UNIT 1. Amplitude modulation Topics :
1. Review of spectral characteristics of periodic and non periodic signals
2. Principles of AM
3. Generation and detection of AM 4. Generation and detection of DSBSC 5. Generation and detection of SSB 6. Generation and detection of VSB
7. Comparison of Amplitude modulation systems 8. Frequency translation
Definition for a Signal:
A signal is defined as a physical quantity that varies with time, space or any other independent variable or variables. It contains some information.
Eg. Electric voltage or current Radio signal, TV Signal, Computer Signal, etc., Signal can be represented either using Time domain approach or Frequency domain approach.
• In time domain representation of signals the amplitude is represented on one axis & the time is represented on the other axis.
• In frequency domain representation the amplitude or power is shown on one axis and frequency is displayed on the other. It specifies the relative amplitudes of the freq component.
• Any signal can be represented on either way.
• Signals can be broadly classified into Continuous Time signal (CT) and Discrete Time Signal (DT).
• A continuous time signal varies in its amplitudes continuously with time. • A DT signal is one in which the amplitude of the signal is discrete with
respect to time.
• A continuous time signal is called as Analog Signal. • A discrete time signal is known ad Digital Signal. Characteristics of a Signal :
The parameters such as amplitude, frequency & phase of the signal are known as characteristics of the Signal.
Energy and power signals: Power Signal :
• A signal is called a power signal if its “average normalized power” is non zero and finite .It has been observed that almost all the periodic signals are power signals.
Energy signals:
• A signal having a finite non zero total normalized energy is called as an energy signal. It is observed that almost all the non periodic signals defined over a finite period , are energy signals. As these signals are defined over a finite period, they are called as time limited signals
Average Normalized Power:
Average normalized power
For periodic signal with a period To the equation 1 and 2 get modified as
For a complexPeriodic signalx ( t) the average normalized power is given by,
Energy:
The total normalized energy for a "real" .signal x ( t) is given by,
……5
However if the signal is complex then the expression for total normalized energy is given by
A Review of Fourier Series and Fourier Transform
• In the field of communication engineering we need to analyze a given signal.
• To do so we have to express the signal in its frequency domain
• The translation of a signal from time domain to frequency domain is obtained by using the tools such as Fourier series' and Fourier transform
Fourier Series:
• Sine waves and cosine waves are the basic building functions for any periodic signal.
• That means any periodic signal basically consists of sine waves having different amplitudes, of different frequencies and having different relative phase shifts.
• Fourier.series represents a periodic waveform in the form of sum of infinite number of sine and cosine terms. It isa representation of the signal in a time domain series form.
• Fourier series is a "tool" used to analyze any periodic signal. After the "analysis” we obtain the following information. about the signal :
(i) All the frequency components present in the signal (ii) Their amplitudes and
(iii) The relative phase difference between these frequency components.
All the "frequency components" are nothing else but .sine waves at those frequencies
Exponential Fourier Series [OR Complex Exponential Fourier Series :
• Substituting the sine and cosine functions in terms of exponential function in the expression for the quadrature fourier series, we can obtain another type of Fourier series called the exponential Fourier series.
• A periodic signal x ( t) is expressed in the exponential Fourier series form as follows :
Amplitude and Phase spectrum:
• The amplitude spectrum of the signal X(t) is denoted by,
The Phase of the spectrum is denoted by,
• The amplitude spectrum is a symmetric or even function That means ICn I = IC_n I. But the phase spectrum is an asymmetric or odd function. That means arg ( Cn ) = - arg ( C_n ).
Fourier Transform :
• A Fourier transform is the limiting case of Fourier series. It is used for the analysis of non-periodic signals.
• The Fourier transform of a signal x ( t) is defined as follows.
………5 This equation is known as analysis equation.
Inverse Fourier Transform:
• The signal X(t) can be obtained back from fourier transform X(f) by using the inverse fourier transform. The inverse transform (IFT) is defined as follows:
……..6 Amplitude and Phase spectrums:
• The amplitude and phase spectrums are continuous rather than being discrete in nature. Out of them, the amplitude spectrum of a real valued function X(t) exhibits an even symmetry and
• The phase spectrum has an odd symmetry. X(f)=X(-f) ……….6
……….7
Problems:
Ex.1 Obtain the Fourier transform of a rectangular pulse of duration T and amplitude A as shown in the fig
The rectangular puse shown can be expressed mathematically as
This is also known as gate function Therefore the Fourier transform will be
………….1
As per the Euler’s theorem
Applying this in equation (1) we get
……….2
Multiply and divide the RHS of equation 1 by T to get
……….3
In the above equation
…………4
Amplitude spectrum:
The amplitude spectrum of the rectangular function is as shown in fig below As, sinc(0) = 1
Therefore AT sinc(0) = AT
The sinc function will have zero value for the following values of “fT”:
The phase spectrum has not been shown as it has zer value for all the values of f ,
To absorb negative values of X(f) in the phase shift:
The negative amplitude of the amplitude spectrum has been absorbed by introducing a ±180º phase shift as shown in the figure below
EX. 2: For the sinc function shown in the fig obtain the fourier transform and plot the spectrum.
Soln: The sinc signal shown in the figure can be expressed as X(t)= Asinc(2wt)
To evaluate the fourier transform of this function we are going to apply the duality and time domain properties of the Fourier transform.Refering to the example 1, where we have obtained
The Fourier transform of a rectangular pulse of amplitude A and duration T, as,
Using the duality property we can write that
Comparing equation (3) with the RHS of Equation (1) which states the expression for X(t), as
• Thus a sinc pulse in the time domain is transformed into a rectangular pulse in the frequency domain. The spectrum of the sinc pulse is shown in the figure.
Fourier Transform for the Periodic signals:
• Sometimes it is essential to obtain the FT of periodic signals .For example, the sampling theorem
• FT of a periodic signal is given by
Where Cn is the Fourier coefficient given by
Fourier Transforms of Standard signals:
The FT of Some signals is given in the following table.
Sr.No Signal Mathematical
representation
Fourier transform
8 Cosine signal X(t) = cos(2πfct)
9 Sine signal X(t) = sin(2πfct)
10 Signum function X(t) = sgn(t) X(f)=1/jπf 11 Unit step X(t) = u(t)
Power and energy theorem: The theorems are:
1. Parseval’s power theorem 2. Rayleigh’s energy theorem.
Parseval’s Power theorem:
This theorem relates the average power of a periodic signal to its “fourier series” coefficients. This theorem states that the total average power of a periodic signal X(t) is equal to the sum od the average powers of the individual fourier coefficients i.e Cn
Average Power of X(t)=(Power of C1) + (Power of C2) +……. Or total average power
Rayleigh’s energy theorem:
This is analogous to the Parseval’s power theorem.It states that the total energy of the sinal X(t) is equal to the sum of energies of the individual spectral components in the frequency domain. The total normalized energy of a signal X(t) is given by,
The normalized energy:
Definition for Communication:
• Electronic Communication System – defined as the whole mechanism of sending and receiving as well as processing of information electronically from source to destination.
• Example – Radiotelephony, broadcasting, point-to-point, mobile communications, computer communications, radar and satellite systems.
Introduction to Communication:
• Communication – Basic process of exchanging information from one location (source) to destination (receiving end).
• Refers – process of sending, receiving and processing of information/signal/input from one point to another point.
NEED FOR COMMUNICATION:
• Interaction purposes – enables people to interact in a timely fashion on a global level in social, political, economic and scientific areas, through telephones, electronic-mail and video conference.
• Transfer Information – Tx in the form of audio, video, texts, computer data and picture through facsimile, telegraph or telex and internet.Broadcasting – Broadcast information to masses, through radio, television or teletext
Terms Related To Communications:
• Message – physical manifestation produced by the information source and then converted to electrical signal before transmission by the transducer in the transmitter.
• Input Transducer – placed at the transmitter which convert an input message into an electrical signal.
Example – Microphone which converts sound energy to electrical energy
Output Transducer – placed at the receiver which converts the electrical signal into the original message.
Example – Loudspeaker which converts electrical energy into sound energy
Signal – electrical voltage or current which varies with time and is used to carry message or information from one point to another
Elements of a Communication System
The basic elements are : Source, Transmitter, Channel, Receiver and Destination
Function of each Element
• The message produced by the information source is not electrical in nature; It may be a voice signal, picture signal etc. Hence a transducer is required to convert the original physical message into a time varying electrical signal.
• These signals are called as Base band signals or Message Signals or modulating Signals.
• Transmitter comprises of electrical and electronic components that converts the message signal into a suitable form for propagating over the communication medium. .
• Channel provides the connection between sources and destinations. It can be of many forms like coaxial cable, microware link, Radio leave link or Optical fiber.
• The receiver extracts the message signal from the degraded version of transmitted signal.
• At the destination, another transducer is used to convert the electrical signal into the appropriate message.
Base band transmission:
• Baseband signal is the information either in a digital or analogue form.
• Transmission of original information whether analogue or digital, directly into transmission medium is called baseband transmission. • Example: intercom (figure below)
Baseband signal is not suitable for long distance communication because of the following reasons:
• Hardware limitations
• Requires very long antenna
• Baseband signal is an audio signal of low frequency. For example voice, range of frequency is 0.3 kHz to 3.4 kHz. The length of the antenna required to transmit any signal at least 1/10 of its wavelength (λ). Therefore, L = 100km (impossible!)
• Interference with other waves
Simultaneous transmission of audio signals will cause interference with each other. This is due to audio signals having the same frequency range and receiver stations cannot distinguish the signals.
In Order to overcome this disadvantage of Baseband transmission we go for Modulation where the low frequency message signal is converted to high frequency signal.
Modulation & Need for modulation
Modulation is the process of changing the characteristics of a high frequency carrier signal in proportion with the instantaneous value of the modulating signal.
Need for modulation 1. Antenna Height:
For communication the antennas are needed to transmit & receive the signals. The antenna radiates effectively when its height is of the order of wavelength of the signal to be transmitted.
χ c Antenna Height = ––– = –––
2 2f
f → frequency of the signal. c → Velocity of the light. For a low frequency signal say 1KHz.
3 x 108
o Antenna height = ––––––––– = 150 km 2 x 1 x 103
Where as for a high frequency signal say, 3 x 108
o 1MHz Antenna height = ––––––––– = 150 m 2 x 1 x 103
This height is practically achievable.Hence modulation is needed . 2. Narrow Banding:
Say we are transmitting a baseband signal in the range of 50Hz to 10KHz. The ratio of highest frequency to lowest freq. will be 103 x 103 / 50 = 200.
It we design an antenna for 50 Hz. It will be too large for 10KHz. Once we modulate this signal range using a 1MHz carrier. The ratio of highest freq. will be (104 + 106) / 106 + 50 = 1.01/1 ≈ 1.
3. Multiplexing :
If more than one signal uses a single channel then modulation may be used to translate different signal to different spectral location, thus, enabling the severer to select the desired signal.
4. To overcome equipment limitations:
When ever we are designing the equipment, it will be designed for fixed range of freq. By modulation we can make any signal to pass through the same equipment.
5. Modulation to reduce noise and interference:
It is not possible to eliminate noise and interference in communication system. But can be minimized using modulation technique.
Amplitude Modulation:
It is the process of changing the amplitude of a relatively high frequency carrier signal in proportion with the instantaneous value of the modulating signal (Information, Message).
Though there are 3 types of Am Double side band full carriers is the most commonly used and is also know as conventional Am or simply Am.
Fig 1. a) Message signal b) carrier signal
Principles of Amplitude Modulation: AM envelope and the equation:
• Consider a message signal em= Em sin 2πfmt.
• Let the carrier Signal be ec= Ec sin 2πfct.
• According to the definition the Amplitude modulated wave can be indicated as
Eam=(Ec+Em sin 2πfmt.) sin 2πfct
The shape of the modulated wave is called the Am envelop.
Depth of Modulation/Modulation Index:
Coefficient of modulation and percent modulation:
If is defined as the ratio of maximum amplitude of the message signal to the maximum amplitude of the carrier signal.
Em
m = ––––– Ec
Percent modulation is indicated ad M Em
M = ––––– x 100 or M = m x 100 Ec
Relationship b/w m, Em & Ec From the figure below.
EC = ½ (Emax + Emin)
½ (Emax - Emin) Emax - Emin
M = –––––––––––––– x 100 = –––––––––– x 100 ½ (Emax + Emin) Emax + Emin
• Based on the modulation index modulation can be either, (i). Critical Modulation
(ii). Over Modulation (iii). Under Modulation
• When Em = Ec modulation goes to 100% this situation is known as critical
modulation.
• Em < Ec leads to under modulation.
AM frequency Spectrum & Bandwidth :
• Am envelope is a complex wave made up of a dc, voltage, the carrier freq. & the sum (fc + fm) and difference (fc - fm) frequencies. (Cross Products)
• The sum and difference frequencies are displaced from the carrier frequency by an amount equal to the modulating signal.
• The effect of modulation is to translate the modulating signal in the frequency domain.
• The figure 2 shown the frequency spectrum of Am. • It extends from fc -fm (max) to fc + fm (max).
• The band of frequencies b/w fc and fc - fm (max) is called lower side band
[LSB] and any frequency within this band is called lower side frequency [LSF].
• The band of frequencies b/w fc and fc + fm (max) is called upper side band
[VSB] and any frequency within this and is called upper side frequency [USF]
Bandwidth of AM.
The Bandwidth of Am wave is equal to the difference b/w the highest upper side frequency and lowest lower side frequency.
B = fc + fm (max) – [fc - fm (max)]
= fc + fm (max) - fc + fm (max)
BW = 2fm (max)
Ex. 1 :
For an Am DSBFC modulator with a carrier frequency fc = 100 KHz and
maximum modulating signal frequency fm (max) = 5 KHz, determine.
a. Frequency limits for upper and lower sidebands. b. Bandwidth.
c. Upper and lower side frequencies produced when modulating a signal in a signal frequency 3 KHz tone.
d. Draw the freq spectrum. Soln :
fc = 100 KHz
fm = 5 KHz
a. Lower side band Freq. = fc - fm = 95 KHz
Upper side band Freq. = fc + fm = 150 KHz
b. B.W = 2 fm (max)
= 10 KHz.
For a 3 KHz msg signal.
LSF = 100 k - 3KHz → 97 KHz USF = 100 k + 3KHz → 103 KHz
AM Voltage Distribution :
• The carrier signal can be described as , Vc cts = Ec sin 2πfct
Vc cts → Time varying voltage of carrier.
Ec → Peak carrier amplitude.
Fc → Carrier freq in
• The modulation signal can be expressed as, Eam = Vam cts = (Ec + Em sin 2πfmt) sin 2πfct
= Ec sin 2πfct + Em sin 2πfmt sin 2πnfct
Em Em
= Ec sin 2πfct – –––– cos 2π (fc+fm) t + –––– cos 2π (fc+fm) t
2 2
Em Em
Eam = Ec sin 2πfct – –––– cos 2π (fc+fm) t + –––– cos 2π (fc+fm) t
2 2 Ec sin 2πfct → Carrier signal (volts) -mEc
–––– Cosπ (fc + fm) t. → Upper side frequency signal (volts).
2
+mEc Cosπ (fc - fm) t. → Lower side frequency signal (volts).
2
V (max) = Ec + Ec/2 + Ec/2 = 2Ec
V (min) = Ec - Ec/2 - Ec/2 = OV
• The peak change in the amplitude of the o/p wave is the sum of the voltages from the upper and lower side frequencies.
Hence Em = Eusf + Elsf
Ex. 2 :
One i/p to a conventional Am modulator is 500 KHz carrier with an amplitude of 20 Vp. The second i/p is a 10 KHz modulating signal that is sufficient to cause a change in the o/p wave of ± 7.5vp Determine.
a. Upper and Lower side frequencies.
b. Modulation coefficient and percent modulation
c. Peak amplitude of the modulated carrier and the upper and lower side frequency voltages.
d. Maximum and minimum amplitudes of the envelope. e. Expression for the modulated wave.
f. Draw the o/p spectrum. g. Sketch the o/p envelop.
Soln : a. fusf = 500 KHz + 10 KHz = 510 KHz Flsf = 500 KHz - 10 KHz = 490 KHz b. m = Em / Ec = 7.5 / 20 = 0.375 M = 0.375 x 100 = 37.5% c. Ec = 20 VP EVSF = ELSF = mEc / 2 = 0.375 x 20 /2 = 3.75 Vp d. Vmax = Em + Ec = 27.5 Vp Vmin = Ec - Em = 12.5 Vp
e. Vam lts = 20 sin 2π 500 kt – 3.75 cos (2π 510 kt) + 3.75 cos 2π 490 kt
Am power Calculation :
The power of the carrier is Ec2
Pc = –––
2R
Pc → Carrier power.
R → Load resistance (mEc/2)2 m2Ec2 PUSB = PLSB = ––––––– = –––––– 2R 8R m2 E c2 PUSB = PLSB = ––––– =–––––– 4 2R m2 = –––– PC 4 Pt = PUSB + PLSB + PC m2 Pc m2Pc Pt = Pc + ––––––– + –––––– 4 4 m2 Pt = Pc 1 + –––– 2 Ex. 3 :
An Am transmitter operating at a carrier freq of 1 MHz and a modulating frequency of 5 KHz and modulated at 60% depth delivers a carrier power of 6kw into 50Ω.
a. Obtain the total average power of the modulated signal in DB watts & dsm.
b. Obtain the RMS voltage of the modulated signal. Soln :
a. Pt = Pc (1+m2 /2)
= 6 ( 1 + 0.36 / 2) = 10.8kw = 40.334 dB. b. The Modulated signal power.
V2(rms) = 2 x RL x P Signal.
= 2.5 x 10.8 x 103 = 1.028 kV.
Ex. 4 :
For a Am DSBFC wave with a peak unmodulated carrier voltage V1 = 10Vp, a load resistance Rc =10Ω. and modulation coefficient m=1, determine
a. Power of the carrier and the upper and lower sidebands b. Total solebard power
c. Total power of the modulated wave. d. Draw the power spectrum.
e. Repeat the above for m=0.5. Soln : Ec2 102 100 a. Pc = –––– = –––––– = –––––– =5w 2R 2(10) 20 m2Pc PUSB = PLSB = –––––– = ¼ x 5 = 1.25w 4
b. Total sideband power = PUSB + PLSB = 1.25 x 2 = 2.50w
c. The total power in the modulated wave is found by, Pt = Pc( 1+ m2/2) = 7.5ω
d. The power spectrum is given by. Am Current Calculations
Pt It2R It2 m2
––– = –––– = ––– = 1 + –––– Pc Ic2R Ic2 2
Pt → Total transmit Power
Pc → Carrier Power
Ic → Carrier Current
m → Modulation index R → Antenna Resistance It2 = Ic2 (1+m2/2)
It2 = Ic2 √1+m2/2)
Modulation by a complex information signal :
• If the modulating signal contains two frequencies say fm1 & fm2, the
modulated wave will contain the carrier and two sets of side frequencies. Spaced symmetrically about the carrier.
Vam (t) = sin 2π fct + ½ cos 2π (fc - fm1) t - ½cos 2π (fc+ fm1) t
+ ½cos 2π (fc- fm2) t - ½cos 2π (fc+ fm2) t
• The coefficient of modulation or modulation index is given by mt = √m12 + m22
• In general for n different signals mt = √m12 + m22 + . . . mn2
• Pusbt = Plsst = Pcmt2 / 4
• Pt = Pc (1+mt2 / 2)
Ex. 5 :
Find the power in each side band of a DSBSC signal with the carrier signal at 1 MHz and of a peak signal voltage on 100V modulated simultaneously by 3 different signals. The freq. of the modulating signal are 2KHz, 3KHz and 5KHz respectively and Peak modulating vaoltages are 10V, 20V and 30V respectively. Assume a load resistance of 100Ω.
Soln :
Given fm1 = 2KHz; fm2 = 3KHz ; fm3 = 5KHz
m1 = 10/100 = 0.1 m2 = 20/100 = 0.2 m3 = 30/100 = 03 mt = m12 + m22 + m32 = 0.374 PSB = Pc x m2/4 = Vc2 (Peak) / 2RL x m2/4 1002 x 0.3742 = –––––––––––– = 1.75ω 2 x 100 x 4 AM modulating Circuits
• Based on the location in the transmitter Am modulating circuits are classified as
a. Low level AM modulator b. High level AM modulator
Difference b/w low level and High level AM mod.
Low level AM modulator High level AM modulator 1. Modulation takes place prior to
the final stage of the transmitter
1. Modulation takes place in the final element of final stage. 2. Less modulating signal power
is required
2. More modulating signal power is required.
Low level AM modulator
• Class A amplifier can perform amplitude modulation.
• Amplifier must have 2 inputs one for the carrier signal & second for modulating signal.
• Without modulating signal the carrier signal is just amplified.
• The carrier is applied the base and the modulating signal to the emitter. Hence it is also called as Emitter Modulation.
• The modulating signal varies the gain of the amplifier at a sinusoidal rate equal to the frequency of the modulating signal.
• The depth of modulation achieved is proportional to the amplitude of the modulating signal.
• The voltage gain for an emitter modulator is expressed as, Av = Aq (1 + m sin 2πfmt)
Av → Amplifier voltage gain with modulation.
Aq → Amplifier quiescent (without modulation) voltage gain.
sin 2πfmt varies form + 1 to -1 Hence, Av = Aq (1±m)
Advantages of Low level modulation:
1. Less modulating signal power is required to obtain high percentage modulation.
2. Modulating circuit is designed for low power. Disadvantage of Low level modulation
Amplifiers following modulator stage must be linear. At high operating powers linear amplifiers are very inefficient.
High power AM modulator / Medium Power AM modulator.
• The class C amplifier is used. It operates nonlinear and is capable of nonlinear mixing (modulation).
• This is known as collector modulator because modulating signal is applied to the collector.
• When the amplitude of the carrier exceeds the barrier potential (0.7V) Q1 turns on collector current flows.
• When carrier voltage drops below 0.7V Q1 turns off and collector current cases.
• When the modulating signal is applied it adds up with the Vcc and gets
submitted from Vcc producing an Am o/p.
Advantages of high level modulators:
• There is no constraint of linear operation on amplifiers preceding modulator stage.
• Power efficiency is good
Disadvantages of high level modulators: • High modulating power is required.
• Final modulating signal amplifier has to supply all the sideband power.
AM transmitters Low level Transmitter
• Modulating signal is got from an acoustical transducer (Converts voice or music). Such as microphone a magnetic tape, CD or a phonograph record.
• Bufferamplifier : Class a linear voltage amplifier. It raises the amplitude of the source.
• Driver-amplifier The information signal to an adequate level to sufficiently drive the modulator.
• Buffer amplifier: It is a low gain, high input impedance linear amplifier. • Matching Network: matches the o/p impedance of the final power
amplifier to the transmission line and antenna.
Application: used in low capacity system such as wireless intercoms, Remote control units, pagers, shot range talkie.
High level Transmitters:
• Here modulating signal power should be higher than the low level. • The amplification takes place prior to modulation.
• Used for long distance communications. AM Detector circuits :
• Figure shows the circuit and the i/p and o/p waveforms.
• Initially at time t=0 the diode remains off and the capacitor is completely discharges Vc = OV.
• The diode remains off until the i/p voltage exceeds the barrier voltage. • When Vin reaches the Barrier voltage the diode turns on, the diode current
flows, charging the capacitor. To the max amplitude.
• When i/p voltage begins to decrease, the diode turns off. The capacitor begins to discharge through the resistor bur RC time constant is made sufficiently long so that the capacitor cannot discharge as rapidly as Vin is
decreasing.
• The diode remains off until the next i/p cycle when Vin goes 0.3V more +ve
than Vc, the diode turns on the capacitor charges to the maximum value.
• This sequence repeats itself on each successive positive peak of Vin and
the capacitor voltage follows the +ve peak of Vin. Hence it is called as
peak detector.
• The output waveform resembles the shape of the i/p envelope. Hence the name shape detector.
• The o/p wave form has a high frequency ripple that is equal to the carrier freq. This is due to the diode turning on during the positive peak of the envelope.
• This can be removed by the audio amplifiers. Amplitude Modulation Classification:
• Double side band full Carrier (DSBFC)
• Double side Band suppressed Carrier (DSBSC) • Single Side Band Suppressed Carrier (SSBSC) • Vestigial side Band (VSB)
• In the frequency spectrum, the carrier frequency is not carrying any information hence can be suppressed and is called Double side band with suppressed carrier ( DSBSC) or simply Double side Band(DSB)
• Both the sidebands are carrying the same information hence only one sideband is sufficient to convey the message. So we can suppress one sideband and transmit the other - Called as the Single side band with suppressed carrier (SSBSC) or single side band (SSB).
• In some cases only a portion (vestige) of the modulated signal will be carrying the information hence we can transmit only that portion and suppress the rest and this type is called as vestigial side band (VSB). DSBSC system:
It is a technique where it is transmitting both the sidebands without the carrier (carrier is being suppressed/cut)
Characteristics:
Power content less Same bandwidth
Disadvantages - receiver is complex and expensive SSB System
• Improved DSBSC and standard AM, which waste power and occupy large bandwidth
• SSB is a process of transmitting one of the sidebands of the standard AM by suppressing the carrier and one of the sidebands
Advantages: Saving power
Reduce BW by 50%
Increase efficiency, increase SNR
Generation and Demodulation of DSBSC :
A circuit that produces a double sideband suppressed carrier signal is balanced modulator.
Balanced modulator / Balanced lattice Modulator.
• Has two i/p and the carrier and the modulating signal.
• The amplitude of carrier must be sufficiently greater than the amplitude of the modulating signal to ensure the on and off condition of 4 diodes.
• When modulating signal is +ve. The carrier signal is as shown then the diodes
D1 & D2 are forward biased (on)
D3 & D4 are reverse biased (off)
• When the modulating signal is Zero & the carrier signal is in the positive half cycle, the Diode D1 & D2 are forward biased and D3 & D4 are reverse
• The current divides equally in the upper and lower portions of the primary winding of T2. This produces a magnetic field which is equal in magnitude
but in opposite dissection in the upper and lower portions of primary winding hence they cancel each other.
• IIIrly when the carrier signal is in the negative half cycle the diodes D3 & D4
are forward biased and D1 & D2 are reverse biased.
• Here also magnetic fields in primary winding are equal and opposite canceling each other. Thus the carrier is suppressed.
• The Diodes D1 to D4 are the electronic switches that control whether the
modulating signal is passed from T1 to T2 as it is or with 1800 phase shift.
• When the carrier is in +ve half cycle the message signal is transferred across the closed switches to T2 without a phase reversal.
• When the carrier is in -ve half cycle the message signal is transferred across the closed switches to T2 with a 1800 phase reversal.
Coherent detection of DSBSC waves:
The coherent detector for the DSBSC signal as shown in the figure.
• DSBSC wave S(t) is applied to a Product modulator in which it is multiplied with the locally generated carrier
• The locally generated carrier is exactly coherent in frequency and phase with the original carrier. Hence the method is called as coherent detection or synchronous detection.
• The output of the product modulator is applied to the low pass filter which eliminates the unwanted frequency components to produce the original message signal.
Costas loop detection for DSBSC modulated wave:
• It consists of 2 coherent detectors with same input(the DSBSC). • The local oscillator signals for individual detectors will be in phase
and quadrature with respect to each other.
• The local oscillator is adjusted to the carrier frequency.
• The detector in the upper path is known as in-phase coherent detector or I-channel .
• The detector in the lower path is known as Quadrature –phase coherent detector of Q-channel.
• These two detectors are coupled together to form negative feedback system (to maintain local oscillator in synchronous with the carrier wave).
• If the local oscillator signal is same as that of the carrier, I-channel output contains the desired demodulated output and Q-channel output is zero.
• Else Q-channel contains the output.
• Assume that the local oscillator drifts in phase by a small value φ radians, the output of I-channel will remain same but the Q-channel will produce a small voltage as its output, which is proportional to
• The outputs of I and Q channel are combined in the phase discriminator, which is a multiplier followed by a low pass filter. • The phase discriminator produces a DC voltage proportional to the
error φ. The dc voltage is applied to the input of the VCO to correct the frequency and phase of the VCO automatically to reduce the phase.
Single Sideband signal:
Since both the sidebands are carrying the same information it is sufficient to transmit only one side band. Such a transmission is called as Single side band transmission.Figure below shows the SSBSC system
Advantages of SSB:
• Since only single sideband is transmitted the bandwidth of the transmitter and channel is only fm.This is half of the BW of DSBFC system.
• The power of the suppressed sideband is saved. • The effect of noise at the receiver is reduced.
• Fading effect which arises because of the interference of carrier and two sidebands is removed in SSB.
Generation of SSB:
Suppression of unwanted sideband:
• The balanced modulator produces DSB o/p. This DSB signal contains both the sidebands.
• This is given to sideband suppression filter to remove unwanted sidebands.
• The filter must have a flat pass band and extremely high attenuation outside the passband.
Phase shift method to generate SSB :
• Consists of 2 Balanced modulators1 and M2.
• One Modulator say M1 has the direct modulating signal and 900 phase
shifted carrier signal
• Hence the o/p of modulator M1 is given as
• The modulator M2 gets the i/p of direct carrier signal and 900 phase shifted
message signal, the o/p of M2 is given by,
y = cos ( wc - 90 ) - wm – cos (wc + 90) + wm ---- (2)
At the summer we will have,
x + y = cos (wc - wm) - 90 – cos (wc + wm) + 90
cos (wc - wm) + 90 – cos (wc + wm) + 90
x + y = - 2cos (wc + wm) + 90
Thus one side band is totally eliminated while retaining the other. Vestigial Sideband ,Transmission:
Definition : One of the sideband is partially suppressed and vestige (portion) of the other sideband is transmitted, This vestige (portion) compensates the suppression of the sideband. It is called vestigial sideband transmission.
Generation and demodulation of VSB:
• Fig.shows the generation of VSB. The product modulator generators DSB-SC signal from the message and carrier.
• The bandpass filter is designed in such a way that. it suppresses one side band partially and passes a portion (vestige) of other sideband.
• The output of the bandpass filter is VSB signal.
Magnitude Response of VSB Filter
Fig. shows the magnitude response of VSB filter.
• Here observe that fc to fc+W is USB. It's portion from fc to fc +fv is suppressed partially. fc to fc - W is LSB. It's portion from fc -fv to fc is transmitted as vestige.
• Observe that H(fc)=1/2. And the frequency response fc-fv<=H(f) <= fc+fv exhibits odd symmetry.
The sum of any two frequency components in, the range. Is
equal to unity. i.e H(f-fc) + H(f+fc) = 1 • Phase response is linear.
Transmission bandwidth
From Fig. the transmission bandwidth of VSB modulation is, Br = fc +W
Applications and Advantages of VSB Advantages:
1. Low frequencies, near fc are, transmitted without any attenuation. 2. Bandwidth is reduced compared to DSB.
Applications:
VSB is mainly used for TV transmission, since low frequencies near fc represent significant picture details. They are unaffected due toVSB.
Frequency translation:
• In communication system the frequency of the modulated wave is translated either upward or downward. So that the modulated wave occupies a new slot in the frequency spectrum.
• Mixer is a device which carries out the frequency translation of the modulated wave.
• The operation of frequency translation is called as mixing or heterodyning. • The mixing is alinear operation in which it preserves the relation between
the sidebands of the incoming signal with the carrier.
Fig a) Spectrum of modulated signal at the input of the mixer b)Spectrum of modulated signal at the output of the mixer .
Frequency division multiplexing:
Channel 1 Channel 2 Channel 3 Channel 4
Source Information Source Information Source Information Source Information 100 KHz 105 KHZ 110 KHz 115 KHz 120 KHz Fig 1
• FDM is analog multiplexing scheme.
• A familiar example is the commercial Am Broadcast band. Which occupies a freq spectrum from 535 KHz to 1605 KHz.
• Each Broadcast station carries an information signal that occupies a Bandwidth b/w 0Hz to 5 KHz.
• If the information is transmitted with original freq spectrum, it will be impossible to separate one stations transmission from the other.
• Each station amplitude modulates a different carrier frequency and produces a 10 KHz signal.
• With FDM each narrow band channel in converted to a different location in the total frequency spectrum.
• The channels are staked on top of one another in frequency domain. • In the figure, a simple FDM system where four 5 KHz channel are
frequency division multiplexed into a single 20 KHz channel (Combined). • Channel 1 amplitude modulates a 100 KHz carrier in a Balanced
Modulator. The o/p of Balanced modulator is 10 KHz DSBSC. This is passed through BPF where it is converted into a SSB signal for this it will be
• 100 KHz - 105 KHz.
IIIrly for Channel 2 → 105 KHz to 110 KHz ,, ,, → 110 KHz to 115 KHz ,, ,, → 115 KHz to 120 KHz
• The combined o/p spectrum by combining the o/p and from the four BFP is shown which has a total Bw of 20 KHz. With each channel
The operation can be explained with the above block diagram
• The input message signals from various sources are passé through the LPF to obtain a band limited signal .
• Then the output of this is Amplitude modulated using different carrier frequencies in the modulator.
• The output of the modulator is a DSBSC signal. This is passed through a BPF to obtain a SSB signal.
• The output of n different BPF s are multiplexed and passed through a single channel.
• At the receiver The original signal is recovered by using the same carriers used in the transmitter
Application of FDM 1. Commercial FM
2. Television broad casting. 3. High-volume telephone. 4. Data communication System. 5. Cable Television.
TUTORIAL Problem :
1. An Audio frequency signal 10 sin 2π x 500 t is used to amplitude modulate a carrier signal of 50 sin 2π x 105t calculate.
1. Modulation index 2. Sideband frequencies
3. Amplitude of each sideband frequencies 4. Bandwidth required
5. Total Power delivered to the load of 600 Ω Soln : 1. 0.2 or 20% 2. wm = 2π x 500 → fm = 500 Hz wc = 2π x 105 → f c = 105 Hz or 100 KHz. fusb = fc + fm = 100 KHz + 500 Hz = 100.5 KHz flsb = fc - fm = 100 KHz - 500 Hz = 99.5 KHz
1. Amplitude of side bands = mEc / 2 = 0.2 x 50 / 2 = 5 V 2. Bandwidth of AM = 2 fm = 2 x 500 Hz = 1 KHz.
3. Total Power delivered to the load
Ec2 m2 502 (0.2)2 Ptotal = ––––– 1 + ––– = –––––––– 1 + ––––––
2R 2 2 x 600 2 Ptotal = 2.125 watts
Problem :
2. A 400w carrier is modulated to a depth of 80% calculate the total power in the modulated wave.
Soln :
Pc = 400w m = 0.8
= 528 W.
Problem :
3. A broad cast transmitter radiates 20 Kw when the modulation % is 75 calculate carrier power & Power of each side bard.
Soln : PTotal = 20,000W & m = 0.75 m2 Ptotal = Pc 1+ ––– 2 (0.75)2 20,000 = Pc 1+ ––––––– 2 Pc = 15.6 Kw m2 Ptotal = Pc 1+ ––– = Pc + Pcm2 /2 2 PSB = Pcm2 / 4 PSB = 2.2 kw. Problem :
4. The total antenna current of an Am transmitter is 5A. If modulation index is 0.6, Calculate the carrier current in antenna.
Soln : M2 (0.6)2 I Total = Ic 1+ –––– => 5 = Ic 1 + ––––– 2 2 Ic = 4.6A Problem :
5. Calculate the total modulation index if the carrier wave is amplitude modulated by three modulating signals with modulation Indies of 0.6, 0.3 & 0.4 respectively. Soln : Mt = √ m12 + m22 + m32 = √ 0.62 + 0.32 + 0.42 Mt = 0.781 Problem :
6. An Am transmitter radiator 10 kw with the carrier and 11.8 kw when the carrier is sinusoidally modulated calculate the modulation index. If another sinewave corresponding to 30% modulation, is transmitted simultaneously determine the total radiated power. .
PTotal M = 2 –––––– - 1 Pc 11.8 M = 2 –––––– - 1 = 0.6 10
m1 = 0.6 the another signal modulates 30% Hence m2 = 0.3. The
combined total modulation index due to two signal.
Soln : : Mt = √ m12 + m22 = √ 0.62 + 0.32 mt2 (0.67)2 P Total = Pc 1 + –––– = 10 1+ ––––– 2 2
Problem :
7. A complex modulating waveform consisting of a sin wave of amplitude 3V and frequency 1 KHz plus a cosine wave of amplitude 5 V and freq 3 KHz. Amplitude modulates a 500 KHz and 10V peak carrier voltage plot the spectrum of modulated wave and determine the average power when the modulated wave is fed into 50Ω load.
em = 3 sin (2π x 1000) t + 5 cos (2π x 3000) t ec = 10 sin (2π x 500 x 103) t Soln : m1 = 3/10 = 0.3 ; m2 = 5/10 = 0.5 mt = √ m12 + m22 = 0.58 Problem :
1. A telephone transmitter using Am has unmodulated carrier o/p power of 20kw and can be modulated to a max depth of 80% by a sinusoidal voltage without causing a overloading find the value to which unmodulated carrier power may be increased without resulting is overloading if the maximum permitted modulating index is restricted to 60% determine the carrier swing the maximum and minimum frequencies altained, and the modulating index of the Fm signal generated by frequency modulation at 101.6 MHz carrier with an 8 KHz sine wave causing a frequency deviation of 24 KHz. Given : fm = 8 KHz fc = 101.6 MHz ∆f = 40 KHz ∆f 40 KHz Mf = ––––– = –––––––– = 5 Fm 8 KHz
For modulation index 5, n = 8 Max freq = fc + n fm = 101.6 MHz + 8 x 8 KHz = 101.664 MHz Min freq = fc + 8 fm = 101.6MHz - 8 x 8 KHz = 101.664 MHx
Min freq = Max freq - Min freq
= 101.664 MHz - 101.536 MHz = 128 KHz.
UNIT 2
ANGLE MODULATION SYSTEM
TOPICS:
1. PHASE AND FREQUENCY MODULATION 2. SINGLE TONE FM
3. NARROW BAND AND WIDE BAND FM 4. TRANSMISSION BANDWIDTH
Angle Modulation Definition
We know that amplitude, frequency or phase of the carrier can be varied by the modulating signal. Amplitude is varied 'in AM. When frequency or phase of the carrier is varied by the modulating signal, then it is called angle modulation, There are two types of angle modulation.
1. Frequency Modulation :
When frequency of the carrier varies as per amplitude variations of modulating signal, then it is called Frequency Modulation (FM). Amplitude of the modulated carrier remains constant.
2. Phase Modulation :
When phase of the carrier varies as per amplitude variations of modulating signal, then it is called Phase Modulation (PM). Amplitude of the modulated carrier remains constant,
Frequency Modulation:
The frequency of the high frequency carrier signal is carried in accordance with the modulating signal.
Vm = Em sin 2πfmt
Vc = Ec sin 2πfct
Vfm = Ec sin (2πfct + mf sin 2πfmt)
Vfm = Ec sin (wct + mf sin wmt)
mf → modulating index of fm
Relationship/Difference between FM and PM:
• The basic difference between FM and PM lies in which property of the carrier isdirectly varied by modulating signal. Note that when frequency of the carrier varies,phase of the carrier also varies and viceversa.
• But if frequency is varied directly, thenit .is called FM., • And if phase is varied. directly, then it is called PM.
The instantaneous phase deviation is denoted by θ (t). It is the instantaneous change in phase of the carrier with respect to reference phase. The instantaneous phase of the carrier is precise phase of the carrier at a given instant .It is mathematically expressed as,
Instantaneous phase =
...(1)
Here θ(t) is the instantaneous phase deviation and ωc is the carrier frequency. Now the instantaneous frequency deviation is defined as
...(2)
Definition for instantaneous frequency deviation: It is the instantaneous change in carrier frequency. It is equal to the rate at which instantaneous phase deviation takes place.
Definition of instantaneous frequency:It is the frequency of the carrier t a given instant of time. It is given as
...(3)
Instantaneous phase deivation θ(t) is proportional to modulating signal voltage
-...(4) Where K is the deviation sensitivity of phase
Similarly the instatneous frequency deviation is proportional to modulating Signal voltage.
...(5) Where k1 is the deviation sensitivity of frequency. From equation (2)
We have
...(6) Let the modulating signal be given as
Using the equation in equation (6)
...(7) The angle modulated wave is mathematically expressed as
...(8) Using the value of θ(t) in the above equation from equation (7)
....(9) Similarly using the value of θ(t) from equation (5) in equation (8) we get
FM and PM waveforms:
From the above waveform we can note the following
• For FM signal maximum frequency" deviation takes Place when Modulating signal is at positive .and negative peaks.
• For PM signal the maximum frequency. deviation takes place near zero crossings of the modulating signal.
Definition of Modulation index of PM and FM
The modulation index of PM is given as M=KEm
For FM It is the ratio of maximum frequency deviation (δ) to the modulating frequency (fm).
Maximum frequency deviation δ mf = ––––––––––––––––––––––––––––– = ––––
Modulating frequency fm
• The maximum frequency deviation is the shift from centre frequency fc
when the amplitude of message is maximum. ∆ f = K1 Em (Hz)
K1 = Deviation sensitivity.
The Bandwidth of FM:
• By Carson’s rule the Bandwidth needed by fm is given as, Bω = 2 (δ + fmmax)
δ → Maximum frequency Deviation fmmax is Maximum modulating frequency.
Deviation Ratio :
The modulation index corresponding to maximum modulating frequency is called deviation ratio.
Maximum frequency deviation Deviation Ratio = –––––––––––––––––––––––––––––
Maximum modulating frequency Frequency Spectrum of angle modualted wave :
• FM and PM analysis is quite complicated. It is derived with the help of Bessel function.
Efm = Ec sin (wct + mf cos wmt)
Efm = A {Jomf sin wct + J1mf [sin (wc + wm)t – sin (wc - wm)t]
+ J2mf [sin (wc + 2wm)t – sin (wc - 2wm)t] + J3mf [sin (wc + 3wm)t
– sin (wc - 3wm)t] + J4mf [sin (wc + 4wm)t – sin (wc - 4wm)t] …..}
J0, J1, J2, J3 …. Are Bessel functions. The value of this depends on
modulation index mf.
From the figure the Bandwidth of FM is given by B = fc + nfm – fc + nfm
BW = 2nfm Bessel Function Table :
m J0 J1 J2 J3 J4 J5 J6 J7 J8 J9 J10 0 1 - - - - 0.25 0.98 0.12 - - - - 0.5 0.94 0.24 0.03 - - - - 1 0.77 0.44 0.11 0.02 - - - - 1.5 0.51 0.56 0.23 0.06 0.01 - - - - 2 0.22 0.58 0.35 0.13 0.03 - - - - 2.5 -0.05 0.50 0.45 0.22 0.07 0.02 - - - - - 3 -0.26 0.34 0.49 0.31 0.13 0.04 0.01 - - - - 4 -0.04 -0.07 0.36 0.43 0.28 0.13 0.05 0.02 - - - 5 0.18 -0.33 0.05 0.31 0.39 0.25 0.13 0.05 0.02 - -
Problems: Ex.1 :
Determine the Bω occupied by a sinusoidally frequency modulated carrier for which the modulation index is 2.4 & maximum frequency deviation is 15 KHz. Soln : mf = 2.4 ∆f = 15KHz ∆f mf = ––––––––– => fm (max) ∆f 15 KHz fm(max) = ––––– = –––––––––– = 6250 Hz mf 2.4 Bω = 2 (∆f + fm(max)) = 42.5 KHz.
Given fm modulator with following parameter,
K1 = 1'5 KHz / V Fc - 500 KHz Vm = 2 sin 2π 2kt
Detersive modulation index, o/p spectrum, change the signal amplitude to 4 Vp repeat 1.
Ex.2 :
For an fm modulator with a peak frequency deviation ∆f = 10 KHz, a modulating signal frequency fm = 10 KHz, Vc = 10 V and a 500 KHz carrier is
applied Determine.
a. Achial minimum Bw from Bessel table. b. Bandwidth using casson’s rule
c. Modulation Index. Soln :
a. ∆f
10 KHz mf = ––––––– = 1
10 KHz
From the Bessel table, for the modulation index = 1, The n value is 3. Bw = 2 (3 x fm) = 2 ( 3 x 10 ) = 60 KHz.
b. Bw using Carson’s rule. Bw = 2 ( ∆f + fm )
= 2 (10 k + 10 k) = 40 KHz. Ex.3 :
In a fm system the frequency deviation is 1 KHz / V. A sinusoidal
modulating voltage of amplitude 15 & frequency 3 KHz is applied find, a. The maximum frequency deviation
b. Modulation index.
Soln :
∆f = 1 KHz / V
Modulating voltage is 15V at 3 KHz.
Maximum frequency deviation = 1 KHz / V. 15V = 15 KHz. Af 15 KHz m = ––––– = –––––––– = 5 fm 3KHz m = 5 Ex.4 :
Determine the peak frequency deviation ∆f and modulation index (m) for an Fm modulator with a deviation sensitivity K1 = 5 KHz / V and a modulating
Signal Vm(t) = 2 cos (2π 2000t) ∆f = KIVm
5 KHz = –––––– x 2 V = 10KHz. V ∆ f 10KHz = –––– = –––––––– = 2. fm 5KHz Classification of FM: 1. Narrowband FM 2. Wide band FM Narrow band FM:
When the modulation index is less than I, it is called narrowband FM. The FM Equation given by eq. 9 can also be expressed as,
………(1)
(2) For narrowband FM, the modulation index, m is very small therefore following approximations can be considered.
Using this in equation (2)
Expanding
This equation gives the spectrum of narrowband FM. Observe that there is carrier frequency fc, upper sideband (fc + fm) and lower sideband (fc - fm).
Wide band FM
If the modulation index is higher than 10 it is called as wide band FM
then the above equation becomes
The above integral is known as the nth order Bessel function of the first kind. It is given as
Using the value of Cn in equation (2)
Using the value x(t) in equation (1)
………(3)
The Fourier transform of the above equation becomes
This equation shows that there are infinite number of components located fc±fm, fc±2fm,fc ±3fm……….
Comparison between narrowband and wideband FM
Sr.no Narrow band FM Wide band FM
1 Modulation index is < 1 Modulation index > 10 2
3 Spectrum contains 2 sidebands and carrier
Spectrum cont6ains infinite number of sidebands and carrier
4 BW=2fm
5 It is used for mobile communication It is used for broadcasting and entertainment
6 Maximum deviation =75Hz Maximum deviation = 5 Hz 7 Range of modulating frequency
30Hz to 15 Kz
Range of modulating frequency 30Hz to 3 Kz
Comparison between FM and PM
Frequency modulation Phase modulation
1 The maximum frequency
deviation depends upon amplitude of modulating voltage and modulating frequency
The maximum phase deviation depends only upon the amplitude of modulating voltage
2 Frequency of the carrier is modulated by modulating signal
Phase of the carrier is modulated by modulating signal
3 Modulation index is increased as modulation frequency is reduced and vice versa
Modulation index remains same if modulating frequency is changed 4 Noise immunity is bette than AM
and PM
Noise immunity is better than AM but worse than FM
5 FM is widely used PM is used in some mobile systems.
Generation of FM waves:
Fm Modulators: There are 2 types of FM modulators. 4. Direct Method
5. Indirect Method
Direct FM Modulators : In this type the frequency of the carrier is varied derectly by the modulating signal.
Indirect FM Modulators: In this type FM is obtained by phase modulatiuon of the carrier.
Generation of Narrow band FM:
Direct FM reactance modulator.
• It behaves as reactance across terminal A-B.
• The terminal A-B of the circuit may be connected across the tuned circuit of the oscillator to get fm o/p.
• The varying voltage (modulating voltage) V, across the terminals A-B changes the reactance of FET.
• This charge in reactance can be inductive or capacitive.
• Neglecting the gate current, let the current through C & R be I1.
• At the carrier freq. the reactance of C is much larger than V
R & I1 = ––––––––––
R + 1/ jwc Jwc >> R
I1 = jwcV
From the Circuit,
Vg = I1R = jwcrv
Id = gmvgs = gmVg
Id = jwcRgm V
From the circuit impedance of the FET is, V Z = –––– Id V 1 1 = ––––––––––– = ––––––––––– = ––––––––– jwCR gm V jw (gmCR) jw (Ceq)
• The impedance of FET is capacitive.
• By carrying the modulating voltage across FET, the operating paint gm can
be varied and hence Ceq.
• This change in the capacitance will change the frequency of the oscillator.
• We know that the junction capacitance of the varactor diode changes as the reverse bias across it is varied.
• L1 & C1 forms the tank circuit of the carrier oscillator.
• The capacitance of the varactor diode depends on the fixed bias set by R1
& R2 & AF modulating signal.
• Either R1 or R2 is made variable.
• The radio frequency choke [RFC] has high reactance at the carrier frequency to prevent carrier signal from getting into the modulating signal. • At +ve going modulating signal adds to the reverse bias applied to the
varactor diode D, which decreases its capacitance & increases the carrier frequency.
• A –ve going modulating signal subtracts from the bias, increasing the capacitance, which decreases the carrier frequency.
• Fig. shows the FM Crosby transmitter with an AFC loop. (Automatic frequency correction loop).
• The Frequency modulator can be either a reactance modulator or voltage controlled oscillator.
• The carrier freq is 5.1MHz. which multiplies by 18 in three steps to produce a final frequency of 91.8 MHz.
• When the frequency modulated carrier is multiplied, its frequency & phase deviations are also multiplied.
• The rate at which the carrier is deviated is unaffected by the multiplication process. Hence the modulation index is multiplied.
• When an angle modulated carrier is heterodyned with another freq in a non linear mixer, the carrier can either be up converted or down converted.
• The purpose of the AFC loop is the achieve near crystal stability of the transmit carrier freq. without using a crystal in the carrier oscillator.
• The cassier frequency is mixed with a local oscillator freq and then down converted in freq. & the fed to a frequency discriminator.
• Frequency discriminator is a device whose o/p voltage is proportional to difference b/w i/p freq and its resonant freq.
• Discriminator responds to low freq changes in the carrier center freq because of master oscillator freq drift.
• When the discriminator responds to frequency deviation, the feedback loop would cancel the deviation and this remove the modulation.
• The dc correction voltage is added to the modulating signal to automatically adjust the master oscillator’s centre frequency to compensate for low freq drift.
Ex. :
A crossby direct Fm transmitter model is used. The total freq multiplication is 20 & Transmit carrier frequency ft = 88.8 MHz. determine
1. Master oscillator center frequency.
2. Frequency deviation at the o/p of the modulator for a freq deviation of 75 KHz at the antenna.
3. Deviation ratio at the o/p of the modulator for a maximum modulating signal freq fm = 15 KHz.
4. Deviation ratio at the Antenna. Ft 88.8 MHz
N1N2N3 20 ∆ Ft 75 KHz Af = ––––––––– = ––––––––––– = 3750 Hz N1N2N3 20 ∆ f max 3750 Dr = ––––––––– = –––––––– = 0.25 f m (max) 15 k Dr = 0.25 x 20 = 5. PLL Direct FM transmitter:
• Fig shows a wide band FM transmitter.
• The VCO o/p freq is divided by N & fed bark to the PLL phase comparator, where it is compared to a stable reference freq.
• The phase comparator generator a correction voltage that is proportional to the difference b/w the 2 frequencies.
• The correction voltage is added to the modulating signal & applied to the VCO i/p.
• The correction voltage adjusts the VCO centre freq to its proper value. • The LPF prevents the changes in the VCO o/p frequency due to the
• The LPF also prevents the loop from locking onto a side frequency.
Indirect Fm transmitter
• Here the modulating signal directly deviates the phase of the carrier, which indirectly changes the frequency.
• The carrier source is a crystal oscillator hence stability can be achieved without a AFC.
• A carrier is phase shifted to 900 & fed to the Balanced modulator. Where it is mixed with the i/p modulating signal.
• The o/p of Balanced modulator is combined with original carrier in the combining N/W. to produce a low index, phase modulated wavefrom. • Fig (b) shows phasor of original carrier, modulating signal and the
resultant Vector.
• Fig (b) shows the phasors for the side freq. components of the suppressed carrier wave. As suppressed carrier is out of phase with Vc, the upper & Lower side bands combine to produce Vm – 90o with Vc.
• The phase modulated signal is obtained by vector addition of carrier and modulating signal.
• Modulating signal vector adds to the carrier OA with 900 phase Shift. • The resultant phase modulated vector is OB with phase shift θ.
• This works only if both have the same frequency. The means carrier & modulating signal should have same frequency. Under this condition phase modulation produces FM o/p.
FM Demodulators / Detectors
FM demodulator must satisfy the following requirements
• It must convert the frequency variations into amplitude variations • This conversion must be linear and efficient.
• The demodulator circuits must be insensitive to amplitude changes. • It should not be too critical in its adjustment and operation.
Types of FM demodulator:
• Round Travis Detector or Balanced discriminator. • Foster – Seley Discriminator or Phase discriminator. • Ratio Detector.
• Consists of 2 identical circuit connected back to back. • FM signal is applied to the tuned LC circuit.
• Two tuned LC circuits are connected in series.
• The inductance of the secondary tuned LC circuit is coupled with the inductance of the primary LC circuit this forms a tuned transformer.
• Upper tuned circuit is T1 & lower tuned circuit is T2.
• I/P side LC is tuned to be
T1 is tuned to fc + δf - max freq fm.
T2 is tuned to fc - δf - max freq fm.
• Secondary of T1 & T2 are connected to diodes D1 & D2 with RC loads.
• When i/p freq is fc, both T1 & T2 produce the same voltage hence o/p = 0
• When i/p freq is fc + δf, the upper circuit T1 produces maximum voltage
since it is tuned to this freq. Hence this produces maximum votalge. V01 is high compared to V02.
Vout = V01 - V02 is positive for fc + δf.
• When i/p freq is fc - δf. T2 produces maximum signal since it is tuned to it.
But T1 produces minimum voltage. Hence o/p Volt = V01 – V02 is negative.
Thus we get a modulating signal. Foster - Seeley Discriminator :
• The primary voltage is coupled through C3 & RFC to the centre tap on the
secondary.
• The capacitor C3 passes all the frequencies of Fm. The voltage V1 is
generated across RFC.
• The voltage V1 thus appears across centre tap of secondary and ground
also.
• The voltage of secondary is V2 & equally divided across upper half & lower
half of the secondary.
• In the figure the voltage across diode D1 is VDI = V1 + 0.5 V2 and that
across D2 is VD2 = V1 + 0.5 V2 .
• The o/p of upper rectifier is V01 and lower rectifier is V02.
• The net o/p V0 = V01 – V02 ≅ V0 = | VD1 | - | VD2 |
• At carrier frequency VD1 x VD2 are equal hence the net o/p of the
discriminator will be zero.
• When the i/p frequency increases above fc the phase shift b/w V1 & V2
reduces | VD1 | > | VD2 | hence V01 = | VD1 | - | VD2 | will be +ve.
• When the i/p frequency reduces below fc then | VD1 | > | VD2 | hence V01 =
| VD1 | - | VD2 | will be –ve.
Ratio detector :
Ratio detector can be obtained by sight modifications in the foster-Seeley discriminator. Fig shows the circuit diagram of ratio detector. As shown in the diagram the diode D2 is reversed, and output is taken from different points. In the
above circuit the regular conversion from frequency to phase shift and phase shift to amplitude takes place as in faster–Seeley discriminator. The polarity of voltage in the lower capacitor is reversed. Hence the voltages V01 and V02 across
