EC-702-A Microwave Engineering - Dec 2024 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aList out various applications of Microwave and briefly explain any two of them.
   How to answer

   • Define microwave frequency range
   • List 6-8 applications: radar, communication, heating, medical, etc.
   • Explain any two in brief with principle/use
2. 7 Marks
   bAn open wire transmission line has the following primary constants $R = 4 \Omega/\text{km}$, $L = 2.5 \text{ mH/km}$, $C = 0.009 \text{ } \mu\text{F/km}$, $G = 0.29 \text{ } \mu\text{mho/km}$ and Frequency of operation is $1 \text{ kHz}$. Determine the following parameters

   1. i)$Z_0$
   2. ii)$\alpha$
   3. iii)$\beta$
   4. iv)Phase Velocity
   How to answer

   • Write primary constants $R,L,G,C$ and $\omega=2\pi f$
   • Formula $Z_0=\sqrt{(R+j\omega L)/(G+j\omega C)}$
   • Formula $\gamma=\alpha+j\beta=\sqrt{(R+j\omega L)(G+j\omega C)}$
   • Compute $v_p=\omega/\beta$
3. 7 Marks
   aA rectangular waveguide with dimension of $3 \times 2 \text{ cms}$ operates in $TM_{11}$ mode at $10 \text{ GHz}$. Determine the characteristic wave impedance.
   How to answer

   • Compute cutoff frequency/wavelength for $TM_{11}$ with $a=3$ cm, $b=2$ cm
   • Formula for $TM$ wave impedance $Z_{TM}=\eta\sqrt{1-(f_c/f)^2}$
   • Substitute $f=10$ GHz, $\eta=377 \Omega$
   • Obtain numerical value
4. 7 Marks
   bDraw the structure and explain the velocity modulation process in two cavity klystron amplifier.
   How to answer

   • Draw two-cavity klystron: electron gun, buncher, catcher, collector
   • Explain velocity modulation by RF gap voltage
   • Explain bunching in drift space and energy extraction
   • Mention amplification condition
5. 7 Marks
   aFor the dominant mode of operation in an air filled circular waveguide of inner diameter $4 \text{ cms}$. Find :

   1. i)Cut off wavelength
   2. ii)Guided wave length
   3. iii)Cut off frequency
   How to answer

   • Identify dominant mode $TE_{11}$ in circular waveguide
   • Formula cutoff wavelength $\lambda_c=1.706D$ for $TE_{11}$
   • Formula cutoff frequency $f_c=c/\lambda_c$
   • Formula guided wavelength $\lambda_g=\lambda/\sqrt{1-(f_c/f)^2}$
6. 7 Marks
   bDiscuss the dominant and higher order modes in strip line structure.
   How to answer

   • Describe stripline geometry
   • Explain dominant TEM mode
   • Discuss higher order TE/TM modes and cutoff
   • Mention suppression/operation constraints
7. 7 Marks
   aList different types of Magnetron. Explain mechanism of oscillations of Magnetron Oscillator with diagram.
   How to answer

   • List types: conventional, coaxial, frequency-agile, etc.
   • Explain crossed E and B electron interaction
   • Explain bunching and oscillation build-up
   • Include magnetron diagram
8. 7 Marks
   bAn air-filled circular waveguide has a radius of $2 \text{ cm}$ and is to carry energy at a frequency of $10 \text{ GHz}$. Find all the TE and TM modes for which energy transmission is possible.
   How to answer

   • Compute cutoff frequencies $f_c$ for TE and TM modes using Bessel roots $p'_{np}, p_{np}$
   • Condition $f>f_c$ for propagation at 10 GHz
   • List all allowed TE modes
   • List all allowed TM modes
9. 7 Marks
   aExplain the coupling factor and directivity of the four ports directional coupler. Also derive the S-matrix for completely matched four-port directional coupler.
   How to answer

   • Define coupling factor and directivity with formulas
   • Write S-matrix form for 4-port
   • Apply matched, lossless, reciprocal conditions
   • Derive ideal directional coupler S-matrix
10. 7 Marks
    bMentioned the symbol and schematic diagram of microwave circulator. Explain the working of the same using geometry containing two magic tee and one phase shifter along with its simplified S-matrix.
    How to answer

    • Show circulator symbol and schematic
    • Explain two magic-tee plus phase shifter geometry
    • Explain circulation operation
    • Write simplified 3-port S-matrix
11. 7 Marks
    aMentioned the basic Principle of IMPATT and TRAPATT diodes.
    How to answer

    • Define IMPATT impact ionization avalanche principle
    • Define TRAPATT trapped plasma principle
    • Compare construction/operation basics
    • Mention microwave generation use
12. 7 Marks
    bWhat is standing wave? Derive the equation of Voltage Standing Wave Ratio (VSWR) in terms of reflection coefficient.
    How to answer

    • Define standing wave from incident+reflected superposition
    • Derive $V_{max}, V_{min}$ in terms of $|\Gamma|$
    • Obtain $VSWR=(1+|\Gamma|)/(1-|\Gamma|)$
    • Interpretation for matched/short/open
13. 7 Marks
    aDiscuss the reasons due to which the measurement of Z, Y, h and ABCD parameter are difficult at microwave frequencies. Elaborate the S-parameters for the multi-port network along with any two properties.
    How to answer

    • Give reasons: lumped elements, parasitics, open/short difficult at microwave
    • Define S-parameters for multi-port
    • Explain incident/reflected wave formulation
    • State any two properties: reciprocal, unitary, etc.
14. 7 Marks
    bThe S-parameters of a two-port network are given by $S_{11} = 0.2 \angle 0^\circ$, $S_{22} = 0.1 \angle 0^\circ$, $S_{12} = 0.6 \angle 90^\circ$, $S_{21} = 0.6 \angle 90^\circ$

    1. i)Prove that the network is reciprocal but not lossless.
    2. ii)Find the return loss at port 1 when port 2 is short-circuited.
    How to answer

    • Check reciprocity $S_{12}=S_{21}$
    • Check losslessness $ [S]^\dagger[S]=[I]$ / power condition
    • Conclude reciprocal but not lossless
    • Compute return loss with port-2 shorted using $\Gamma_{in}$ formula
15. 14 Marks
    Write short note (Any four)

    1. a)MASER
    2. b)Tuned Detectors
    3. c)BARITT
    4. d)Microwave resonators
    5. e)Power measurement bridges
    6. f)TWT Amplifier
    How to answer

    • Select any four topics
    • Give principle/diagram for each
    • Mention applications/advantages
    • Conclude briefly