Conventional Paper I (a) (i) What are ferroelectric materials? What advantages do they have over conventional dielectric materials?

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1 Conventional Paper I-03.(a) (i) What are ferroelectric materials? What advantages do they have over conventional dielectric materials? (ii) Give one example each of a dielectric and a ferroelectric material having high relative. permittivity ( ) r P-n junction transistors can be fabricated using the materials Germanium and Silicon. However silicon is preferred to Germanium. Explain. Find the power spectral density if autocorrelation function is given as: x ( ) α τ R τ = e for < τ <. Find v and v by writing a single supernode equation for the given circuit. 4Ω V V 3Ω V 6Ω Ω 4V Figure: Q. ( d) (e) Two concentric spherical shells ( r 5cm and r 30cm) = = are applied with -0 V and 0 V respectively. The dielectric medium between the shells has r =.. Find the charge densities. Determine the location where the V=50V. (f) (g) Three signals (0. GHz, GHz and 0 GHz) are available for propagation. Will it be possible to send all of them through a parallel plate air filled waveguide with a separation of cm between the plates? In an oscilloscope X- and Y-signals both are saw-tooth waves of same amplitudes and time periods but different phase angles. If Y-input is leading the X-input by 90, draw the pattern traced on the CRO screen. Take the saw-tooth signals with positive slopes. (h) (a) Explain in brief the working of the circuit shown when (i) The switch S is ON (ii) The switch S is OFF. What will be the output Vo when Vi is 5sin00π t and India s No. institute for GATE Training Lakh Students trained till date 65 Centers across India 09

2 (i) S is OFF (ii) S is ON S ON S OFF S ON S OFF S R R V i V o R S Figure: Q. ( h). (a) What are the expressions for series and parallel resonances of the equivalent circuit of a quartz crystal oscillator? A quartz crystal oscillator has an equivalent inductance of L = 0 mh and series and parallel capacitances of Cs = 0µ F and Cp = 0µ F. Find the series and parallel resonant frequencies of this oscillator. (e) (f) (g) Show schematically the static characteristics of a thyristor identifying clearly various regions. What is a direct band gap and an indirect band gap semiconductor? Explain why a silicon diode cannot be used as a LED but it is useful as a photodiode? If Si diode is used as a photodiode find the maximum value of responsivity and maximum wavelength up to which it can be used. A magnetically levitated train travels between the city centre and the airport in Shanghai, China. Which peculiar property of super-conductivity is taken advantage of in this application? India s No. institute for GATE Training Lakh Students trained till date 65 Centers across India 0

3 3. (a) A Zener diode regulates at 50 V over a range of diode circuits from 5 ma to 40 ma. Supply voltage V = 00V. (i) (ii) Calculate the value of R to allow voltage regulation from a load current IL = 0 upto I max, the maximum possible value of I L. What is I max? A half wave rectifier having a diode with an internal resistance of 0Ω is to supply power to a kω load from a 0 V (rms) source of supply. Do the following: (a) Draw a schematic that represents the above description of the circuit. Also calculate: Peak load current DC load current AC load current (e) DC diode voltage. Find the circuit shown, neglecting base currents find I0 and I, I, I 3. 6V 0KΩ I I I 3 I 0.4K R0 300Ω 400Ω 500Ω R R R3 In the following circuit: Fig.Q.3 ( c) 6V V DD Q 3 Q I ref Q V out V m Figure: Q.3 ( d ) India s No. institute for GATE Training Lakh Students trained till date 65 Centers across India

4 If VDD = 0V, Vtn = Vtp = V, µ Co = µ Co = 0µ A / v, W = 00 µ m, n x p x L = 0µ m and VA = Early voltage = 00V both for n and p devices, Iref = 00 µ A, find the small signal voltage gain. at E of the signal ( ) ( ) 4. (a) Find the energy x x t = e u t. Determine the frequency W (rad/sec) so that the energy contributed by the spectral components of all frequencies below W is 95% of the signal energy. Given that X( w) is the Fourier transform of ( ) following in terms of X( w ) : (i) x ( t) = x ( t) x ( t) (ii) x ( t) = x ( 4t 5) (iii) x ( t) = ( t ) d x 3 dt x t. Find the Fourier transform of 4t The output y( t ) of a continuous time LTI system is found to be 3e u ( t) input x ( t) is u ( t ). (i) Find the impulse response h ( t ) of the system. (ii) t Find the output y( t ) when the input x ( t) is e u ( t). when the Consider the discrete time system as shown in the figure below: x ( n) Σ K/4 q ( n ) z q ( n) K/5 Figure: Q.4 ( d ) Σ y ( n) For what value of K is the system BIBO stable. 5. (a) State and prove maximum power transfer theorem for a circuit with source V s and source resistance R s and a variable load resistance R L. India s No. institute for GATE Training Lakh Students trained till date 65 Centers across India

5 If R L is fixed and EC-Conventional Paper-I IES-03 R s is varied will the formula be valid? Prove. For the circuit shown determine Z L that will draw maximum power from the source. jω jω 0 0V jω zl 0Ω Figure: Q.5 ( c) Determine the h-parameters of the network shown. i 0Ω 3v x i 50 Ω Vx V V Figure: Q.5 ( d ) 6. (a) A pair of isolated parallel power lines of cm radius with a separation of 90 cm have a voltage difference of 440 V. These power lines are 60 cm above a pair of telephone lines. Find the voltage difference between the telephone lines due to induction from power lines. The telephone lines are separated by 0 cm. Two coils kept on a common axis are separated by cm. Coil A has 0 turns of radius 4 cm with a current of A. Coil B has 5 turns of wire with a radius of 6 cm. The current in Coil B is to be determined such that the induced magnetic field due to this current cancels the magnetic field at the center of Coil A generated by Coil A. B n= 5turns I B =? A n= 0turns 4cm 6cm IA = A Figure: Q.6 ( b) India s No. institute for GATE Training Lakh Students trained till date 65 Centers across India 3

6 Derive the expression for the power required to move a current carrying conductor at a rotational frequency of N rev/min if it is placed in a magnetic field of flux density B a ˆ. Find the value with the given data. o r Bo = 0.6T; I = 0 A; L =.m; N = 5 rev / min, r = cm. From this determine the magnetic flux density to be applied if the power is to be.5 W. Z Y X A plane wave travelling in the z direction in free space ( z < 0) is normally incident at z = 0 on a conductor ( z > 0) for which σ = 6.7MS / m, µ r =. The free space wave has a frequency of.5 MHz. The E field amplitude is.5 V/m at the interface. Find the expression for H in the conductor. 7. (a) In the circuit shown, R is a resistive transducer. The bridge is balanced and the output, Vo = 0 when R3 = R. Now R is changing in response to a physical variable. Show R R that the output voltage Vo V = R R R R V R I ( ) Figure: Q.6 C R R R R 3 V o R R R Figure: Q.7 ( a) where R is the change in the value of R. India s No. institute for GATE Training Lakh Students trained till date 65 Centers across India 4

7 In the circuit shown, the output voltage is found to be 5 mv. If the optical power input is at a wavelength, λ =.3µ m. Calculate the optical power in µ W. Take the quantum efficiency of the photo-diode to be 65%. 5V K 0K I p K V o Figure: Q.7 ( b) Overall quantum efficiency of GaAs light emitting diode shown in the circuit is 70%. ON state diode voltage is.8 V. V 5V V 0 = 0V. V is a binary signal with ( ) = and ( ) i Find the logic levels of the optical binary output. Take band-gap energy for GaAs =.43 ev. 50Ω 0V V i 0V Figure: Q.7 ( c) K India s No. institute for GATE Training Lakh Students trained till date 65 Centers across India 5