## RF Modelling and Antennas - Dec 2012

### 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 lossless co-axial cable has wavelength of electric and magnetic field of l=20cm of 960MHz. Find the relative dielectric of insulation.(5 marks)
**1 (b)** 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 (c)** For a parallel copper plate transmission line operated at 1GHz, the following parameters are given:

W=6mm, d=1mm, σ_{dielectric}=0.125mS/m, ε_{r}=2.25.

. Find the line parameters R, L, G and C per unit length.(5 marks)
**1 (d)** A lossless 50 Ω 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 50Ω . (5 marks)
**2 (a)** A transmission line of characteristic impedance of Z_{0}=50A transmission line of characteristic impedance of Z_{0}=50Ω and length d=0.15? is terminated into load impedance of Z_{L} =(25-j30)Ω.

Find τ_{0},Z_{in}(d) and SWR. (10 marks)
**2 (b)** A lossless transmission line with Z_{0}=50Ω is 10cms long f=800MHz, v_{p}=0.77c. If the input impedance is Z_{in}=j60Ω, find C_{L}. What length of a short circuited transmission line would be needed to replace Z_{L}. (10 marks)
**3 (a)** To suppress noise in a digital communication system a bandpass RF filter is required with a passband from 1.9GHz to 2GHz. The minimum attenuation of filter at 2.1GHz and 1.8GHz should be 30dB. Assuming that a 0.5dB ripple in passband can be tolerated, design a filter that would be using minimum number of components(10 marks)
**3 (b)** Derive expression for internal, external and loaded quality factors for standard series and parallel resonant circuit. (10 marks)
**4 (a)** The intrinsic carrier concentration is typically recorded at room temperature.

For GaAs we find at T=300^{o}K the effective densities of state

N_{c}=4.7x10^{17} cm^{-3},

N_{v}=7.0x10^{18} cm^{-3}. .

Assuming that the bandgap energy of 1.42eV remains constant,

(a) Find the intrinsic carrier concentration at room temperature.

(b)Compute ni at T=400°K.

(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)** Explain Ebers-Moll model of a large signal BJT. Also give details of transport representation. (10 marks)
**6 (a)** Explain in brief the determination of AC parameters of bipolar transistors.(10 marks)
**6 (b)** Show that in the fig d12.1, the feedback capacitance C_{cb} can be expressed as

C_{M1}=C_{cb}(1-v_{ce}/v_{be}) and C_{M2}=C_{cb}(1-v_{be}/v_{ce}), on the input and output port

Assume that the input and output voltages are approximately constant, and keep in mind that v_{ce} is negative under CE configuration. (10 marks)

### Write short notes on:

**7 (a)** DC characterization of BJT.(5 marks)
**7 (b)** Realization of RF filters using Kuroda s identities. (5 marks)
**7 (c) ** Terminations used in microstrip line. (5 marks)
**7 (d) ** Equivalent circuits of resistors, inductors and capacitors.(5 marks)