signal at transmitter increases the S0 / N0 ratio at the detector output and it becomes large enough to improve the threshold level over the entire message band. (vi) Thus, the artificial boosting of higher modulating frequencies is called as pre-emphasis. The preemphasis circuit at the transmitter is a high pass network which behaves like a differentiator. (vii) As f m increases, reactance of C decreases and modulating voltage applied to FM modulator goes on increasing. The frequency response characteristic of the RC high pass network is shown in figure. The corner frequency for the RC high-pass network is 2,122 Hz. The rate of increase in output is 6 dB/octave.

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Noise in AM & FM

Fig. Pre-emphasis characteristics Assuming R2  R1 in the pre-emphasis circuit, its transfer function is given by

 f  1 H p ( f )  1  j   where f1  R1C  f1  (viii) The pre-emphasis is carried out at the transmitter as shown in the following block diagram.

Fig. FM transmitter including the pre-emphasis

In commercial broadcast FM system, the output SNR are typically 40-50 dB with pre-emphasis network. There is an improvement in output SNR by 6-7 dB, that is approximately 15%. 18.2 De-emphasis : (i) The artificial boosting given to the higher modulating frequencies in the process of pre-emphasis is nullified or compensated at the receiver by a process called de-emphasis. (ii) The high frequency components of the message signal reproduced by the detector are at a raised amplitude level, and therefore, amplitude distribution of the baseband is distributed. An inverse action is needed at the discriminator output to bring back the original level of high frequency components, and restore the amplitude distribution of message band. (iii)This is done by another RC network known as de-emphasis circuit. The de-emphasis circuit at the receiver is a low pass RC network which behaves like an integrator.

Fig. De-emphasis circuit (iv) An FM system equipped with the facility of pre-emphasis and de-emphasis has a block diagram just like phase modulation system.

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(v) The demodulated FM is applied to the de-emphasis circuit. With increase in f m the reactance of C goes on decreasing and the output of de-emphasis circuit will also reduce as shown in figure. The rate of decrease in output is  6 dB/octave.

Fig. De-emphasis characteristics The transfer function of de-emphasis circuit is given by Hd ( f ) 

1 1 where f1  1  j ( f / f1 ) R1C

The transfer functions H d ( f ) of de-emphasis circuit and H p ( f ) of pre-emphasis circuit have inverse relationship, so that their product is constant for the entire message band i.e. H d ( f ).H p ( f )  K . (vi) The de-emphasis is carried out at the receiver as shown in the following block diagram.

Fig. FM receiver including the de-emphasis

The time constant of de-emphasis circuit at FM transmitter must be kept same as that in pre-emphasis circuit at FM transmitter. Solved Example 1 A Gaussian filter has the characteristics H ( f )  e k f   f   (a) Calculate the 3-dB bandwidth. (b) Calculate the noise bandwidth. 2

Sol.

Given : H ( f )  e k

2

f2

2

  f  

Maximum value of H ( f ) is H (0)  1 2 2 H (0)  e k f H 2

where f H  3-dB frequency

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GATE ACADEMY PUBLICATIONS TM 2 2 1  e k f H 2 0.58  fH  k Noise bandwidth is given by,

BN 

2



1  k 2 f H 2 2

Ans.



1 H (0)

 log e

Noise in AM & FM



H ( f ) df  2

0

1 2 k 2 f 2 e df 12 0

Put 2k 2 f 2  x  4k 2 fdf  dx  df 

dx 2k 2 x



BN 

1 1 1 1 e x x 1/2 dx      2k 2 0 2k 2 2 2k 2 

Definition of gamma function, n   e  x x n 1dx 0



BN 

1  k 8

Ans.

Solved Example 2 The two-sided power spectral density of noise n(t ) is shown in below figure.

(i) Plot the power spectral density of the product n(t ) cos 2f1t . (ii) Calculate the normalized power of the product in the frequency range ( f 2  f1 ) to ( f 2  f1 ) . (iii)Repeat parts (i) and (ii) for the product n(t )cos 2( f 2  f1 ) / 2 t . Sol.

(i) The power spectral density of n(t ) is given by Gn ( f ) . PSD n(t )   Gn ( f )

The power spectral density of the product n(t ) cos 2f1t is given by, PSD n(t ) cos 2f1t  

Gn ( f  f1 )  Gn ( f  f1 ) 4

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(ii) Normalized power in the frequency range ( f 2  f1 ) to ( f 2  f1 ) is given by, P  Area of noise power spectral density   ( f 2  f1 )  ( f 2  f1 )   

P

 8

 ( f 2  f1 ) 4

Ans.

( f  f )  (iii)PSD of n(t ) cos 2  1 2 t  2   ( f  f2 )  ( f1  f 2 )    ( f  f 2 )  PSD 1    n(t ) cos 2  1 t    Gn  f  1   Gn  f   2 4  2 2     

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Noise in AM & FM

Normalized power in the frequency range ( f 2  f1 ) to ( f 2  f1 ) is given by,  ( f  f ) ( f 2  f1 )   P  Area of noise power spectral density   2 1    4 2 2  

P

 ( f 2  f1 ) 4

Ans.

Solved Example 3 Compute the transmission bandwidth BT and the required transmitted power ST of DSB, SSB and AM systems for transmitting an audio signal which has a bandwidth of 10 kHz with an output SNR of 40 dB. Assume that the channel introduces a 40 dB power loss and channel noise is AWGN with power spectral density (psd)  / 2  109 W/Hz . Assume  2 S X  0.5 for AM. Sol.

Noise PSD,

  109 W/Hz Signal bandwidth, B  10 kHz 2

S Output SNR,    40 dB  N 0 Power loss, PL  40dB





S 10log10    40  N 0

10log10 PL  40





S 4    10 N  0

PL  104

The transmission bandwidth requirements are :

2 B  20 kHz for DSB and AM BT    B  10 kHz for SSB For DSB and SSB : For the transmitter power of DSB and SSB systems, we have

Ans.

Si S  104     N 0 f m

Si  f m 104  (2 10 9 ) 104 104  0.2 W Power loss in channel is given by, PL 

ST Si

The transmitted power is, ST  PL Si  0.2 104  2 kW

Ans.

For AM : For an AM system using envelope detection with  2 S X  0.5, we have

2 S X S    2  N 0 1   S X

 Si  1  Si       f m  3  f m 

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S Si  3f m    3  (2 109 ) 104 104  0.6 W  N 0 The transmitted power is, ST  PL Si  0.6 104  6 kW

Ans.

Hence, the required transmitted power in AM is 3 times than that for the DSB or SSB system.

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Q.1

Noise in AM & FM

The minimum value of m f for an FM system required to produce a noticeable improvement in over a comparable AM system with m = 1 is (A)

Q.2

Q.3

3

(B)

2

(C) 1

1 2

(D)

S ratio N

[IES-1991] 1

3

If the transmission bandwidth is doubled in FM, then the SNR is [IES-1993] (A) also doubled (B) improved four - fold (C) decreased by one fourth (D) unaffected Assertion (A) : Frequency modulation (FM) is preferable to amplitude modulation (AM) for transmitting high quality music. Reason (R) : FM signals have higher noise immunity [IES-1996] (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true but R is NOT the correct explanation of A (C) A is true but R is false (D) A is false but R is true

Q.4

Match List-I (Modulation) with List-II (Characteristic) and select the correct answer using the codes given below the Lists : [IES EC 1997] List – I List – II A. AM 1. Mobile communication B. FM 2. Constant carrier frequency C. Noise in FM 3. Triangular noise power spectrum D. Noise in AM and FM 4. Rectangular noise-power spectrum Codes : A B C D (A) 2 1 4 3 (B) 1 2 3 4 (C) 1 2 4 3 (D) 2 1 3 4 Q.5 Assertion (A) : AM has better noise performance than FM. [IES EC 1998] Reason (R) : AM results in an increase in signal power. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true but R is NOT a correct explanation of A (C) A is true but R is false (D) A is false but R is true Q.6 Which one of the following statements regarding the threshold effect in demodulators is correct? [IES EC 2000] (A) It is exhibited by all demodulators when the input signal to noise ratio is low (B) It is the rapid fall in output signals to noise ratio when the input signal to noise ratio falls below a particular value  GATE ACAD EMY PUB L ICATIONS  GATE ACAD EMY PUBL ICATIONS  GATE ACAD EMY PUBL ICATIONS  GATE ACAD EMY PUBL ICATIONS  Copyrights © All rights reserved by GATE ACADEMY PUBLICATIONS. No part of this booklet may be reproduced or utilized in any form without the written permission.

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(C) It is the property exhibited by all AM suppressed carrier coherent demodulators (D) It is the property exhibited by correlation receivers Q.7 Assertion (A) : The demodulated output power spectral density is parabolic over the range |f| < w for FM where w is the signal bandwidth. [IES EC 2002] Reason (R) : FM demodulation is essentials a differentiation process (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true and R is not a correct explanation of A (C) A is true but R is false (D) A is false but R is true. Q.8

Which one of the following blocks is not common in both AM and FM Receiver? [IES EC 2006] (A) RF amplifier (B) Mixer (C) IN amplifier (D) Slope detector Q.9 Match List-I (Communication Service) with List-II (Bandwidth) and select the correct answer using the code given below [IES EC 2006] List-I List-II A. AM Broadcast 1. 10 kHz B. Telephone 2. 4 kHz C. Wideband FM 3. 200 kHz D. TV 4. 7 MHz Code : A B C D (A) 1 2 3 4 (B) 3 4 1 2 (C) 1 4 3 2 (D) 3 2 1 4 Q.10 Why does an FM radio station perform better than an AM station radiating the same total power? [IES EC 2007] (A) FM is immune to noise (B) AM has only two sidebands while FM has more (C) FM uses larger bandwidth for large modulation depth (D) Capture effect appears in FM Q.11

The threshold effect in demodulators is (A) The rapid fall of output SNR when the input SNR falls below a particular value (B) Exhibited by' all the demodulators when the input SNR is low (C) Exhibited by all AM suppressed carrier coherent demodulators (D) Exhibited by correlation receivers



Answers to Multiple Choice Questions 1.

D

2.

B

3.

A

9.

A

10.

A

11.

A

4.

D

5.

D

6.

B

7.

[IES EC 2012]

A

8.

D

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

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Noise in AM & FM

Scan for solution of important GATE questions based on amplitude modulation :



Explanation of Multiple Choice Questions

S  S  Sol.1 The output of signal to noise Ratio  0   3(m f ) 2  0   N0  FM  N0  AM 1 For improvement to be noticeable, 3(m f )2  1 (or) m f  3 Hence, the correct option is (D). Sol.2 Band width of FM  2(  1) f m

For WBSM   1 so bandwidth  2f m 

BW 2 fm

f m is constant. As transmission bandwidth increases,  also increases proportionally. Thus if bandwidth is doubled  also gets doubled. But figure of merit of FM SNR O/P 3 2 FOM    SNR I/P 2 Thus when  is doubled FOM increases four fold. The question is appropriate if the word SNR is replaced by FOM. Hence, the correct option is (B). Sol.3 The frequency modulation (FM) is always preferable compared to amplitude modulation (AM) for transmitting high quality music. Because FM signals have higher noise immunity. Hence, the correct option is (A). Sol.4 A. AM 2. Constant carrier frequency B. FM 1. Mobile communication C. Noise in FM 3. Triangular noise power spectrum D. Noise in AM and FM 4. Rectangular noise-power spectrum Hence, the correct option is (D). Sol.5 FM has better noise performance than AM. AM required more power for signal transmission. Hence, the correct option is (D). S Sol.6 The loss of message at low prediction is called threshold effect. N S The name comes about because, there is some value of input , above which signal distortion due to noise N is negligible and below which the system performance deteriorates rapidly. Hence, the correct option is (B). Sol.7 Let the incoming signal for the FM demodulator be A cos ct  ni (t ). 

x(t )  A cos ct  nc (t ) cos ct  ns (t )sin ct

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 [ A  nc (t )]cos ct  ns (t )sin ct The instantaneous angle (t )

 n (t )   tan 1  s   A  nc (t )  under low noise condition, nc (t )  A and ns (t )  A Considering that, under small '  ' .

tan   , (t ) 

ns (t ) A

The instantaneous frequency d (t ) ns (t ) i   dt A Output of an FM demodulator  i of the input signal.  output noise component n0 (T ) 

ns (t ) n (t ) i.e. n0 (t )    s A A

This can be considered as

2 2    input PSD A2 Thus, the output noise PSD, varies as square of the frequency. This variation is a parabolic variation. In FM demodulation, the incoming signal is differentiated to convert input frequency variations into amplitude variations and that is applied to a diode detector. Hence, the correct option is (A). Output PSD 

Sol.8

Slope detection is the principle of demodulation of FM, where the frequency variations are converted into amplitude variations and then detected using envelope detector. Hence, the correct option is (D). Sol.9 As per FCC regulations, the bandwidth of each AM broadcasting channel is 10 kHz. A. AM Broadcast 1. 10 kHz B. Telephone 2. 4 kHz C. Wideband FM 3. 200 kHz D. TV 4. 7 MHz Hence, the correct option is (A). Sol.10 FM receivers can be fitted with amplitude limiters to remove the amplitude variations caused by noise. This makes FM reception is more immune to noise than AM reception. Hence, the correct option is (A).

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