ECE 407 – ELECTROMAGNETIC COMPATIBILITY
ECE
Advanced Electromagnetic Fields and Waves I
1. A dipole antenna lies on the z-axis between −?/2 and ?/2 in free space.
Let’s consider a triangular distribution for the cu
ent over the dipole:
?(?) = ?0 (1 − |
?
?/2
|)
a) Derive the far field radiated by the dipole.
) Derive the radiation resistance and plot the radiation resistance as a function
of the length for 0 < ?/2 ≤ 1. The involved integral for this question should
e calculated numerically.
c) Assume that ?/2 ≪ 1 and determine an approximate formula for the
adiation resistance. Compare this to the result for a linear dipole antenna
from Chapter 2 of the notes. Compare the numerical value to that obtained in
part (b) for ? = λ/10.
2. Consider a Hertzian dipole at the origin of a cartesian system and oriented along
a generic direction �̂�.
(a) Derive the radiated field.
(b) Derive the equivalent cu
ents over the surface of a sphere centered with the
dipole and with a radius of 5λ.
3. Consider a sphere with center at the origin of a cartesian system and with radius 5
λ. The following electric (?) and ( �⃗⃗⃗�) magnetic cu
ent distributions are provided
over the surface of the sphere:
? = ?0 sin ? ?
�⃗⃗⃗� = ?0 ζ sin ? �̂�
With ?0 a constant and ζ the characteristic impedance in free space.
(a) (15 pts) Derive the field radiated by such a distribution in a generic point in
free space within and outside the sphere. Hint: Link these cu
ents to the point
(b) of Ex. 2 for a dipole along the z-axis.
(b) The far-field distance associated to such distribution.