dBuV= dBm+90 + [20*log (of the square root of system impedance)].
or
For a 50 ohm system:
dBuV= dBm+90 + [20*log (of the square root of 50 ohms)]
dBuV= dBm+90 + [20*log (7.071067812)]
dBuV= dBm+90 + [20*.849485]
dBuV= dBm+90 + 16.9897
dBuV= dBm+106.9897
Noise floor of -174 at 50 ohms would therefore be -67.01 uV.
Free space impedance is approximately equal to 377 ohms (some would
argue 328), and thus the math works out as follows:
For a 377 ohm system:
dBuV= dBm+90 + [20*log (of the square root of 377 ohms)]
dBuV= dBm+90 + [20*log (19.416487)]
dBuV= dBm+90 + [20*1.288170675]
dBuV= dBm+90 + 25.7634135
dBuV= dBm+116.7634135
At 1 Hz the noise floor is -173.977 dBm, the minimum detectable
signal is a function of system bandwidth, and of the noise inflicted
by the instrument making the measurement. This is why we want to use
a preamplifier in front of the instrument to not only lift our
signals out of the noise, and to over come the losses caused by the
low value attenuator, and limiter circuits. TSCM folks commonly run a
3 or 5 dB attenuator, and loose another 2 to 3 dB from the limiter,
and front end connections so my the time your signals hits the first
distorting circuit in the system you have already lost over half your signal.
This is the reason why we punch up the low noise amplifiers on the
front end, and isolate specific chunks for the spectrum with
extremely sharp, and extremely deep filtering. If your spectrum
analyzer hits you with a noise figure of 25 dB, and you always run
with a 5 dB attenuator (to protect the SA) and the cables and
connectors outside the SA kick you for another 6 dB, you are already
36 dB down from where you need to be, and about the only thing you
can do is put a 40 dB LNA as close to the antenna as practical.
If this did annoy you enough then you have to consider if you use a
fast scanning IF bandwidth of 300 kHz you are losing a another 54 dB
of signal in addition to the 36 dB you lost in the above mention for
a total system loss of 90 dB. This 54 dB of signal loss is actually
the amount of noise that switching from a narrow window of 1 Hz to a
wider window of 300 kHz caused you. This means that you are could be
loosing 1,000,000,000 times more signal then you should be loosing
(or compensating for), and even if you are 3 inches form the bug you
might not see it with even $300,000 in equipment.
Here is an exercise... figure out the "distortion" in your system by
first determining the response curves of your antennas or
transducers, then the loss involved in your cables, and then the
attenuation and noise present in your SA or receiver. Remember that
this number is going to drastically change with frequency, draw up
some correction charts, but compensate for all loss and distortion...
don't just document it.
A 50 dB low noise amplifier (NF of less then 3 dB across the
spectrum), and some extremely deep and extremely sharp bandpass
filters will go a long way to get your equipment down into the grass.
Then use the best quality cables and connectors you can find and get
the bandpass filter actually ON the antenna, not on the SA, and then
get the LNA close to the antenna, but far enough back so that you do
not get feedback from the amplifier back into the antenna, then
filter again on the back end of the amplifier (yes, you been TWO
filters) and dumps the signal into your SA. If you feel lucky, and
are extremely good at what you do you can bypass the limiters and
attenuators in your SA, but do so with extremely caution. Kepe your
cables as short as possible, but long enough to get you and your
equipment far enough away from the place or thing that you are trying
to measure so that you are screwing up the measurements with your
body or equipment.
Modern equipment being produced in the last couple of years lets us
get our equipment well down into the grass (noise) so that you can
get down to -160 or -164 dBm with even cheap equipment, and with
spread spectrum analysis equipment we can get at least 50 to 60 dB
well into the noise, and process gains of over 60 and 80 dB are not
uncommon on the more "covert" and wider band digital eavedropping systems.
-jma
At 01:58 PM 5/19/2007, James M. Atkinson wrote:
>Conversion formula for dBm to dBuV
>
>dBuV= dBm+90 + [20*log (of the square root of system impedance)].
>
>dBmV= dBm+30 + [20*log (of the square root of system impedance)].
>
>dBm= dBmV-30 - [20*log (of the square root of system impedance)].
>
>dBm= dBuV-90 - [20*log (of the square root of system impedance)].
>
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Granite Island Group Fax: (978) 546-9467
127 Eastern Avenue #291 Web:
http://www.tscm.com/
Gloucester, MA 01931-8008 E-mail: mailto:jm..._at_tscm.com
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Received on Sat Mar 02 2024 - 00:57:19 CST