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 Antenna is a structure designed for radiating and receiving EM energy in a prescribed manner  Far field region ( the distance where the receiving antenna is located far enough for the transmitter to appear as a point source)  The shape or pattern of the radiated field is independent of r in the far field.  Normalized power function or normalized radiation intensity 2

 Directivity is the overall ability of an antenna to direct radiated power in a given direction.  An antenna’s pattern solid angle:  Total radiated power can be written as  Antenna efficiency e is measured as 3

 If the current distribution of a radiating element is known, we can calculate radiated fields.  In general, the analysis of the radiation characteristics of an antenna follows the three steps below: 1. Determine the vector magnetic potential from known of assumed current on the antenna. 2. Find the magnetic field intensity from. 3. Find the electric field intensity from. 4

From the point form of Gauss’s law for magnetic field, Define therefore we can express as where J d = current density at the point source (driving point) R = distance from the point source to the observation point (m) 5

 From here we can determine, then find in free space.  We can then find the electric field from  The time-averaged radiated power is The subscript “0” represents the observation point. W/m 2. 6

1. Hertzian dipole (electric dipole) 2. Small loop antenna (magnetic dipole) 3. Dipole antenna 7

 A short line of current that is short compared to the operating wavelength. This thin, conducting wire of a length dl carries a time-harmonic current A and in a phasor form A. 8

The current density at the source seen by the observation point is A differential volume of this current element is dV = Sdz. 9

Therefore Then Where at the observation point. For short dipole, R  r, thus we can write Conversion into the spherical coordinate gives 10

Therefore We can then calculate for 11

Multiply  2 to both nominator and denominator, so we have We are interested in the fields at distances very far from the antenna, which is in the region where or 12

Under a far-field condition, we could neglect and Then and Finally, W/m 2. 13

Since the current along the short Hertzian dipole is uniform, we refer the power dissipated in the radial distance R rad to I, or m. 14

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16 a)P max at r = 100 m

b) What is the time-averaged power density at P (100,  /4,  /2)? c) Radiation resistance 17

Assume a << A complicate derivation brings to 18 If the loop contains N-loop coil then S = N  a 2

 Longer than Hertizian dipole therefore they can generate higher radiation resistance and efficiency. 19 Divide the dipole into small elements of Hertzian dipole. Then find and. Figure of dipole

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The current on the two halves are Symmetrical and go to zero at the ends. We can write Where Assume  = 0 for simplicity. 21

From 22 In far field but since small differences can be critical.

We can write 23

From In our case 24

where 25

1. Find P n (  ), calculate F(  ) over the full range of  for length L in terms of wavelength then find F max (this step requires Matlab) 2. Find  p 3. D max (Directivity) 4. R rad 26

 Link to Matlab file Link to Matlab file 27

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Using Matlab, we get 29  p = D max = 1.64 R rad = 73.2  This is much higher than that of the Hertzian dipole.