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RF Modelling and Antennas : Question Paper Dec 2013 - Electronics & Telecomm (Semester 5) | Mumbai University (MU)

## RF Modelling and Antennas - Dec 2013

### Electronics & Telecomm. (Semester 5)

TOTAL MARKS: 80
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks.
1 (a) A typical PCB substrate consists of Al2O3 with a relative dielectric constant of 10 and a loss tangent of 0.0004 at 10 GHz. Find the conductivity of the substrate. (5 marks) 1 (b) Draw the lumped element circuit model for a transmission line. Derive the expression for voltage and current travelling waves.(5 marks) 1 (c) Explain current flow in p-n junction and give the expression for Idiff in terms of diffusion constant and Vdiff in terms of doping concentration. (5 marks) 1 (d) A lossless 50Ω microstrip line is terminated into a load with admittance of 0.05mS. What additional impedance has to be placed in parallel with load to assure impedance of 50 Ω. (5 marks) 2 (a) A short circuited 50Ω transmission line section operated at 1GHz and possesses a phase velocity of 75% of the speed of light. Use both the analytical and the Smith chart approach to determine the shortest length required to obtain:
(i) 5.6 pF capacitor
(ii) 4.7 nH inductor.
(10 marks)
2 (b) Explain various terminations used in Microstrip transmission lines.(10 marks) 3 (a) Starting with the equation for normalized admittance-
y=g+jb= 1-τ/1+τ
Prove that the circle equations for the Y-smith chart are given by the following two formulas:
For the constant conductance circle as $${\left(τ_r+\frac{g}{g+1}\right)}^2={τ_i}^2{\left(\frac{1}{g+1}\right)}^2$$
(ii)For the constant susceptance circle as $${\left(τ_r+1\right)}^2+{\left(τ_i+\frac{1}{b}\right)}^2={\left(\frac{1}{b}\right)}^2$$
(10 marks)
3 (b) Explain with equivalent circuits the RF behavior of resistor,inductor and capacitor. (10 marks) 4 (a) State and prove Kuroda's four Identities. (10 marks) 4 (b) Explain in brief the principle of operation of HEMT and RF FET along with their construction. (10 marks) 5 (a) Design a prototype low pass Butterworth filter that will provide at least 20dB attenuation at f=2f3dB. Compute and plot the amplitude response for 0 to 5GHz. (10 marks) 5 (b) What is Miller Effect? Show that:
$$C_{M1}=C_{cb}\left(1-\frac{V_{ce}}{V_{be}}\right)\ \\ \text{on the input port and } C_{M2}=C_{cb}\left(1-\frac{V_{be}}{V_{ce}}\right)$$on the output port.
(10 marks)
6 (a) Derive expression for internal, external and loaded quality factors for standard series and parallel resonant circuit. (10 marks) 6 (b) Explain functionality of BJT. (10 marks)

### Write short notes on:

7 (a) Butterworth filter. (5 marks) 7 (b) Chip components. (5 marks) 7 (c) Schottky contacts.(5 marks) 7 (d) Richard's transformations.(5 marks)

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