Point Sources

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Antenna Design
Chapter 4 Point Sources

• Cheng-Chi Yu

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Contents

• Point source radiators
• Power patterns
• Isotropic sources
• Radiation intensity
• Example of power patterns
• Field patterns
• Phase patterns

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Point source

• Our observations are made at a sufficient
  distance (far field), any antenna, regardless of
  its size or complexity, can be represented in
  this way by a single point source.
• As shown in Fig. 4-1b, if Rgtgtd, Rgtgtb, and Rgtgt?,
  the distance d between the two centers has a
  negligible effect on the field patterns at the
  observation circle. However, the phase patterns
  will generally differ, depending on d. As d is
  increased, the observed phase shift becomes
  larger.

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Power patterns

• The time rate of energy flow per unit area is the
  Poynting vector, or power density (Watt/m2).
• For a point source (or in the far field of any
  antenna), the Poynting vector S has only a radial
  component Sr with no components in either the ?
  or ? directions (S? S?0).

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Power patterns

• A source that radiates energy uniformly in all
  directions is an isotropic source.
• For a isotropic source, the radial component Sr
  of the Poynting vector is independent of ? and ?.
• A graph of Sr at a constant radius as a function
  of angle is a Poynting vector (or power-density)
  pattern, but is usually called a power pattern.

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Power pattern of isotropic source

• The 3-D power pattern for an isotropic source is
  a sphere. In 2-D the pattern is a circle.

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Absolute power patterns vs.relative power pattern

• Absolute power pattern Sr is expressed in W/m2
• Relative power pattern Sr is expressed in terms
  of its value in some reference direction
• A relative power pattern with a maximum of unity
  is also called a normalized pattern.

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A power theorem and its application to an
isotropic source

• 4

Sr ? 1/r2
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Radiation intensity
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Power theorem

• The total power radiated is given by the integral
  of the radiation intensity over a solid angle of
  4? steradians.
• Power patterns can be expressed in terms of
  either the Poynting vector (power density) or the
  radiation intensity.
• The total radiation power of an isotropic source
  is
• P 4?Uo (W)
• Where Uo radiation intensity of isotropic
  source, W/sr

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Example of power patterns

• Calculating D of various power patterns
• Unidirectional cosine power pattern
• Bidirectional cosine power pattern
• Sine (doughnut) power pattern
• Sine-squared (doughnut) power pattern
• Unidirectional cosine-squared power pattern
• Pencil beam with minor lobes

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ltsolgt

• The maximum radiation intensity Um of the
  unidirectional cosine source is 4 times the
  radiation intensity Uo from an isotropic source
  radiation the same total power.

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ltsolgt

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• By sufficiently reducing the step size, the
  summation can be made as precise as the available
  data will allow.
• The directivity can be expressed as D 4?/?A
  A/a

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Relation of the Poynting vector S and electric
field of the far field

• For far field (point source)
• Poynting vector radial ( Sr component only )
• Electric field transverses to the wave direction
  ( E? and E? components only ) and so magnetic
  field does.
• E and H perpendicular to each other, and in
  phase.
• E/H Z 377 ?

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Relation of the Poynting vector S and electric
field of the far field

• The Poynting vector and the electric field at a
  point of the far field are related in the same
  manner as they are in a plane wave, since, if r
  is sufficiently large, a small section of the
  spherical wave front may be considered as a
  plane.
• The relation between the average Poynting vector
  and the electric field at a point of the far
  field is

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Field pattern

• A pattern showing the variation of the electric
  field intensity at a constant radius r as a
  function of angle (? ,? ) is called a field
  pattern.
• Absolute field pattern the field intensity is
  expressed in V/m
• Relative field pattern the field intensity is
  expressed in units relative to its value in some
  reference direction

relative field pattern of the E? component
relative field pattern of the E? component
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Field pattern

• The magnitudes of both E? and E? of the far field
  vary inversely as the distance from the source.
• E? and E? may be different functions, F1 and F2,
  of the angular coordinates ? and ? ,
• The relative total power pattern

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• The polarity of the lobes alternate ( and -)
• When the magnitude of the field of one lobe ()
  and the adjacent lobe (-) are equal, the total
  field goes to zero, producing a null.

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