EEL 4512 – Communication Systems
Added on 2020-04-15
21 Pages3588 Words165 Views
0CommunicationSystems
Table of ContentsProblem-1.............................................................................................................................................2(a)Free space path loss.............................................................................................................2(b)Local oscillator.....................................................................................................................3Determine the frequency ratio....................................................................................................3Determine the image frequency..................................................................................................4(c)Auto correlation function....................................................................................................4Problem-2.............................................................................................................................................4(a)Frequency re-use in cellular system.......................................................................................4(b)Duplexer in cellular system.....................................................................................................6(c)Multiple access technique........................................................................................................6Problem-3.............................................................................................................................................9(a)Find the power spectral density of the output Sy(f)..............................................................9(b)Auto correlation of the output signal R(y)τ.........................................................................10(c)Output signal p y....................................................................................................................10Problem -4..........................................................................................................................................10(a) Determine the overall noise figure of the cascade......................................................................10(b) Input power..................................................................................................................................11(c ) Suppose amplifier 1 and 2 are interchanged. the noise figure cascade is F1 =6,F2=0............11Problem- 5..........................................................................................................................................11(a)Overall nosie factor......................................................................................................................11(b)The overall noise figure if a preamplifier....................................................................................12( c) The overall noise figure if the amplifier.....................................................................................12Problem -6..........................................................................................................................................12(a)Auto correlation function......................................................................................................12(b)Power spectral density...........................................................................................................12Problem – 7........................................................................................................................................12(a) Briefly explain the role of the blocks labelled RF amplifier and Limiter in the diagram.......12(b)Find the bandwidths required for the RF amplifier, IF amplifier, and of the audio amplifier.............................................................................................................................................15(c)Larger bandwidth..................................................................................................................16Problem- 8..........................................................................................................................................16(a)Briefly explain what is meant by an ergodic random process............................................16(b)Determine whether or not the random process X (t) is an ergodic random process.........17(c)Random process is uniformly distribution is X (t) an ergodic random process................18
Problem-1(a)Free Space Path LossGiven Data:Frequency (f) = 1 MHZDistance (d) = 10 KmThe free space path loss equation is expressed as:FSPL = (4πdfc)2Decibel (db) is expressed as mentioned below:Distance in decibel (db) = 20 log10(4πdfc)Solution:Wavelength (λ) = cfWe know that, The light’s speed (c) = 3×108 m/sPut the value of c and f in wavelength equation:Wavelength (λ) = 3000001000000λ= 0.3 m The distance doubled the value, where the value of distance is in decibel.Distance in decibel (db) = 20 log10(4πdfc)= 20 log10(4π×20×1000000300000)=20 log10(251327412.2300000)=20 log10 (251.3274122)Distance in decibel (db)= 48 db(b)Local OscillatorGiven Data:Lower frequency = 540 kHzHigher frequency = 1700 kHz1
Intermediate frequency (IF) = 455 kHzSolution:Determine the Frequency RatioThe frequency ratio is defined by the highest to lowest frequency ratio of the local oscillator frequency fLO. Local oscillator frequency ratio is the difference between the highest ratio and the lowest ratio. fLO = highest ratio – lowest ratio/2 = 1700-540/2 =1160/2Ratio = 580 Determine the Image Frequency To find the value of frequency (f), F = 12π√LC =12π√109 =165.59 = 0.01524Image frequency (fimg)fimg = {f+2fIF if fLO > f (high side injection) }, {f−2fIF if fLO <f (low side injection) } = { (0.0152) + 2 (45), (0.0152) – 2 (45) = {90.0152 , -89.984Image frequency in fall time = 90.0152(c)Auto Correlation Function The appropriate autocorrelation function is characterised as follows, Autocorrelation function ρ(h) = γ(h)/ γ(0)| ρ(h)| ≤ 1Therefore, the appropriate autocorrelation function is given by the following equation, R(τ) = {1−|τ|,∨τ∨≤11+|τ|,∨τ∨≥12
Problem-2(a)Frequency re-use in Cellular SystemCellular Frequency Reuse- PrinciplesThe cellular frequency allocated the service named re-used in the areas of regularpattern, known as “Cells”. Every single cell is converted by one BS (base station). Such cellsare hexagonal in nature, in the mobile telephonenets. Similar, the rhombic cells has led to theradio broadcasting concept. For ensuring mutual inference between the users remain belowlaved, and the adjacent cell use different frequencies. For the cluster of each C adjacent cells,the set of frequencies such as {f1, ..., fC}are used. In a regular pattern, the cluster patterncorresponding frequencies are re-used.C= 3’s Frequency reuse plan, with hexagonal cells (i=1,j=1)C= 7’s Frequency reuse plan with (i=2,j=1).The system’s total bandwidth isCtimes the bandwidth that a single cell occupies. A cell is acellular base station that allocates radio channel within the group of small geographic area.3
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