F
Fred Abse
- Jan 1, 1970
- 0
OK, but can we talk about electric power density as isolated from the
magnetic density or voltage density?
Your terminology is confusing. Power has density (per unit area),
electromagnetic fields (voltage and magnetizing force) have intensity or
strength (per unit length). Consider a simple example: a capacitor has
two parallel plates, separated by one meter. The PD between the plates is
one volt, hence the field between the plates is one volt per meter
intensity.
At what distance does electric power density stop falling as the inverse
of distance and begin to fall as the square of distance? (This is the
definition of 'near field' / 'far field', yes?)
Power density *always* follows an inverse square law.
Field intensity follows a first power law.
My current misunderstanding is that for an (admittedly theoretical)
isotropic radiator, that distance is 'several wavelengths'.
See below.
If that is true, can we reasonably expect to see the shape of the near
field be the same as the shape of the far field in the radiation pattern
of an anisotropic transmitting antenna, though the *sizes* of those fields
be quite different.
Is this correct?
No, see below
Even within the near field? (Electric power density only)
There's no such thing as electric power density. Get these things straight
in your mind, I think you're getting confused, there is:
Electric field intensity - B Volts per meter.
Magnetic field intensity - H Amps (or amp turns if you like) per meter.
Power density - Watts per square meter.
All three are inseparable, and are linked by the intrinsic impedance of
free space = 377 ohms. It's just like Ohm's Law.
The near field has two components.
Firstly, an inductive component, which merely stores energy, returning it
to the antenna each half cycle. Analogous to a resonant circuit.
The inductive field *does not radiate power*, hence does not contribute to
power density. Its electric and magnetic components are antiphase.
Secondly, a component which radiates power as a field having an electric
(E) component, and a magnetic (H) component, mutually at right angles in
space, and in phase.
Energy flow (the Poynting vector) is at right angles to both E and H, and
flows away from the antenna, into space, and is equal to the vector
product of E and H.
In the far field, only the radiation component exists.
Kraus gives the near field boundary as R=2L^2/lambda (meters), where L is
the antenna physical length.
The electric and magnetic components of the *inductive* field have
different spatial patterns. The electric component is concentrated around
the open end (where voltage is maximum), while the magnetic component is
concentrated around the point of maximum current.
The radiating field has both components spatially co-located.
Hence, the near and far field polar patterns are not the same.
Definitely get a copy of Kraus, and bone up on cylindrical and spherical
coordinate systems.