19 Ecb2173 Electromagnetic Theory

8/13/2019 19 Ecb2173 Electromagnetic Theory

1/7

UNIVERSITITEKNOLOGIPETRONAS

COURSEDATETIME

ECB2173 - ELECTROMAGNETIC THEORYsrH SEPTEMBER 2o1l (wEDNESDAv)2.30 PM - 5.30 PM (3 hours)

INSTRUCTIONS TO CANDIDATES1.2.3.4.

5.

Answer ALL questions from the euestion Booklet.Begin EACH answer on a new page in the Answer Booklet.Indicate clearly answers that are cancelled, if any.Where applicable, show clearly steps taken in arriving at the solutions andindicate ALL assumption.Do not open this Question Booklet until instructed.

Note I There are sEVEN (7) pages in ths euestion Booklet incrudingthe cover page and an appendix.Smith chart will be provided.l

FINAL EXAMINATIONMAY 2012 SEMESTER

Universiti Teknologi PETRONAS


2/7

a.1.ECB 2173

An infinitely long line of charge with uniform charge density, p,,isplaced along the y -axis as shown in FIGURE Q1.

,rrrrrrrtlr

FIGURE QI

Pt

Using the Gauss's law in differential form, deriveform.

Based on the integral form of Gauss's law, derive an expressionfor the electric field, , in free space due to the lne chargegiven in FIGURE Q1.

[10 marks]b. State the FOUR (4) Maxwell equations in differential form.

[4 marks]

il


3/7

a..EC 2173

F|GURE Q2 shows a coaxial capacitor of length l:6cm with insulatingdielectric material of t,:9 . The radii of the cylindrical conductors are0.5 cm and 1 cm. The voltage applied across the capacitor is

v(t':15gsin (tso nr)

FIGURE Q2Based on FIGURE Q.2, the electric field E in the dielectric spacebetween the cylindrical conductors is gven byE: - = Q =.2nerl'Develop an expression for the potential difference, V, betweenthe outer and inner conductor.

[5 marks]Develop an expression for the capacitance C of the coaxial line.

[3 marks]Assuming that the coaxial capacitor is lossless, determine thedisplacement current when the voltage V(t) is applied.

[B marks]Given two waves characterized byy,(r,t)= 3 cos(2or - 30x)Yr(*,t): -3 cos(20 t +30x)determine the wave which is leading and by what phase angle.

il

ilt

1-+l

[4 marks]


4/7

3.ECB 2173

A 1O-kHz sound wave is traveling in the x-direction in air. This sound has adifferential pressure p(*,r):I2Nf m2 al x:0 and t=4g/s. The velocity ofsound in air is 330 mf s . The reference phase of p(x,t) is equal to 42. .a. Derive the expression for p(t,t).

[12 marks]

construct the waveform for at least 2 cycres, the pressure wave p(r,t)versus distance, x at time, f = 0. [4 marks]

construct the waveform for at least 2 cycres, the pressure wave p(*,t)versus time, f at distance, x = 0.

[4 marks]

b.

c.


5/7

a..ECB 2173

A 1.25-GHz generator circuit with internal impedanc e z;-10o andvoltage source given byV*(t) : 10 sin( wt * 30 ) V

is connected to a load Z through s0-o, 67-cm long losslesstransmission line. The phase velocity of the line is 0.7c, where c isvelocity of light in vacuum.

il

Derive v(z,t) along the lne.Derive i(z,t) along the line [5 marks]

[5 marksJ

lossless microstripfabrication. Justify

b. The measurement wth a Zo: so o slotted line terminated in anunknown load impedance had produced voltage standing waveratio value of 3.0.The distance between successive voltage minima isfound to be 30 cm and the first voltage minimum was located at '12 cmfrom the load. Determine the impedance of the load,21.

[5 marks]c Specify the electromagnetic

line that suitable for printedyour answer.

characteristics of thecircuit boards (PCB)

[5 marks]


6/7

5.ECB 2173

a. Explain the importance of Smith chart applications in electricalengineering.

[3 marks]State the requirements of matching network in transmission lines andpropose THREE (3) suitable techniques that can be applied to matchthe impedance between the load and feed line.

[5 marks]A load impedance ZL: 30-j25 O is connected to a 50-O transmissionlne as shown in FIGURE Q5c. A shunt element is inserted to eliminatereflections towards the sending end of the lines. The signalsourceoperates at/=100 MHz. Using Smith chart solution,

Feedline

FIGURE Q5cspecify the insert location of dt and dz(in wavelength) from Z,

ii. specify the type of the element and its value. [8 marksJ[2 marks]

A 50-O lossless transmission line is to be matched to a resistive loadimpedance with Z:100 O. Construct a quarter wavelength network toeliminate the reflection along the feed line.

b.

c.

YL

d.

- END OF PAPER -[2 marks]


7/7

ECB 2173APPENDIX I

Permeability in free space: po = 4frx10-7 Hf mPermittivity in free space: so :8.854 xl0-12 Ff m

Documents

19 Ecb2173 Electromagnetic Theory