## Advanced Microwave Engg - May 2014

### Electronics & Telecomm. (Semester 8)

TOTAL MARKS: 100

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **four** from the remaining questions.

(3) Assume data wherever required.

(4) Figures to the right indicate full marks.
**1(a)** Define signal to noise ration and noise figure with help of a noisy network. Explain test set up to measure signal to noise ratio.(5 marks)
**1(b)** Prove that scattering matrix is symmetrical and reciprocal.(5 marks)
**1(c)** Explain unilateral figure of merit.(5 marks)
**1(d)** Explain the terms conversion loss and Isolation with reference to mixer.(5 marks)
**2(a)** Consider two power BJT amplifiers used in circuit configuration shown below having following specification:

Amplifier | Go(dB) | Gi(dB) | PidB(dBm) |

1 | 8 | 7 | 27 |

2 | 10 | 9 | 22 |

Assume that operating frequency is 1 Ghz and input power is 5.5 dBm. Specify correct BJT amplifiers that must be used at each stage to obtain 29.5 dBm output power. Assume each two way divider/combiner has 0.5 dB insertion loss.(10 marks)

**2(b)**Discuss amplifier linearisation methods.(10 marks)

**3(a)**For an ideal transformer with turns ratio n=n

_{1}/n

_{2}prove that the scattering matrix is $$ S= \begin{bmatrix}\frac {n^2-1}{n^2+1} & \frac {2n}{n^2 +1} \\ \frac {2n}{n^2+1} & \frac {1-n^2}{n^2+1} \end{bmatrix} $$ (10 marks)

**3(b)**Define and explain noise correlation matrix for general noisy two port network. What is congruence transformation?(10 marks)

**4**Design a transistor oscillator at 6GHz using an FET in CS configuration driving a 50Ω load on drain side. The S-parameters at 50 Ω are $$ S= \begin{bmatrix} 0.9 \angle 150 &0.2 \angle -15 \\ 2.6 \angle 50 & 0.5 \angle 105 \end{bmatrix} $$ Calculate and plot output stability circle for $$|\Gamma_{IN}| >> 1. \ Choose \ \Gamma_T \ so \ that \ |\Gamma_{IN}|>>1 $$ Design load and terminating networks. (20 marks)

**5 (a)**Discuss various mixer topologies. Compare performance of various topologies.(10 marks)

**5 (b)**Discuss generalised single ended mixer design approach. Give design consideration.(10 marks)

**6 (a)**For a two port network the ABCD matrix is given as: $$ \begin{bmatrix} A &B \\C &D \end{bmatrix}= \begin{bmatrix}0.5 &j1.6 \\j1.6 &0.5 \end{bmatrix} $$ Find scattering matrix if Zo=50 Ω. Find condition of reciprocity. (10 marks)

**6 (b)**Discuss generator tuning networks for microwave oscillators.(10 marks)

**7 (a)**A GaAs FET is biased for minimum noise figure and has following S parameters and noise parameter at 4 Ghz (Zo=50 Ω). $$ S= \begin{bmatrix}0.6 \angle -60 &0.05 \angle 26 \\ 1.9 \angle 81 & 0.5 \angle -60 \end{bmatrix} \\ F\min =1.6 dB \ \Gamma_{opt}=0.62 \angle 100 \ R_N=20 \Omega $$ Design an amplifier with 2dB noise figure and maximum gain compatible with this noise figure. Assume device is unilateral (15 marks)

**7 (b)**Consider the amplifier circuit shown below. The input and output matching network are to be designed using open circuited stubs for Γ

_{S}=0.5 ∠120 and Γ

_{L}=0.4∠90. User Smith Chart. (5 marks)