anteena

1. Chapter 3: Radiation Integrals
and Auxiliary
Potential Functions

2. The block diagram for computing fields radiated by
electric and magnetic sources are given below,

3. Integration path 1 (Difficult Approach)
Using this method, we can calculate electric and magnetic fields
as below,
Here Y = 1/Z and k are the admittance and
propagation constant of the background medium,
respectively.

4. Integration Path 2 : Source placed at
origin

5. THE VECTOR POTENTIAL A FOR AN
ELECTRIC CURRENT SOURCE J
The electromagnetic field generated by a given harmonic electric
current J (M = 0) can be computed using the following relations,

6. THE VECTOR POTENTIAL F FOR A
MAGNETIC CURRENT SOURCE M
The electromagnetic field generated by a given harmonic magnetic current
M (J = 0 ) can be computed using the following relations,

7. ELECTRIC AND MAGNETIC FIELDS FOR
ELECTRIC (J) AND MAGNETIC (M)
CURRENT SOURCES
In case if we have non-zero electric and magnetic current sources then we
can combine the electromagnetic fields generated by J and M as below,

8. Source located not at origin

9. Linear current densities/only currents
If and represent linear current densities (1/m),
For electric and magnetic currents and ,

10. FAR-FIELD RADIATION

11. Continued

12. Continued

13. Continued

14. Continued

15. Continued

16. Continued

17. Continued

18. Continued

19. Continued

20. Continued

21. FAR-FIELD RADIATION (Summary)
Neglecting higher order terms of (1∕r)n, the radiated E- and H-fields
due to electric current source J (or A) have only 𝜃 and 𝜙 components,

22. FAR-FIELD RADIATION (Summary)
In a similar manner, the far-zone fields due to a magnetic source M
(potential F) can be written as,
It is clear that the corresponding far-zone E- and H-field components
are orthogonal to each other and form TEM (to r) mode fields.