1. TC303 Antenna & Propagation
Lecture 4
Antenna Radiation Pattern and Power Density
Reference: Antenna Theory, 3rd edition, by Constantine A. Balanis

2. Overview
Field regions
Radiation patterns
Directional antenna

4. Spherical coordinate component ranges

5. Field regions (2) Reactive near-field Radiating near-field: Fresnel
Far-field: Fraunhofer

6. Field regions

7. Evolution of pattern from near to far field

8. Reactive near-field
In the reactive near-field, the relationship between the strengths of the E and H fields is often too complex to predict.
Either field component (E or H) may dominate at one point, and the opposite relationship dominate at a point only a short distance away.
Phase of electric and magnetic fields are nearly quadrature thus
Highly reactive wave impedance
High content of non-propagating stored energy near antenna
Very close to the antenna, in the reactive region, energy of a certain amount, if not absorbed by a receiver, is held back and is stored very near the antenna surface. This energy is carried back and forth from the antenna to the reactive near-field by electromagnetic radiation of the type that slowly changes electrostatic and magnetostatic effects. For example, current flowing in the antenna creates a purely magnetic component in the near-field, which then collapses as the antenna current begins to reverse, causing transfer of the field's magnetic energy back to electrons in the antenna as the changing magnetic field causes a self-inductive effect on the antenna that generated it. This returns energy to the antenna in a regenerative way, so that it is not lost. A similar process happens as electric charge builds up in one section of the antenna under the pressure of the signal voltage, and causes a local electric field around that section of antenna, due to the antenna's self-capacitance. When the signal reverses so that charge is allowed to flow away from this region again, the built-up electric field assists in pushing electrons back in the new direction of their flow, as with the discharge of any unipolar capacitor. This again transfers energy back to the antenna current.
Because of this energy storage and return effect, if either of the inductive or electrostatic effects in the reactive near-field transfers any field energy to electrons in a different (nearby) conductor, then this energy is lost to the primary antenna. When this happens, an extra drain is seen on the transmitter, resulting from the reactive near-field energy that is not returned. This effect shows up as a different impedance in the antenna, as seen by the transmitter.

9. Radiating near-field Fields are predominantly in phase.
Fields do not yet display a spherical wave front: thus a pattern varies with distance.
These are regions where near-field measurements are made.

10. Far-field
Fields exhibit spherical wavefront, 𝑒 −𝑗𝑘𝑟 𝑟 , thus ideally, the pattern does not vary with distance.
E and H Fields are in time-phase and spatial quadrature.
Wave impedance is ideally real.
Power predominantly real; propagating energy.

11. Identifying the near-far field region
Near the antenna,

12. In the parallel ray approximation for far field calculations, the third term is neglected.
This can be expanded by the binomial theorem which for the first three terms, reduces to:
The distance where the far field begins (Rff) (or where the near field ends) is the value of r when the error in R due to neglecting the third term of equation, equals 1/16 of a wavelength.

13. Rff is usually calculated on boresight, so  = 90 and the second term equals zero
(Cos 90 = 0), therefore Rff is found by equating the third term to 1/16 wavelength.

14. General rule of thumbs Far field conditions
r>> D or r >> 

15. Radiation patterns
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.

16. Amplitude radiation patterns
Isotropic, directional, omnidirectional
Principle patterns
Pattern lobes

17. Isotropic antenna
The isotropic antenna radiates EM waves equally in all directions.

18. Directional antenna (1)
The directional antenna radiates and receives EM waves preferentially in some directions.
Normalized electric field pattern:

19. Directional antenna (2)
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

24. Check fig 2.2c , repeating 2.2b

28. Time and spatial variations

29. Radiation power density

31. Ex1 The radial component of the radiated power density of an antenna is given by 𝑊 𝑟𝑎𝑑 = 𝑊 𝑟 𝑎 r = 𝐴 0 𝑠𝑖𝑛𝜃 𝑟 2 𝑎 r W/m2 , determine the total radiated power.