Demo11Hertzian - ECE 3030: Electromagnetic Fields and Waves...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECE 3030: Electromagnetic Fields and Waves Fall 2009 DEMO 11 INSTRUCTOR NOTES: Hertzian Dipole Antennas Reminder: Date: Tuesday 11/10 1. Problem 17.2 The two Hertzian dipoles shown have current densities specified by the phasors: ~ J 1 ( ~ r) = Id 3 ~ r- h 2 z z ~ J 2 ( ~ r) = Id e j 3 ~ r + h 2 z z Assuming A = 1, = , and h = , find the radi- ation pattern in the z- x plane. Sketch p ( , = 0) and indicate the angular location of all the nulls in the radiation pattern. Hint: Make sure you do not miss the sin 2 term that is due to the an- gular dependence of the radiation patterns of the individual dipoles. x z h J 1 J 2 Figure 1: Another two Hertzian dipole array. Solution: The general far-field formula for 2 Hertzian z-directed dipoles (from Slide 9 of Lecture 32) is ~ E ff ( ~ r ) = j kI 1 d 4 r sin e jkr e jk r ~ h 1 + I 2 I 1 e jk r ~ h 2 Make sure the students understand where this comes from...probably you should go back to the vector potential for one Hertzian dipole: ~ A( ~ r ) = o Id 4 r e- jk ( r- r ~ h) noting that this is in the same direction as the current, and yields a magnetic field in the direction (via ~ ~ A) and an electric field in the direction ( to ~ H and ~ r. Remember that r = sin cos x + sin sin y + cos z and that r, , and form an orthogonal set. In the far-field: ~ E( ~ r ) = j kId 4 r sin e- jkr e jk r ~ h ~ H( ~ r ) = j kId 4 r sin e- jkr e jk r ~ h Be careful with the unit vector in the dot product r ~ h. Note | E | / | H | = , and that ~ H ~ E ~ r....
View Full Document

Page1 / 4

Demo11Hertzian - ECE 3030: Electromagnetic Fields and Waves...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online