1. Antennas: from Theory to Practice 4. Antenna Basics
Yi HUANG
Department of Electrical Engineering & Electronics
The University of Liverpool
Liverpool L69 3GJ
This is a general rule, but it may need modification for certain situation.

2. Objectives of this Chapter
Study the basic theory of antennas
Understand how radio waves are generated by antennas
Identify the most important antenna parameters from both the field point of view and the circuit point of view.

3. 4.1 Antennas to Radio Waves
For a single frequency case
Eliminating H, we have
Thus in a open space

4. This equation gives the radiated electric field from a time varying current J (the time factor is omitted here) and is the very foundation of the antenna theory – it reveals how the antenna is related to radiowaves

5. Radiation from a current source IDl
η is about 377 ohms in free space

8. The electric field is always greater than the magnetic field;
When βr >1, the ratio of |E/H| = η
When βr <1, as the distance increases, the electric field reduces at a much faster rate (60 dB/decade) than the magnetic field (40 dB/decade).
When r is fixed, br =1 is still an important point,
The electric field first reduces as b (or frequency) increases to the point br =1 and then changes to increase with b (or frequency) after this point
the ratio of E/H reduces first as b increases to about br = 1; it then becomes a constant for br > 1.

9. Antenna far field

10. Major features of the far field
Just one E field component and one H field component – a local plane wave?
Both fields are inversely proportional to the distance r;
The ratio of E/H is , the intrinsic impedance
E and H fields are orthogonal to each other and the cross product of these two is the power density function which is inversely proportional to the distance square r2:

11. Antenna near field
Simulated near field around a dipole antenna

12. Major features of the near field
The region βr <1 for is normally called the reactive near field. The field changes rapidly with distance.
From its power density function, we can see that
It contains both the radiating energy (the real part) and reactive energy (the imaginary part – it does not dissipate energy which is like a capacitor or inductor). The latter is normally dominant in this region.
It has components in r and f directions. The former is radiating away from the source and the latter is reactive.

13. Antenna near and far fields

14. 4.2 Antenna Parameters from the Field Point of View
Radiation Pattern
a plot of the radiated field/power as a function of angle at a fixed distance which should be large enough to be considered in its far field

15. The half-power beamwidth (HPBW) of the main lobe, also called the 3dB beamwidth; or just the beamwidth (to identify how sharp the beam is);
The 10 dB beamwidth or first null beam width (FNBW) (another one capture the main beam shape);
The first side lobe level (expressed in dB, relative to the peak of the main beam);
The front to back ratio (the peak of the main lobe over the peak of the back lobe, another attempt to identify the directivity of the antenna).
Null positions (sometimes used for anti-interference and positioning).

16. When the patterns are plotted in the logarithmic scale (dB plot), both the normalised field and power patterns are the same

17. Directivity
a measure of the concentration of radiated power in a particular direction. It is defined as the ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions.
Pt is the total radiated power in W, and U is radiation intensity in W/unit solid angle, linked to the averaged radiated power density Sav

18. Example 4.1
The radiated power density of the electrically short current element is given earlier as:
Determine the directivity of the antenna as a function of the directional angles, find the maximum directivity and express it in decibels.

20. Gain Radiation Efficiency
the ratio of the radiation intensity in a given direction from the antenna to the total input power accepted by the antenna Pin divided by 4p:
Radiation Efficiency
the ratio of the radiated power to the input power accepted by the antenna:

21. Example 4.2
If the efficiency of the antenna in Example 4.1 is 50%, VSWR at the antenna input is 3 and the input/supplied power is 1 W, find: a). the power gain; b). the total radiated power

23. Effective Aperture and Aperture Efficiency
EIRP
Effective isotropic radiated power, or EIRP, is the amount of power that would have radiated by an isotropic antenna to produce the peak power density observed in the direction of maximum antenna gain:
Effective Aperture and Aperture Efficiency
The effective aperture Ae is less than the physical aperture Ap, the aperture efficiency is defined as the ratio of these two:
and directivity

24. Example 4.4
The directivity of a pyramidal horn antenna of aperture width a and height b is
Find its aperture efficiency. If the power density around the antenna is 1 W/m2, find the received power.

26. Polarisation Antenna Temperature
The antenna polarisation is the same as the polarisation of its radiating wave: linear or circular in practice.
Two orthogonally polarised antennas cannot communicate with each other.
Antenna Temperature
The radiation from different sources is intercepted by antennas and appears at their terminals as
TB is the brightness temperature of the radiation source

27. Radar Cross Section (RCS)
Antenna factor (AF)
the ratio of the incident electric field E to the induced voltage V0 at the antenna terminal when it is connected to a load/cable (50 ohms by default)
Radar Cross Section (RCS)
the ability of a target to reflect the energy back to the radar and it is the ratio of the backscattered power to incident power density

28. 4.3 Antenna Parameters from the Circuit Point of View
Input Impedance
Antenna input impedance (Za) is the impedance presented by an antenna at its terminals or the ratio of the voltage to current at its terminals

29. Radiation Resistance
the equivalent resistance which would dissipate the same amount of power as the antenna radiates when the current equals the input current at the terminals:
RL is the loss resistance of the antenna.
To match with the source impedance, the condition is:

30. Reflection Coefficient, Return Loss and VSWR

31. Radiation Efficiency
Matching Efficiency
Total Efficiency
source supplied power
This has taken the feed-antenna mismatch into account

32. Bandwidth
It can be defined by a number of things, such as the VSWR
return loss, gain, or even 3dB beam width!

33. Summary of antenna main parameters