Download Model Paper-Advanced Measurements - IESL e

College of Engineering
Institute of Engineers in Sri Lanka (IESL)
EE3001 - Advanced Measurements
Class Test
Answer only Five Questions
Time Allowed: Three Hours
Q(1) (i) A continuous-time signal x(t) is shown in the following Figure.Sketch the signals for
(a) x(t)[u(t) – u(t-2)]
(b) x(t)(t-3/2)
(ii) Find, from first principle, the Fourier transform of the signal
(iii) If the Laplace transform of f(t) shown in Figure (a) is F(s), shown that G(s), the Laplace transform
of g(t)shown in Figure (b) is given by
Figure (a)
Figure (b)
Hint: Remember that
Q(2) (i) Using the definition of z-transform, show that
𝑎𝑘 𝑢(𝑘) ⇔
𝑧
𝑧−𝑎
(ii) Using the z-transform derived in (i), or otherwise, find the z-transform X(z) of the
(iii) Using the z-transform pairs given in the z-transform table, find the inverse z-transform of
(iv) Using the graphical method, find y(t) x(t)*h(t) where x(t) and h(t) are shown in the following
figure.
Q(3) (i) Discuss following errors in a measurement system
(a) Gross error
(b) Systematic Errors
(c) Random Errors
(ii) During a test the current was measured as 30.4 A, flowing in a resistor of 0.105. Later on it is
discovered that the ammeter reading was low by 1.2% and the marked resistance was high by 0.3%.
Determine the true value of power as a percentage of the power that was originally calculated.
(iii) The speed of a hydraulic turbine which is running at 1000 rpm is measured by a tachometer. The
hydraulic turbine is subjected to variations in speed. For a sample of 20 readings at this speed, how
many readings would you expect between 990 rpm and 1010 rpm. Assume that the tachometer gives a
normal set of deviations with precision index of 0.04 at 1000rpm.
Q(4) (i) Linear Time Invariant (LTI) system is specified by system equation
(a) Find the characteristic polynomial, characteristic equation, characteristic roots and characteristic
modes ofthis system.
(b) Find y0(t), the zero-input component of the response y(t) for t ≥ 0, if the initial conditions arey0(0) =
1 and 𝑦0̇ (0) = 1
(ii) Given the initial conditions y0(0) 0 and 𝑦0̇ (0) = 1, find the unit impulse response of a LTI system
specified by the equation
Q(5) (a) State Nyquist Sampling Theorem
(b) A discrete-time LTI system with a sampling frequency of 8kHz is shown in following Figure.
Therectangular boxes with the label z -1 provide one sample period delay to their input
signals.Thecircular components are adders or subtractors. The triangular components provide
lineargain factors of ai or bi, where i is 0, 1 or 2.
(i) Find the difference equation relating the output y[n] and input x[n].
(ii) Derive the system transfer function H(z).
(iii) Given that the gain values are
Find the poles and zeros of this system.
Q(6) (i) Draw a circuit diagram to show the structure of a four bit 'R-2R ladder' type ofdigital to
analogueconverter (DAC). Describe how a binary number is applied to the ladder network and explain
how theappropriate analogue output voltage is generated
(ii)4-bit R-2R DAC has VR=5 V, R= 5 kΩ. Calculate value of Vout for
(a) LSB, 0001
(b) MSB, 1000
(iii) Determine the smallest step size (resolution) of a 4-bit ADC, which has a maximum output voltage of
12 V.
Q(7) (i) The input-output relationship of a finite impulse response filter is given as
(a) Write the z-transfer function of this filter
(b) Show that the filter has a linear phase response
(ii) (a) What do you understand by EMC ?
(b) Describe followings related to Electro Magnetic Interference (EMI)
(1) Inductive coupling
(2) Capacitive Coupling
(3) Mitigation of EMI
Z-Transform Table
Probability Table