THEORY EXAMINATION (SEM–VI) 2016-17 MICROWAVE ENGINEERING

MICROWAVE ENGINEERING (EEC603)

SECTION – A

(10 × 2 = 20 Marks | Short Answers)

(a) Evanescent mode in waveguides

An evanescent mode occurs when the operating frequency is below cut-off frequency. In this mode, waves do not propagate but decay exponentially along the guide.

(b) Properties of E-plane tee

Symmetrical about E-plane

Used as power divider or combiner

Phase reversal occurs between output arms

(c) Cut-off wave number (kc)

Cut-off wave number is defined as:

kc=ω2με−β2k_c = \sqrt{\omega^2 \mu \varepsilon - \beta^2}kc​=ω2με−β2​

For a lossless dielectric:

kc2=ω2μεk_c^2 = \omega^2 \mu \varepsilonkc2​=ω2με 

(d) Threshold field of Gunn diode

Threshold field is the minimum electric field required to initiate negative differential resistance and start Gunn oscillations.

(e) Electron trajectory in magnetron (Hull magnetic field)

When Hull magnetic field is applied, electrons follow cycloidal paths from cathode to anode instead of straight paths, enabling microwave oscillations.

(f) Axial velocity in helical slow-wave structure

Given:
Pitch (p) = 5 cm
Diameter (D) = 10 cm

Axial velocity:

vz=c×pπDv_z = c \times \frac{p}{\pi D}vz​=c×πDp​ vz=3×108×0.05π×0.10≈4.77×107 m/sv_z = 3 \times 10^8 \times \frac{0.05}{\pi \times 0.10} \approx 4.77 \times 10^7 \, \text{m/s}vz​=3×108×π×0.100.05​≈4.77×107m/s 

(g) V-I characteristics of tunnel diode

Tunnel diode exhibits negative resistance region due to quantum tunneling, enabling high-speed switching and microwave oscillations.

(h) Difference between microwave and low-frequency devices

(i) Condition for sustained oscillation in reflex klystron

Total phase shift must be 2πn and loop gain must be ≥ 1.

(j) S-matrix of ideal 3-port circulator

[S]=[001100010][S] = \begin{bmatrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{bmatrix}[S]=​010​001​100​​ 

SECTION – B

(Attempt Any Five | 5 × 10 = 50 Marks)

(a) Microstrip line calculations

Given parameters substituted in standard equations.

(i) Characteristic impedance (Z₀)
Calculated using Wheeler’s formula.

(ii) Surface resistivity

Rs=πfμσR_s = \sqrt{\frac{\pi f \mu}{\sigma}}Rs​=σπfμ​​

(iii) Conductor attenuation (αc)
Depends on surface resistance and current distribution.

(iv) Dielectric attenuation (αd)
Proportional to loss tangent and frequency.

(v) Quality factor

Q=β2(αc+αd)Q = \frac{\beta}{2(\alpha_c + \alpha_d)}Q=2(αc​+αd​)β​ 

(b) Two-cavity klystron amplifier

Working principle:
Velocity modulation → bunching → RF power amplification.

Optimum drift length:

L=34λL = \frac{3}{4}\lambdaL=43​λ

Maximum efficiency ≈ 40%

High voltage gain due to bunching.

(c) Directional coupler

A directional coupler samples power flowing in one direction.

Types:

Two-hole

Multi-hole

Hybrid coupler

2-hole coupler: Uses phase cancellation to achieve directionality.

(d) Microwave measurements

VSWR meter: Measures reflected power using crystal detector.

Insertion loss: Reduction in power due to device insertion.
Attenuation measurement: Done using substitution method on microwave bench.

(e) Microwave amplifiers & Gunn effect

Amplifiers: Klystron, TWT, MASER
Oscillators: Magnetron, Gunn, IMPATT

Gunn effect: Explained using two-valley model showing NDR region.

(f) Microwave isolator & cavity resonator

Isolator: Allows wave transmission in one direction only using ferrites.

Rectangular cavity:

kc=(mπa)2+(nπb)2+(pπc)2k_c = \sqrt{\left(\frac{m\pi}{a}\right)^2 + \left(\frac{n\pi}{b}\right)^2 + \left(\frac{p\pi}{c}\right)^2}kc​=(amπ​)2+(bnπ​)2+(cpπ​)2​

Phase constant:

β=k2−kc2\beta = \sqrt{k^2 - k_c^2}β=k2−kc2​​ 

(g) IMPATT diode

Working: Avalanche multiplication + transit time delay.

Operating frequency:

f=12πτf = \frac{1}{2\pi \tau}f=2πτ1​

Efficiency ≈ 10–20%

(h) Radiation pattern & VSWR measurement

Radiation pattern: Measured using rotating antenna setup.

VSWR < 10: Measured using double-minimum method on slotted line.

SECTION – C

(Attempt Any Two | 2 × 15 = 30 Marks)

 (a) S-parameter matrix problem

Given matched ports:

Pout=∣Sij∣2PinP_{out} = |S_{ij}|^2 P_{in}Pout​=∣Sij​∣2Pin​

With input power = 20 mW, remaining port powers are calculated using S-matrix elements.

(b) Circular waveguide TE₁₁ mode

Given:
Diameter = 12 cm

fc=X11′cπdf_c = \frac{X'_{11}c}{\pi d}fc​=πdX11′​c​

Guide wavelength:

λg=λ1−(λ/λc)2\lambda_g = \frac{\lambda}{\sqrt{1 - (\lambda/\lambda_c)^2}}λg​=1−(λ/λc​)2​λ​

Wave impedance:

ZTE=η1−(fc/f)2Z_{TE} = \frac{\eta}{\sqrt{1 - (f_c/f)^2}}ZTE​=1−(fc​/f)2​η​ 

Reflex klystron & magnetron

Reflex klystron: Explained using Applegate diagram.

Magnetron:
Called cross-field device due to perpendicular E & B fields.

π-mode: Adjacent cavities are 180° out of phase.
Strapping suppresses unwanted modes.

Rectangular waveguide fields

(a) TM mode derivation

Electric and magnetic field components derived from Maxwell’s equations.

(b) Non-existence of TM₀₁ and TM₁₀

Because longitudinal electric field component becomes zero, violating TM condition.