## 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 Al_{2}O_{3} 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 I_{diff} in terms of diffusion constant and V_{diff} 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=2f_{3dB}. 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)