The relationship between power density and power spectral density

Hi!

Is there a relationhsip between power density (Watt/m^2) and power
spectral density (dbm/Hz) ?

Thanks

Suterr

<suterr@gmail.com> wrote in message 
news:1126678071.725462.183830@g44g2000cwa.googlegroups.com...
> Hi!
>
> Is there a relationhsip between power density (Watt/m^2) and power
> spectral density (dbm/Hz) ?
>

One could say "not much" and one could say "oh, yes".

Both should be fairly clear from their units.

Take the output of an antenna as an example:

A waveform received from the antenna at some point in space has power 
density (Watt/m^2).  There is no mention of spectral content and the 
assumption may be it is broadband power (entailing a spectral character) or 
that it is narrowband power (with little or no spectral character).

Given the same situation where there is a signal in the broadband sense then 
not only is there a power density (Watt/m^2) but there is also an 
interesting spectral density (dBm/Hz) associated with the power density.

I suppose one could talk about Watt/m^2/Hz just to make the point.
That's because Watts and dBm relate to the same measure but in different 
terms.
/m^2 refers to power density at a point in space.
/Hz refers to the spectral distribution.

Watts/m^2 is a scalar measure over space due to the beam pattern and 
frequency response of the antenna and the input signal - in the example it 
sums over all frequencies.
dBm/Hz is a scalar measure over frequency - in the example above it varies 
over space due the beam pattern and frequency response of the antenna.
Watts/m^2/Hz is a scalar measure over space and frequency - in the example 
above it can be expressed as a weighted spectral plot at each point in 
space.

Fred 

Not without knowing something about the physical problem. For example,
if you know PSD and you know the area over which the power was
measured, then you could compute power density by integrating PSD over
all frequency and dividing
by the area. 

--RY

suterr@gmail.com wrote:
> Hi!
>
> Is there a relationhsip between power density (Watt/m^2) and power
> spectral density (dbm/Hz) ?

It is no simple connection, you need to bring in some
physics. The radio antenna "drains" some electromagnetic
energy from the atmosphere, and this energy can be expressed
in terms of W/m^2. Through the various physical processes
that happen in the amplifier, this energy is converted
to some electrical signal that has a PSD that can be
expressed in terms of dbm/Hz.

Very general, but that's about it. 

Rune