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- 1. t"{ O6MAT41 USN Fourth Semester B.E. Degree Examination, Dec.2013/Jan.2ol4 Engineering Mathematies - lV Max. Marks:100 Time: 3 hrs. Note: Answer FIVEfull questions, selecting at least TWO questionsfrom euch part. PART _ A d o ! 9. degree term. o ! o b. oX bo- 1. Given {=*+v2-v(0):1. (06 Marks) O, Find y at x: 0.2 using Runge Kutta fourth order method. Given ioo .= a.t x 0 0.2 0.1 [ a= tction f(z) ootr i9 o'' b. a-dV c. aOl o c. Evaluate l r"ot1., dz where 'c' is lz - 1l : ! (r-Y,)' Solve y =0 With usual notation prove that Express xo E 5 a. 1 using Cauchy's residue using the method ofsolution in series - 3x' + x P, (") = 1 d'.) (x' fr# - 1)n in terms of Legendre's polynomials. o o w:2,i,-2. (07 Marks) r 14* r9+ dx' dx Z F i, -1 intothepoint lzl VL lr< (07 Marks) 2- z:1, lz-r)(z-2) 12 b. ;n,l#;r (06 Marks) . (06 Marks) tr> =o 0 t ":11:* au*ly's theorem under complex values tunctiol tl.:rl",t"r. :,". f1z; = < 1, (ii) I <lzl<2.10t Marks) Expand in Laurent's series valid tbr (i) 5.v >'1- 4a. * Findthebilineartransformationwhichmapsthepoints Also find the invariant points of the transformation. qO boio0 o= o-B :2 6"' *l )' ffrl l' = 4lf'@)l' Ay' :u * iv where , = oO 3a. + y). with # = ,,, (07 Marks) / ;) b. dv t.5049 2a. If(z) in a regular tunction of 'z' show that I + L. 1 and 0.3 ! I I .1 169 1.2733 (Use comector formula twice.) :r bO Y(] at -o EE o> !o oe {y - y-*, y(0) : dx y+x (07 Marks) Use Milne's predictor corrector formulae to find y(0.4). Given -ld) 3o by considering the series up to fourlh step size 0.2. d9 *- x:0.1 Applying Taylor's series method, find'y'at o Fit a curve in the form y : at . { theorem. (07 Marks) ffi frx.-/9 Marks) Marks) Marks) tN;e NAg82/ _B PART U* T .7Uy-tn method of least squares for the data given below: x 1 1.5 2 2.5 J 3.5 4 v 1.1 1.3 t.6 2 2.7 3.4 4.1 (06 Marks)
- 2. O6MAT41 5 b. Obtain the two lilnes o 2 1 x v 2 5 ssions for the data given below: a J 4 5 a 8 7 J (07 Marks) between x and y' and hence The contents of the three wns are as given below: Urn 1: 1 white ball,2 red balls, 3 greenballs' lJrn2:2 white, 1 red and 1 greenball' Urn 3: 4 white, 5 red and 3 green --are found to the one white and one Two balls are drawn from randomly chosen urn and (07 Marks) p."u"unirv that the bails so drawn came from the third findffirrelation c. balls' i .1 urn' ;;r. ;;;i;rr. FindthemeanandvarianceofPoissondistribution(06Marks) distributed with mean 5 minutes' In a certairr town the duration of a shower is exponentially (ii) less than pr"u"il1iry that ashower will last for (i) 10 minutes or more' #"; ilil minutes? 10 (07 Marks) and 12 with mean 70 a normal distribution The marks of 1000 students in an examination foilows number.of, students, whose marks will be: and standard deviation of 5. Find the expected iil) between 65 and75 ii) more than z5 i) less than 65 (07 Marks) ffi;;,'iiid;i;#10 c. iCiu", 7a. b. c. 8 a. Test the hypothesis that the coin A coin is tossed 1000 times and head turned up 540 times. (06 Marks) is an unbiased one. r 1 L- 1. 40000 kms is found to be A sample of 200 tyres is taken from 11o1. The mean life of tyres mean life of tltes in the the with standard a.riuiio,.or izoo kms. Is it reasonable to assume limits with in which the mean life of tyres lot as 41000 kms? irro .uuurish 9-5% confidence (07 Marks) in the lot is expected to lie. . andr the , . 1 L- are t. to the in ,i heights -. found Ten individuals are chosen at random from a population light of this data discuss the inches 63,63,66",;,";;,*ei, io,70,7l i"d lt lg-tfre is 66 inches' If the population mean is suggestion that the *"u, height in the population (07 Marks) mean. unknown, obtain q-0%-co"fiae"nce limits foithis The given below: distribution for two random variables x arid y is joint (@ distributions of x and Y, (ii) covariance of x and Y. (06 Marks) regular stochastic matrix Find the unique fixed probability vector of the [o % Y^1 - "-.---' 107Marks) y y, o I| [o I o-l work place every day by motor bike or by car' he never goes - =lI P c. .. A(z:1):0.34i31'. Find the b. . .. A software .ngin.e, goes to his goes by car on a day then he is equally likely to by bike on two .orrrJ*ir. days, but if he transition matrix for the chain of the mode of go by car or by bik;;;the next day. Find t[e is used, (ii) a week find the probability that (i) bike transport. If car is used on the first day of (07 Marks) ;;;'";, o, ,r,. 5,n ;;. {<r,<*** .
- 3. I 10ES42 USN Fourth Semester B.E. Degree Examination, Dec.2013 /Jan.201.4 Microcontrollers Time: 3 hrs. Max. Marks:100 Not e : () o ::;::; ;ir; {::: l :x ;::; :"::;'#f, PART _ A k I (.) o 3e a. Define rrdcrocontroller. Differentiate between microprocessor and microiontroller. b. c. With the ,"ai diugrum, explain the 8051 architecture. Briefly explain the dual functions of port-3 pins of 8051. 2 a. -y. d9 bo loo .=N b. 6 otr dO ?.rr ?a c. a= oO bos >6 6Ecd 3a. A q: !o b. 6.e >. (F ^^o coO o= gU tr> o- c. (r< 4a. -N o '7 (n L (05 Marks) What is addressin!";o0., Put the number OFAH in registers R:, addressing modes. & and R5 in four different (06 Marks) Explain the following in brief, i) The pin that connects external memory. ii) The port that has open-drain output. iii) The register that sequences the program execution. iv) PSW. (08 Marks) Showthe stack contents, sp contentsandContents of anyregister affected after each step of the following sequences of operation: MOV SP. #7OH MOV R5. #3OH MOV A. #44H Add A. R5 MOV R4. A PUSH4 .,,,'"' PUSH 5 ' POP4 ^X o: (05 Marks) (10 Marks) ":$ltx -?() 5 .t3 o-i ,, ' ' "'.",, (06 Marks) ' Explain the different types of conditional and unconditional jump instructions of 8051. Specify the different ranges associated with jump instructions. (08 Marks) Find the address of first two internal RAM locations between 20H and 40H, which contains consecutive numbers. If so, set the carry flag to one, else clear the carry flag. (06 Marks) Write an 8051 assembly time delay subroutine to generate a time delay of 100 prsec when called. Assume crystal liequency as 12 MHz. Show delay calculations. Do not use timers. *"uod Give bit size and data range details for the widely used seven 'C' datat.ypes of 80r::u (04 Marks) b. C^ Write an 8051 ALP to convert packed BCD number 48 to ASCII and display the result on port-2 and port-3. (06 Marks) Write an ALP 8051 program to find the checksum byte of data stream 30H, 4AH, 65H and 10H. Convert the binary value of checksum into decimal and display the value of the BCD digits on ports Po, Pr and Pz. (10 Marks) I of2
- 4. 10ES42 PART 5 a. - B With regard to timers of 8051: i) Explain briefly the difference between the timer and counter operation. ii Indicate how io starVstop the timer if GATE control is also used. (06 lv!'fir':K$r) uo ltfffi,,liit" ::: E-,-r^:- mode-2 nnerqfinn iil) Explain ^^Ao-) operation. with a duty cycle of66"A *ii . an ALp to generate a square wave continuously of 2 kHz ,,rl ,,"1"'t*'. "":4= - u. ..,' create A switch is connected to the pin Pl.2. Write a 'C' program to monitor the swi$ch d ,x ff,6r; following frequencies on pin P1.7: : 0; 500H2 *,.Wh.n SW ii),"lrWhen SW = l;750H2 U-r"i@ir"U mode 1 for both of them. i,-.q..'l n.=,hhs q"'i$: 't' :,. ,,,', , ,:1,*,_ (08 Marks) RS232 in 6 a. what i, ;6id; communication? How serial communication id carried out with (06 Marks) u'''# so51? :: " ' (06 Marks) b. Explain the bit p&;h of SCON register' , " -'%,', -,.= = i) ii) ALP to transfer'se;ia$y letter 'A' continuously' ,,. 8-bits and C program to recelve,pty-tes of data and p,g;!thdfriin Pl. Use 9600 baud rate, 1, mode-2. (08 Marks) one st-op bit, for both t$ailsmission and qe'et$gtion. Use timer "'f' 7 a. b. 8 ,.'::=':iu =t io ftecture. "'':F'r'* (10 Marks) Explain briefly the MSP430 RISC+Q'ru,arc Give details of register of MSP430. Write short notes ..q=[,;.*&_., -" on: .;-' A, RTC ,,E-; fl b. DMA c. DAS d: RF interfaces. (10 Marks) 65'= '.h $ d".; " (20 Marks) _ ._*...] 2 of2 "{ .::!.
- 5. 06ES43 USN Fourth Semester B.E. Degree Examination, Dec. 20l3lJan.2014 Gontrol Systems Max. Marks:100 Time: 3 hrs. Note: 1. Answer FIVEfull questions, selecting atleast TWO questions from each part. 2. Missing data, tf any, muy be suitable assumed. o o o . () o ! ?a oociv -o0 I trca d$ I a. b. PART -A Define a control system. Explain with examples, open loop and clssed loop control systems. (10 Marks) List the merits and demerits of open loop and closed loop control systems. For the mechanieal system shown in Fig. Ql(b), D Draw the medhanical network ii) Write the differential equations describing the system iii) Draw the F - V analogous electrical circuit ater writing the corresponding electrical (l0 Marks) equations. 1 H(J og: eO ()= ai UO o0-c >! Fig. Q1(b) -6 ,o oE :9 ()i. orw 2 a. For the circuit shown in Fig. Q2(a). Draw the 1rr.1ior, -S($ Y (s) block diagram and determine the transfer , using block diagram rules. (10 Marks) aLE !o o.i >,t co" troo .-r c so tr> o- Fig. Q2(a) lr< iat For the system represented by the following equations, find the transfer function (.) o Z ! a E x(s) U(S) by signal flow graph, technique Xt t Cr:U X: i, =-0,x,+xr+crrU Xz =-pzXr +cr,U. (10 Marks)
- 6. 06ES43 3a. Explain the following time domain specifications of a second order systems, with neat sketch i) Peak time ii) Delay time iii) Rise time iv) maximum over shoot v) Settling time. (06 Marks) b. c. * * lgv + 25y(t)= 50x(t) , dt' dt Evaluate the response and maximum output for a step of 2.5 units. In the block shown in Fig. Q3(c) G(s) : A/S2 and H(S) : (ms +n). For A: A system described uv ' values of m and n for a step input with a time constant of30%o. 4a. b. 0.l (08 Marks) 10, determine the sec ; which give a peak over shoot (06 Marks) What are the.difficulties encountered while assessing Routh - Hurwitz criteria and how do you eliminate these difficulties, explain with examples. (06 Marks) ,,, ,r' The open loop transfer function of a feedback control system is given by G(S)H(S) = ------K-S(s+4Xs'+2s+2) i) Using R- H cretarian determine the range of "K'' for which the system will be stable ii) If a zero at S : -4 is added to the forward transfer function, how is the stability affected? (08 Marks) Using R H cretarian, find the stability of a unity feedback system having closed loop - lransfer function G(S) -qr - e =S(s + 2) (06 Marks) 5 a. State the different rules for ttretoriiru.,,:lH;l,o"rr. b. A feedback control system has open loop transfer {hnction G(S)H(S) = * b. 't"'' S(s + 4)(s2"+ 4s + 20) Plot the root locus.fot 6a. K:0 to co indicate all points on (12 Marks) ,, (06 Marks) The opeh loop transfer function of unity feedback control system is given by .,::',.' ,''' K s(l+0.001s)(1+0.25s)(l+0.1s) Determine the value of K, so that the system the gain margin. Use code plot. b. it. Explain co-rel{tion between time domain and frequency domai4 for second order systems. n/QLl/c ta. (08 Marks) : will have a phase margin of 40o, what will State and explain Nyquist stability cretarian. Using Nyquist stability cretarian. find the range of K for closed K>0. G(s)H(s)= . K S(s'+2s+2) ,,,,, be (t4 Marks) (06 Marks) - loop stability , t. (14 . Marks)' li .ri Explain properties and significance of state transition matrix. (10 Marks) A linear time invariant system is characterizedby the homogeneous state equation : ft li l=[, 0l [.1 ] [t r-] Lo, L*,.1 Compute the solution of homogeneous equation assume the initial state ***'k* vector. (10 Marks)
- 7. t0EC44 USN Fourth Semester B.E. Degree Examination, Dec.2013 lJan.2ol4 Signals and Systems Max. Marks:100 ,], Time: 3 hrs. d) o Note: Answer FIVEfull questions, selecting at least TWO questions from esch port. PART _ A Sketch the even and odd part of the signal shown in Fig.Ql(a). Ia. . '!'':;",, ""' ,:', (06 Marks) o d L a a () o L oX 50x> 6e **l =h troo Fig.Ql(a) '..'.,., signals is periodic or not'and if periodic find its fundamental b. Check whether the following period. .-I .= 6l d?! ol: FO c. (i) x(n): (ii) x(t) = [cos(2nt)]2 cos(2Onn) + sin(50nn) Let x(t) and y(t) as shown in Fig.Ql(c). Sketch (i) x(t)y(t 1) (ii) x(t)y(-t -1) - (06 Marks) (08 Marks) Y(r) 6: oO t b0i 2G -o 5!r Fig.Q1(c) Determine the convolution sum of the given sequences and h(n) = {-2,2,-2 x(n) = {1; -2,3, -3} ' 2a. oX o .-i Performthe convolution of the following sequences: b. xl(t):e-at ; 0<t<T 5: to a tr= ,,,::::::: Gi !o ^.= -^o cOO :..:: G. ,q.n " :,," xz(t):1 ; 0<t<27 LTl system is characterized by an impulse input x(n; (r< 3a. o = h1n;=l- l ,(n). Find the |') = / [1]'r,rr. t4t ,./ (06 Marks) Determine the following LT1 systems characterued by impulse reponse is memory, causal and stable. (ii) h(n) : (0.99)'u(n + 6). h(n) : 2u(n) - 2u(n-2) Find the natural response of the system described by a differential equation (i) Z o response, I response of the system for the =o oVL c.i (10 Marks) /rn L 6= oB tr> J (04 Marks) ,l,l rl ll b. d2y(t) dy(t) + 2y(t) *. dr, " d, =2x(t). with y(0) 1 : of2 l. and #1,=, =o (06 Marks) (06 Marks)
- 8. t0EC44 c. Find the difference equation description for the system shown in Fig.Q3(c). Y d. (04 Marks) ("1 Fie.Q3(c) By converting the differential equation to integral equation draw the direct form-I and direct form-Il implementation for the system as d2x(t) d'y(t) * 1 dy(t) (04 Marks) v .*a = x(t) *I u -t -nt/ qJ$* d, dt2 dt' prove the following properties of DTFS: (i) Modulation (ir) Parseval's,ni,%riil;u., dtr 4a. b. State and Find theFourier series coefficients of the signal x(t) shown in Fig.Q4(b) and also draw its (10 Marks) spectra. -Tr Fig.QaG) a. b. c. fl Fie.Qs(b) "...., PART_B . Find the DTFT of the following signals: x(n) :2'u(-n) Determine the signal x(n) if its DTFT is as shown in Fig.Q5(b). Compute the Fourier transform of the signal (i) x(n):unl' lal<1 (iil (08 Marks) (06 Marks) fl+cosnt : lti<l x(t) = 1 |. 0 a. b. c. (06 Marks) : ltl>l Find the frequency respanse of the system described by the impulse response 2t h(t) : a(r) - 2e i(t) and also draw its magnitude and phase spectra. Obtain the Fourier translorm representation for the periodic signal x(t) : sin wot and draw the magnitude and phase. A signal'x(t): cos(20nt) + % cos(30nt) is sampled with sampling period Nyqaisf rate. a. ffiat (08 Marks) (07 Marks) tr. Find the (05 Marks) is region of convergence (ROC)? Mention its properties. (06 Marks) b: ' Determine the z-transform and ROC of the sequence x(n) = riu(n) + riu(-n). C. Determine the inverse z-transform of the function, x(z) = l+z-' l-z-t +0.52-2 ' , (07 Marks) using partial fraction expanslon. 8 a. b. c. (07 Marks) An LT1 system is described by the equation y(n): x(n) + 0.8 x(n- 1) + 0.8x(n -2) -0.49y(n-2) Determine the transfer function H(z) of the system and also sketch the poles and zeros. (06 Marks) Determine whether the system described by the equation y(n):x(n) + by(n- 1) is causal and stablewhere lb l< 1. Find the unilateral z-transform for the sequence y(n) : x(n - 2), where x(n) -r-:;- : o'. (08Marks) (06 Marks)
- 9. 06EC45 USN Fourth Semester B.E. Degree Examination, Dec.2013 lJan.2ol4 Fundamentals of HDL Time: 3 hrs. Max. Marks:100 Note: Answer FIVE full questions, selecting at least TWO questions from each poit. o o PART _ A o L a la. b. Cornpare VHDL and Verilog. What are values that std-logic c. With proper example explain the logical operators of verilog. (.) o 3e 2a. b. N9 c. 7r) oDr traa .= o.l rB+ Ho (VHDL) and nets (verilog) (06 Marks) (06 Marks) can take? (08 Marks) What are the facts of data flow description? (02 Marks) Starting from the basics draw the logic symbol of D'latch exoitation table, K map circuit for D latch and write VI{DL and verilog program for the sr}me. (10 Marks) Write a data flow description (in both VHDL and verilog) of a full adder with enable. If the enable is low (0). the sum and carry are zero; otherwise the sum and carry are usual outputs of the adder. Use a 5 ns delay for any gate inoluding xor. Draw the truth table of this adder and derive the Boolean function after minimization. (08 Marks) FO E= o> 3* 3a. b. With syntax explain different types of loops in VHDL and verilog. (10 Marks) Write a program in VHDL and verilog for JK flip flop using if & else if statements. (10 Marks) a: oO = ad 4 a. b. E(g ,(.) What is binding? Explain the binding between entity and components in VHDL and between two modules in verilog. (10 (t0 Marks) Write VHDL behavioral description of a tristate buffer. Use this as nent for structural of 2 to 4 decoder with tristate output. Marks) or= o; oj o: atE !o 6 .:i 5a. b. 6 a. b. ooo Eil) o= *O tr> ->r :^ (J o z L E Write VHDL procedure and verilog task for N-bit ripple caffy With suita-ble example write VHDL code for writing integers to a (# f/. ) arks) Give an example of a VHDL package. Marks) write the block diagram and function table of a SRAM of 16x8 and writd verilog code for the same. (12 Mark$ , 7 a. o lr< PART _ B b. 8 a. b. How to invoke a verilog module from a VHDL module? Giving an example of a full adder ' --'--^D using two half adders. (10 Marks) Discuss the facts and limitations of mixed language description. (10 Marks) Draw the flow chart and explain the steps involved in synthesis. (10 Marks) Write a program in VHDL and obtain the gate level synthesis for BP and ADH. BP is the input and ADH is the output. BP varies from 0 to 7 and ADH varies from 0 to 16. Assume that if BP is more than 5 the ADH is 0. For BP > 2 and less than 5 the ADH is given by ADH:_5*BP+25 (10 Marks) {<***{<
- 10. I 068C46 USN Fourth Semester B.E. Degree Examination, Dec.2013 lJan.2014 Linear lGs and APPlications Max. Marks:100 Time: 3 hrs. Note: Answer FIVE full questions, selecting at least TlyO questions from each part. o (l PART - A f ftrr -'r' () a I a. () () EP, b. sr c0 .=r .= c! d+ b?p ogl -o 2a. o> b. oO ooi -o >! 3a. a6 !cd J?(J '-^ Define the following opamp parameters and mention their typical values for IC 7 i) Input voltage range ii) CMRR iii) Input offset voltage iv) Slew rate (10 Marks) v) Input impedanee. With a neat circuit diagram, explain direct coupled inverting amplifier. Also, design an inverting amplifier using a,741 opamp. The voltage gain is to be 75 and the output voltage (10 Marks) amplitude is to be 3V. Is1,nu*;: 500nA. Explain a high input impedance capacitof ;oupled voltage follower, with necessary circuit diagram. (10 Nlarks) Oesign a capacitor-coupled inverting amplifier to operate with a +20V supply. The minimum input signal level is, 50mV, the voltage gain is to be 68, the load resistance is (10 Marks) 500Q, and the lower cutoff frequency is to be 2,00 Hz. Use a74l opamp. What are the effects of slew rate on i) Bandwidth ii) Output amplitude and (06 Marks) ' iii) Output pulse rise time. With a neat eircuit diagram, explain Zin Mod technique of frequency compensu,totb. Marks) o'w <): o c. What precautions should be observed for opamp circuit stability? Draw the necessary 'i6 @LE >'! 4a. h. bo" tro0 o= po (08 Marks) With a neat circuit diagram, explain instrumentation amplifier. Explain the operatio, of high lnput impedance full-wave precision rectifier with necessary diagram. Draw the voltage waveforms at various points in the circuit and write the (12 Marks) appropriate equations to show that full-wave rectification is performed. tr> =o: (.) - t< -i c-i o o Z a PART _ B 5a. b. With a neat circuit diagram and waveforms, explain operation of a triangular/rectangular waveform generator with frequency and duty cycle controls. Explain and design an RC phase - shift oscillator with following specifications: supply voltage : +15V. IC 741is to be used. l of 2 (10 Marks) fo:5 kHz, (10 Marks).
- 11. I I 06F,.C46 6 a. b. Explain the operation of an inverting Schmitt trigger circuit with different UTP and LTP levels. Discuss the design procedure and also indicate the input/output characteristics for the same. (10 Marks) Design a second-order high-pass active filter to have a cutoff frequency of 10 kHz. Use a l.5prA. (l0Marks) "''lll 7 "'"" a,. Explain the terms line regulation, load regulation and ripple rejection for a, dc voltage ' i '(06 Marks) :. iegulator. (08Marks) b. W,,tthaneat schematic, explainthe salient features of 723 regulator. (06 Marks) c. Expffilhe principle of operation of a switching regulator. IBrmar): ' . 8 a. b. c. d. ..... Write short notes on the following: 555 timer as mono.stable. multivibrator. Voltage-controlled oscillator. R-2R ladder Oae-,,,,,,.. Servo tracking ADC. " . x**** ; ." .;.'' ' (20 Marks) ,,,., : ..: ::: ',r'' 2 of2

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