EFWA 09 test 2

TEST 2, MAY 2009

Notes: Fields, \Vaves & Antennas: Test 2, Spring 2009

pl	P2	P3	P4	total

Notes:

Student name:

>    Bold lettcrs denotc vectors.

>    Iralics denote scalar variables.

>    Bold Italia denote vector variables.

>    Please specify units in all your answers!

>    IntrinsicimpcdanccofvacuumZ₀ = 120ifl; c= 3*10^sm/s.

>    Maximutn numbcr of points for each problem: 5.

Problem 1:

A piane 2=0 is the boundan between two lossless coaxial lines of cqual diameters a=5 mą 6=3mm. Media filling thesc lines havc following parametcrs: to e, =8,    ft_r = 2y    z<0

II: e_r =36,    //, = 4,    z>0

A wave of frcquency 10 GHz and average incident power 1 W is incidcnt upon this boundary from medium I. Compute:

a)    coefficients of field rcflcction f~_E, r_H and of power reflection ,

b)    coefficients of field transmission T_E, T„ and of power transmission T_p,

c)    density of power of the reflected and transmitted wave,

d)    coefficients of a standing wave SWR in both media.

Skctch the cnvclopcs of the E-. H- D-, and B- fields.

Problem 2:

Design a quartcr-wavc transformer matching the two lines of Problem 1, Skctch the cnvelopes of the E-, H- D-, and B- fields. Calculatc:

a)    density of power of the reflected and transmitted waves in each medium,

b)    coefficients of a standing wave SWR in each medium.

Problem 3:

Codsidcr a coaxial linę of radii 1.5 mm and 3 im filled with air. A travclling wavc propagates in the dircction -fi. and its voltagc amplitudc eąuals U₀.

Wnte down foli exprcsskns for the ełectric and magnetic fields, and conduction and displaccmcnt eurrents Spccify tbcir units and calculatc amplitudę vałues.

Draw the thstnbutions of the electromagnedc field lines and the conduction and displaccmcnt eurrents in the longitudmal soctkm of the linę

Problem 4:

In the linę of Problem 3, a standing wave is generated by temunating a section of the linc with a PEC platc at 2=0. Write down foli expressions for the ełectric and magnetic fields, and conduction and displaccmcnt eurrents. Spociły thcir units and cakailatc amplitudę vahies

Draw the distributkns of the electromagnedc field lines and the conduction and displaccmcnt eurrents in the longitudmal section of the linc for r=0. assunung that at this moment the E_p componcnt rcachcs its maximum.