NOISE IN Analog Communication Part-2 AM SYSTEMS.ppt

ANALOG COMMUNICATION
Course Code:B028411(028)
Part-2 Noise in AM System
Manjeet Singh Sonwani
Assistant Professor
Department of Electronics & Telecomm. Engg.
Government Engineering College Raipur

Course Contents
UNIT-I AMPLITUDE MODULATION
UNIT-II ANGLE MODULATION
UNIT-III MATHEMATICAL REPRESENTATION OF NOISE
UNIT-IV NOISE IN AM SYSTEMS
UNIT-V NOISE IN ANGLE MODULATED SYSTEMS
Text Books:
1. Principles of Communication Systems, Taub and Schilling, 2nd Edition.,
Tata McGraw Hill.(Unit-I,II,III,IV,V)
2. Electronic Communication Systems, George F Kennedy, Tata McGraw Hill.
(Unit-I, II)
3. Communication Systems, Simon Haykins, Wiley India
Reference Books:
1. Communication Systems Engineering, Proakis, 2nd Edition, Pearson Education.
2. Modern Digital and Analog Communication, B.P. Lathi, Oxford University Press.
3. Communication Systems (Analog and Digital), Singh and Sapre, 2nd Edition,
Tata McGraw Hill


UNIT- 3
UNIT-V
Part-2 Noise In Amplitude
Modulation Systems
Manjeet Singh Sonwani
Assistant Professor
Department of Electronics & Telecomm.
Government Engineering College Raipur

4
NOISE IN AMPLITUDE-MODULATION SYSTEMS
Noise calculation (SNR, FOM) of Various AM system:
 Double sideband suppressed carrier AM(DSB-SC)
 Single sideband suppressed carrier AM (SSB-SC)
 AM-FC system (Envelope detector)
 Threshold Effect in Envelope detector.

AMPLITUDE-MODULATION RECEIVER
5
A system for processing an amplitude-modulated carrier and recovering the
baseband Amplitude modulation receiver modulating system is shown in Figure

6
AMPLITUDE-MODULATION RECEIVER…...
 The signal has suffered great attenuation during its transmission over the
 communication channel and hence amplification is needed.
 The input to the system might be a signal furnished by a receiving anten
na which receives its signal from a transmitting antenna.
 The carrier of the received signal is called a radio frequency (RF) carrier
, and its frequency is the radio frequency frf
 The input signal is amplified in an RF amplifier and then passed on to a
mixer.
 In the mixer the modulated RF carrier is mixed (i.e., multiplied) with a si
nusoidal waveform generated by a local oscillator which operates at a fre
quency fosc .
 The process of mixing is also called heterodyning, and since the heterod
yning local-oscillator frequency is selected to be above the radio frequen
cy, the system is often referred to as a superheterodyne system.

7
AMPLITUDE-MODULATION RECEIVER…..
 The process of mixing generates sum and difference frequencies.
 Thus the mixer output consists of a carrier of frequency (fosc + frf ) and
a carrier ( fosc –frf ). Each carrier is modulated by the baseband signal to the
same extent as was the input RF carrier.
 The sum frequency is rejected by a filter. This filter is not shown in Figure
but may be considered to be part of the mixer.
 The difference-frequency carrier is called the intermediate frequency (IF)
carrier, that is, fIF = ( fosc –frf ).
 The modulated IF carrier is applied to an IF amplifier.
 The process in which a modulated RF carrier is replaced by a modulated IF
carrier, is called conversion.The combination of the mixer and local oscillator
is called a converter.
 The IF amplifier output is passed, through an IF carrier filter, to the demodul
ator in which the baseband signal is recovered, and finally through a baseban
d filter. The baseband filter may include an amplifier, not indicated in Figure.

8
AMPLITUDE-MODULATION RECEIVER….
 If synchronous demodulation is used, a synchronous signal source will be re
quired.
 The only operation performed by the receiver is the process of frequency tra
nslation back to baseband.
 This process is the inverse of the operation of modulation in which the base
band signal is frequency translated to a carrier frequency.
 The process of frequency translation is performed in part by the converter
and in part by the demodulator. For this reason the converter is sometimes
referred to as the first detector, while the demodulator is then called the
second detector.
 The only other components of the system are the linear amplifiers and filters
, none of which Would be essential if the signal were strong enough and the
re were no need for multiplexing.
 It is apparent that there is no essential need for an initial conversion before
demodulation. The modulated RF carrier may be applied directly to the
demodu lator.
 However, the superheterodyne principle, which is rather universally incorpo
rated into receivers, has great merit.

9
ADVANTAGE OF THE SUPERHETERODYNE
PRINCIPLE SINGLE CHANNEL
 A signal furnished by an antenna to a receiver may have a power as low as
 some tens of picowatts, while the required output signal may be of the order of
tens of watts.
 Thus the magnitude of the required gain is very large.
 In addition, to minimize the noise power presented to the demodulator, filters
are used which are no wider than is necessary to accommodate the baseband si
gnal. Such filters should be rather flat-topped and have sharp skirts.
 It is more convenient to provide gain and sharp flat-topped filters at low freque
ncies than at high.
 Example: In commercial FM broadcasting, the RF carrier frequency is in the
range of 100 MHz, while at the FM receiver the IF frequency is 10.7 MHz
 Thus, in Fig. 8.1-1 the largest part, by far, of the required gain is provided by t
he IF amplifier, and the critical filtering done by the IF filter.
 While Figure suggests a separate amplifier and filter, actually in physical recei
vers these two usually form an integral unit. For example, the IF amplifier may
consist of a number of amplifier stages, each one contributing to the filtering.

10
PRINCIPLE SINGLE CHANNEL………
 Some filtering will also be incorporated in the RF amplifier.
 But this filtering is not critical It serves principally to limit the total noise po
wer input to the mixer and thereby avoids overloading the mixer with a noise
waveform of excessive amplitude.
 RF amplification is employed whenever the incoming signal is very small.
 This is because of the fact that RF amplifiers are low-noise devices; ie, an
 RF amplifier can be designed to provide relatively high gain while
generating relatively little noise.
 When RF amplification is not employed, the signal is applied directly to the
mixer. The mixer provides relatively little gain and generates a relatively larg
e noise power.
 Calculations showing typical values of gain and noise power generation in
RF, mixer, and IF amplifiers.

11
 Multiplexing
 An even greater merit of the superheterodyne principle becomes apparent
when we consider that we shall want to tune the receiver to one or another
of a number of different signals, each using a different RF carrier.
 If we were not take advantage of the superheterodyne principle,
 we would require a receiver which many stages of RF amplification were e
mployed, each stage requiring tuning.
 Such tuned-radio-frequency (TRF) receivers were, as a matter of fact comm
only employed during the early days of radio communication.
 It is difficult enough to operate at the higher radio frequencies; it is even m
ore difficult to gang-tune the individual stages over a wide band, maintainin
g at the same time a reasonably sharp flat-topped filter characteristic of cons
tant bandwidth .
 In a superhet receiver, however, we need but change the frequency of the
 local oscillator to go from one RF carrier frequency to another.

12
 Whenever fosc is set so that fosc - frf = fif the mixer will convert the
input modulated RF carrier to a modulated carrier at the IF frequency
, and the signal will proceed through the demodulator to the output.
 Of course, it is necessary to gang the tuning of the RE amplifier to the
frequency control of the local oscillator.
 But again this employed. ganging is not critical, since only one or two
RF amplifiers and filters are employed.
 Finally, we may note the reason for selecting fosc higher than frf .
With this higher selection the fractional change in fosc required to
accommodate a given range of RF frequencies is smaller than would
be the case for the alternative selection.

13
SINGLE SIDE BAND SUPRESSED CARRIER(SSB-SC)
 The receiver shown in Figure is suitable for the reception and demodul
ation of all types of amplitude-modulated signals, single sideband or do
uble sideband, with and without carrier.
 The only essential changes required to accommodate one type of signal
or another are in the demodulator and in the bandwidth of the IF carrier
filter.
 The signal input to the IF filter is an amplitude-modulated IF carrier.
 The normalized power (power dissipated in a 1-ohm resistor) of this
signal is Si
 The signal arrives with noise. Added, is the noise generated in the RF
amplifier and amplified in the RF amplifier and IF amplifiers.
 The IF amplifiers and mixer are also sources of noise, i.e., thermal
noise, shot noise, etc., but this noise, lacking the gain of the RF
amplifier, represents a second-order effect.

14
 We shall assume that the noise is Gaussian, white, and of two-sided power spe
ctral density η/2.
 The IF filter is assumed rectangular and of bandwidth no wider than is necessa
ry to accommodate the signal.
 The output baseband signal has a power So , and is accompanied by noise of to
tal power No
 Calculation of Signal Power
 With a SSB-SC signal, the demodulator is a multiplier as shown in Fig. 8.3-1a.
The carrier is Acos 2πfct.
 For synchronous demodulation the demodulator must be furnished with a sync
hronous locally generated carrier cos 2πfct.
 We assume that the upper sideband is being used; hence the carrier filter has a
bandpass, as shown in Fig. 8.3-1b, that extends from fc to fM. where fM is the
baseband bandwidth. The bandwidth of the baseband filter extends from zero t
o fM as shown in Fig. 8.3-1c

SINGLE SIDE BAND SUPRESSED CARRIER(SSB-SC)……..
15

16
 Let us assume that the baseband signal is a sinusoid of angular frequency
 fm (fm ≤ fM )
 The carrier frequency is fc .The received signal considering USB is
 Si(t)=A cos 2π(fc+fm)t.
 We assume that the upper sideband is being used; hence the carrier filter has a
bandpass, as shown in Fig.b,
 that extends from fc to fM. where fM is the baseband bandwidth.
 The bandwidth of the baseband filter extends from zero to fM as shown in
Fig. c
 The output of the multiplier is
 S2(t)=S1(t)cosωc t=(A/2) cos 2π(2fc+fm)t.+(A/2) cos 2πfmt
 Only the difference frequency will pass through the baseband filter.
 Therefore, the output signal is So(t)=(A/2) cos 2πfmt which is modulating sign
al amplified by ½.

17
 The output signal power is So(t)= 0.5(A/2)2 = A2/8=Si/4
 Thus So/Si =1/4
 When the baseband signal were quite arbitrary in waveshape. Then the SSB
 signal generated by this baseband signal may be resolved into a series of ha
rmonically related spectral components.
 The input power is the sum of the powers in these individual components.
 Therefore, the output signal power generated by the simultaneous application
 at the input of many spectral components is simply the sum of the output po
wers that would result from each spectral component individually.
 Hence Si and So, are properly the total powers, independently of whether a
single or many spectral components are involved

18
 Calculation of Noise Power
 When a noise spectral component at a frequency f is multiplied by cos 2πfc t th
e original noise component is replaced by two components, one at frequency(fc
+ f) and one at frequency (fc - f), each new component having one-fourth the po
wer of the original.
 The input noise is white and of spectral density η/2.
 The noise input to the multiplier has a spectral density Gn1 . as shown in fig.
 The density of the noise after multiplication by cos 2πfct is Gn2 as is shown in
Fig
 Finally the noise transmitted by the baseband filter is of density Gno as in Fig.c
The total noise output is the area under the plot in Fig. c. We have,

SSB-SC: Calculation of Noise Power
19

SSB-SC : Use of Quadrature Noise Components
20
It is of interest to calculate the output noise power No, in an alternative manner using th
e transformation of Equation n(t)=nc(t)cos 2πfct -ns(t)sin 2πfct
This eq. is applied to the noise output of the IF filter so that n(t) has the spectral density
Gn1(f).The spectral densities of nc(t) and ns(t) are:
Gnc(f)= Gn1(f)=Gn1(fc-f)+ Gn1(fc+f)
for
0 ≤f≤fM , Gn1(fc-f)=η/2 ; while Gn1(fc+f)=0 so that Gnc(f) and Gns(f) are as shown in
Figure

SSB-SC : Use of Quadrature Noise Components
21
 Multiplying n(t) by cos 2πfct yields
 n(t)cos 2πfct =nc(t)cos 22πfct - ns(t) sin2πfct cos2πfct
 = 0.5nc(t) +0.5 nc(t)cos 4πfct -0.5 ns(t) sin4πfct
 The spectra of the second and third terms in Eq (8.3-10) extend over the ran
ge 2fc-fM to 2fc+fM and are outside the baseband filter.
 The output noise is no(t)=0.5 nc(t)
 The spectral density of no(t) is then Gno= (1/4)Gnc =(1/4)(η/2) =η/8.
 The spectral density Gno is η/8 over the range from -fM to +fM and the total
noise is again No= η fM/4


22
 Calculation of Signal-to-Noise Ratio (SNR)
 Finally Signal-to-Noise Ratio at output is :
 The importance of So/No is that it serves as a figure of merit of the performance
. a communication system.
 Certainly, as So/No increases, it becomes easier to distinguish and to reproduce
the modulating signal without error.If a system of communication allows the us
e of more than a single type of demodulator (synchronous or nonsynchronous),
that ratio So/No , will serve as a figure of merit with which to compare demodul
ators.

23
DOUBLE SIDE BAND SUPRESSED CARRIER(DSB-SC)
 When a baseband signal of frequency range fM is transmitted over a
 DSB-SC system, the bandwidth of the carrier filter must be 2 fM rather
than fM
 Thus, input noise in the frequency range from fc -fM to fc +fM will
contribute to the output noise, rather than only in the range fc to fc +fM
as in the SSB case.
 This situation is illustrated in figure.which shows the spectral density,
Gn1 (f) of the white input noise after the IF filter. This noise is multiplied
by cos 2πfct.

24

25
The multiplication results in a frequency shift by ±fc and a reduction of
power in the PSD of the noise by a factor of 4.
Thus,the noise in region d of Figure(a) shifts to regions(d)shown in Fig.(b)
, Similarly regions a, b, and c of Fig. 8.4-1a are translated by ±fc and are a
lso attenuated by 4 as shown in fig(b).
 Note that the noise-power spectral density in the region between -fM to+fM
is η/4.while the nose density in the SSB case is only η/8
 Hence the output of noise power in twice as large as ourput noise power f
or SSB.The output noise for DSB after baseand filtering is

26
For equal received powers the ratio So/No for DSB would be only half the
corresponding ratio for SSB.
 Let us assume a sinusoidal baseband signal of frequency
 To keep the received powers the same as in the SSB case that is, Si= A2 /2
we write Si (t) =√2 A cos 2πfmt cos 2πfct
=(A/√2) cos 2π(fc+fm)t + (A/√2) cos 2π(fc-fm)t
The received power is then
Si (t) =0.5(A/√2)2 + 0.5(A/√2)2 =(A2/2)
 In the demodulator (multiplier) Si (t) is multiplied by cos ωct
 The upper- sideband term yields a signal within the passband of the baseba
nd filter given byS’o (t) =(A/2√2) cos 2πfmt
 The lower- sideband term yields S’’o (t) =(A/2√2) cos 2πfmt

27
 S’o (t) and S’’o (t) are in phase and hence the output signal is
 So (t) = S’o (t) +S’’o (t) =(A/√2) cos 2πfmt
 Which has the power So =(A2/4)= Si/2
 When a received signal of fixed power is split in to two sideband compone
nts each of half power, the output signal power increases by a factor of 2.
 A doubling in amplitude causes a fourfold increase in power. Thus the
overall improvement in output signal power is by a factor of 2
 Calculation of Signal to Noise Ratio
 The signal power So =(A2/4)= Si/2
 The Noise power
 So S/N ratio is

28
DSB-SC: Arbitrary Modulated Signal
 It is often convenient to have an expression for the power of a DSB-SC
signal in terms of the arbitrary waveform m(t) of the baseband modulating
signal. Hence let the received signal be Si (t) = m(t) cos 2πfct
The power of Si (t) is
 Now m(t) can always be represented as a sum of sinusoidal spectral
components.
 Hence m2(t) cos4 πfct consists of a sum of sinusoidal waveforms in the fre
quency range 2 fc ± 2fM
 The average value of such a sum is zero, and we therefore have
 When the signal Si (t) is demodulated by multiplication by cos 2πfct ,and p
assed through the baseband filter ,the output is So (t) = m(t)/2
 The output power is

29
DSB-SC: Arbitrary Modulated Signal…….
 Use of Quadrature Noise Components to Calculate N0
 It is again interesting to calculate the output noise power No using the tran
sformation of Equation n(t)=nc(t)cos 2πfct -ns(t)sin 2πfct
 The power spectral densities of nc(t) and ns(t) are:
 Gnc(f)= Gns(f)=Gn1(fc-f)+ Gn1(fc+f)
 In the frequency range |f|≤fM , Gn1(fc-f)= Gn1(fc+f)= η/2 ;
 Thus Gnc(f)=Gns(f)=η , |f|≤fM
 The result of multiplying n(t) by cos 2πfct yields
 n(t)cos 2πfct =nc(t)cos 22πfct - ns(t) sin2πfct cos2πfct
 = 0.5nc(t) +0.5 nc(t)cos 4πfct -0.5 ns(t) sin4πfct
Baseband filtering eliminate the second and third terms,leaving no(t)=0.5nc(t)
The power spectral densities of no(t) is then Gno(f)= (1/4)Gnc(f)= η/4
-fM ≤ f≤fM
The output noise power N0 is

30
AM-FC System
 Demodulation is achieved synchronously as in SSB-SC and DSB-SC.
 The carrier is used as a transmitted reference to obtain the reference signal
cosωct .
 The carrier increases the total input-signal power but makes no contributio
n to the output-signal power.
 we replace Si by SSB
i, where SSB
i is the power in the sidebands alone.
 Then

 Suppose that the received signal is
 Si(t)=A[1+m(t)]cos2πfct = A cos2πfct+Am(t)cos2πfct
 Where m(t) is the the baseband signal which amplitude-modulates the
 carrier A cos 2πfc t. The carrier power is A2/2. The sidebands are contained
in the term A m(t) cos 2πfc t.
 The power associated with this term is (A2/2) Where is the
 time average of the square of the modulating waveform. The total input
 power is

31
DOUBLE SIDE BAND WITH CARRIER……..
 Eliminating A2 ,we have,
 In terms of the carrier power Pc ≡ A2 /2 we get,
 If the modulation is sinusoidal,with m(t)=m cos2πfmt ,then
 Si (t)=A(1+m cos2πfmt) cos2πfct
 When the carrier is transmitted only to synchronize the local demodulator
waveform cos2πfct ,little carrier power need be transmitted.
 In this case m>>1.m2/(2+m2) ≈1, and the signal-to-noise ratio is not greatl
y replaced by the presence of the carrier.For envelop detector,
 m<<1. and for m=1,m2/(2+m2) ≈1/3 power transmitted

32
Figure of Merit
 In each demodulation system the ratio Si/ηfM appeared in the expresion for
output SNR
 To give the product ηfM some physical significance, we consider it to be th
e noise power NM at the input, measured in a frequency band equal to the b
aseband frequency
 Thus NM is the true input noise power only in the case of single sideband
which is transmitted through the IF lter only when the IF filter bandwidth is
f M. For the purpoe of comparing systems,The figure of merit defined by th
e ratio of output signal to noise ratio to input signal noise ratio denoted by γ
is introduced.
 The results given above may be summarized as follows:

33
Figure of Merit………..
 A point of interest in connection with double-sideband synchronous
demodulation is that,for the purpose of suppressing output-noise power,the
carrier filter of Fig. 8.3-1 is not necessary,
 A noise spectral component at the input which lies outside the range
(fc ±fM ) will, after multiplication in the demodulator, lie outside the pass
band of the baseband filter.
 On the other hand, if the carrier filter is eliminated, the magnitude of the
noise signal which reaches the modulator may be large enough to overload
the active devices used in the demodulator.
 Hence such carrier filters are normally included, but the purpose is overloa
d suppression rather than noise suppression. In single sideband, of course,
the situation is different, and the carrier filter does indeed suppress noise.

34
The ENVELOPE DETECTOR
 We again consider an AM signal with modulation |m(t)| <1
 To demodulate this DSB signal we shall use a network which accepts the m
odulated carrier and pro vides an output which follows the waveform of the
emelope of the carrier
 The diode demodulator of Sec. 3.6 is a physical circuit which performs the r
equired operation to a good approximation As usual, as in Fig H1
 The demodulator is preceded by a bandpass filter with center frequency fc, a
nd bandwidth 2fM and is followed by a low-pass baseband filter of bandwidt
h fM .
 It is convenient in the present discussion to use the noise representation give
n in Eq. n(t)= nc(t) cos ωct-ns(t) sinωct
 If the noise n(t) has ower spectral density η/2 in the range 1f and is zero els
ewhere as shown in Fig. 8.4-1, then, as explained in See 712,
 both n(t) and n,(t) have the spectral density η/ in the frequency range -fM to
+fM

35
The ENVELOPE DEMODULATOR........
 At the demodulator input, the input signal plus noise is
 S1(t)+n1(t)=A[1 + m(t)] cos ωct+ nc(t) cos ωct-ns(t) sinωct
 = {A[1 + m(t)]+ nc(t)} cos ωct-ns(t) sinωct

 where A is the carrier amplitude and m(t) the modulation.
 In a phasor diagram the first term of Eq. (8.7-2b) would be represented by a
phasor of amplitude {A[1 + m(t)]+ nc(t)} while the second term would be re
prescnted by a phasor per pendicular to the first and of amplitude ns(t).
 The phasor sum of the two terms is then represented by a phasor of amplitud
e equal to the square root of the sum of the squares of the amplitudes of the t
wo terms.
 Thus, the output signal plus noise just prior to baseband filtering is the envel
ope (phasor sum):
 S2(t)+n2(t)={(A[1 + m(t)]+ nc(t))2 + n2
s(t)}
 = {(A2[1 + m(t)]2+ 2A[1 + m(t)] nc(t) + n2
c(t)} + n2
s(t)}1/2

36
The ENVELOPE DEMODULATOR.......
 We should now like to make the simplification in above Eq. that would be a
llowed if we might assume that both |nc(t)| and |ns(t)| were much smaller tha
n the carrier amplitude A.
 The difficulty is that nc, and ns, are noise "waveforms" for which an explicit
time function may not be written and which are described only in terms of t
he statistical distributions of their instantaneous amplitudes
 No matter how large A and how small the values of the standard deviation o
f ntn or nit), there is always a finite probability that |nc(t)|, |ns(t))| or both, wi
ll be comparable to, or even larger than, A. On the other hand, if the standar
d deviation. of nc(t) and ns(t)are much smaller than A. the likelihood that nc,
or ns, will approach or exceed A is rather small.
 Assuming then that that |nc(t)|<< A and |ns(t)|<< A, the " noise-noise " terms
n2
c(t) and n2
s(t) may be dropped, leaving us with the approximation
 S2(t)+n2(t) ≈{(A2[1 + m(t)]2+ 2A[1 + m(t)] nc(t)}1/2
 = A[1 + m(t)]{1+2nc(t)/(A[1 + m(t)])}1/2

37
The ENVELOPE DEMODULATOR.......
 Using now the further approximation that (1 + x) 1/2 ≈(1+ x/2) for small
 x we have finally that S2(t)+n2(t) ≈ A[1 + m(t)] + nc(t)
 The output-signal power measured after the baseband filter, and neglecting dc
terms, is So =A2 m2(t)
 Since the spectral density of nc(t)=η. the output-nose power after baseband filt
ering is No = 2ηfM
 Again using the symbol NM(≡ηfM )N to stand for the noise pOwer at the input
in the baseband range fM, and using Eq. (8.5-31, we find that
 The result is the same as given in Eq. (8.5-13) for synchronous demodulation.
 To make a comparison with the square-law demodulator,
 we assume m2(t)<<1. In this case, Si≈ Pc, and above Eq. reduces to Eq.
 So/No =m2(t)Pc/ηfM .Hence we have the important result that above threshold t
he synchronous demodulator, the square-law demodulator, and the envelope d
emodulator all perform equally well provided m2(t)<<1

38
The ENVELOPE DEMODULATOR......
 Threshold: Like the square-law demodulator, the envelope demodulator
exhibits a threshold.
 As the input signal-to-noise ratio decreases, a point is reached where the sign
al to-noise ratio at the output decreases more rapidly than at the input. The cal
culation of signal-to-noise ratio is quite complex, and we shall therefore be co
ntent to simply state the result' that for Si/NM << 1 and m2(t)<<1
 Above Equation is obviously indicates a poorer performance than indicated b
y γ,which applies above threshold.
 Comparison between square-law demodulator and the envelope demodulator
 In square-law demodulator m2(t)<<1 then
 Since both square-law demodulation and envelope demodulation exhibit a thr
eshold, a comparison is of interest. We had assumed in square-law demodulat
ion that m2(t) <<1. Then, as noted above, Si≈ A2/2=Pc, the carrier power,
 and Eq. (S/N)out becomes So/No =(m2(t)/1.1)(Pc/NM)2 which is to be compare
d with Eq So/No =(4/3)m2(t)(Pc/NM)2 giving So/No, below threshold for the sq
uare-law demodulator. The comparison indicates that, below threshold, the sq
uare-law demodulator performs better than the envelope detector.

Threshold in Envelop Demodulator-2
39
Comparison:
(i)Square law demodulator has lower threshold and
(ii)also performs better below threshold

COMMUNICATION SYSTEMS,
BY SIMON HAYKINS, WILEY INDIA
NOISE IN AM SYSTEMS
.
40

41
Effect of Noise on a Baseband System
 Since baseband systems serve as a basis for comparison of various
modulation systems, we begin with a noise analysis of a baseband
system.
 In this case, there is no carrier demodulation to be performed.
 The receiver consists only of an ideal lowpass filter with the
bandwidth W.
 The noise power at the output of the receiver, for a white noise
input, is
 If we denote the received power by PR, the baseband SNR is given
by
(6.1.2)
W
N
df
N
P
W
W
n 0
0
2
0

 
W
N
P
N
S R
b 0








42
White process (Section 5.3.2)
 White process is processes in which all frequency components
appear with equal power, i.e., the power spectral density (PSD),
Sx(f), is a constant for all frequencies.
 the PSD of thermal noise, Sn(f), is usually given as
(where k is Boltzrnann's constant and T is the temperature)
 The value kT is usually denoted by N0, Then
2
)
( kT
n f
S 
2
0
)
( N
n f
S 

43
Effect of Noise on DSB-SC AM
 Transmitted signal :
 The received signal at the output of the receiver noise-
limiting filter : Sum of this signal and filtered noise
 Recall from Section 5.3.3 and 2.7 that a filtered noise process
can be expressed in terms of its in-phase and quadrature
components as
(where nc(t) is in-phase component and ns(t) is quadrature
component)
 
t
f
t
m
A
t
u c
c 
2
cos
)
(
)
( 
)
2
sin(
)
(
)
2
cos(
)
(
)
2
sin(
)
(
sin
)
(
)
2
cos(
)
(
cos
)
(
)]
(
2
cos[
)
(
)
(
t
f
t
n
t
f
t
n
t
f
t
t
A
t
f
t
t
A
t
t
f
t
A
t
n
c
s
c
c
c
c
c















44
 Received signal (Adding the filtered noise to the
modulated signal)
 Demodulate the received signal by first multiplying r(t)
by a locally generated sinusoid cos(2fct + ), where  is
the phase of the sinusoid.
 Then passing the product signal through an ideal
lowpass filter having a bandwidth W.
     
t
f
t
n
t
f
t
n
t
f
t
m
A
t
n
t
u
t
r
c
s
c
c
c
c 

 2
sin
)
(
2
cos
)
(
2
cos
)
(
)
(
)
(
)
(






45
 The multiplication of r(t) with cos(2fct + ) yields
 The lowpass filter rejects the double frequency components and
passes only the lowpass components.
 
   
   
       
   
   
     
 












































t
f
t
n
t
f
t
n
t
n
t
n
t
f
t
m
A
t
m
A
t
f
t
f
t
n
t
f
t
f
t
n
t
f
t
f
t
m
A
t
f
t
n
t
f
t
u
t
f
t
r
c
s
c
c
s
c
c
c
c
c
c
s
c
c
c
c
c
c
c
c
c
4
sin
)
(
4
cos
)
(
sin
)
(
cos
)
(
4
cos
)
(
cos
)
(
2
cos
2
sin
)
(
2
cos
2
cos
)
(
2
cos
2
cos
)
(
2
cos
)
(
2
cos
)
(
2
cos
)
(
2
1
2
1
2
1
2
1
     
 


 sin
)
(
cos
)
(
cos
)
(
)
( 2
1
2
1
t
n
t
n
t
m
A
t
y s
c
c 



46
 In Chapter 3, the effect of a phase difference between the
received carrier and a locally generated carrier at the receiver is
a drop equal to cos2() in the received signal power.
 Phase-locked loop (Section 6.4)
 The effect of a phase-locked loop is to generate phase of the received
carrier at the receiver.
 If a phase-locked loop is employed, then  = 0 and the demodulator is
called a coherent or synchronous demodulator.
 In our analysis in this section, we assume that we are
employing a coherent demodulator.
 With this assumption, we assume that  = 0
 
)
(
)
(
)
( 2
1
t
n
t
m
A
t
y c
c 


47
 Therefore, at the receiver output, the message signal and the
noise components are additive and we are able to define a
meaningful SNR. The message signal power is given by
 power PM is the content of the message signal
 The noise power is given by
 The power content of n(t) can be found by noting that it is the
result of passing nw(t) through a filter with bandwidth Bc.
M
c
o P
A
P
4
2

n
n
n P
P
P c
4
1
4
1
0



48
 Therefore, the power spectral density of n(t) is given by
 The noise power is
 Now we can find the output SNR as
 In this case, the received signal power, given by Eq. (3.2.2), is
PR = Ac
2PM /2.


 


otherwise
W
f
f
f
S c
N
n
0
|
|
)
( 2
0
0
0
2
4
2
)
( WN
W
N
df
f
S
P n
n 


 



0
2
0
4
1
4
0
0 2
2
2
0
WN
P
A
WN
P
P
P
N
S M
c
M
A
n
c










49
 The output SNR for DSB-SC AM may be expressed as
 which is identical to baseband SNR which is given by Equation (6.1.2).
 In DSB-SC AM, the output SNR is the same as the SNR for a
baseband system
 DSB-SC AM does not provide any SNR improvement over
a simple baseband communication system
W
N
P
N
S R
DSB 0
0








50
Effect of Noise on SSB AM
 SSB modulated signal :
 Input to the demodulator
 Assumption : Demodulation with an ideal phase reference.
 Hence, the output of the lowpass filter is the in-phase
component (with a coefficient of ½) of the preceding signal.
)
2
sin(
)
(
ˆ
)
2
cos(
)
(
)
( t
f
t
m
A
t
f
t
m
A
t
u c
c
c
c 
 

   
     
t
f
t
n
t
m
A
t
f
t
n
t
m
A
t
f
t
n
t
f
t
n
t
f
t
m
A
t
f
t
m
A
t
n
t
f
t
m
A
t
f
t
m
A
t
r
c
s
c
c
c
c
c
s
c
c
c
c
c
c
c
c
c
c








2
sin
)
(
)
(
ˆ
)
2
cos(
)
(
)
(
2
sin
)
(
2
cos
)
(
)
2
sin(
)
(
ˆ
)
2
cos(
)
(
)
(
)
2
sin(
)
(
ˆ
)
2
cos(
)
(
)
(












 
)
(
)
(
)
( 2
1
t
n
t
m
A
t
y c
c 


51
Effect of Noise on SSB AM
 Parallel to our discussion of DSB, we have
 The signal-to-noise ratio in an SSB system is equivalent to that
of a DSB system.
0
2
0
0 0
WN
P
A
P
P
N
S M
c
n








M
c
U
R P
A
P
P 2


b
R
N
S
W
N
P
N
S
SSB














0
0
M
c
o P
A
P
4
2

n
n
n P
P
P c
4
1
4
1
0


0
0
2
2
)
( WN
W
N
df
f
S
P n
n 


 




52
Effect of Noise on Conventional AM
 DSB AM signal :
 Received signal at the input to the demodulator
 a is the modulation index
 mn(t) is normalized so that its minimum value is -1
 If a synchronous demodulator is employed, the situation is basically
similar to the DSB case, except that we have 1 + amn(t) instead of m(t).
 After mixing and lowpass filtering
)
2
cos(
)]
(
1
[
)
( t
f
t
am
A
t
u c
n
c 


   
   
t
f
t
n
t
f
t
n
t
am
A
t
f
t
n
t
f
t
n
t
f
t
am
A
t
n
t
f
t
am
A
t
r
c
s
c
c
n
c
c
s
c
c
c
n
c
c
n
c






2
sin
)
(
)
2
cos(
)
(
)]
(
1
[
2
sin
)
(
2
cos
)
(
)
2
cos(
)]
(
1
[
)
(
)
2
cos(
)]
(
1
[
)
(











 
)
(
)
(
)
( 2
1
t
n
t
am
A
t
y c
n
c 


53
 Received signal power
 Assumed that the message process is zero mean.
 Now we can derive the output SNR as
  denotes the modulation efficiency
 Since , the SNR in conventional AM is always
smaller than the SNR in a baseband system.
 
n
M
c
R P
a
A
P 2
2
1
2


 
b
b
M
M
R
M
M
M
A
M
M
M
c
n
M
c
N
S
N
S
P
a
P
a
W
N
P
P
a
P
a
W
N
P
a
P
a
P
a
W
N
P
a
A
P
P
a
A
N
S
n
n
n
n
n
c
n
n
n
c
n
AM





























2
2
0
2
2
0
2
2
2
2
0
2
2
4
1
2
2
4
1
0
1
1
1
1
2
2
n
n M
M P
a
P
a 2
2
1


54
 In practical applications, the modulation index a is in the range of
0.8-0.9.
 Power content of the normalized message process depends on the
message source.
 Speech signals : Large dynamic range, PM is about 0.1.
 The overall loss in SNR, when compared to a baseband system, is a
factor of 0.075 or equivalent to a loss of 11 dB.
 The reason for this loss is that a large part of the transmitter power
is used to send the carrier component of the modulated signal and not
the desired signal.
 To analyze the envelope-detector performance in the presence of
noise, we must use certain approximations.
 This is a result of the nonlinear structure of an envelope detector,
which makes an exact analysis difficult.

55
 In this case, the demodulator detects the envelope of the
received signal and the noise process.
 The input to the envelope detector is
 Therefore, the envelope of r ( t ) is given by
 Now we assume that the signal component in r ( t ) is much
stronger than the noise component. Then
 Therefore, we have a high probability that
   
t
f
t
n
t
f
t
n
t
am
A
t
r c
s
c
c
n
c 
 2
sin
)
(
)
2
cos(
)
(
)]
(
1
[
)
( 



  )
(
)
(
)]
(
1
[
)
( 2
2
t
n
t
n
t
am
A
t
V s
c
n
c
r 



  1
)]
(
1
[
)
( 

 t
am
A
t
n
P n
c
c
)
(
)]
(
1
[
)
( t
n
t
am
A
t
V c
n
c
r 



56
 After removing the DC component, we obtain
 which is basically the same as y(t) for the synchronous
demodulation without the ½ coefficient.
 This coefficient, of course, has no effect on the final SNR.
 So we conclude that, under the assumption of high SNR
at the receiver input, the performance of synchronous
and envelope demodulators is the same.
 However, if the preceding assumption is not true, that is, if we
assume that, at the receiver input, the noise power is much
stronger than the signal power, Then
)
(
)
(
)
( t
n
t
am
A
t
y c
n
c 


57
 (a) : is small compared with the other components
 (b) : ;the envelope of the noise process
 Use the approximation
, where
 
   
 
 
)
(
1
)
(
)
(
)
(
)
(
1
)
(
)
(
1
)
(
)
(
1
)
(
)
(
)
(
2
1
)
(
)
(
)]
(
1
)[
(
2
)
(
)
(
)]
(
1
[
)
(
)
(
)]
(
1
[
)
(
2
2
2
2
2
2
2
2
2
2
2
t
am
t
V
t
n
A
t
V
t
am
t
V
t
n
A
t
V
t
am
t
n
t
n
t
n
A
t
n
t
n
t
am
t
n
A
t
n
t
n
t
am
A
t
n
t
n
t
am
A
t
V
n
n
c
c
n
n
n
c
c
n
b
n
s
c
c
c
s
c
a
n
c
c
s
c
n
c
s
c
n
c
r



































2
2
)]
(
1
[ t
am
A n
c 
)
(
)
(
)
( 2
2
t
V
t
n
t
n n
s
c 


 
small
for
,
1
1 2


  
)
(
1
)
(
)
(
)
(
2
2
2
t
am
t
n
t
n
t
n
A
n
s
c
c
c





58
 Then
 We observe that, at the demodulator output, the signal and
the noise components are no longer additive.
 In fact, the signal component is multiplied by noise and is
no longer distinguishable.
 In this case, no meaningful SNR can be defined.
 We say that this system is operating below the threshold.
 The subject of threshold and its effect on the performance
of a communication system will be covered in more detail
when we discuss the noise performance in angle
modulation.
 
)
(
1
)
(
)
(
)
(
)
( t
am
t
V
t
n
A
t
V
t
V n
n
c
c
n
r 



NOISE IN Analog Communication Part-2 AM SYSTEMS.ppt

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