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EEN 303 Communication Systems BETM (Fall 2009)
Frequency Modulation Engr. Humera Rafique Assistant Professor (CS & Engineering) Bahria University, Karachi Campus
[email protected] Course web: http://dcs.telecom.googlepages.com/communicatio http://dcs.telecom.googlepages.com/communication nsystems
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CH:4 FM EEN303 Communication Systems
Text and Reference
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Text 1. Communication Electronics: Electronics: (2/e) Louis E. Frenzel 2. Modern Electronic Communication Communication:: (8/e) Beasley/Miller
Reference 1. Principles of Electronic Communication Systems (3/e) Louis E. Frenzel 2. Electronic Communication Systems (4/e) Canedy
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Chapter Contents • CH4:
1. 2. 3. 4. 5. 6. 7.
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Fundamentals of Frequency Modulation
Angle Modulation Basic principle of Frequency modulation Principle of Phase modulation Modulation index and sidebands Noise suppression effects of FM FM versus AM Disadvantages of FM
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Angle Modulation
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Angle Modulation
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Three parameters of a carrier sinusoid can be varied to allow it to carry a low frequency intelligence signal: 1. 2. 3.
Amplitude Frequency Phase
1. Amplitude modulation 2.3. Angle modulation Angle Modulation: Super imposing the intelligence signal on a high frequency carrier so that its phase angle or frequency is altered as a function of amplitude of intelligence signal Types of Angle Modulation: a. Frequency modulation b. Phase modulation 4-Dec-09
Fig. 4-1: AM, FM & PM
CH:4 FM EEN303 Communication Systems
Angle Modulation
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Frequency Modulation: ‘An angle modulation in which an information signal changes the frequency of a carrier proportional to its amplitude’ Phase Modulation: ‘An angle modulation where the phase angle of a carrier is caused to depart from its reference value by an amount proportional to the modulating signal’s amplitude’ •
Usually PM is not used as the transmission signal , but – Helps in generating FM – Helps to understand noise characteristics of FM as compared to AM
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FM: Basic Principle
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Basics Principle of FM
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Fig. 4-2: AM & FM Techniques
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Basics Principle of FM Time domain AM & FM waveforms
Intelligence
1 0.5 0 -0.5 -1
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
1
AM
0.5 0 -0.5 -1
1
FM
0.5 0 -0.5 -1
Fig. 4-3: Modulation Techniques: AM & FM (constant amplitude intelligence) 4-Dec-09
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Basics Principle of FM
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Fig. 4-4: FM: Variable amplitude intelligence 4-Dec-09
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Basics Principle of FM •
In FM, the carrier amplitude remains constant & the carrier frequency is changed by the modulating signal
•
As the amplitude of the intelligence signal varies, the carrier frequency shift proportionally
•
if vm(t) ↑ => the fc ↑ & relationship is also allowed)
•
When intelligence signal = 0 => fc = fc = centre or resting frequency of carrier frequency
•
As the modulating signal’s amplitude varies between +ve & -ve peaks, passing via zero values, carrier frequency changes above & below its normal, ‘centre’, or ‘resting’ value
if vm(t) ↓ => the fc ↓
(Note: The reverse
Frequency deviation • The amount of change in carrier frequency occurs due to modulating signal (max deviation @ maximum amplitude) 4-Dec-09
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Basics Principle of FM
Information
Frequency deviation rate: • How many times per second the carrier frequency deviates above & below the carrier/centre frequency Time domain FM signals 1 • fm determines fd i.e., if modulating signal: fm , then, 0 fc shifts above & below the centre -1 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 frequency, fm times per second Carrier
1
0
-1
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
FM
1
0
-1
Fig. 4-5: FM
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Basics Principle of FM A simple FM generator: • Simple FM transmitter • Components: i. ii. iii.
LC tank circuit Oscillator FM transmitting antenna
Oscillator
Fig. 4-6: Modulation Techniques •
The capacitance of LC tank circuit is not a standard capacitor, but a capacitor microphone (or condenser mike i.e., a variable capacitor)
•
With no sound waves at mike, its capacitor remains constant while for sound waves, its plates move in and out alternatively and its capacitance goes up and down around its centre value
•
The rate of capacitance change is equal to frequency of the sound waves striking the mike and the amount of capacitance change is proportional to the amplitude of the sound waves
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Basics Principle of FM
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FM Generation Mechanism:
Fig. 4-6 (a): FM Generation mechanism
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Basics Principle of FM
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FM Generation Mechanism: Time: 0 – T1: • Intelligence signal = zero amplitude • Carrier remains unchanged Time: T1 – T2: • Intelligence signal’s amplitude: zero to +ve peak • Oscillator’s frequency changes from its centre value to highest value respectively Time: T2 – T3: • Intelligence signal’s amplitude gradually decreases from +ve peak to zero • Oscillator's frequency its highest value to centre value Time: T3 – T4: • Intelligence signal’s amplitude goes from zero to –ve peak • Oscillator's frequency gradually decreases from centre value to a lowest value 4-Dec-09
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Basics Principle of FM
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FM Generation Mechanism (contd..): Time: T4 – T5: • Intelligence signal’s amplitude goes zero again • Oscillator's frequency gradually goes to its central value
•
The relationship of FM generation with capacitor microphone is:
f out = f c + kvm
intelligence signal . . . . . (4-1)
deviation constant
instantaneous output frequency carrier frequency • • 4-Dec-09
k : “how much the carrier frequency will deviate for a given modulating input voltage level” (kHz/volt) k vm = total deviation CH:4 FM EEN303 Communication Systems
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Basics Principle of FM FM Generation Mechanism:
Time domain AM & FM waveforms 1
Intelligence
0.5
0
-0.5
-1
Fig. 4-6 (b): FM signal with square wave as intelligence
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
1
FM
0.5
0
-0.5
-1
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Basics Principle of FM
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FM Generation Mechanism:
Fig. 4-6 (c): FM signal with variable square wave 4-Dec-09
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Basics Principle of FM FM Generation Mechanism:
Time domain FM waveform 1
Intelligence
0.5
0
-0.5
-1
Fig. 4-6 (d): FM signal with saw tooth wave as intelligence
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
1
FM
0.5
0
-0.5
-1
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Basics Principle of FM
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Example (4-1): (Miller) A 25-mV sinusoid at a frequency of 400 Hz is applied to a capacitor microphone FM generator. If the deviation constant for the capacitor microphone FM generator is 750 Hz/10mV, determine: (a) (b) (c)
The frequency deviation generated by an input level of 25 mV The rate at which the carrier frequency is being deviated Output frequency, if fc = 50 kHz
Example (4-2): (Frenzel 2/e p.71) 71) For a carrier of 50 MHz, find the total frequency deviation, if the peak amplitude of the modulating signal causes a maximum frequency shift of 200 kHz.
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Basics Principle of FM
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Example (4-3): (Frenzel 3/e) p.153 A transmitter operates on a frequency of 915 MHz. The maximum FM deviation is +/- 12.5 kHz. What are the maximum and minimum frequencies that occur during Modulation?
Example (4-4): An FM signal has a centre frequency of 100 MHz, but is swinging between 100.001 MHz & 99.999 MHz at a rate of 100 times per second. Determine: (a) (b) (c)
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fm Vm What happens to amplitude of intelligence if the frequency deviation changes to between 100.002 & 99.998 MHz.
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PM: Basic Principle
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Basics Principle of PM •
A method to produce FM, by varying the amount of phase shift of a constant frequency carrier in accordance with a modulating signal
•
Phase shift: a time separation between two (sine) waves of same frequency
•
A Phase modulator is a circuit that causes a phase shift in a sinusoid in accordance with the amplitude of a modulating signal such that
•
The amplitude of the intelligence ↑, the phase shift ↑ and vise versa
•
Further, for positive amplitudes of modulating signal: lagging phase shift and, for negative values, a leading phase shift
•
In other words, the output of a phase shifter (PM) is delayed, delay increases with the amplitude of modulating signal, if the input is a ‘constant-frequencyconstant-amplitude’ sinusoid carrier
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Basics Principle of PM
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Fig. 4-7: PM 4-Dec-09
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Basics Principle of PM
Fig. 4-8: Modulations: (a) AM 4-Dec-09
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(b) FM (c) PM
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Basics Principle of PM
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Fig. 4-9: PM: variable amplitude intelligence 4-Dec-09
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Modulation Index & Sidebands
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Modulation Index & Sidebands
Frequency Spectrum of FM FM:: • All modulation processes produce sidebands • Like AM, in FM/PM, side bands are ‘sum & difference of the carrier & modulating frequencies’ • Other (theoretical) infinite pairs of upper & lower side bands • FM/PM wider than equivalent AM (broadband FM) • Special signal, whose BW slightly wider than that of AM (Narrowband FM) Carrier USBs
LSBs
fc-7fm
fc-5fm
fc-3fm
fc - fm
fc
fc+2fm
fc+4fm
fc+6fm
Fig. 4-10 : Frequency spectrum of FM signal (single frequency modulating) 4-Dec-09
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Modulation Index & Sidebands
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Frequency Spectrum of FM (Contd.. (Contd..)): • Frequency will change if the amplitude of modulating signal varies •
Number of side bands produced , their amplitudes & their spacing depend on: i. Frequency deviation (δ) ii. Modulating signal’s frequency ( fm )
•
Among infinite number of side bands, only larger amplitude side bands carry useful information
•
An insignificant side band’s amplitude < 1% of un-modulated carrier’s amplitude
•
The above fact narrows the FM spectrum to a finite extent
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CH:4 FM EEN303 Communication Systems
Modulation Index & Sidebands
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Modulation Index of FM : • The ratio of frequency deviation (δ) to the modulating frequency ( fm )
mf =
δ
Maximum frequency shift in carrier caused by intelligence
fm
. . . . . . . . . (4-2)
Modulation Index Modulating frequency
•
↑ mf, wider the FM band width
•
Modulation index is called ‘deviation ration’ if computer using equation (4-2)
•
If mf is known, amplitudes and number of significant side bands can be computed, using ‘Bessel function’
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Modulation Index & Sidebands
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Bessel function function::
Table 4-1 : Bessel function based carrier & side band amplitudes for different values of mf 4-Dec-09
CH:4 FM EEN303 Communication Systems
Modulation Index & Sidebands
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Total band width of FM : • Two methods: i. Total bandwidth of an FM signal can be determined by mf & ‘Bessel function table’ BW = 2 Nf m . . . . . . . . . (4-3) max
N : number of significant side bands
ii. Carson’s rule: rule: An equation to approximate the bandwidth of an FM signal:
(
BW 2 δ max + f mmax
)
. . . . . . . . (4-4)
max. frequency shift caused by the intelligence signal 4-Dec-09
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Modulation Index & Sidebands
Measurement of frequency deviation: deviation: • Method is called ‘zero zero carrier amplitude amplitude’ • Generated FM is observed on spectrum analyzer • At the point where carrier’s amplitude becomes zero, number of side bands are noted down • Number of side bands -> Modulation index (Bessel function table) Carrier mf = 0.5
Carrier mf = 1.0 Carrier mf = 2.0
Fig. 4-11: FM Spectrum 4-Dec-09
CH:4 FM EEN303 Communication Systems
Modulation Index & Sidebands
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Example (4-5): Highest modulating frequency = 2 kHz, carrier deviation = 5 kHz. Find the number of usable side bands. Example (4-6): Frenzel Find the modulation Index: (a) The maximum frequency deviation of a carrier in FM is ± 25 kHz with modulating frequency is 10 kHz . (b) The maximum frequency deviation of a carrier in FM is ± 75 kHz with modulating frequency is 15 kHz . Example (4-7): Frenzel Highest modulating frequency = 2.5 kHz, modulation index = 2. Find the total bandwidth occupied by FM signal. Example (4-8): In zero carrier amplitude method, 9 side bands are visible on a spectrum analyzer showing FM signal. If modulating frequency = 100 kHz, find frequency deviation. 4-Dec-09
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Modulation Index & Sidebands
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Example (4-9): Determine the bandwidth required to transmit an FM signal, if maximum deviation δ = 20 kHz : (a) fm = 10 kHz (b) fm = 5 kHz Example (4- 10) 10): For broadcast FM radio, compute DR. Example (4-11 11)): (a) Determine the permissible range in maximum modulation index for commercial FM that has 30 Hz – 15 kHz modulating frequencies (b) Repeat for a narrow band system that allows a maximum deviation of 1 kHz and 100 Hz to 2 kHz modulating frequency (c) Determine the deviation ratio for the system in part (b) Example (4-12) 12): Determine the relative and total power of the carrier & side frequency bands when mf = 0.25 for a 10 kW FM transmitter. 4-Dec-09
CH:4 FM EEN303 Communication Systems
FM Classification
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Broadband FM (BBFM/WBFM): (BBFM/WBFM): • Standard FM broadcast bandwidth: 200 kHz for each station (one FM band may contain many AM channels) •
Such a large allocation is needed: – High Fi modulating signal up to 15 kHz – Having superior noise performance
• •
Maximum allowed deviation in fc : ± 75 kHz for significant side bands Guard bands” to help minimizing inter-channel interference: 25 kHz 200 kHz
-75 kHz
Carrier 1 +75 kHz
200 kHz
-75 kHz
Carrier 2 +75 kHz
Fig. 4-12: Commercial FM bandwidth allocation for two adjacent stations 4-Dec-09
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FM Classification
Broadband FM (contd.. (contd..)): • DR: (deviation ratio): maximum possible frequency deviation over the maximum input frequency:
DR = • •
max. possible freq. deviation δ max = max. input freq. f m(max)
. . . . . . . . (4-4)
If DR > 1 => wideband FM system If DR < 1 => narrow band FM system
Narrowband FM (NBFM): (NBFM): • Band allocation : 10-30 kHz • Modulation index: 0.5 – 1.0 • Use for voice transmission (intelligence of 3 kHz) in systems such as Applications: Police help line, Aircrafts, Taxi cabs, Weather services, Private industrial networks 4-Dec-09
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Analysis of FM & PM
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Analysis of FM & PM Maximum phase shift by the intelligence signal (radians)
Phase modulated instantaneous voltage
vφ ( t ) = A p sin( ω c t + m p sin ω m ) Carrier frequency (radians) Peak value of un-modulated carrier
. . . . . . . (4-5)
Modulating frequency (radians)
Modulating index of FM (measure of maximum frequency phase shift in carrier’s frequency)
vFM (t ) = Ap sin(ωc t + m f sin ωm )
. . . . . . . (4-6)
Frequency modulated instantaneous voltage Carrier frequency (radians)
Modulating frequency (radians)
Peak value of un-modulated carrier
mf = 4-Dec-09
δ
Maximum frequency shift in carrier caused by intelligence
fi
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Analysis of FM & PM •
FM is not sensitive to intelligence signal’s frequency but PM
•
In FM the amount of frequency deviation produced in carrier, does not depend on the intelligence’s frequency but in PM
•
The amount of deviation is proportional to the intelligence signal’s amplitude for both PM & FM f
0
FM
Deviation (δ)
Deviation (δ)
f
Vm
0
fm
Fig. 4-11: Relationship b/w deviation & modulating signal amplitude & frequency for FM & PM 4-Dec-09
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Analysis of FM & PM
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Example (4-13) 13): An FM signal, 2000 sin(2π 108 t + 2 sin (π 104 t)), is applied to a 50-Ω antenna. Determine: (a) fc (b) fm (c) PT (d) mf (e) BW (f) Power in the largest & smallest sidebands predicted by table (4-1)
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Noise Suppression Effects of FM
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Noise Suppression Effects of FM •
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Noise : an interference by: – Lightning – Motors – Automotive ignition systems – Transient signals by power line switching
• • •
Such noise is typically narrow spikes of voltage with very high frequencies Add to a signal and interfere with it Usually changes its amplitude
• •
FM has superior noise characteristics than AM e.g., static noise is rarely heard on FM (although quite common in AM)
FM limiters: • A stage in FM receivers that removes any amplitude variations of the received signal before next stage • If limiters do not remove all noise completely, the remaining noise spikes produce a small frequency variations or phase shifts 4-Dec-09
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Noise Suppression Effects of FM
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FM Limiter/ Detector
AM Detector
Fig. 4-12: FM, AM noise comparison 4-Dec-09
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Noise Suppression Effects of FM • •
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This unwanted noise produces PM, which in terns produce unwanted FM The amount of frequency deviation (FM) caused by PM is:
Frequency deviation
Modulating frequency
δ = φ × fm
. . . . . . . (4-7)
Phase shift in radians
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FM Noise analysis
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S : desired signal N : noise signal = ½ S => S/N = 2:1 R : resultant signal • The phase shift b/w noise and signal is given by:
N S
φ = sin −1
. . . . . . . (4-8)
Rotating vector
½S Φ
Φ S
Fig. 4-13: (a) 4-Dec-09
S
Phase shift as a result of noise (b) Maximum phase shift condition CH:4 FM EEN303 Communication Systems
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FM Noise analysis
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General equation for phase shift:
δ ( worst ) = (φrad ) f m
. . . . . . . (4-9
The maximum phase shift occurs when the noise & signal phasors are at a right angle to each other (worst case):
( )
φ = sin −1 1 2 = 30o = 0.5236 rad Then, worst case frequency deviation (from eq(4-7)):
δ ( worst ) = 0.5236 f m . . . . . . . (4-9-a) For improved SNR of an FM system:
N freq. dev. produced by noise . . . . . . . (4-10) = S max. allowed dev.
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FM Noise analysis
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Example (4-14) 14): If modulating frequency = 15 kHz, find worst case deviation in FM system, if input SNR is 2. Example (4-15) 15): Modulating frequency = 800 Hz. The SNR = 3:1. Determine the frequency deviation produced. Example (4-16) 16): Determine the worst case output SNR for a broadcast FM that has a maximum modulating frequency of 5 kHz. The input SNR is 2. Example (4-17) 17): The input SNR of an FM receiver is 2.8. the modulating frequency is 1.5 kHz. The maximum permitted deviation is 4 kHz. Find: (a) Frequency deviation caused by the noise (b) The improved output SNR 4-Dec-09
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Pre--Emphasis Pre • •
A voice signal is band limited to 3 kHz (low frequency) Musical instruments have almost low frequency components but some of them contain high frequency components as well
•
Thus an audio Hi Fi system must have wider band width to represent all
• •
Noise interfere FM signal, particularly at higher frequencies Noise primarily is sharp spikes of energy, it contains a lot of harmonics & other high frequency components These components are larger in magnitude than the high frequency components of modulating signal
•
•
High frequency components of information signals are usually at low amplitude levels
•
To overcome this problem, most FM systems use a technique ‘Pre-Emphasis’ to deal with high frequency noise problem
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Pre--Emphasis Pre C
fu =
R1 + R2 2π R1 R2C
R1
FM Modulator
R2
Pre-emphasis circuit
Pre-emphasis FM output
Fig. 4-14: (a) FM with pre-emphasis circuit
A(dB) dB/octave ≥ 30 kHz 3 dB 0 dB f1 4-Dec-09
fu
f (Hz)
Fig. 4-14 (b) : Pre-emphasis curve
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Pre--Emphasis Pre FM in
FM demodulator
De-emphasis circuit
R
Audio out
C
fL =
1 2π RC
Fig. 4-15 (a) : FM demodulator with De-emphasis circuit A(dB) 0 dB -3 dB
Fig. 4-15 (b) : De-emphasis curve f (Hz)
fL 4-Dec-09
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Pre--Emphasis Pre A(dB)
+3 dB 0 dB -3 dB
fa
f (Hz)
Fig. 4-16: Combined frequency response
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