HP 54710A User's Reference Manual page 342

Computation of dBm
The vertical units of the FFT functions are dBm, and 0 dBm is defined as a
1 mW signal. The formula for converting a signal of power P into dBm is:
dBm = 10 log   
P

1mW
 
A handier formula, and the one that is used in the oscilloscope, is for
calculating dBm from the peak voltage.


V
dBm = 20 log p


0.316228 V


The bottom term, 0.316228 Volts, is the peak voltage of a 1 mW signal into a
50-Ω resistor. The calculation is:
√  
P×R
V
rms
= =
V
P
0.707107 0.707107
1 mW × 50 Ω
√  
=
0.707107
= 0.316228V
If you are measuring the power of a signal, then terminate the source into
50 Ω in order to get the correct dBm reading. However, if you are measuring
voltage, then you do not need to terminate source impedance into 50 Ω. The
equation above for dBm as a function of peak voltage still applies.
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