Transcript Angle modulation Frequency Modulation

Angle Modulation
Introduction
 There are three parameters of a
carrier that may carry information:
 Amplitude
 Frequency
 Phase
 Frequency and Phase modulation
are closely related and grouped
together as Angle modulation
Frequency Modulation
 In this the instantaneous frequency of the carrier
is caused to vary by an amount proportional to
the amplitude of the modulating signal. The
amplitude is kept constant.
Simple FM generation
Resistant to Some Noise
time
Some key Observations
 More complex than AM this is because it involves
minute changes in frequency
 Power in an FM signal does not vary with
modulation
 FM signals do not have an envelope that
reproduces the modulation
 FM is more immune to effects of noise
Frequency Deviation
e(t) = E sin (t +)
 Frequency deviation
of the carrier is
proportional to the
amplitude of the
modulating signal
as illustrated
kf= frequency deviation/V = kf kHz/V
  k Em   Maximum freq deviation
f
Deviation ratio Kf
•This shift in frequency compared with the amplitude of the
modulating voltage is called the deviation ratio.
•Example
Given that the deviation constant is 1kHz/10mV, what is
the shift in frequency for a voltage level of 50 mV?
•Frequency deviation =
50 
1
 5kHz
10
Mathematical Expression for FM
e(t) = E sin (t +)
eFM  ECSin ct 
  k Em
f
 
K f Em Sinmt
fm
Maximum freq deviation
eFM  ECSin ct 
Sin t
m
fm
eFM  ECSin ct  mfSinmt
Where modulation index is


fm

 mf

% modulation FM
% Modulation = Actual freq deviation/ allowed freq deviation
Example:
An FM broadcast-band transmitter has a peak deviation of ±60
kHz for a particular input signal. Determine the percentage of
modulation.
Important Definitions
 -Frequency Deviation is maximum departure of instantaneous freq. of
FM wave from career frequency
Maximum Freq of FM is
fmax= fc+

is independent of modulating freq. and proportional to only

amplitude of information
  KfEm

fm
 mf
Modulation index is proportional to deviation and
inversely proportional to modulating freq.
This decides the BW of the FM wave also decides the no of side
bands In FM the modulation index can be greater than 1
Deviation Ratio
DR =Maximum deviation /maximum modulating freq
in FM
is 75KHz
 max is 15KHz
DR 
 max
fm max
fm max
Examples
In an FM system when the audio frequency is 300 Hz and the
audio voltage is 2.0V, the deviation is 5kHz. If the audio
voltage is now increased to 6V what is the new deviation? If
the voltage is now increased to 9V and the frequency dropped
to 100Hz what is the deviation? Find the modulation index in
each case.
  Vm
 5
Vm

mf 
2

fm
 2.5kHz / V

5
 16.67
0.3
when V  6v
  2.5  6  15kHz
mf 

fm

15
 50
0.3
when V  9v
  2.5  9  22.5kHz

22.5
mf 

 225
f m 0.1
Find the carrier and modulating frequencies, the
modulating index, and the max. deviation of an FM wave
below. What power will the wave dissipate in a 10 ohm
resistor?
v  12 sin 6  10 t  5 sin 1250 t 
8
Compare this with:



v  A sin   ct  sin  mt 
fm


 c 6  108
fc 

 95.5MHz
2
2
 m 1250
fm 

 199Hz
2
2
Modulating index =5 as given.
2
Power,
12 
 72
Vrms 
2
 
P

 7.2W
R
10
10
Frequency spectrum of FM Wave –
eFM  ECSin ct  mfSinmt

Sin of sin function is solved by Bessel function
eFM  EC  J 0mf Sinct
 J 1mf Sin c  m t  Sin c  m t 
 J 2mf Sin c  2m t  Sin c  2m t 
 J 3mf Sin c  3m t  Sin c  3m t 
 J 4mf Sin c  4m t  Sin c  4m t .......
J0Ec
J3Ec
Fc3fm
J2Ec
Fc2fm
J1Ec
Fcfm
J1Ec
J2Ec
fc
Fc+
fm
Fc+
2fm
J3Ec
Fc+3
fm

Jn
Modulation index
Carson’s Rule
This is an approximate method used to predict the required bandwidth
necessary for FM transmission
BW  2 max  f s max 
About 98% of the total power is included in the approximation.
What bandwidth is required to transmit an FM signal with intelligence
at 12KHz and max deviation 24 kHz
mf 

fm

24
2
12
Consult Bessel function table to note that for modulating index of 2,
components which exist are J1,J2,J3,J4 apart from J0.
This means that apart from the carrier you get J1 at +/-10kHz, J2 at +/20kHz, J3 at +/- 30kHz and J4 at +/- 40 kHz.
Total bandwidth is therefore 2x40=80kHz.
For an FM signal given by
v  60 sin 4  10 t  2 sin 2  10 t 
8
If this signal is input into a 30 ohm antenna, find
the carrier frequency
•the transmitted power
•the modulating index
•the intelligence frequency
•the required bandwidth using Carson's rule and tables
•the power in the largest and smallest sidebands
3
AM Vs FM systems
In both systems a carrier wave is modulated by an audio signal to produce
a carrier and sidebands. The technique can be applied to various
communication systems eg telephony and telegraphy
Special techniques applied to AM can also be applied to FM
Both systems use receivers based on the superheterodyne principle
•In AM, the carrier amplitude is varied whereas in FM the carrier frequency is
varied
•AM produces two sets of sidebands and is said to be a narrowband system.
FM produces a large set of sidebands and is a broad band system
•FM gives a better signal to noise ratio than AM under similar operating
conditions
•FM systems are more sophisticated and expensive than AM systems
Transmitters
In an AM transmitter, provision must be made for varying the carrier amplitude
whilst for FM the carrier frequency is varied.
AM and FM modulators are therefore essentially different in design. FM can be
produced by direct frequency modulation or by indirectly phase modulation.
The FM carrier must be high usually in the VHF band as it requires large
bandwidth which is not available in the lower bands.
Receivers
The FM and AM receivers are basically the same, however the FM receiver uses a limiter
and a discriminator to remove AM variations and to convert frequency changes to
amplitude variations respectively. As a result they (FM) have higher gain than AM.
FM receivers give high fidelity reproduction due to their large audio bandwidth up to 15
kHz compared with about 8 kHz for AM receivers.
Frequency Modulation Index
 Another term common to FM is the modulation index,
as determined by the formula:
mf 

fm
Phase Modulation
 In phase modulation, the phase shift is proportional to the
instantaneous amplitude of the modulating signal,
according to the formula:

kp 
em
Relationship Between FM and Phase
Modulation
 Frequency is the derivative of phase, or, in other
words, frequency is the rate of change of phase
 The modulation index is proportional to frequency
deviation and inversely proportional to modulating
frequency
Modulating Signal
Frequency
Converting PM to FM
 An integrator can be
used as a means of
converting phase
modulation to frequency
modulation
This solution may be shown to be given by
v  A{J o m f sin  ct
 J1 m f [sin  c   m t  sin  c   m t ]
 J 2 m f [sin  c  2 m t  sin  c  2 m t ]
 J 3 m f [sin  c  3 m t  sin  c  3 m t ]
 J 4 m f [sin  c  4 m t  sin  c  4 m t ]...}
To evaluate the individual values of J is quite tedious and so tables are used.
Observations
•Unlike AM where there are only three frequencies, FM has an infinite
number of sidebands
•The J coefficients decrease with n but not in any simple form and
represent the amplitude of a particular sideband. The modulation index
determines how many sideband components have significant
amplitudes
•The sidebands at equal distances from fc have equal amplitudes
•In AM increase depth of modulation increases sideband power and
hence total transmitted power. In FM total transmitted power remains
constant, increase depth of modulation increases bandwidth
•The theoretical bandwidth required for FM transmission is infinite.