1.5 The voltage V is given as V=RI, where R and I are resistance matrix and I current vector. Evaluate V given that

Transcription

1 Sheet (1) 1.1 The voltage across a discharging capacitor is v(t)=10(1 e 0.2t ) Generate a table of voltage, v(t), versus time, t, for t = 0 to 50 seconds with increment of 5 s. 1.2 Use MATLAB to evaluate the complex number (3 + jj6)(6 + jj4) ZZ = jj10 (2 + jj1)(jj2) 1.3 Write a function-file to obtain the dot product and the vector product of two vectors a and b. Use the function to evaluate the dot and vector products of vectors x and y, where x = (1 5 6) and y = (2 3 8). 1.4 Write a function-file that can be used to calculate the equivalent resistance of n parallel connected resistors. In general, the equivalent resistance of resistors R1, R2, R3,, Rn is given by 1 = RR eeee RR 1 RR 2 RR 3 RR nn 1.5 The voltage V is given as V=RI, where R and I are resistance matrix and I current vector. Evaluate V given that RR = and I = Use MATLAB to simplify the expression y=0.5+j6+3.5e j0.6 +(3+j6)e j0.3π 1.7 Write a function file to evaluate n factorial (i.e. n!); where n!=n(n 1)(n 2) (2)(1) Use the function to compute x = 7! 3!4! 1.8 For a triangle with sides of length a, b, and c, the area A is given as AA = SS(SS aa)(ss bb)(ss cc) where S=(a+b+c)/2 Write a function to compute the area given the sides of a triangle. Use the function to compute the area of triangles with the lengths: (a) 56, 27 and 43 (b) 5, 12 and 13.

2 Sheet(2) 2.1 Plot the voltage across a parallel RLC circuit given as v(t) = 5e 2t sin(1000πt) 2.2 Obtain the polar plot of z=r n e jnθ for θ = 15 o and n = 1 to A function f (x) is given as f(x)=x 4 +3x 3 +4x 2 +2x+6 (a) Plot f (x) and (b) Find the roots of f (x) 2.4 A message signal m(t) and the carrier signal c(t) of a communication system are, respectively: m (t) = 4 cos( 120πt)+2 cos(240πt ) and c(t) =10 cos(10,000πt ) A double-sideband suppressed carrier s(t) is given as s(t) = m(t)c(t) Plot m(t), c(t) and s(t) using the subplot command. 2.5 The voltage v and current I of a certain diode are related by the expression i =Is exp[ v/ (nvt )] If Is = 1.0x10 14 A, n = 2.0 and VT = 26 mv, plot the current versus voltage curve of the diode for diode voltage between 0 and 0.6 volts. 2.6 The resonant frequency f (in Hz) for the circuit shown is given by: Given L= 0.2 H, C= 2 μf, make the following plots: (a) f versus R2 for 500 RR ΩΩ, given R1=1500 ΩΩ (b) f versus R1 for 500 RR ΩΩ, given R2=1500 ΩΩ Plot both plots on a single page (two plots in a column).

3 Sheet(3) 3.1 Write a MATLAB program to add all the even numbers from 0 to Add all the terms in the series until the sum exceeds Print out the sum and the number of terms needed to just exceed the sum of The Fibonacci sequence is given as Write a MATLAB program to generate the Fibonacci sequence up to the twelfth term. Print out the results. 3.4 The table below shows the final course grade and its corresponding relevant letter grade. For the course grades: 70, 85, 90, 97, 50, 60, 71, 83, 91, 86, 77, 45, 67, 88, 64, 79, 75, 92, and 69 (a) Determine the number of students who attained the grade of A and F. (b) What are the mean grade and the standard deviation? 3.5 Write a script file to evaluate y[1], y[2], y[3] and y[4] for the difference equation: y[n]=2y[n 1] y[n 2]+x[n] for n 0. Assume that x[n]= 1 for n 0, y[ 2]=2 and y[ 1]= The equivalent impedance of a circuit is given as ZZ eeee (jjjj) = jjjjjj + 1 jjjjjj If L = 4 H and C = 1 μf, (a) Plot Zeq(jw ) versus w. (b) What is the minimum impedance? (c) With what frequency does the minimum impedance occur?

4 Sheet(4) 4.1 The triangular waveform, shown in Figure P4.1 can be expressed as Where w0=1/tp Figure P4.1 Triangular Waveform If A = 1, T = 8 ms, and sampling interval is 0.1 ms. (a) Write MATLAB program to resynthesize g(t) if 20 terms are used. (b) What is the root-mean-squared value of the function that is the difference between g(t) and the approximation to g(t) when 20 terms are used for the calculation of g(t)? 4.2 A periodic pulse train g(t) is shown in Figure P4.2. Figure P4.2 Periodic Pulse Train If g(t) can be expressed by Equation (4.3), (a) Derive expressions for determining the Fourier Series coefficients an and bn. (b) Write a MATLAB program to obtain an and bn for n = 0, 1,..., 10 by using Equations (4.5) and (4.6). (c) Resynthesis g(t) using 10 terms of the values an and bn obtained from part (b). 4.3 For the half-wave rectifier waveform, shown in Figure P4.3, with a period of 0.01 s and a peak voltage of 17 volts.

5 (a) Write a MATLAB program to obtain the exponential Fourier series coefficients cn for n = 0, 1,..., 20. (b) Plot the amplitude spectrum. (c) Using the values obtained in (a), use MATLAB to regenerate the approximation to g(t) when 20 terms of the exponential Fourier series are used. Figure P4.3 Half-Wave Rectifier Waveform 4.4 Figure P4.4(a) is a periodic triangular waveform. Figure P4.4(a) Periodic Triangular Waveform (a) Derive the Fourier series coefficients an and bn. (b) With the signal v(t) of the circuit shown in P4.4(b), derive the expression for the current i(t).

6 Figure P4.4(b) Simple RL Circuit (c) Plot the voltages VR(t), VL(t) and also the sum of VR(t),and VL(t) (d) Compare the voltages of VR(t)+VL(t) to V(t). 4.5 The unit sample response of a filter is given as h[n]=( ) (a) Find the discrete Fourier transform of h[n]; assume that the values of h[n] not shown are zero. (b) If the input to the filter is x[n] = sin[ nn ] u[n]. find the output of the filter g(t)=sin(200πt)+sin(400πt) (a) Generate 512 points of g(t). Using the FFT algorithm, generate and plot the frequency content of g(t). Assume a sampling rate of 1200 Hz. Find the power spectrum. (b) Verify that the frequencies in g(t) are observable in the FFT plot. 4.7 Find the DFT of g(t) = e 5t u(t) (a) Find the Fourier transform of g(t). (b) Find the DFT of g(t) using the sampling interval of 0.01 s and time duration of 5 seconds. (c) Compare the results obtained from parts (a) and (b).

7 Sheet(5) 5.1 Use the iteration technique to find the voltage VD and the ID of Figure P5.1. Assume that T = 25 o C, n = 1.5, Is = A. Stop current the iteration when Vn Vn-1 <10-9 V. Figure P5.1 A Diode Circuit 5.2 A forward-biased diode has the following corresponding voltage and current. (a) Plot the static I-V characteristics. (b) Determine the diode parameters Is and n. (c) Calculate the dynamic resistance of the diode at Vs = 0.5 V. Forward Voltage,V Forward Current, A 7.54e e e e e e For a full-wave rectifier circuit with smoothing capacitor shown in Figure 5.17, if vv ss (tt) = 100sin(120πt) V, R = 50KΩ, C = 250μF, using MATLAB (a) Plot the input and output voltages when the capacitor is disconnected from the load resistance R. (b) When the capacitor is connected across load resistance R, determine the conduction time of the diode. (c) What is the diode conduction time?

8 Sheet(6) Consider a modulating wave mm(tt) that consists of a single tone or frequency component; that is, mm(tt) = AA mm cos(2ππff mm tt) where AA mm is the amplitude of the sinusoidal modulating wave and ff mm is its frequency (see Fig. p.1(a)). The sinusoidal carrier wave has amplitude AA cc and frequency ff cc (see Fig. p.1(b)). The corresponding AM wave is therefore given by ss(tt) = AA cc [1 + μμ cos (2ππff mm tt)] cos(2ππff cc tt) (6.7) Where μμ = kk aa AA mm The dimensionless constant μμ is called the modulation factor, or the percentage modulation when it is expressed numerically as a percentage. To avoid envelope distortion due to overmodulation, the modulation factor μμ must be kept below unity, as explained previously. FIGURE p.1 Illustration of the time-domain (on the left) and frequency-domain (on the right) characteristics of amplitude modulation produced by a single tone. (a) Modulating wave. (b) Carrier wave. (c) AM wave.

9 1- It s required to write a MATLAB program to model the AM-DSB-LC communication system in time and frequency domains? 2- It s required to write a MATLAB program to model the AM-DSB-SC communication system in time and frequency domains? Please wait for the remaining questions