1. Theory, characteristics, and implementations
Antennas
Theory, characteristics, and implementations
Chris Allen
Course website URL people.eecs.ku.edu/~callen/823/EECS823.htm

2. Topics Role of antennas Theory Antenna types Characteristics
Radiation pattern – beamwidth, pattern solid angle
Directivity, gain, effective area
Bandwidth
Friis’ transmission formula
Implementations
Dipole, monopole, and ground planes
Horn
Parabolic reflector
Arrays
Terminology

3. The role of antennas Antennas serve four primary functions
Spatial filter
directionally-dependent sensitivity
Polarization filter
polarization-dependent sensitivity
Impedance transformer
transition between free space and transmission line
Propagation mode adapter
from free-space fields to guided waves
(e.g., transmission line, waveguide)

4. Spatial filter
Antennas have the property of being more sensitive in one direction than in another which provides the ability to spatially filter signals from its environment.
Directive antenna.
Radiation pattern of directive antenna.

5. Polarization filter
Antennas have the property of being more sensitive to one polarization than another which provides the ability to filter signals based on its polarization.
In this example, h is the antenna’s effective height whose units are expressed in meters.

6. Impedance transformer
Intrinsic impedance of free-space, E/H
Characteristic impedance of transmission line, V/I
A typical value for Z0 is 50 .
Clearly there is an impedance mismatch that must be addressed by the antenna.

7. Propagation mode adapter
In free space the waves spherically expand following Huygens principle: each point of an advancing wave front is in fact the center of a fresh disturbance and the source of a new train of waves.
Within the sensor, the waves are guided within a transmission line or waveguide that restricts propagation to one axis.

8. Propagation mode adapter
During both transmission and receive operations the antenna must provide the transition between these two propagation modes.

9. Antenna types Antennas come in a wide variety of sizes and shapes
Helical antenna
Horn antenna
Parabolic reflector antenna

10. Theory Antennas include wire and aperture types.
Wire types include dipoles, monopoles, loops, rods, stubs, helicies, Yagi-Udas, spirals.
Aperture types include horns, reflectors, parabolic, lenses.

11. Theory
In wire-type antennas the radiation characteristics are determined by the current distribution which produces the local magnetic field.
Yagi-Uda antenna
Helical antenna

12. Theory – wire antenna example
Some simplifying approximations can be made to take advantage the far-field conditions.

13. Theory – wire antenna example
Once Eq and Ef are known, the radiation characteristics can be determined.
Defining the directional function f (q, f) from

14. Theory – aperture antennas
In aperture-type antennas the radiation characteristics are determined by the field distribution across the aperture.
Horn antenna
Parabolic reflector antenna

15. Theory – aperture antenna example
The far-field radiation pattern can be found from the Fourier transform of the near-field pattern.
Where Sr is the radial component of the power density, S0 is the maximum value of Sr, and Fn is the normalized version of the radiation pattern F(q, f)

16. Theory
Reciprocity
If an emf is applied to the terminals of antenna A and the current measured at the terminals of another antenna B, then an equal current (both in amplitude and phase) will be obtained at the terminals of antenna A if the same emf is applied to the terminals of antenna B.
emf: electromotive force, i.e., voltage
Result – the radiation pattern of an antenna is the same regardless of whether it is used to transmit or receive a signal.

17. Characteristics Radiation pattern
Radiation pattern – variation of the field intensity of an antenna as an angular function with respect to the axis
Three-dimensional representation of the radiation pattern of a dipole antenna

18. Characteristics Radiation pattern
Spherical coordinate system

19. Characteristics Radiation pattern

20. Characteristics Radiation pattern

21. Characteristics Radiation pattern

22. Characteristics Radiation pattern

23. Characteristics Radiation pattern

24. Characteristics Beamwidth and beam solid angle
The beam or pattern solid angle, p [steradians or sr] is defined as
where d is the elemental solid angle given by

25. Characteristics Directivity, gain, effective area
Directivity – the ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions.
[unitless]
Maximum directivity, Do, found in the direction (, ) where Fn= 1
and or
Given Do, D can be found

26. Characteristics Directivity, gain, effective area
Gain – ratio of the power at the input of a loss-free isotropic antenna to the power supplied to the input of the given antenna to produce, in a given direction, the same field strength at the same distance
Of the total power Pt supplied to the antenna, a part Po is radiated out into space and the remainder Pl is dissipated as heat in the antenna structure. The radiation efficiency hl is defined as the ratio of Po to Pt
Therefore gain, G, is related to directivity, D, as
And maximum gain, Go, is related to maximum directivity, Do, as

27. Characteristics Directivity, gain, effective area
Effective area – the functional equivalent area from which an antenna directed toward the source of the received signal gathers or absorbs the energy of an incident electromagnetic wave
It can be shown that the maximum directivity Do of an antenna is related to an effective area (or effective aperture) Aeff, by
where Ap is the physical aperture of the antenna and ha = Aeff / Ap is the aperture efficiency (0 ≤ ha ≤ 1)
Consequently
[m2]
For a rectangular aperture with dimensions lx and ly in the x- and y-axes, and an aperture efficiency ha = 1, we get
[rad]
[rad]

28. Characteristics Directivity, gain, effective area
Therefore the maximum gain and the effective area can be used interchangeably by assuming a value for the radiation efficiency (e.g., l = 1)
Example: For a 30-cm x 10-cm aperture, f = 10 GHz ( = 3 cm) xz  0.1 radian or 5.7°, yz  0.3 radian or 17.2° G0  419 or 26 dBi
(dBi: dB relative to an isotropic radiator)

29. Characteristics Bandwidth
The antenna’s bandwidth is the range of operating frequencies over which the antenna meets the operational requirements, including:
Spatial properties (radiation characteristics)
Polarization properties
Impedance properties
Propagation mode properties
Most antenna technologies can support operation over a frequency range that is 5 to 10% of the central frequency
(e.g., 100 MHz bandwidth at 2 GHz)
To achieve wideband operation requires specialized antenna technologies
(e.g., Vivaldi, bowtie, spiral)

30. Friis’ transmission formula
At a fixed distance R from the transmitting antenna, the power intercepted by the receiving antenna with effective aperture Ar is
where Sr is the received power density (W/m2), and Gt is the peak gain of the transmitting antenna.

31. Friis’ transmission formula
If the radiation efficiency of the receiving antenna is hr, then the power received at the receiving antenna’s output terminals is
Therefore we can write
which is known as Friis’ transmission formula

32. Friis’ transmission formula
as Friis’ transmission formula can be rewritten to explicitly represent the free-space transmission loss, LFS
which represents the propagation loss experienced in transmission between two lossless isotropic antennas. With this definition, the Friis formula becomes

33. Friis’ transmission formula
Finally, a general form of the Friis’ transmission formula can be written that does not assume the antennas are oriented to achieve maximum power transfer
where (t, t) is the direction of the receiving antenna in the transmitting antenna coordinates, and vice versa for (r, r).
An additional term could be included to represent a polarization mismatch between the transmit and receive antennas.

34. Implementation Dipole, monopole, and ground planes Horns
Parabolic reflectors
Arrays

35. Implementation Dipole, monopole, and ground plane
For a center-fed, half-wave dipole oriented parallel to the z axis
(V/m)
(W/m2)
Tuned half-wave dipole antenna

36. Dipole antennas
Versions of broadband dipole antennas

37. Dipole antennas

38. Monopole antenna q q Ground plane
Mirroring principle creates image of monopole, transforming it into a dipole
Radition pattern of vertical monopole above ground of (A) perfect and (B) average conductivity

39. Ground plane
A ground plane will produce an image of nearby currents. The image will have a phase shift of 180° with respect to the original current. Therefore as the current element is placed close to the surface, the induced image current will effectively cancel the radiating fields from the current.
The ground plane may be any conducting surface including a metal sheet, a water surface, or the ground (soil, pavement, rock).
Horizontal current element
Conducting surface (ground plane)
Current element image

40. Implementation Horn antennas

41. Implementation Horn antennas

42. Implementation Parabolic reflector antennas
Circular aperture with uniform illumination. Aperture radius = a.
Ap = p a 2
where
where
J1( ) is the Bessel function of the first kind, zero order

43. Implementation Antenna arrays
Antenna array composed of several similar radiating elements (e.g., dipoles or horns).
Element spacing and the relative amplitudes and phases of the element excitation determine the array’s radiative properties.
Linear array examples
Two-dimensional array of microstrip patch antennas

44. Implementation Antenna arrays
The far-field radiation characteristics Sr(, ) of an N-element array composed of identical radiating elements can be expressed as a product of two functions:
Where Fa(, ) is the array factor, and Se(, ) is the power directional pattern of an individual element.
This relationship is known as the pattern multiplication principle.
The array factor, Fa(, ), is a range-dependent function and is therefore determined by the array’s geometry.
The elemental pattern, Se(, ), depends on the range-independent far-field radiation pattern of the individual element. (Element-to-element coupling is ignored here.)

45. Implementation Antenna arrays
In the array factor, Ai is the feeding coefficient representing the complex excitation of each individual element in terms of the amplitude, ai, and the phase factor, i, as
and ri is the range to the distant observation point.

46. Implementation Antenna arrays
For a linear array with equal spacing d between adjacent elements, which approximates to
For this case, the array factor becomes
Note that the e-jkR term which is common to all of the summation terms can be neglected as it evaluates to 1.

47. Implementation Antenna arrays
By adjusting the amplitude and phase of each elements excitation, the beam characteristics can be modified.

48. Implementation Antenna arrays

49. Implementation Antenna arrays

50. Implementation Example: 2-element array Isotropic radiators

51. Implementation Example: 2-element array Isotropic radiators

52. Implementation Example: 2-element array Half-wave dipole radiators

53. Implementation Example: 2-element array Half-wave dipole radiators

54. Implementation Example: 6-element array Half-wave dipole radiators
grating lobes
d ≥ l produces two grating lobes

55. Antenna arrays Beam steering effects
Inter-element separation affects linear array gain and grating lobes
The broadside array gain is approximately where d is the inter-element spacing and N is the number of elements in the linear array
To avoid grating lobes, the maximum inter-element spacing varies with beam steering angle or look angle, , as

56. Antenna arrays Beamwidth and gain
An 2-D planar array with uniform spacing, N x M elements in the two dimensions with inter-element spacing of /2 provides a broadside array gain of approximately
The beamwidth of a steered beam from a uniform N-element array is approximately (for N > ~5) where b is the window function broadening factor (b = 1 for uniform window function) and d is the inter-element spacing

57. Conclusions
Antennas play an important role in microwave remote sensing systems.
There are both art and science aspects to antennas.
Antenna arrays enable the radiation characteristics to be changed electronically (i.e., very rapidly) unlike conventional mechanically-steered antennas.
Digital beamforming (dedicated transmit or receive electronics for each element) enable simultaneous realization of multiple antenna beams and/or multiple independent signals.

58. Terminology
Antenna – structure or device used to collect or radiate electromagnetic waves
Array – assembly of antenna elements with dimensions, spacing, and illumination sequency such that the fields of the individual elements combine to produce a maximum intensity in a particular direction and minimum intensities in other directions
Beamwidth – the angle between the half-power (3-dB) points of the main lobe, when referenced to the peak effective radiated power of the main lobe
Directivity – the ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions
Effective area – the functional equivalent area from which an antenna directed toward the source of the received signal gathers or absorbs the energy of an incident electromagnetic wave
Efficiency – ratio of the total radiated power to the total input power
Far field – region where wavefront is considered planar
Gain – ratio of the power at the input of a loss-free isotropic antenna to the power supplied to the input of the given antenna to produce, in a given direction, the same field strength at the same distance
Isotropic – radiates equally in all directions
Main lobe – the lobe containing the maximum power
Null – a zone in which the effective radiated power is at a minimum relative to the maximum effective radiation power of the main lobe
Radiation pattern – variation of the field intensity of an antenna as an angular function with respect to the axis
Radiation resistance – resistance that, if inserted in place of the antenna, would consume that same amount of power that is radiated by the antenna
Side lobe – a lobe in any direction other than the main lobe