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Midterm Exam for ECE 3065: Electromagnetics and Waveguides, February 2006 - Prof. Emmanoui, Exams of Guiding Electromagnetic Systems

Georgia Institute of Technology - Main CampusGuiding Electromagnetic Systems
Prof. Emmanouil Tentzeris

The problems and solutions for the midterm exam of the ece 3065 course focused on electromagnetics and waveguides. The exam covers topics such as cutoff wavelength and frequency calculation for different waveguide modes, transverse-wave impedance, power efficiency, reflection and transmission coefficients, and rfid circuit analysis.

Typology: Exams

Pre 2010

Uploaded on 09/17/2009

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ECE3065
MIDTERM2/2006
Problems
1.ArectangularwaveguideusedforWiMaxapplicationshasacross-section1:1in£0:5inand is
¯lledwithasilicon-based nonmagneticlossless materialwith¹r=1 and ²r=12.
(a)Calculatethe cuto®wavelength¸ocand the cuto®frequencyfcoforthedominant,the¯rst two
higher-orderTEmodesand the¯rst twohigher-orderTMmodes.(10%)
(b)Determinethetransverse-waveimpedance forthedominant,the¯rsthigher-orderTEand the
¯rsthigher-orderTMmodesatf=3:5GHz.HowclosearetheytotheTEMvalue?Whatwill bethe
valueofthetransverse-waveimpedance ofthedominantmodeatadual-band short-rangebroadband
moduleoperating atf=50GHz(DONOT CALCULATEIT!!)and why?(10%)
(c)Therehavebeenthree proposedfrequenciesforWiMaxoperations:1.7GHz,2.5GHzand 3.5
GHz.Whichone(s)wouldoperatewiththebestpowere±ciencyforthiswaveguideand why?(10%)
(d)After removingthesidewalls(shortside),recalculatethe cuto®frequencyforthedominantand
the¯rst two-highermodes,afteridentifyingthem.(10%)
2.Aperpendicularlypolarizedmonochromaticlaserwaveinairisobliquelyincidentuponaplanar
LTCC-Airinterface atanincidence angleof60o,asitisusedfordefectdetectionof3D(multilayer)
integratedceramic3G-telecom modules.Thewavefrequencyis5THz(1THz=1012 Hz),and the
dielectric constantofLTCC is5.6(assumethatLTCC isanonmagneticlossless ceramicmaterial).
Ifthe electric¯eldamplitudeoftheincidentwaveis20 mV/m,determine:
(a) there°ectionand transmissioncoe±cients,(15%)and
(b)howmanydb'sit'slowerthantheincident¯eld(5%)
(c) theMAGNETIC¯eldamplitudeofthetransmittedwave(15%).
(d) theangleofminimumpower re°ection.Wouldthisanglehaveadi®erentvalueiftheincident
wavewereparallel-polarized?(10%)
3.(a)Find theABCDand ZmatricesofanRFIDwhose electronicsconsistofashuntopen-circuit
stub oflength8.85 cmbuiltonanonmagneticlossless °exibleorganic(LCP)materialwith²r=3:0
and Zo=125-and aseriesinductorL=62.5nH,usedasaresonantstructureat0.9GHz.(10%)
(b)Isthisareciprocaland/orlossless structureand why?(10%)
(c)Givethe¿-and the¼-equivalentcircuit.(10%)
(d)Whatisthe exactresonantfrequencyofthisgeometry?Doesitneedtobemodi¯edforane®ective
RFIDoperation?(5%)
GOODLUCK!!!
1

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ECE 3065

MIDTERM 2/

Problems

  1. A rectangular waveguide used for WiMax applications has a cross-section 1: 1 in £ 0 : 5 in and is ¯lled with a silicon-based nonmagnetic lossless material with ¹r=1 and ²r=12.

(a) Calculate the cuto® wavelength ¸oc and the cuto® frequency fco for the dominant, the ¯rst two higher-order TE modes and the ¯rst two higher-order TM modes. (10%)

(b) Determine the transverse-wave impedance for the dominant, the ¯rst higher-order TE and the ¯rst higher-order TM modes at f = 3: 5 GHz. How close are they to the TEM value? What will be the value of the transverse-wave impedance of the dominant mode at a dual-band short-range broadband module operating at f = 50GH z (DO NOT CALCULATE IT!!) and why? (10%)

(c) There have been three proposed frequencies for WiMax operations: 1.7 GHz, 2.5 GHz and 3. GHz. Which one(s) would operate with the best power e±ciency for this waveguide and why? (10%)

(d) After removing the side walls (short side), recalculate the cuto® frequency for the dominant and the ¯rst two-higher modes, after identifying them. (10%)

  1. A perpendicularly polarized monochromatic laser wave in air is obliquely incident upon a planar LTCC-Air interface at an incidence angle of 60o, as it is used for defect detection of 3D (multilayer) integrated ceramic 3G-telecom modules. The wave frequency is 5 THz (1 THz = 10^12 Hz), and the dielectric constant of LTCC is 5.6 (assume that LTCC is a nonmagnetic lossless ceramic material). If the electric ¯eld amplitude of the incident wave is 20 mV/m, determine:

(a) the re°ection and transmission coe±cients, (15%) and

(b) how many db's it's lower than the incident ¯eld (5%)

(c) the MAGNETIC ¯eld amplitude of the transmitted wave (15%).

(d) the angle of minimum power re°ection. Would this angle have a di®erent value if the incident wave were parallel-polarized? (10%)

  1. (a) Find the ABCD and Z matrices of an RFID whose electronics consist of a shunt open-circuit stub of length 8.85 cm built on a nonmagnetic lossless °exible organic (LCP) material with ²r = 3: 0 and Zo = 125- and a series inductor L=62.5nH, used as a resonant structure at 0.9 GHz. (10%)

(b) Is this a reciprocal and/or lossless structure and why? (10%)

(c) Give the ¿- and the ¼- equivalent circuit. (10%)

(d) What is the exact resonant frequency of this geometry? Does it need to be modi¯ed for an e®ective RFID operation? (5%)

GOOD LUCK!!!