# How to change Vrms to dBm?

Discussion in 'Electronic Design' started by [email protected], Mar 18, 2008.

1. ### Guest

Hello,

I have a power spectra in dB relative to 1Vrms / sqrt(Hz) and I want
to change units to dBm (dB power relative to 1mW). Signal was measured
at 1 kOhm load. How to change this units?

E.C.

2. ### GPGGuest

http://www.sengpielaudio.com/calculator-volt.htm

3. ### John O'FlahertyGuest

To convert 1 Vrms / sqrt(Hz) to power, you need to specify bandwidth.
If you just want power spectral density, that's in W / Hz. The figure
1 Vrms / sqrt(Hz) at 1000 ohms is a PSD of 1 mW / Hz, or 0 dbm / Hz
(by (E/sqrt(Hz))^2 / R).
If your spectrum has a point specified at +10 dB relative to 1 Vrms /
sqrt(Hz) @ 1Kohm, then at that point it should have +10 dBm / Hz, with
the same 1 Kohm impedance, since dBs represent a power ratio.
If you want actual power, and if the spectrum is flat, you can
multiply the PSD by the bandwidth, e.g., +10 dBm / Hz is 10 mW / Hz.
If BW is 1 kHz, power is 10 W, or +40 dBm.

4. ### Tom BruhnsGuest

John O' gave you a very nice concise answer with everything you need,
assuming you have only the spectrum to work with. If you have access
to the analyzer and can re-run the measurement, you should be able to
put the analyzer into a mode where it displays dBm directly, though
perhaps not at 1kohm impedance. An impedance change can be accounted
for through a constant dB offset: for example, since P=V^2/R,
doubling the resistance halves the power, which is nominally -3dB. In
dBm at the assumed Rref load (commonly 600 ohms for audio, or 50 or 75
ohms for RF; settable to an arbitrary "user" value in some analyzers
that then do the math for you).

In general, if you are measuring a broadband signal, either a band
power or a power spectral density measurement is appropriate. If you
are measuring one or more discrete frequencies--carriers, tones,
sidebands resulting from single-tone modulation--it's better to use a
straight spectral measurement.

Cheers,
Tom

5. ### Robert BaerGuest

Depends on the impedance and standard.
In audio there two standards: Western Electric which i think was 500
ohms, and modern audio which i think is 600 ohms; if i am wrong,then
switch the numbers.
In RF, there are nominally two standards: 50 ohms and 75 ohms.
If you did your work at a different impedance level (say 93 or 110
ohms) then use that.

6. ### Jim ThompsonGuest

I have a little Windows utility that calculates dBm from VPP and Zo,
and vice versa... written by oldest son Aaron.

If you like a copy drop me an E-mail.

...Jim Thompson  