[Elecraft] XG1

[Bob-AG5Q]

> A comment in an earlier email wondered where the -107dBm came from. From
an
> old handbook, I pulled the following:
>
> dBm = 10 log {20*(Vrms)^2}
>
>  where "log" is base 10
>
> If you plug in the 1 microvolt into that equation and solve it, you cill
> come up with -107dBm. Please don't ask me to derive the equation <g>. Too
> many years have passed....
>
> 73
> Ken Wagner
> K3IU
>

dBm means the power is measured relative to one milliwatt.  A one milliwatt
signal is zero dBm and a 1 watt signal would be +30 dBm.

If a signal has a power level of 1mw and the load is 50 ohms, Vrms=0.2236V.
In the general case, for any load resistance, Vrms = SQRT(power*resistance)

The factor of 20 accounts for the load resistance of 50 ohms. It corresponds
to  (1/50)*1000 = 0.020*1000
The quantity inside the curly brackets of Ken's equation is the power in
milliwatts, hence the factor of 1000.

Example:

A 1 uv  rms signal into 50 ohms has a power level of:

Power = 10*log(Vrms*Vrms/resistance) = 10* log( ( 1e-6) * (1e-6)/50 )
  -137 dB relative to one watt or :

( -137 + 30 ) = -107 dB relative to one milliwatt.  That is, it's 107 dB
weaker than a 1 milliwatt signal.

73/ Bob - AG5Q