Hertzian Dipole Antenna Radiation : The Whole Story

[barton]

I've been trying to learn the details of electromagnetic radiation from a hertzian dipole antenna, but all the information that I find only gives me a patchy understanding. This is what I have so far:

Near-Field: Charges oscillate past each other in a center-fed hertzian dipole. This creates rapidly expanding and collapsing E and H fields around it. These fields a 90 degrees apart in time. When the charges rush past each other at the center, the magnetic field is at a maximum when the electric field is fully collapsed. When the charges are at maximum separation, the electric field is at a maximum, and the magnetic field is fully collapsed. The fields are oriented at right angles to each other.
See http://www.phy.davidson.edu/instrumentation/Files/NEETS/Mod10%20-%20Wave%20Propagation%20Transmission%20Lines%20and%20Antennas.pdf" , Page 62

Far-Field: Somehow these expanding and collapsing E and H fields create waves of E and H fields further out in space. This time, they are 0 degrees apart in time. They are still however, oriented orthogonally to each other.

Maxwell's Equations - Method of Propagation: A changing electric field at a point creates a curl of magnetism around it. This creates a changing magnetic field in the points surrounding that original point, in turn causing a curl of electric fields further out. The process continues, creating a propagating wave.

Maxwell's Equations - Prediction of Sinusoidal Waves: When Maxwell reduced his equations to one-dimension, he found the wave function. It just so happened that the variable in the wave function that determines the speed of the wave was 1/sqrt(e*u). He predicted that electromagnetic waves are sinusoids, and was able to predict their speed. No mention on how they are generated from an antenna.

Bubbling Out Electric Fields - The charges in the dipole move so fast that the electric field lines around them bend, forming closed loops. These loops then bubble out from the antenna, for whatever reason. http://www-antenna.ee.titech.ac.jp/~hira/hobby/edu/em/smalldipole/smalldipole.html" . No mention of the near magnetic field.

Near Field and Far Field Distances - Somehow the near fields diminish as 1/r^3, but the far fields diminish as 1/r. I'm not quite sure what that means.



Can anyone explain the whole story of electromagnetic waves emanating from a dipole antenna? Or point me in the direction of a good reference?

 

[jtbell]

Intermediate-level undergraduate E&M textbooks cover dipole radiation fairly extensively. See for example Griffiths, or Purcell, or Corson & Lorraine.

 

[barton]

Thanks for the references. I looked at both Griffiths and Corson & Lorraine, and both texts describe dipole radiation using retarded vector potentials. I was hoping for a description using just electric and magnetic fields.

 

[turin]

The 1/r^3 dependence is the typical static dipole field dependence. The 1/r dependence is the square-root of the dependence of power flow density from a point source and the field strengths are basically like square-roots of power flow. This is conceptually what distinguishes near-field from far field. In the near field, the antenna looks like a quasi-static finite-sized line of current. In the far-field, the antenna looks like a single point.

I was hoping for a description using just electric and magnetic fields.

You can try Jefimenko's eqs.. Set the charge density to zero, and choose the current density to represent the Hertzian dipole. Then, alternate two mutually exclusive approximations in the equations. For the near field, approximate r<<c/f, where r is the distance from the antenna, c is the speed of light, and f is the frequency at which the antenna operates. For the far field, approximate r>>c/f, and r>>L, where L is the length of the antenna.