How to change Vrms to dBm?

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.

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John

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 general it will be 10*log10(Rref/Rload)--you add that to your measured 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

I think it depends on your 'dBm' definition. The usual definition is mW into a 600 ohm load (this is an old telephone standard) and you might want to worry about confusion with the old moving-needle meters that converted V to dBm with that different load (the AC scale on an old Simpson 260 VOM for instance).

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.

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

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|  James E.Thompson, P.E.                           |    mens     |
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