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www.studymaterialz.in EC8491 COMMUNICATION THEORY UNIT I AMPLITUDE MODULATION Amplitude Modulation- DSBSC, DSBFC, SSB, VSB - Modulation index, Spectra, Power relations and Bandwidth – AM Generation – Square law and Switching modulator, DSBSC Generation – Balanced and Ring Modulator, SSB Generation – Filter, Phase Shift and Third Methods, VSB Generation – Filter Method, Hilbert Transform, Pre-envelope & complex envelope –comparison of different AM techniques, Superheterodyne Receiver UNIT II ANGLE MODULATION Phase and frequency modulation, Narrow Band and Wide band FM – Modulation index, Spectra, Power relations and Transmission Bandwidth - FM modulation –Direct and Indirect methods, FM Demodulation – FM to AM conversion, FM Discriminator - PLL as FM Demodulator. UNIT III RANDOM PROCESS Random variables, Random Process, Stationary Processes, Mean, Correlation & Covariance functions, Power Spectral Density, Ergodic Processes, Gaussian Process, Transmission of a Random Process Through a LTI filter. UNIT IV NOISE CHARACTERIZATION Noise sources – Noise figure, noise temperature and noise bandwidth – Noise in cascaded systems. Representation of Narrow band noise –In-phase and quadrature, Envelope and Phase – Noise performance analysis in AM & FM systems – Threshold effect, Pre-emphasis and de-emphasis for FM. UNIT V SAMPLING & QUANTIZATION Low pass sampling – Aliasing- Signal Reconstruction-Quantization - Uniform & non-uniform quantization - quantization noise - Logarithmic Companding –PAM, PPM, PWM, PCM – TDM, FDM. TEXT BOOKS: 1. J.G.Proakis, M.Salehi, ―Fundamentals of Communication Systems‖, Pearson Education 2014. (UNIT I-IV 2. Simon Haykin, ―Communication Systems‖, 4th Edition, Wiley, 2014.(UNIT I-V) REFERENCES: 1. B.P.Lathi, ―Modern Digital and Analog Communication Systems‖, 3rd Edition, Oxford University Press, 2007. 2. D.Roody, J.Coolen, ―Electronic Communications, 4th edition PHI 2006 3. A.Papoulis, ―Probability, Random variables and Stochastic Processes‖, McGraw Hill, 3rd edition, 1991. 4. B.Sklar, ―Digital Communications Fundamentals and Applications‖, 2nd Edition Pearson Education 2007 5. H P Hsu, Schaum Outline Series - ―Analog and Digital Communications‖ TMH 2006 6. Couch.L., "Modern Communication Systems", Pearson, 2001. www.studymaterialz.in EC8491 ENGINEERING COLLEGES 2016 – 17 Even Semester IMPORTANT QUESTIONS & ANSWERS (IQA) Department of ECE SUBJECT CODE: EC 6402 SUBJECT NAME: COMMUNICATION THEORY Regulation: 2013 Year and Semester: II/IV Prepared by Sl. No. 1 2 3 4 5 6 Name of the Faculty Designation DEPARTMENT OF ECE Mr. V. Parvathinathan AP SUBJECT CODE : EC8491 Affiliating College SCADCET SUBJECT NAME : COMMUNICATION THEORY REGULATION :2017 YEAR : II Verified by DLI, CLI an d Approved by SEM the Centralized Monitoring Team dated :IV EC8491 EC8491 www.studymaterialz.in COMMUNICATION THEORY LTPC 3003 1. Aim and Objective of the Subject The student should be made To introduce the concepts of various analog modulations and their spectral characteristics. To understand the properties of random process. To know the effect of noise on communication systems. To study the limits set by Information Theory. 2. Need and Importance for Study of the Subject The student will be able to understand the working of simple communication systems 3. Industry Connectivity and Latest Developments Industry Connectivity: The following companies (Industries) are linked to communication systems: BSNL, TATA Communications Latest Developments: LIFI if fast data transfer in networking. New revolution in 5G, 6G in all the smart phones, smart televisions, etc. Network on chip. AM and FM Modulation Schemes. LTE were introduced almost in all the home appliances. 4. Industrial Visit (Planned if any): -Nil- www.studymaterialz.in EC8491 SCAD GROUP OF INSTITUTIONS DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING Detailed Lesson Plan Name of the Subject & Code: EC8491 COMMUNICATION THEORY Name of the Faculty: 1. Mr. Parvathinathan V, AP/ECE, SCADCET TEXT BOOKS: 1. J. G. Proakis, M. Salehi, “Fundamentals of Communication Systems”, Pearson Education 2006. 2. S. Haykin, “Digital Communications”, John Wiley, 2005. REFERENCES: 1. B. P. Lathi, “Modern Digital and Analog Communication Systems”, 3rd Edition, Oxford University Press, 2007. 2. B. Sklar, “Digital Communications Fundamentals and Applications”, 2nd Edition Pearson Education 2007 3. H P Hsu, Schaum Outline Series - “Analog and Digital Communications” TMH 2006 4. Couch.L., "Modern Communication Systems", Pearson, 2001. TOPIC TOPIC NAME No. of Cumulative Books Periods Hour Referred 1 1 R1,T1 2 Introduction to Communication Systems Generation of Amplitude modulation 1 2 T1, T2 3 Demodulation of AM 1 3 T1, T2 4 Double side band suppressed carrier modulation Double side band suppressed carrier demodulation Single side band suppressed carrier modulation 1 4 T1, T2 1 5 T1 1 6 T1 NO. 1 5 6 www.studymaterialz.in EC8491 7 8 9 Single side band suppressed carrier demodulation Vestige side band modulation & demodulation Comparison of AM modulation 1 7 T1 1 8 T1 1 9 T1 systems 10. Super heterodyne Receiver 1 10 T1 12 Phase Modulation 1 11 T1 13 Frequency Modulation 1 12 T1 14 Single tone FM 1 13 T1 15 Narrow band FM 1 14 T1 16 Wide band FM 1 15 T1 17 Generation of FM 2 17 T1 18 Demodulation of FM 2 19 T1 19 Transmission Bandwidth of FM 1 20 T1 20 Review 1 21 T1 of probability, random process 21 Central limit Theorem 1 22 T1 22 Stationary Processes 1 23 T1 23 Mean, Correlation 1 24 T1 & Covariance functions 24 Power Spectral Density 1 25 T1 25 Ergodic Processes 1 26 T1 26 Gaussian Process 1 27 T1 27 Transmission of a Random Process 1 28 T1 Through a LTI filter 28 Noise sources and types 1 29 T1 29 Noise figure and noise temperature 1 30 T1 30 Noise in cascaded systems 1 31 T1 31 Narrow band noise 1 32 T1 32 PSD of in-phase and quadrature 1 33 T1 noise www.studymaterialz.in EC8491 33 Noise performance in AM systems 3 34 T1 34 Noise performance in FM systems 1 35 T1 35 Pre-emphasis and de-emphasis 1 36 T1 36 Capture effect and threshold effect 1 37 T1 34 Introduction to Information 1 38 T2 35 Entropy & Average information 1 39 T2 36 Discrete Memory less channels & 1 40 T2 Channel Capacity 37 Hartley - Shannon law 1 41 T2 38 Source coding 2 43 T2 theorem 39 Huffman coding 2 45 T2 40 Shannon - Fano codes 2 47 T2 EC8491 www.studymaterialz.in INDEX S. NO. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 TABLE OF CONTENT TITLE AMPLITUDE MODULATION PART A PART B Super heterodyne Receiver DSBSC Amplitude Modulation Envelope Detector Filter and phase shift method Weaver method Comparison of AM PART C Hilbert Transform VSB Problem 2. ANGLE MODULATION PART A PART B Comparison of NBFM & WBFM Generation of FM-Direct method Generation of FM-Indirect method FM detector Foster –Seeley discriminator NBFM & WBFM PART C Comparison of AM and FM Problems Single tone FM 3. RANDOM PROCESS PART A PART B Differentiate SSS with WSS Ergodicity Principle Power spectral density Central limit theorem Covariance and auto correlation function PART C Problems PAGE NO. 1 3 6 9 11 12 14 14 15 16 18 19 21 22 23 23 25 27 31 32 33 36 37 39 41 43 44 47 EC8491 www.studymaterialz.in 4. NOISE CHARACTERIZATION 28 29 30 31 32 33 34 35 36 37 38 39 40 41 PART A PART B Noises Pre-emphasis & De-emphasis NB Noise Figure of merit of FM system Noise performance of AM receiver using envelope detection PART C Problems 5. INFORMATION THEORY PART A PART B Shannon laws Rate distortion theory Huffman Theory Mutual Information Problem PART C Problems Previous Year Question Papers 51 52 56 58 64 71 75 77 78 79 81 83 85 93 97 EC8491 www.studymaterialz.in UNIT I AMPLITUDE MODULATION PART A 1. Define modulation and what are the types of analog modulation? Modulation is a process by which some characteristics of high frequency carrier signal is varied in accordance with the instantaneous value of the modulating signal. Types: Amplitude modulation. Angle Modulation Frequency modulation Phase modulation. 2. What is the need for modulation and what are the degrees of modulation? (or) What are the advantages of converting low frequency signal in to high frequency signal? ( MAY/JUNE 2013) Needs for modulation: Ease of transmission Multiplexing Reduced noise Narrow bandwidth Frequency assignment Reduce the equipments limitations Degrees of modulation Under modulation, m<1 Critical modulation, m=1 Over modulation m>1 3. Define Heterodyning. (APRIL/MAY 2015) Heterodyning means the translating or shifting in frequency. By heterodyning the incoming signal at ωRF with the local oscillator frequency ωLO, the message is translated to an intermediate frequency ωIF, which is equal to either the sum or the difference of ωRF and ωIF. 4. What are the advantages of converting low frequency signal in to high frequency signal? (or) What are the advantages of modulation? (NOV/DEC 2016) Reduction in the height of antenna Avoids mixing of signals Increases the range of communication Multiplexing is possible Improves quality of reception 5. How to calculate the average power of a periodic signal? (MAY/JUNE 2016) For a periodic signal, its average normalized power is equal to the power over one period. 𝑃 = 1 𝑇 𝑥(𝑡) 2 𝑑𝑡 5. What is Super Heterodyne Receiver? The super heterodyne receiver converts all incoming RF frequencies to a fixed lower frequency, called intermediate frequency (IF). This IF is then amplitude and detected to get the original signal. 1 www.studymaterialz.in EC8491 6. What is single tone and multi tone modulation? If modulation is performed for a message signal with more than one frequency component then the modulation is called multi tone modulation. If modulation is performed for a message signal with one frequency component then the modulation is called single tone modulation. 7. Compare bandwidth and power requirement for AM with DSB-SC and SSBSC? (MAY/JUNE 2013) S. No 1 2 3 AM signal DSB-SC SSB-SC Bandwidth = 2fm Contains USB, Carrier Bandwidth = 2fm Bandwidth = fm LSB, Contains USB,LSB USB,LSB Power required is less er required is less More Power is required for than than Transmission that of AM. AM &DSB-SC 8. Define Demodulation. Demodulation or detection is the process by which modulating voltage is recovered from the modulated signal. It is the reverse process of modulation. The devices used for demodulation or detection are called demodulators or detectors. For amplitude modulation, detectors or demodulators are categorized as, Square-law detectors Envelope detectors 9. What are the advantages of VSB-AM? (APRIL/MAY 2011) It has bandwidth greater than SSB but less than DSB system. Power transmission greater than DSB but less than SSB system. No low frequency component lost. Hence it avoids phase distortion. 10. Define SSB-SC and DSB-SC SSB-SC stands for Single Side Band Suppressed Carrier When only one sideband is transmitted, the modulation is referred to as Single side band modulation. It is also called as SSB or SSB-SC. DSB-SC: After modulation, the process of transmitting the sidebands (USB, LSB) alone and suppressing the carrier is called as Double Side Band-Suppressed Carrier. 11. Define Coherent Detection (APRIL/MAY 2013) During Demodulation carrier is exactly coherent or synchronized in both the frequency and phase, with the original carrier wave used to generate the DSB-SC wave. This method of detection is called as coherent detection or synchronous detection. 12.What is image frequency? (NOV/DEC-2014) The local oscillator frequency (fo), input signal frequency (fs) and intermediate frequency (fi) are related as f0 – fs=fi that is f0=fs+fi .If some other frequency fsi=fs+2fi appear at the input of mixer, it produces fi at the output of mixer.This interferes with the desired IF,since it is same as IF.The frequency is called image frequency. Thus image image frequency gets converted to IF range and it is amplified by IF amplifier. 2 www.studymaterialz.in EC8491 13. Draw the frequency spectrum of VSB. Where it is used?(APRIL/MAY 2015) VSB is used for TV transmission, since low frequencies near f c represents picture details. They are unaffected by VSB. 14.A transmitter radiates 9 kW without modulation and 10.125 kW after modulation. Determine depth of modulation. (APR/MAY 2013) Depth of modulation: Therefore, =1.125-1 =0.125 ma2=0.125X2 =0.250 ma=0.50 15. Suggest a modulation scheme for the broadcast video transmission and justify. (NOV/DEC 2016) Vestigial Sideband modulation (VSB) is used for video transmission for the following reasons: 1. Video signal exhibits a large bandwidth and significant low-frequency content which suggests the use of VSB. 2. The circuitry for demodulation in the receiver should be simple and therefore cheap. PART-B 1.Explain With Block Diagram Super Heterodyne Receiver? (April/May 2015, MAY/JUNE 2016) In a broadcasting system whether it is based on amplitude modulation or frequency modulation, the receiver not only have the task of demodulating the modulated signal, but it is also required to perform some other system functions. Carrier frequency tuning, the purpose of which is to select the desired signal (i.e.) desired radio or TV station) Filtering, which is required to separate the desire signal from other modulation signals that may be picked up along the way. 3 EC8491 www.studymaterialz.in Amplification, which is intended to compensate for the loss of signal power incurred in the course of transmission. R.F Section The incoming amplitude modulated wave is picked up by the receiving antenna and is fed to the RF section. The RF section consists of a pre selector and an RF Amplifier. The pre selector is a band pass filter with an adjustable centre frequency that is tuned to the desired carrier frequency of the incoming signal. The main use of the preselected is to provide sufficient band limiting to prevent undesired ratio in frequency signal or image signal. The effectiveness of suppressing unwanted image signals increases as the number of selective stages in the RF section increases and as the ratio of intermediate to signal frequency increases. R.F amplifiers are used for better selectivity. Fig. 1 Super Heterodyne Receiver Frequency Changer The combination of mixer and local oscillator provides a heterodyning function whereby the incoming signal is converted to a predetermined fixed intermediate frequency, usually lower than the incoming carrier frequency. This frequency translation is achieved without disturbing the relation of the sidebands to the carrier. The result of heterodyning is to produced an intermediate frequency carrier defined by fIF = flo –fRF Where fLO is the frequency of the local oscillator and fRF is the carrier frequency of the incoming RF signal. Since the output of the frequency his neither the original input frequency not the final baseband frequency, it is called as intermediate frequency. Sometimes the frequency changer circuits are referred to as the first detector, in which case the demodulator i s called as second detector. IF Section The IF section consists of one or more stages of turned amplification with a bandwidth corresponding to that required for the particular type of modulation that the receiver intended to handle. The IF section provides most of the amplification purpose of which is to recover the baseband or message signal. If coherent detection is used, then a coherent signal source must be provided in the receiver. 4 EC8491 www.studymaterialz.in Audio Amplifiers The final stage of the super heterodyne receiver consists of one or more audio amplifiers which is used for the power amplification of the recovered message signal. Image frequency and its rejection ratio In a super heterodyne receiver, the mixer will develop and intermediate frequency output when the input signal frequency is greater or less than the local oscillator frequency by an amount equal to intermediate frequency. Amplitude Limiter The basic difference between AM and FM super heterodyne receiver lies in the use of an FM Demodulator such as limiter frequency discriminator. In FM system the message signal is transmitted by the instantaneous value of carrier signal & its amplitude remain constant. Therefore any variation of the carriers amplitude at the receiver input must result from noise or interference. An amplitude limiter following the IF section is used to remove amplitude variations by clipping the modulated wave is rounded by a band pass filter that suppresses harmonics of the carrier frequency. Thus the filter output is again sinusoidal, with an amplitude that in practically independent of the carrier amplitude of the receiver input. The Fig shows basic block diagram of FM super heterodyne receiver. Performance Parameters of Receivers The performance of a Radio receiver is measured on the basic of its selectivity, sensitivity, fidelity and image frequency rejection selectivity. Selectivity The selectivity is the ability of the receiver to select a signal of a desired frequency while rejecting all others. The selectivity of the receiver is obtained partially by RF amplifier and mainly by IF amplifiers. The selectivity shows the attenuation that the receiver offers to signals at frequencies near to the one to which it is tuned. Fig. shows the typical selectivity curve of the receiver. The selectivity depends upon tuned LC circuits used in RF and IF stages, fr is the resonating (tuned) frequency and Q is quality factor of these LC Circuits, As shown in Fig. bandwidth should be narrow for better selectivity. Hence Q of the coil should be high. Sensitivity The ability of the receiver to pick up weak signals and simplify them is called sensitivity. It is often defined in terms of the voltage that must be applied to the receiver input terminals to give the standard output power, measured at the output terminals. As the gain of the receiver is increased, sensitivity is also increased. The sensitivity is expressed in micro volts or decibels. Fig.shows the typical sensitivity curve of a receiver. As shown in the Fig., the sensitivity is decreased (i.e., voltage is increased) at high frequencies. Fidelity Fidelity is a measure of the ability of a communication system to produce at the output of the receiver, an exact replica of the original source information. This may also be defined as the degree to which the system accurately reproduces at the output, the essential characteristics of signals that are impressed upon the input. 5 EC8491 www.studymaterialz.in Signal to noise Ratio Signal to noise Ratio may be defined as the ratio of signal power to noise power at the receiver output. A good receiver should have high signal to noise ratio (SNR) which indicates negligible noise present at the output. Image Frequency Rejection We know that local oscillator frequency is made higher than the signal frequency such that f0 – fs = fi . Here fi is IF. That is f0 = fs + fi. The IF stage passes only fi . If the frequency fi = fs +2fi appears at the input of the mixer, then the mixer will produce different frequency equal to fi . This is equal to IF. The frequency fsi is called image frequency and is defined as the signal frequency plus twice the IF. The image frequency is converted in the IF stage and it is also amplified by IF amplifiers. This is the effect of two stations being received simultaneously. The image frequency rejection is done by tuned circuit in the RF stage. It depends upon the selectivity of the RF stage. The image rejection should be done before the RF stage. 2.With The Help Of Neat Diagram Explain The Generation Of DSB-SC Using Balanced Modulator And Ring Modulator. (Nov/Dec 2010, MAY/JUNE 2016,NOV/DEC 2016) In DSB – SC, the transmitted wave consists of only upper and lower sidebands. Transmitted power is saved here through the suppression of the carrier wave because it does not contain any useful information, but the channel bandwidth required is the same as before. Expression for DSB –SC: Let the modulating signal, The carrier signal Comparing equation (1.57) and (1.58) the carrier terms Vc sin ωct is missing and only upper and lower sidebands are present. Fig.2 Spectrum of DSB-SC 6 EC8491 www.studymaterialz.in In this fig, the carrier term fc is suppressed. It contains only two sideband terms having the frequency of (fc – fm) and (fc + fm). Generation of DSB – SC – AM There are two ways of generating DSB – SC – AM such as , (i) Balanced modulator, (ii) Ring modulator. Balanced Modulator The circuit that is very commonly used for DSB – SC generation. In balanced modulator, two non-linear devices are connected in the balanced mode, so as to suppress the carrier wave. It is assumed that the two transistors are identical and the circuit is symmetrical. Since the operation is confined in non-linear region of its transfer characteristics. Fig.3 Balanced modulator modulating voltage across the two windings of a centre-tap transformer is equal, The and opposite in phase, i.e., Vm = V'm Ring Modulator (or) Diode Balanced Modulator Introduction: The one of the most popular method of generating a DSB – SC wave is ring modulator. The circuit employs diodes as non-linear devices and the carrier signal is connected between centre taps of the input and output transformers. There is no need for a band pass filter at the output. The four diodes are controlled by a carrier Vc(t) of frequency fc The carrier signal acts as a switching signal to alternate the polarity of the modulating signals at the carrier frequency. For better understanding of the operation, assume that the modulating input is zero. Only carrier signal is present. Fig. 4 Diode Balanced modulator 7 www.studymaterialz.in EC8491 Positive Half Cycle of Carrier: Diodes D1 and D2 are form ward biased. AT this time D3 and D4 are reverse biased and act like open circuits. The current divides equally in the upper and lower portions of the primary winding of T12 . The current in the upper part of the winding produces a magnetic field that is equal and opposite to the magnetic field produced by the current in the lower half of the secondary. Therefore, these magnetic fields cancel each other out and no output is induced in the secondary. Thus the carrier is effectively suppressed. Negative Half Cycle of Carrier: When the polarity of the carrier reverses. Diodes D1 and D2 are reverse biased and diodes D3 and D4 conduct. Again the current flows in the secondary winding of Tr1 and the primary winding of Tr2. The equal and opposite magnetic fields produced in Tr2 cancel each other out and thus result in zero carrier output. The carrier is effectively balanced out. Principle of Operation: When both the carrier and the modulating signals are present, during positive half cycle of the carrier, diodes D1 and D2 conduct, while diodes D3 and D4 does not conduct. During negative half cycle of the carrier voltage diodes D3 and D4 conduct and D1 and D2 does not conduct. Fig. 5. Graphical representation of DSB-SC signals Phase Reversal When polarity of the modulating signal changes, the result is a 180 phase reversal. 8 EC8491 www.studymaterialz.in At the time, during the positive half cycle of the carrier, diodes D3 and D4 are in forward bias and the negative half cycle of the carrier, diodes D1 and D2 are in reverse bias. Consider the modulating signal Vm (t) and carrier signal Vc (t) , such that, The equation (1.76) shows that the output is free from the carrier and other higher order terms, and it contains upper and lower sidebands only. The ring modulator circuit is also known as double balanced modulator because comparing to balanced modulator here two more diodes are used. Advantages: 1. DSB –SC is more efficient in transmitted power as compared to DSBFC . 2. DSB –SC has better signal to noise ratio as compared to single side band (SSB) transmission. Disadvantage: Even though the carrier is suppressed the bandwidth of DSBSC remains same as DSBFC. 3.i). Define amplitude modulation. How an amplitude modulated signal can be generated using a non linear modulator circuit.(NOV/DEC 2012,NOV/DEC 2016) Amplitude modulation: Amplitude modulation is the process by which amplitude of the carrier signal is varied in accordance with the instantaneous value of the modulating signal,but frequency and phase remains constant. Non linear modulator circuits: A simple diode can be used as a non linear modulator by restricting its operation to non linear operation of its characteristics. The undesired frequency terms are filtered out by a band pass filter. The methods for generation of AM waves using non linear property are broadly divided into two types (a)square law modulator (b)Balance modulator (a)Square law modulators: Any device operated in non linear region of its output characteristics is capable of producing amplitude modulated waves when the carrier and modulating signals are fed at the input. Thus a transistor, a triode tube,a diode etc. may be used as the square law modulator. A square law modulator circuit consists of the following: (i) A non linear device (ii) A bandpass filter (iii)A carrier source and modulating signal 9 EC8491 www.studymaterialz.in Fig.6 The square law modulator Consider a non linear device to which a carrier c(t)= A cos(2Π fct) and an information signal m(t) are fed simultaneously as shown in figure1. The total input to the device at any instant is As the level of the input is small very small, the output can be considered up to square of the input Taking Fourier transform on both sides we get, Therefore the square law device output Vo consists of the dc component at f=0 The information signal ranging from 0 to W Hz and its second harmonics Signal at fc and 2fc Frequency band centered at fc with a deviation of ± W Hz. The required AM signal with a carrier frequency fc can be separated using a bandpass filter at the output of the square law device. The filter should have a lower cutoff frequency ranging between 2W and (fc - W) and upper cut-off frequency between (fc+W) and 2fc Therefore the filter output is 10 EC8491 www.studymaterialz.in The output AM signal is free from distortion and attenuation only when(f c-W)2W or fc<3W 3 ii)Draw An Envelope Detector Circuit Used For The Demodulation Of Am And Its Operation. (MAY/JUNE 2012,MAY/JUNE 2013,APRIL/MAY 2010,APRIL/MAY 2015) Diode Detector or Envelope Detector The most commonly used AM detector is simple diode detector as the shown in Fig. The AM signal at fixed IF is applied to the transformer primary. The signal at secondary is half wave rectified by diode D. This diode is the detector diode. The resistance R is load resistance to rectifier and C is the filter capacitor. In the positive half cycle of AM signal diode conducts and currents flows through R, whereas in negative half cycle, the diode is reverse biased and no current flows. Therefore only positive half of the AM wave appears across resistance R as shown in figure. The capacitor across capital R provides low impedance at the carrier frequency and much higher impedance at the modulating frequency. Therefore capacitor reconstructs the original modulating signal as shown in figure and high frequency carrier is removed. Fig 7 Diode detector Negative peak clipping in diode detector: This is the distortion that occurs in the output of diode detector because of unequal ac and dc load impedances of the diode. The modulation index is defined as Em /Ec. Fig.8 Diode detector waveforms 11 EC8491 www.studymaterialz.in Therefore it can also be defined as Im /Ic with Im = and Ic = Here is audio diode load impedance and is the dc diode resistance. The audio load resistance of the diode is smaller than the dc resistance. Hence the AF current is larger, in proportion to dc current. This makes the modulation index in the demodulated wave relatively higher than that of modulated wave applied at the detector input. This introduces the distortion due to over modulation in the detector signal for modulation index near 100%. This is illustrated in Fig. In the figure observe that the negative peak of the detected signal takes place because of over modulation effect taking place in detector. Diagonal Clipping in Diode Detector As the modulating frequency is increased, the diode ac load impedance, Zm does not remain purely resistive. It does have reactive component also. At high modulation depths, the current changes so fast that the time constant of the load does not follow the changes. Hence the current decays slowly as shown in fig. The output voltage follows the discharge law of RC circuit. This introduces distortion in the detected signal and it is called diagonal peak clipping. Fig.9 Diagonal peak clipping 4.(i) Explain The Filter Method And Phase Shift Method To Produce SSB. SSB – SC – AM waves can by generated in two ways. 1. Frequency discrimination (or) Filler method 2. Phase discrimination method. Phase discrimination method itself can be divided into two types. 1. Phase shift method. 2. Modified phase shift (or) weaver's method. Suppression of Unwanted Sideband In the previous subsection we studied the techniques to suppress the carrier. To generate single sideband suppressed carrier (SSBSC), we have to suppress the carrier as well as one of the sidebands. In this section let us consider the techniques to suppress one of the sidebands. These techniques are (i) filter method, (ii) phase shift method and (iii) The 'third' method. Filter Method to Produce SSB Fig.shows the block diagram of filter method to suppress one sideband. As shown in the block diagram, the balanced modulator produces DSB output. This DSB 12 EC8491 www.studymaterialz.in signal contains both the sideband. The filter must have a flat pass band and extremely high attenuation outside the pass band. In order to have this type of response the Q of the tuned circuits must be very high. The required value of Q factor increases as the difference between modulating frequency and carrier frequency increases. Carrier frequency is usually same as the transmitter frequency increases. Carrier frequency is usually same as the transmitter frequency. For higher transmitting frequencies them required value of Q is so high that there is no practical way of achieving it. In such situation, initial modulation is carried out at a low frequency carrier say 100 kHz by the balanced modulator. Then the filter suppresses one of the sidebands. The frequency of the SSB signal generated at output of filter is very low as compared to the transmitter frequency. The frequency is boosted up to the transmitter frequency by the balanced mixer and crystal oscillator. This process of frequency booting is also called as up conversion. The SSB signal having frequency equal to the transmitter frequency is then amplified by the linear amplifiers. Fig.10 Filter method to suppress sideband Phase Shift Method to Generate SSB Fig. 11shows the block diagram of phase shift method to generate SSB. The carrier signal is shifted by 90 and applied to the balanced modulator M1. The modulating signal is also directly applied to the balanced modulator M2. The modulating signal is phase shifted by 90 and applied to balanced modulator M2. Both the modulators produce an output consisting of only sidebands. The upper balanced modulator (M1 ) generates upper sideband and lower sideband, but upper sideband is shifted by +90 whereas lower sideband is shifted by -90.The output of balanced modulators are added by the summing amplifier. Since upper sidebands of both the modulators are phase shifted by +900, they are in phase and add to produce double amplitude signal. But lower sideband of the balanced modulator s are (+90 , -90 ) 180 out of phase and hence cancel each other. Thus the output of summing amplifier contains only upper sideband SSB signal. The carrier is already suppressed by balanced modulators. Fig.11 phase shift method to generate SSB 13 www.studymaterialz.in EC8491 4 (ii) How SSB Can Be Generated Using Weaver’s Method.(MAY/JUNE 2012) Weaver's Method or Third Method of SSB Generation Principle: It uses two carriers: One is audio subcarrier at frequency fo and other is RF carrier at frequency fc . Block diagram and operation Fig. 1.30 shows the block diagram of weaver's method. The input to the modulator is s(t) = cos( 2 fmt). It is the modulating signal of frequency fm. Fig.12 Block diagram of weaver's method 5. Write The Comparison Of Amplitude Modulation Systems.(MAY/JUNE 2012) Description AM with carrier DSB – SC – AM SSB – SC on AM Band width 2fm Power Saving for Sinusoid al 33.33% Power Saving for 33.33% non Sinusoidal Generation methods Easier to generate Detection methods Simple & Inexpensive 2fm fm VSB - AM fm <BW<2fm 66.66% 83.3% 75% 50% 75% 75% Not difficult Difficult More difficult Difficult. But to easier to generate generate than SSB-SC More difficult Difficult 14 EC8491 www.studymaterialz.in PART C 1. Explain Hilbert Transform With An Example. (APRIL/MAY 2015) Hilbert Transform If every frequency components of a signal f(t) is shifted by (-π/2) the resultant signal fh (t) is the Hilbert transform of f(t). Fig.13 phase shifting system A signal f(t) is passed through a phase shift system H(ω) and the output fh (t) shown in fig. The characteristics of the of the system specified as follows: i) The magnitude frequency components present in f(t) remains unchanged when it is passed through the system that is H(ω) = 1 and ii) The phase of the positive frequency components if shifted by -π/2 . Since the phase spectrum (ω) has an odd symmetry, the phase of the negative frequency components is shifted by π/2. H(ω) and (ω) are plotted in Fig by continuous and dotted lines respectively. Fig.14 Transfer function -π/2 phase shifter Properties of Hilbert transform Hilbert transform has the following properties 1. A signal f(t) and its Hilbert transform have the same magnitude spectrum. 2 A signal f(t) and its Hilbert transform sh(t) have the same energy density spectrum. 3 If the Hilbert transform of fh(t) is –f(t), then fh(t) is Hilbert transform of s(t) that is if Where H denotes the Hilbert transform. 15 EC8491 www.studymaterialz.in 4. A signal f(t) and its Hilbert transform fh(t) are mutually orthogonal over the time interval (-∞,∞) that is 5. A signal f(t) and its Hilbert transform fh(t) have the same auto correlation function. Some useful Hilbert transform. Application of Hilbert transform pair Generation of SSB signal Design of minimum phase type filters Representation of band pass signals. 2. With suitable block diagrams and equations show how will you generate VSB signals (NOV/DEC 2013) Generation of VSB signals: A vestigial-sideband system is a compromise between DSB and SSB It inherits the advantages of DSB and SSB but avoids their SSB. It inherits the advantages of DSB and SSB but avoids their disadvantages. VSB signals are relatively easy to generate and their bandwidth is VSB signals are relatively easy to generate and their bandwidth is only slightly (typically 25 percent) greater than that of SSB signals. In VSB, instead of rejecting one sideband completely as in SSB, a gradual cutoff of one sideband is accepted. All of the one sideband is transmitted and a small amount (vestige) of the other sideband is transmitted The filter is allowed to have a nonzero transition band. The roll-off characteristic of the filter is such that the partial suppression of the transmitted sideband in the neighborhood of the carrier is exactly compensated for by the partial transmission of the carrier is exactly compensated for by the partial transmission of the corresponding part of the suppressed sideband. Our goal is to determine the particular H( f ) required to produce a modulated signal s( t) with desired spectral characteristics such with desired spectral characteristics, such that the original baseband signal m( t) may be recovered from s( t) by coherent detection. 16 EC8491 www.studymaterialz.in Fig. 15 Filtering scheme of the generation of VSB modulated wave Fig. 16 Spectrum of VSB SC Amplitude response of VSB filter: To obtain baseband signal m(t) at coherent detector output, we require V o(f) to be a scaled version of M(f),Therefore we can write Now equation(a) can be written as 17 EC8491 www.studymaterialz.in 18 EC8491 www.studymaterialz.in UNIT 2 ANGLE MODULATION PART A 1. What do you understand by narrowband FM? When the modulation index is less than 1, the angle modulated systems are called low index. The bandwidth requirement of low index systems is approximately twice of the modulating. 2. Define frequency modulation and modulation index of frequency modulation and phase modulation? (MAY/JUNE 2013) (NOV/DEC 2016) Frequency modulation: Frequency modulation is defined as the process by which the frequency of the carrier wave is varied in accordance with the instantaneous amplitude of the modulating or message signal. Modulation index of frequency modulation. It is defined as the ratio of maximum frequency deviation to the modulating β = δf/fm Phase modulation: Phase modulation is defined as the process of changing the phase of the carrier signal in accordance with the instantaneous amplitude of the message signal. 3. What are the types of Frequency Modulation? Based on the modulation index FM can be divided into types. They are Narrow band FM and Wide band FM. If the modulation index is greater than one then it is wide band FM and if the modulation index is less than one then it is Narrow band FM 4. What is the basic difference between an AM signal and a narrowband FM signal? In the case of sinusoidal modulation, the basic difference between an AM signal and a narrowband FM signal is that the algebraic sign of the lower side frequency in the narrow band FM is reversed. 5. What are the two methods of producing an FM wave? Basically there are two methods of producing an FM wave. They are, i) Direct method: In this method the transmitter originates a wave whose frequency varies as function of the modulating source. It is used for the generation of NBFM ii) Indirect method: In this method the transmitter originates a wave whose phase is a function of the modulation. Normally it is used for the generation of WBFM where WBFM is generated from NBFM. 6. Compare WBFM and NBFM. (APRIL/MAY 2011,2015) (NOV/DEC-2013) S.NO WBFM NBFM 1 Modulation index is greater than 1 Modulation index less than 1 2 Frequency deviation 75 KHz Frequency deviation 5 KHz 3 Bandwidth 15 times NBFM Bandwidth 2fm 4 Noise is more suppressed Less suppression of noise 5 Used in broadcasting Used in mobile communication 19 EC8491 www.studymaterialz.in 7.Define phase deviation and frequency Deviation? APRIL/MAY 2014) Phase deviation: The maximum phase deviation of the total angle from the carrier angle is called phase deviation. Frequency Deviation: The maximum departure of the instantaneous frequency from the carrier frequency is called frequency deviation. 8. State the Carson’s rule.(APRIL/MAY 2015, NOV/DEC 2015) An approximate rule for the transmission bandwidth of an FM Signal generated by a single tone-modulating signal of frequency f m (max) is defined as ∴ BW=2[δ + fm(max)] 9.What is the use of crystal controlled oscillator? The crystal-controlled oscillator always produces a constant carrier frequency thereby enhancing frequency stability. 10.How will you generate message from frequency-modulated signals? First the frequency-modulated signals are converted into corresponding amplitude-modulated signal using frequency dependent circuits. Then the original signal is recovered from this AM signal. 11.What are the disadvantages of balanced slope detector? Amplitude limiting cannot be provided Linearity is not sufficient It is difficult to align because of three different frequency to which various tuned circuits to be tuned. The tuned circuit is not purely band limited. 12. What are the applications of phase locked loop (PLL)? (NOV/DEC 2013) Phase locked loops are used for various purposes in AM and FM communication. (i)Automatic frequency correction in FM transmitter uses PLL to keep carrier frequency constant. (ii)PLL is used direct FM Transmitter to generate WBFM signals. (iii) PLL is also used in FM demodulators. 13.Differentiate phase and frequency modulation. S.No Phase Modulation(PM) 1 Phase of the carrier varies as per amplitude variations of modulating signal. 2 Instantaneous phase deviation, ϕ(t ) = k Em(t ) Frequency Modulation (FM) Frequency of the carrier varies as per amplitude variations of modulating signals. Instantaneous frequency deviation, ∆ (t ) = k Em(t ) 3 Modulation index = k Em Modulation index = k Em 20 EC8491 www.studymaterialz.in 14.A 80 MHz carrier is frequency modulated by a sinusoidal signal of 1V amplitude and the frequency sensitivity is 100 Hz/V. Find the approximate bandwidth of the FM waveform if the modulating signal has a frequency of 10 kHz. (APR/MAY 2010) Ans: Frequency Sensitivity = 100 Hz/ volt. Amplitude of modulating signal = 1V Hence maximum frequency deviation, δ =100 Hz / volt ×1V= 100 kHz Frequency of modulating signal, fm = 10kHz ∴ BW = 2 [δ + fm (max)]= 2 [100 +10×103 ] BW = 20.2 kHz 15. What is the need for Pre-emphasis? (MAY/JUNE 2016,NOV/DEC 2016) Pre emphasis is a process used to boost the input frequency range which is most susceptible to noise. PART B Write The Comparison Of Wideband And Narrowband FM (NOV/DEC 2011, MAY/JUNE 2013 ) 1. SI. Parameter No Characteristics 1. Modulation index 2. Maximum deviation 3. Range of modulating Frequency 4. Bandwidth 5. Maximum modulation 6. Pre-emphasis and De-emphasis 7. Noise Wideband FM Greater than 1 75 KHz Narrowband FM 30 Hz to 15 KHz 30 Hz to 3 KHz Less than (or) slightly greater than 1 5 KHz Large, about 15 times higher Small. Approximately same than BW of narrow band as that of AM. BW=2fm FM. BM=2(ΔF+F m) 5 to 2500 Slightly greater than 1 Needed Needed Noise is more suppressed Less suppressing of noise 8. Applications Entertainment broadcasting FM mobile communication 9. Side bands Spectrum contains infinite number of side bands and carrier Spectrum contains two sidebands and carrier. 21 EC8491 www.studymaterialz.in 2.Explain With Diagram The Generation Of FM Using Direct Method. (APRIL/MAY 2015, NOV/DEC 2016) Direct FM Direct FM can be obtained by using FET and varactor diode. These methods are discussed next. (i).FET Reactance Modulator Fig shows the basic circuit of FET reactance modulator. It behaves as reactance across terminals A-B. The terminals A-B of the circuit may be connected across the tuned circuit of the oscillator to get FM output. The varying voltage (modulating voltage) V, across terminals A-B changes reactance of the FET. This change in reactance can be inductive or capacitive. Fig.1 FET reactance modulator (ii).Frequency Modulation using varactor Diode All the diodes exhibit small junction capacitance in the reverse biased condition. The varactor diodes are specially designed to optimize this characteristic. The junction capacitance of the varactor diode changes as the reverse bias across it is varied. The variations in capacitance of this diode are wide and linear. The varactor diodes provide the junction capacitance in the range of 1 to 200 pF. Fig shows how varactor diode can be used to generate FM. L1 and C1 form the tank circuit of the carrier oscillator. The capacitance of the varactor diode depends upon the fixed bias set by R1 and R2 and the AF modulating signal. Either R1 or Rs is made variable so that the center carrier frequency can be adjusted over a narrow range. The Radio Frequency Choke (RFC) has high reactance at the carrier frequency to prevent the carrier signal from getting into the modulating signal circuits. At positive going modulating signal adds to the reverse bias applied to the varactor diode D, which decreases its capacitance and increases the carrier frequency. A negative going modulating signal subtracts from bias, increasing the capacitance, which decreases the carrier frequency. Fig.2 Varactor diode for FM generation The frequency of the LC oscillator changes due to temperature effects. Hence crystals are used in FM generators to provide frequency stability. 22 EC8491 www.studymaterialz.in 3. Explain Indirect Method Of Generating FM Signal (APRIL/MAY 2015,NOV/DEC2016,MAY/JUNE 2016) Indirect method (Armstrong method) In this method of FM generation, the modulating signal is integrated and it is phase modulated by crystal oscillator to get narrow band FM signal which later passed on to a frequency multiplier to get a wideband FM signal. The block diagram of an Armstrong method is shown in Fig Fig.3 Block diagram of Armstrong method for generating wideband FM signal Fig.4 Block diagram of Frequency multiplier Advantages: i) FM is generated from PM indirectly. ii) Modulation takes place at low carrier frequency. 4.(i). Explain The Function Of Any Two FM Detector Circuit.(MAY/JUNE 2014,NOV/DEC 2016) The FM receivers also super heterodyne receivers. But they have different types of demodulators or detectors. FM receivers have amplitude limiters which are absent in AM receivers. The AGC system of FM receivers is different than that of AM receivers. RF amplifiers, mixers, local oscillators IF amplifiers, audio amplifiers etc. all are present in FM receivers The detection of FM is totally different compared to AM. The FM detector should be able to produce the signal whose amplitude is proportional to the deviation in the frequency of signal. Thus the job FM detector is almost similar to frequency to voltage convertor. Here we will discuss these types of FM detectors. Slope detectors, phase discriminator and ratio detector. 23 EC8491 www.studymaterialz.in Round – Travis detector or balanced slope detector (frequency Discriminator) Fig.5 shows the circuit of balanced slope detector. It consist of two identical circuit connected back to back . The FM signal is applied to the turned LC circuit. Two turned LC circuits are connected in series . The inductance of this secondary turned LC circuit is coupled with inductance of the primary (or input side) LC circuit . Thus it forms a turned transformer. In fig., the upper turned circuit is shown as T1 and lower turned circuit is shown as T2. The input side LC circuit is turned to fc, carrier frequency. T1 tuned to fc- , which represents the minimum frequency of FM signal. The input FM signal is coupled to T1 and T2 180 out of phase. The secondary side tuned circuits (T1 and T2) are connected to diodes D1 and D2 with RC loads. The total output is equal to difference between and , since they subtract Fig. shows the characteristic of the balanced slope detector. It shows with respect to input frequency. Fig.5 Balanced Slope detector Fig.6 Characteristic of balanced slope detector, or 'S' curve Frequency Discriminator Fig.shows the block diagram of a frequency discriminator which is based on the principle of slope detection. There are two slope circuits in Fig. Their transfer functions are as follows: Fig.7 frequency discriminator 24 EC8491 www.studymaterialz.in 4.(ii) With The Phasor Representation Explain The Foster Seeley Discriminator And Ratio Detector. (APRIL/MAY 2015,MAY/JUN 2016, NOV/DEC 2016) Foster-Seeley Discriminator (Phase Discriminator) The phase shift between the primary and secondary voltages of the tuned transformer is a function of frequency. It can be shown that the secondary voltage lags primary voltage by 90 degree at the carrier center frequency. The carrier frequency ) is the resonance (or tuned) frequency of the transformer. Foster-Seeley discriminator utilizes this principle for FM detection. Fig shows the circuit diagram of basic Foster-Seeley discriminator. In the figure observe that capacitor C3 passes all the frequencies of FM. Fig. 8 Foster-Seeley discriminator The output of upper rectifier is V01 and lower rectifier is V02. The net output V0=V01-V02. Since V01 │VD1│ and V02 |VD2| output V0 | V01| |VD1|.Thus the net output depends upon the difference between magnitudes of VD1and VD2 . At the centre frequency both VD1and VD2 will be equal, since V2 will have 90 phase shift with V1. Fig.shows how VD1and VD2 are generated from V1 and V2. It shows that |VD1|=|VD2|. Hence the net output of the discriminator will be zero. Now consider the situation when input frequency increases above fc. Hence the phase shift between V1 and V2 reduces. Therefore |VD1| is greater than |VD2|. This is shown by vector addition in Fig.. Hence the net output V0=V01-V02 will be positive. Thus the increase in frequency increases output voltage. Now consider the situation when frequency reduces below fc. This makes |VD1| less than |VD2|. This is shown is Fig.8 Hence the output V0=V01-V02 will be negative. Thus the Foster- Seeley discriminator produces output depending upon the phase shift, The linearity of the output depends upon the linearity between frequency and induced phase shift. The characteristic of the Foster-Seeley discriminator (i.e. S-curve) is similar to that shown in Fig.8 with more linearity in the operation. Phase shift between V1 and V2. 25 EC8491 www.studymaterialz.in Ratio Detector: Ratio detector can be obtained by slight modifications in the Foster -Seeley discriminator. Fig. shows the circuit diagram of ratio detector .As shown in diagram the diode D2 is reversed, and output is taken from different points. The polarity of voltage in the lower capacitor is reversed, since connections of diode D2 are reversed. Hence the voltages V01 and V02 across two capacitors add. We know that when V01 increases, V02 decreases and vice-versa as we have seen in FosterSeeley circuit. Since V‟0 is sum of V01 and V02, it remains constant. Fig. 9 Ratio Detector Advantages: 1) As compared to Foster – Seeley circuit, this circuit does not respond to amplitude variations. 2) The output is bipolar (i.e., positive as well as negative). Disadvantages: 1) Ratio detector does not tolerate variation in signal strength over performed period. 2) It requires an ACC signal. 26 EC8491 www.studymaterialz.in 27 EC8491 www.studymaterialz.in 28 EC8491 www.studymaterialz.in 29 EC8491 www.studymaterialz.in 30 EC8491 www.studymaterialz.in PART C 1. Compare Am and FM in detail. AM FM AM stands for Amplitude Modulation AM method of audio transmission was first successfully carried out in the mid 1870s. In AM, a radio wave known as the "carrier" or "carrier wave" is modulated in amplitude by the signal that is to be transmitted. The frequency and phase remain the same. AM has poorer sound quality compared with FM, but is cheaper and can be transmitted over long distances. It has a lower bandwidth so it can have more stations available in any frequency range. AM radio ranges from 535 to 1705 KHz (OR) Up to 1200 bits per second. Twice the highest modulating frequency. In AM radio broadcasting, the modulating signal has bandwidth of 15kHz, and hence the bandwidth of an amplitude-modulated signal is 30kHz. Equidistant FM stands for Frequency Modulation Complexity Transmitter and receiver are simple but syncronization is needed in case of SSBSC AM carrier. Noise AM is more susceptible to noise because noise affects amplitude, which is where information is "stored" in an AM signal. Transmitter and receiver are more complex as variation of modulating signal has to beconverted and detected from corresponding variation in frequencies.(i.e. voltage to frequency and frequency to voltage conversion has to be done). FM is less susceptible to noise because information in an FM signal is transmitted through varying the frequency, and not the amplitude. Stands for Origin Modulating differences Pros and cons Frequency Range Bandwidth Requirements Zero crossing in modulated signal FM radio was developed in the United states in the 1930s, mainly by Edwin Armstrong. In FM, a radio wave known as the "carrier" or "carrier wave" is modulated in frequency by the signal that is to be transmitted. The amplitude and phase remain the same. FM is less prone to interference than AM. However, FM signals are impacted by physical barriers. FM has better sound quality due to higher bandwidth. FM radio ranges in a higher spectrum from 88 to 108 MHz. (OR) 1200 to 2400 bits per second. Twice the sum of the modulating signal frequency and the frequency deviation. If the frequency deviation is 75kHz and the modulating signal frequency is 15kHz, the bandwidth required is 180kHz. Not equidistant 31 EC8491 www.studymaterialz.in 32 EC8491 www.studymaterialz.in 4. Explain in detail about single tone FM.(MAY/JUNE 2016, NOV/DEC 2016) For the single tone frequency modulation,i.e the modulating signal x(t) be a sinusoidal signal of amplitude Em and frequency fm . Therefore, x(t) = Em cos (2πfmt) The unmodulated carrier is represented by the expression :ec = Ec sin (ωct + φ). Instantaneous frequency of an FM wave In FM, the frequency f of the FM wave varies in accordance with the modulating voltage . Thus, Where Δf = kf Em and it is called as frequency deviation. Frequency Deviation (Δf) Frequency deviation Δf represents the maximum departure of the instantaneous frequency fi(t) of the FM wave from the carrier frequency fc . 33 EC8491 www.studymaterialz.in Since Δf = kf Em, the frequency deviation is proportional to the amplitude of modulating voltage (Em) and it is independent of the modulating frequency fm . Maximum frequency of FM Wave: The maximum frequency of FM wave is given by : fmax = fc ± Δf Mathematical Expression for FM: FM wave is a sine wave having a constant amplitude and a variable instantaneous frequency . As the instantaneous frequency is changing continuously, the angular velocity ω of an FM wave is the function of ωc and ωm . Therefore, the FM wave is represented by, As shown in fig.10, Ec sin Θ(t) is a rotating vector . If Ec is rotating at a constant velocity ‘ω’, then we could have written that Θ(t)=ωt . Fig.10 Phasor of single tone FM 34 EC8491 www.studymaterialz.in But, in FM , this velocity is not constant. In fact, it is changing continuously. The angular velocity of FM wave is given as, Modulation Index The modulation index of an FM wave is defined as under : The modulation index is very important in FM because it decides the bandwidth of the FM wave which we will discuss later . The modulation index also decides the number of sidebands having significant amplitudes . In AM, the maximum value of the modulation index m is 1 . But, for FM, the modulation index can be greater than 1. Deviation Ratio In FM broadcasting, the maximum value of deviation is limited to 75 kHz. The maximum modulating frequency is also limited to 15 kHz. The modulation index corresponding to the maximum deviation and maximum modulating frequency is called as the deviation ratio . Percentage Modulation of FM Wave The percent modulation is defined as the ratio of the actual frequency deviation produced by the modulating signal to the maximum allowable frequency deviation . Thus, 35 EC8491 www.studymaterialz.in UNIT – III RANDOM PROCESS PART A 1. Define random variables? (MAY/JUNE 2012,NOV/DEC2010,NOVDEC 2015) A random variable, usually written X, is a variable whose possible values are numerical outcomes of a random phenomenon. Random variable consists of two types they are discrete and continuous type variables. 2. What is meant by probability distribution? The probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values. It is also sometimes called the probability function or the probability mass function. 3. What are the conditions applied in the central limit theorem? The mean of the population of means is always equal to the mean of the parent population from which the population samples were drawn. The standard deviation of the population of means is always equal to the standard deviation of the parent population divided by the square root of the sample size (N). The distribution of means will increasingly approximate a normal distribution as the size N of samples increases. 4. Define stationary process. Stationary process is a stochastic process whose joint probability distribution does not change when shifted in time. Consequently, parameters such as the mean and variance, if they are present, also do not change over time and do not follow any trends. 5. Write the equation for correlation? The population correlation coefficient ρX,Y between two random variables X and Y with expected values μX and μY and standard deviations ςX and ςY is defined as: 6. What is meant by covariance? Covariance is a measure of how much two variables change together, and the covariance function, or kernel, describes the spatial covariance of a random variable process or field. 7. Define random process.(APR/MAY-2010) (NOV/DEC-2011) A random process X(t) is a Gaussian process if for all n and all (t1 ,t2 ,…,tn ), the random variables have a jointly Gaussian density function. 36 www.studymaterialz.in EC8491 8. Write the equation of Autocorrelation?(MAY/JUNE 2016) The autocorrelation function of the output random process Y (t). By definition, we have RY (t, u) = E[Y (t)Y (u)] where t and u denote the time instants at which the process is observe 9. Write the applications of random process? The available noise power is directly proportional to temperature and it is independent of value of resistance. This power specified in terms of temperature is called as noise temperature. It is denoted by Te . It is given as, Te =(F−1)T A Gaussian process can be used as a prior probability distribution over functions in Bayesian inference. 10. What are the properties of a autocorrelation function? Autocorrelation function of a stationary random process X(t) is defined as, Rx(τ)=E[X(t + τ) X(t)] for all t (i).The mean square value of the process may be obtained from R x(τ) by simply putting τ=0 in the above equation 2 Rx(0)=E [X (t)] (ii)The auto correlation function Rx(τ) is an even function of Rx(τ)= Rx(-τ) From this property we can redefine auto correlation function like this. Rx(τ)= E[X(t) . X(t-τ) (iii)The autocorrelation function Rx(τ) has its maximum magnitude as τ = 0 11.State Central limit theorem.( NOV/DEC 2016,MAY/JUNE 2016) The central limit theorem states that the sampling distribution of the mean of any independent random variable will be normal or nearly normal, if the sample size is large enough. PART-B 1.Differentiate The Strict-Sense Stationary With That Of Wide Stationary Process. (APR/MAY 2015,MAY/JUN 2016) In mathematics and statistics, a stationary process or strict stationary process or strong stationary process) is a stochastic process whose joint probability distribution does not change when shifted in time. Consequently, parameters such as the mean and variance, if they are present, also do not change over time and do not follow any trends. Stationarity is used as a tool in time series analysis, where the raw data is often transformed to become stationary; for example, economic data are often seasonal and/or dependent on a non stationary price level. An important type of non- 37 www.studymaterialz.in EC8491 stationary process that does not include a trend like behavior is the cyclo-stationary process. A "stationary process" is not the same thing as a "process with a distribution”. Indeed, there are further possibilities for confusion with the use of "stationary" in the context of stochastic processes; for example a "time-homogeneous" Markov chain is sometimes said to have "stationary transition probabilities". Besides, all stationary Markov random processes are time-homogeneous. Strict-sense Stationary Process A random process X (t ) is called strict-sense stationary (SSS) if its probability structure is invariant with time. In terms of the joint distribution function, X (t ) is called SSS if (x , x ..., x ) F F X ( t ), X ( t )..., X ( t 1 2 ) 1 2 X ( t t ), X ( t t )..., X ( t t n n 1 0 2 0 n )0 (x1 , x2 ..., xn ) n N , t 0 and for all choices of sample points t1 , t 2 ,...tn . Thus the joint distribution functions of any set of random variables does not depend on the placement of the origin of the time axis. This requirement is a very strict. Less strict form of stationarity may be defined. Particularly, F (x , x (x , x X ( t ), X ( t )..... X ( t ) 1 2 .....xn ) FX ( t t ), X ( t t )..... X ( t t ) 1 2 .....xn ) for n 1,2,.., k, if then X ( t1 ), X ( t 2 ), ..., X ( tn ) 12 n 1 0 2 0 X (t ) is called kth order stationary. If X (t ) is stationary up to order 1 F (x ) F (x ) t T X (t1 ) X (t1 t0 ) 1 1 n 0 0 Let us assume t 0 t1. Then FX ( t1 ) (x1 ) FX (0) (x1 ) which is independent of time. As a consequence EX (t1 ) EX (0) X (0) constant F If X (t ) is stationary up to order 2 (x , x .) F X (t1 ), X (t2 ) Put t0 t2 F 1 2 (x , x ) X (t1 t0 ), X (t2 t0 ) (x , x ) F X ( t1 ), X ( t 2 ) 1 2 1 2 (x , x ) X ( t1 t 2 ), X (0) 1 2 This implies that the second-order distribution depends only on the time-lag t1 t2 . As a consequence, for such a process R X (t1 , t 2 ) E ( X (t1 ) X (t2 )) x1 x2 f X (0) X ( t1 t2 ) ( x1 , x2 )dx1 dx2 = R X (t1 t2 ) Similarly, C X (t1 , t 2 )= CX (t1 t2 ) Therefore, the autocorrelation function of a SSS process depends only on the time lag We can also define the joint stationary of two random processes. Two processes t1 t2 . X (t ) and Y (t) are called jointly strict-sense stationary if their joint probability distributions of any Z (t ) X (t ) 38 www.studymaterialz.in EC8491 order is invariant under the translation of time. A complex process jY (t ) is called SSS if X (t ) and Y (t) are jointly SSS. Wide-sense stationary process It is very difficult to test whether a process is SSS or not. A subclass of the SSS process called the wide sense stationary process is extremely important from practical point of view. A random process { X ( t)} is called wide sense stationary process (WSS) if EX (t) X constant and EX (t1 ) X (t 2 ) R X (t1 t 2 ) is a function of time lag t1 t2 . (Equivalently, Cov ( X (t1 ) X (t 2 )) CX (t1 t 2 ) is a function of time lag t1 t2 ) 2. Explain in detail about Ergodicity Principle If the time averages converge to the corresponding ensemble averages in the probabilistic sense, then a time-average computed from a large realization can be used as the value for the corresponding ensemble average. Such a principle is the ergodicity principle to be discussed below: Mean ergodic process Thus for a mean ergodic process X (t), lim E X T X T and lim var X T T 0 We have earlier shown that E X X T and var X 1 2T C X ( ) 1 d 2T 2T 2T Therefore, the condition for ergodicity in mean is T lim 1 2T C ( ) 1 X T 2T 2T d 0 2T If CX ( ) decreases to 0 for 0 , then the above condition is satisfied. Further, 2T 2T CX ( ) d C X ( ) 1 d 2T 2T 2 T 2T 2T Therefore, a sufficient condition for mean ergodicity is 1 2T 2T 1 C X ( ) d 39 www.studymaterialz.in EC8491 Example Consider the random binary waveform{ X ( t)} discussed in Example .The process has the auto-covariance function for Tp given by 1 CX ( ) Tp Tp 0 otherwise Here 2T 2T C X ( ) d 2 C X ( ) d 2 T 0 Tp 1 2 0 2T p 2Tp 3 d Tp T3 p 2 3T p T2 p T p C X ( ) d Hence { X ( t)}is not mean ergodic. Autocorrelation ergodicity R ( ) 1 T X (t ) X (t )dt X T 2T T If we consider Z (t ) X (t ) X (t ) so that, Z RX ( ) Then { X ( t)} will be autocorrelation ergodic if {Z (t)} is mean ergodic. Thus { X ( t)} will be autocorrelation ergodic if 2T lim 1 1 1 C ()d 0 T Z 1 1 2T 2T 2T where CZ ( 1 ) EZ (t )Z (t 1 ) EZ (t )EZ (t 1 ) 2 EX (t ) X (t ) X (t ) X (t 1 ) RX ( ) Involves fourth order moment. Hence the condition for autocorrelation ergodicity of a jointly Gaussian process is found. Thus X (t) will be autocorrelation ergodic if 2T lim 1 1 C ( )d 0 T z 2T 2T 2T Now C ( ) EZ (t )Z (t ) R2 () Z X Hence, X (t) will be autocorrelation ergodic 40 www.studymaterialz.in EC8491 If lim T 1 2T 1 Ez (t )z (t ) R2 ( ) d 0 X 2T 2T 2T 3.Derive The Equation For Finding The Power Spectral Density Of A One To One Differential Function Of A Given Random Variable. (NOV/DEC 2013) Consider a random process Z ( t ) which is sum of two real jointly WSS random processes X(t) and Y(t). RZ ( ) R X ( ) RY ( ) R XY ( ) RYX ( ) If we take the Fourier transform of both sides, S Z ( ) S X ( ) SY ( ) FT ( RXY ( )) FT ( RYX ( )) where FT (.) stands for the Fourier transform. Thus we see that SZ () includes contribution from the Fourier transform of the crosscorrelation functions RXY ( ) and RYX ( ). These Fourier transforms represent cross power spectral densities. Definition of Power Spectral Density Given two real jointly WSS random processes X(t) and Y(t), the cross power spectral density (PSD) SXY () is defined as S FTX ( ) FTY () XY () lim E 2T T T T whereFTX T ( ) and FTYT () are the Fourier transform of the truncated processes X (t) X(t)rect( t ) and Y (t) Y(t)rect( t ) respectively and denotes the complex T T 2T 2T conjugate operation. We can similarly define SYX () by S YX () lim E FTY ( ) FTX T () T 2T Proceeding in the same way as the derivation of the Wiener-Khinchin-Einstein theorem for the WSS process, it can be shown that T S XY ( ) R XY ( ) e j d and SYX ( ) RYX ( ) e j d The cross-correlation function and the cross-power spectral density form a Fourier transform pair and we can write R XY ( ) S XY ( ) e and RYX ( ) SYX ( ) e j j d d 41 www.studymaterialz.in EC8491 Properties of the PSD The PSD is a complex function of the frequency . Some properties of the CPSD of two jointly WSS processes X(t) and Y(t) are listed below: (1) S XY ( ) SYX* () Note that R XY ( ) RYX ( ) S XY ( ) R XY ( ) e j d RYX ( ) e j d j d RYX ( ) e * = S () YX (2) Re( SXY ()) is an even function of and Im( SXY ()) is an odd function of We have S XY ( ) R XY ( )(cos j sin ) d R XY ( ) cos d j R XY ( )sin ) d Re(S XY ( )) j Im(S XY ()) where Re(S XY ( )) R XY ( ) cos d is an even function of and Im(S XY ( )) R XY ( )sin d is an odd function of and (3) X(t) and Y(t) are uncorrelated and have constant means, then S XY ( ) SYX ( ) X Y () Observe that R XY ( ) EX (t )Y (t) EX (t )EY (t) XY YX RXY ( ) S XY ( ) SYX ( ) X Y () (4) If X(t) and Y(t) are orthogonal, then S XY ( ) SYX () 0 If X(t) and Y(t) are orthogonal, R XY ( ) EX (t )Y (t) 0 RXY ( ) S XY ( ) SYX () 0 (5) The cross power PXY between X(t) and Y(t) is defined by P XY lim T 1 2T T E X (t )Y (t )dt T 42 www.studymaterialz.in EC8491 Applying Parseval’s theorem, we get P XY T 1 E X (t )Y (t )dt T 2T T 1 lim E X T (t )YT (t )dt T 2T 1 1 * lim E FTX T ( ) FTYT ( ) d T 2T 2 lim P XY 1 lim 2 T 1 EFTX * ( ) FTY () T T 2T d S XY ( ) d 2 1 S XY ( ) d 2 Similarly, P YX 1 SYX ( ) d 2 1 S * ( ) d 2 PXY* XY 4. Explain Central limit theorem and its Convergence to the limit. In probability theory, the central limit theorem states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined expected value and welldefined variance, will be approximately normally distributed, regardless of the underlying distribution. A simple example of this is that if one flips coin many times, the probability of getting a given number of heads should follow a normal curve, with mean equal to half the total number of flips. It is used to define a sum of many independent and identically distributed random variables, or alternatively, random variables with specific types of dependence, will tend to be distributed according to one of a small set of attractor distributions. In contrast, the sum of a number of random variables with power law tail −α−1 distributions decreasing as |x| where 0 < α < 2 (and therefore having infinite variance) will tend to an alpha-stable distribution with stability parameter (or index of stability) of α as the number of variables grows. Classical Central limit theorem Let {X1, ..., Xn} be a random sample of size n —∞ that is, a sequence of independent and identically distributed random variables drawn from distributions of 2 expected values given by µ and finite variances given by σ . Sn=X1+…….+Xn/n Suppose we are interested in the sample average of these random variables. By the law of large numbers, the sample averages converge in probability and almost surely to the expected value µ as n → ∞. 43 EC8491 www.studymaterialz.in Convergence to the limit The central limit theorem gives only an asymptotic distribution. As an approximation for a finite number of observations, it provides a reasonable approximation only when close to the peak of the normal distribution; it requires a very large number of observations to stretch into the tails. 3 If the third central moment E((X1 − μ) ) exists and is finite, then the above convergence is uniform and the speed of convergence is at least on the order of 1/2 1/n (see Berry-Esseen theorem). Stein's method can be used not only to prove the central limit theorem, but also to provide bounds on the rates of convergence for selected metrics. The convergence to the normal distribution is monotonic, in the sense that the entropy of Zn increases monotonically to that of the normal distribution. The central limit theorem applies in particular to sums of independent and identically distributed discrete random variables. A sum of discrete random variables is still a discrete random variable, so that we are confronted with a sequence of discrete random variables whose cumulative probability distribution function converges towards a cumulative probability distribution function corresponding to a continuous variable (namely that of the normal distribution). This means that if we build a histogram of the realizations of the sum of n independent identical discrete variables, the curve that joins the centers of the upper faces of the rectangles forming the histogram converges toward a Gaussian curve as n approaches infinity, this relation is known as de Moivre–Laplace theorem. The binomial distribution article details such an application of the central limit theorem in the simple case of a discrete variable taking only two possible values. 5.(i). Write Short Notes On Covariance Function. COVARIANCE FUNCTIONS: In probability theory and statistics, covariance is a measure of how much two variables change together, and the covariance function, or kernel, describes the spatial covariance of a random variable process or field. For a random field or stochastic process Z(x) on a domain D, a covariance function C(x, y) gives the covariance of the values of the random field at the two locations x and y: The same C(x, y) is called the auto covariance function in two instances: in time series (to denote exactly the same concept except that x and y refer to locations in time rather than in space), and in multivariate random fields (to refer to the covariance of a variable with itself, as opposed to the cross covariance between two different variables at different locations, Cov(Z(x1), Y(x2))). 44 EC8491 www.studymaterialz.in A function is a valid covariance function if and only if this variance is nonnegative for all possible choices of N and weights w1, …, wN. A function with this property is called positive definite. 5. (ii).Write Short Notes On Auto Correlation Function. In statistics, dependence is any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence. Familiar examples of dependent phenomena include the correlation between the physical statures of parents and their offspring, and the correlation between the demand for a product and its price. Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling; however, statistical dependence is not sufficient to demonstrate the presence of such a causal relationship. Formally, dependence refers to any situation in which random variables do not satisfy a mathematical condition of probabilistic independence. In loose usage, correlation can refer to any departure of two or more random variables from independence, but technically it refers to any of several more specialized types of relationship between mean values. There are several correlation coefficients, often denoted ρ or r, measuring the degree of correlation. The most common of these is the Pearson correlation coefficient, which is sensitive only to a linear relationship between two variables. Other correlation coefficients have been developed to be more robust than the Pearson correlation that is, more sensitive to nonlinear relationships. Mutual information can also be applied to measure dependence between two variables. Pearson's correlation coefficient: The most familiar measure of dependence between two quantities is the Pearson product-moment correlation 45 EC8491 www.studymaterialz.in coefficient, or "Pearson's correlation coefficient", commonly called simply "the correlation coefficient". It is obtained by dividing the covariance of the two variables by the product of their standard deviations. Karl Pearson developed the coefficient from a similar but slightly different idea by Francis Galton. The population correlation coefficient ρX,Y between two random variables X and Y with expected values μX and μY and standard deviations ςX and ςY is defined as: where E is the expected value operator, cov means covariance, and, corr a widely used alternative notation for the correlation coefficient. The Pearson correlation is defined only if both of the standard deviations are finite and nonzero. It is a corollary of the Cauchy– Schwarz inequality that the correlation cannot exceed 1 in absolute value. The correlation coefficient is symmetric: corr(X,Y) = corr(Y,X). The Pearson correlation is +1 in the case of a perfect direct (increasing) linear relationship (correlation), −1 in the case of a perfect decreasing (inverse) linear relationship (autocorrelation), and some value between −1 and 1 in all other cases, indicating the degree of linear dependence between the variables. As it approaches zero there is less of a relationship (closer to uncorrelated). The closer the coefficient is to either −1 or 1, the stronger the correlation between the variables. If the variables are independent, Pearson's correlation coefficient is 0, but the converse is not true because the correlation coefficient detects only linear dependencies between two variables. For example, suppose the random variable X is symmetrically distributed about zero, and Y = X2. Then Y is completely determined by X, so that X and Y are perfectly dependent, but their correlation is zero; they are uncorrelated. However, in the special case when X and Y are jointly normal, uncorrelatedness is equivalent to independence. If we have a series of n measurements of X and Y written as xi and yi where i = 1, 2, ..., n, then the sample correlation coefficient can be used to estimate the population Pearson correlation r between X and Y. where x and y are the sample means of X and Y, and sx and sy are the sample standard deviations of X and Y. 46 EC8491 www.studymaterialz.in PART C 47 EC8491 www.studymaterialz.in 48 EC8491 www.studymaterialz.in 49 EC8491 www.studymaterialz.in 50 www.studymaterialz.in EC8491 UNIT IV- NOISE CHARACTERIZATION PART A 1. Define noise. Noise is defined as any unwanted form of energy, which tends to interfere with proper reception and reproduction of wanted signal. 2. What are types of internal noise? Internal noise can be classified into 1. Thermal noise 2. Shot noise 3. Transit time noise 4. Miscellaneous internal noise 3. Define flicker noise. Flicker noise is the one appearing in transistors operating at low audio frequencies. Flicker noise is proportional to the emitter current and junction temperature and inversely proportional to the frequency. 4. Define thermal noise. Give the expression for the thermal noise voltage across a resistor. The electrons in a conductor possess varying amounts of energy. A small fluctuation in this energy produces small noise voltages in the conductor. These random fluctuations produced by thermal agitation of the electrons are called thermal noise. 5. Define equivalent noise temperature. (MAY/JUNE-2010,NOV/DEC2014,MAY/JUN 2016,NOV/DEC 2016) The available noise power is directly proportional to temperature and it is independent of value of resistance. This power specified in terms of temperature is called as equivalent noise temperature. It is denoted by Te. It is given as, Te = (F −1) T0 Where F-noise figure T0-Absolute temperature 6. What is shot noise? (MAY/JUNE-2013) When current flows in electronic device, the fluctuations number of electrons or holes generates the noise. It is called shot noise. Shot noise also depends upon operating conditions of the device. 7. What is narrowband noise? The receiver of a communication system usually includes some provision for pre-processing the received signal. The pre-processing may take the form of a narrowband filter whose bandwidth is large enough to pass modulated component of the received signal essentially undistorted but not so large as to admit excessive noise through the receiver. The noise process appearing at the output of such filter is called narrow band noise. 51 EC8491 www.studymaterialz.in 8. Define noise equivalent bandwidth. The noise equivalent bandwidth of the filter is defined as the bandwidth of an ideal filter at which the noise power passed by real filter and ideal filter is same. 9. What is FM threshold effect? (NOV/DEC-2011,APR/MAY2015,NOV/DEC 2015) As the carrier to noise ratio is reduced, clicks are heard in the receiver output. As the carrier to noise ratio reduces further, crackling, or sputtering sound appears at the receiver output. Near the breaking point, the theoretically calculated output signal to noise ratio becomes large, but its actual value is very small. This phenomenon is called threshold effect. 10. Define pre-emphasis and de-emphasis. (NOV/DEC-2010,MAY/JUNE2013,APR/MAY 2015) Pre-emphasis: It artificially emphasizes the high frequency components before modulation.This equalizes the low frequency and high frequency portions of the PSD and complete band is occupied. De-emphasis: This circuit attenuates the high frequency components. The attenuation characteristic is exactly opposite to that of pre-emphasis circuit. De-emphasis restores the power distribution of the original signal. The signal to noise ratio is improved because of pre-emphasis and de-emphasis circuits. 11.Define SNR. (APR/MAY-2015) Signal to noise ratio(SNR) is the ratio of signal power to the noise power at the same point in a system. 12.Define noise figure. (MAY/JUNE-2013,APR/MAY-2015,NOV/DEC 2015MAY/JUNE 2016) Noise figure is defined as the ratio of signal to noise power at the input to the signal to noise power at the output. 13.Define white noise (or) Gaussian noise. (MAY/JUNE-2013)(APR/MAY2011) (NOV/DEC-2010) (MAY/JUNE-2014) Many types of noise sources are Gaussian and have flat spectral density over a wide frequency range. Such spectrum has all frequency components in equal portion, and is therefore called white noise, the power spectral density of whit noise is independent of the operating frequency. PART-B 1. Write Short Notes On Shot Noise, Thermal noise, White Noise .(APRIL/MAY 2015,MAY/JUNE 2013,NOV/DEC 2016) Noise is random, undesirable electrical energy that enters the communications system via the communicating medium and interferes with the transmitted message. However, some noise is also produced in the receiver. With reference to an electrical system, noise may be defined as any unwanted form of energy which tends to interfere with proper reception and reproduction of wanted signal. Noise may be put into following two categories. 52 www.studymaterialz.in EC8491 External noises, i.e. noise whose sources are external. External noise may be classified into the following three types: Atmospheric noises Extra-terrestrial noises Man-made noises or industrial noises. Internal noise in communication: Noises which get, generated within the receiver or communication system. Internal noise may be put into the following four categories. Thermal noise or white noise or Johnson noise Shot noise. Transit time noise Miscellaneous internal noise. External noise cannot be reduced except by changing the location of the receiver or the entire system. Internal noise on the other hand can be easily evaluated mathematically and can be reduced to a great extent by proper design. Explanation of External Noise Atmospheric Noise: Atmospheric noise or static is caused by lighting discharges in thunderstorms and other natural electrical disturbances occurring in the atmosphere. These electrical impulses are random in nature. Hence the energy is spread over the complete frequency spectrum used for radio communication. Atmospheric noise accordingly consists of spurious radio signals with components spread over a wide frequency range. These spurious radio waves constituting the noise get propagated over the earth in the same fashion as the desired radio waves of the same frequency. Accordingly at a given receiving point, the receiving antenna picks up not only the signal but also the static from all the thunderstorms, local or remote. Extra-terrestrial noise: Solar noise Cosmic noise Solar noise: This is the electrical noise emanating from the sun. Under quite conditions, there is a steady radiation of noise from the sun. This results because sun is a large body at a very high temperature (exceeding 6000°c on the surface), and radiates electrical energy in the form of noise over a very wide frequency spectrum including the spectrum used for radio communication. The intensity produced by the sun varies with time. In fact, the sun has a repeating 11-year noise cycle. During the peak of the cycle, the sun produces some amount of noise that causes tremendous radio signal interference, making many frequencies unusable for communications. During other years. The noise is at a minimum level. 53 EC8491 www.studymaterialz.in Cosmic noise: Distant stars are also suns and have high temperatures. These stars, therefore, radiate noise in the same way as our sun. The noise received from these distant stars is thermal noise (or black body noise) and is distributing almost uniformly over the entire sky. Noise is received from the centre of our own galaxy (The Milky Way) from other distant galaxies and from other virtual point sources such as quasars and pulsars. Man-Made Noise (Industrial Noise): By man-made noise or industrial- noise is meant the electrical noise produced by such sources as automobiles and aircraft ignition, electrical motors and switch gears, leakage from high voltage lines, fluorescent lights, and numerous other heavy electrical machines. Such noises are produced by the arc discharge taking place during operation of these machines. Such man-made noise is most intensive in industrial and densely populated areas. Man-made noise in such areas far exceeds all other sources of noise in the frequency range extending from about 1 MHz to 600 MHz Explanation of Internal Noise in communication: Thermal Noise: Conductors contain a large number of 'free" electrons and "ions" strongly bound by molecular forces. The ions vibrate randomly about their normal (average) positions, however, this vibration being a function of the temperature. Continuous collisions between the electrons and the vibrating ions take place. Thus there is a continuous transfer of energy between the ions and electrons. This is the source of resistance in a conductor. The movement of free electrons constitutes a current which is purely random in nature and over a long time averages zero. There is a random motion of the electrons which give rise to noise voltage called thermal noise. Thus noise generated in any resistance due to random motion of electrons is called thermal noise or white or Johnson noise. The analysis of thermal noise is based on the Kinetic theory. It shows that the temperature of particles is a way of expressing its internal kinetic energy. Thus "Temperature" of a body can be said to be equivalent to the statistical rms value of the velocity of motion of the particles in the body. At -273°C (or zero degree Kelvin) the kinetic energy of the particles of a body becomes zero .Thus we can relate the noise power generated by a resistor to be proportional to its absolute temperature. Noise power is also proportional to the bandwidth over which it is measured. From the above discussion we can write down. 54 EC8491 www.studymaterialz.in Transit Time Noise: Another kind of noise that occurs in transistors is called transit time noise. Transit time is the duration of time that it takes for a current carrier such as a hole or current to move from the input to the output. The devices themselves are very tiny, so the distances involved are minimal. Yet the time it takes for the current carriers to move even a short distance is finite. At low frequencies this time is negligible. But when the frequency of operation is high and the signal being processed is the magnitude as the transit time, then problem can occur. The transit time shows up as a kind of random noise within the device, and this is directly proportional to the frequency of operation. Miscellaneous Internal Noises Flicker Noise: Flicker noise or modulation noise is the one appearing in transistors operating at low audio frequencies. Flicker noise is proportional to the emitter current and junction temperature. However, this noise is inversely proportional to the frequency. Hence it may be neglected at frequencies above about 500 Hz and it, Therefore, possess no serious problem. 55 EC8491 www.studymaterialz.in Transistor Thermal Noise: Within the transistor, thermal noise is caused by the emitter, base and collector internal resistances. Out of these three regions, the base region contributes maximum thermal noise. Partition Noise: Partition noise occurs whenever current has to divide between two or more paths, and results from the random fluctuations in the division. It would be expected, therefore, that a diode would be less noisy than a transistor (all other factors being equal) If the third electrode draws current (i.e.., the base current). It is for this reason that the inputs of microwave receivers are often taken directly to diode mixers. Shot Noise: The most common type of noise is referred to as shot noise which is produced by the random arrival of 'electrons or holes at the output element, at the plate in a tube, or at the collector or drain in a transistor. Shot noise is also produced by the random movement of electrons or holes across a PN junction. Even through current flow is established by external bias voltages, there will still be some random movement of electrons or holes due to discontinuities in the device. An example of such a discontinuity is the contact between the copper lead and the semiconductor materials. The interface between the two creates a discontinuity that causes random movement of the current carriers. 2. Explain the Capture effect, threshold effect Pre-emphasis and de-emphasis (APR/MAY-2013,NOV/DEC2015,MAY/JUNE 2016) 3. Capture effect: In the frequency modulation, the signal can be affected by another frequency modulated signal whose frequency content is close to the carrier frequency of the desired FM wave. The receiver may lock such an interference signal and suppress the desired FM wave when interference signal is stronger than the desired signal. When the strength of the desired signal and interference signal are nearly equal, the receiver fluctuates back and forth between them, i.e., receiver locks interference signal for some times and desired signal for some time and this goes on randomly. This phenomenon is known as the capture effect. FM Threshold Effect: The output signal to noise ratio of FM receiver is valid only if the carrier to noise ratio is measured at the discriminator input is high compared to unity. It is observed that as the input noise is increased so that the carrier to noise ratio decreased, the FM receiver breaks. At first individual clicks are heard in the receiver output and as the carrier to noise ratio decreases still further, the clicks rapidly merge in to a crackling or sputtering sound. FM threshold reduction: This can be achieved by using an FM demodulator with negative feedback (FMFB) or by using a phase locked loop demodulator. Fig.1 FM Threshold reduction 56 EC8491 www.studymaterialz.in The conventional local oscillator is replaced by VCO. To understand the operation of this receiver, suppose that VCO is removed from the circuit and the feedback path is left open. Assume that the wide band FM is applied to the receiver input, and a second FM from the same source but with a modulation index a fraction smaller is applied to the VCO terminal of the product modulator. The output of the product modulator consists of sum and difference frequency components. The IF filter is designed to pass only difference frequency component. The frequency deviation of the IF filter output would be small, although the frequency deviation of both input FM wave is large, since the difference between their instantaneous deviations is small. Hence, the modulation indices would subtract, and the resulting FM wave at the IF filter output have a smaller modulation index than the input FM waves. This means that the IF filters bandwidth in fig above need only be a fraction of that required for either wideband FM wave. It is now apparent that Second wide band FM waves replaced by VCO feed by o/p of low pass filter. Pre-Emphasis and De-Emphasis in an FM system Fig. 2 Pre-emphasis and De-emphasis in FM In this method, we artificially emphasize the high frequency components of the message signal prior modulation in the transmitter before the noise is introduced in the receiver. The low frequency and high frequency portions of the PSD of the message are equalized in such a way that the message fully occupies the frequency band allotted to it. Then, at the discriminator output in the receiver perform the inverse operation by de-emphasizing the high frequency components to restore the message. In this process, the high frequency noise is reduced thereby effectively increasing the output SNR of the system. 57 EC8491 www.studymaterialz.in MAY/JUNE 2016 58 EC8491 www.studymaterialz.in 59 EC8491 www.studymaterialz.in 60 EC8491 www.studymaterialz.in 61 EC8491 www.studymaterialz.in 62 EC8491 www.studymaterialz.in 63 EC8491 www.studymaterialz.in (NOV/DEC 2016) 64 EC8491 www.studymaterialz.in 65 EC8491 www.studymaterialz.in 66 EC8491 www.studymaterialz.in 67 EC8491 www.studymaterialz.in 68 EC8491 www.studymaterialz.in 97 EC8491 www.studymaterialz.in 98 EC8491 www.studymaterialz.in 99 EC8491 www.studymaterialz.in 100 EC8491 www.studymaterialz.in 101 EC8491 www.studymaterialz.in 102 EC8491 www.studymaterialz.in 103 EC8491 www.studymaterialz.in 104 EC8491 www.studymaterialz.in 105 EC8491 www.studymaterialz.in 106 EC8491 www.studymaterialz.in 107 EC8491 www.studymaterialz.in 108 EC8491 www.studymaterialz.in 109 EC8491 www.studymaterialz.in 110