Question:

Question 1

A differential equation didt?0.2i=0didt-0.2i=0 is applicable over ?10

Question 2

Consider a signal defined by

x(t)={ej10t0for |t|?1for |t|>1xt=ej10tfor t?10for t>1

Its Fourier Transform

Question 3

The coils of a wattmeter have resistances 0.01?? and 1000??; their inductances may be neglected. The wattmeter is connected as shown in the figure, to measure the power consumed by a load, which draws 25A at power factor 0.8. The voltage across the load terminals is 30V. The percentage error on the wattmeter reading is?

Question 4

A buck converter feeding a variable resistive load is shown in the figure. The switching frequency of the switch S is 100 kHz and the duty ratio is 0.6. The output voltage V0V0 is 36 V. Assume that all the components are ideal, and that the output voltage is ripple-free. The value of R (in Ohm) that will make the inductor current (iL) just continuous is?

Question 5

For the switching converter shown in the following figure, assume steady-state operation. Also assume that the components are ideal, the inductor current is always positive and continuous and switching period is TsTs. If the voltage VLVL is as shown, the duty cycle of the switch S is?

Question 6

In the given rectifier, the delay angle of the thyristor T1T1 measured from the positive going zero crossing of VsVs is 30. If the input voltage VsVs is 100sin(100?t)V100sin?(100?t)V, the average voltage across R (in Volt) under steady-state is?

Question 7

For linear time invariant systems, that are Bounded Input Bounded stable, which one of the following statement is TRUE?

Question 9

The z-Transform of a sequence x[n]x[n] is given as X(z)=2z+4?4/z+3/z2X(z)=2z+4?4/z+3/z2. If y[n]y[n] is the first difference of x[n]x[n] , then Y(z)Y(z) is given by?

Question 10

Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of +Q is placed at a distance of d from both sheets. The net force on the charge is Q24??0Kd2Q24??0Kd2 where K is given by?

Question 11

In the following sequential circuit, the initial state (before the first clock pulse ) of the circuit is Q1Q0Q1Q0= 00. The state (Q1Q0Q1Q0), immediately after the 333rd333rd clock pulse is?

Question 12

A Boolean funcation f(A,B,C,D)=f(A,B,C,D)= ??(1, 5, 12, 15) is to be implemented using an 81 multiplexer (A is MSB). The inputs ABC are connected to the select inputs S2S1S0S2S1S0 of the multiplexer respectively. Which one of the following options gives the correct inputs to pins 0,1,2,3,4,5,6,7 in order?

Question 13

The saturation voltage of the ideal op-amp shown below is 10 V. The output voltage v0v0 of the following circuit in the steady-state is?

Question 14

The incremental costs (in Rupees/MWh) of operating two generating units are functions of their respective powers P1P1 and P2P2 in MW, and are given by

dC1dP1=0.2P1+50dC1dP1=0.2P1+50

dC2dP2=0.24P2+40dC2dP2=0.24P2+40

Where

20MW?P1??P1?150 MW

20MW?P2??P2?150MW.

For a certain load demand, P1P1 and P2P2 have been chosen such that dC1/dP1dC1/dP1 = 76 Rs/MWh and dC2/dP2dC2/dP2 = 68.8 Rs/MWh. If the generations are rescheduled to minimize the total cost, then P2P2 is?

Question 15

A composite conductor consists of three conductors of radius R each. The conductors are arranged as shown below. The geometric mean radius (GMR) (in cm) of the composite conductor is kR. The value of k is?

Generation of random sequences: While deterministic signals such as square pulses, sinc waveforms, sinuses and cosines are used in specific applications, almost all other real-life signals from econometric series to radar returns, from genetic codes to multimedia signals in consumer electronics are information-bearing random signals. Time sequences: Generate a sequence of 1000 equally spaced samples of a Gauss- Markov process using the recursive relation: An = ax-1 + Wnin = 1,2, .., 1000. Here assume that X0 = 0, and {w,} is a sequence of independent identically distributed Gaussian random variables. You can use the randn function in MATLAB to generate zero-mean, unit-variance random variables. Below is given a low-pass filter (a>0) excited by a white noise sequence, and the filter has a real pole at z= a. Plot the output waveform for the following values of a: a= 0.5, a = 0.95, a = 0.995. Comment on the effect of the selection of a on the resulting time sequence. Autocorrelation function: In order to estimate the autocorrelation function of this discrete process, one can apply the formula: Rx(m) = lim = En=1*n*n-m = E(XXn-m). However, since we have a finite number of samples an approximation would be Rx(m) = -EMFxxn-mim = 0,1,...,64. Notice we shorten the data and consider only the overlapping samples in the window starting at n=1 and the window starting at n=m+1. The theoretical autocorrelation for such a signal model is also known as: Rx(m) = opalml, where on is the input process variance. Plot the autocorrelation sequence in three separate graphs for the values of a= 0.5, a = 0.95, a = 0.995, but superpose in each graph the analytical and estimated Rx(m) and Rx(m) correlation functions.1. Consider the Markov chain with three states, S={1,2,3), that has the following transition matrix: 0.6 0.3 0.1 P = 0.5 0.0 0.5 0.2 0.4 0.4 with initial distribution 7 = (0.7;0.2; 0.1). 1) Plot state transition diagram of the Markov Chain; 2) Find the Markov transition matrix after 2 steps; 3) Find the Markov Chain distribution after two steps; 4) Find the Markov chain realization: P(1=E3 , (3=El , 84=E2, 87=ED). 5) Find the stationary distribution of the Markov Chain - (co).. Consider a zero-mean WSS complex Gauss-Markov process of order 1 defined by the following equation r =-ar _tv, n=0,1,.... where v ~ /(0, o') and Ela, v* ] = 0 for 1 = +1, 12, .... Multiply both sides by * and take expectation values to find Er, *]. Note that E[rv*] = Ex*v,]. Multiply both sides by r* and take expectation values to show R., [0] = -aR_ [-1] + 0) = -aR* [1]+02. This process is also known as the auto-regressive process of order 1 and is denoted by AR(1). . Now multiply both sides by e* , I = 1, 2...., and take expec- tation values to show R, [!] = -aR,, [[ - 1], 1 =1, 2. .... This result, for a Gauss-Markov process of order P, or an AR(P) process. forms the basis for high resolution spectral estimation of zero-mean WSS random signals.Qs.3 [25 pts] a. If a Random Process (RP) is 5" order SSS: - Is it also 2nd order SSS? Is it also WSS? b. Given two RPs X(t) and Y(t), define what it means for them to be - Uncorrelated - Orthogonal - Independent c. What makes a Random Process a Gauss-Markov process? d. Using appropriate sketches and equations, describe what it means to say a WSS RP is also Ergodic - i.e. time averages equal ensemble averages. Your answer should not exceed a page including figures e. A real valued RP X(t) has a PSD Sex(f) i. What are the units for the PSD? Sketch an arbitrary (but valid) PSD and indicate how you would compute the power in the RP for a limited band of frequencies, say from f, to f2