1. 1

2.  E z = 0 From Expanding for z-propagating field gets where 2

3.  In the x-direction Since E y = 0, then from we have at x = 0 and x = a 3

4.  In the y-direction Since E x = 0, then from we have at y = 0 and y = b 4

5. Assume then we have 5

6. 1.in the x-direction at x = 0, at x = a, 6

7. 7

8. 2. in the y-direction at y = 0, at y = b, 8

9. Properties of TE wave in y-direction of rectangular WGs (2) For lossless TE rectangular waveguides, 9

10. 10

11.  For TE mode, either m or n can be zero, if a > b, is a smallest eigen value and f c is lowest when m = 1 and n = 0 (dominant mode for a > b) 11

12.  For TM mode, neither m nor n can be zero, if a > b, f c is lowest when m = 1 and n = 1 12

13. 13

14. 14

15.  General properties  Radiation fields and patterns  Antenna performance 15

16.  A structure designed for radiating and receiving EM energy in a prescribed manner.  The importance of the shape and size of the structure › the efficiency of the radiation › the preferential direction of the radiation 16

17.  Complex antenna impedance Z ant needs to be matched to the system impedance. 17

18.  Far field region (the distance where the receiving antenna is located far enough for the transmitter to appear as a point source) In the far field where  0 = 120  . Time-averaged power density: or W/m 2. 18

19.  Total power radiated by the antenna can be expressed as W 19

20.  The shape or pattern of the radiated field is independent of r in the far field.  Radiation patterns usually indicate either electric field intensity or power intensity.  A transmit-receive pair of antennas must share the same polarization for the most efficient communication.  Normalized power function or normalized radiation intensity 20

21.  The isotropic antenna radiates EM waves equally in all directions so that 21

22.  The directional antenna radiates and receives EM waves preferentially in some directions.  Normalized electric field pattern: 22

23.  E-field pattern is plotted as a function of  for constant .  H-field pattern is plotted as a function of  for  =  /2.  In decibels, E-field pattern and Power pattern are similar. and 23

24.  The overall ability of an antenna to direct radiated power in a given direction.  Pattern solid angle: A steradian (sr) is defined by an area r 2 at the surface. A differential solid angle d , in sr, is defined as 24

25. The solid angle of a sphere is found by integrating d  such that  An antenna’s pattern solid angle: Comparing  p for two Radiation patterns. 25

26.  Normalized power’s average value:  Directivity gain D( ,  ) is defined as  The maximum directive gain is called Directivity D max : 26

27.  Total radiated power can be written as therefore we have or 27

28. 28

29.  The antenna resistance R ant consists of the radiation resistance R rad and a dissipative resistance R diss that arises from ohmic losses in the metal conductor.  Assume so we can write  For maximum radiated power, R rad must be as large as possible but still easy to match with the feed line. 29

30.  Dissipated power P diss can be written as  Antenna efficiency e is measured as  The power gain can then be expressed as 30