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## Conversion of Receiver Sensitivity From Microvolts to dBm

### by James W. Hebert

Voice communication receiver sensitivity is often stated in terms of the radio-frequency voltage level at the input necessary to produce a particular signal-to-noise ratio of the desired signal at the audio-frequency output. Conversion of this voltage level to a power level in decibels referenced to one-milliwatt (dBm) can be useful when analyzing radio circuits. The formula for circuit analysis predicts a certain received power level. Conversion of rated receiver sensitivity in micro-volts to a power level in dBm will help assess the receiver performance for a particular predicted level of received signal. We must also assume a particular resistance in the antenna, R, normally about 50-ohms.

Power (P), voltage (E), and resistance (R) are related by Ohm's Law;

(1) P = E2 / R

If we express power in terms of dB relative to one milliwatt, we get:

(2) dBm = 10 LOG ( E2 / R ) + 30

Separating the first term into components we have

(3) dBm = 10 LOG ( E2 ) + 10 LOG ( R-1 ) + 30

Further simplifying we get

(4) dBm = 20 LOG E - 10 LOG (R) + 30

Here E is in volts. If Eµ is the same voltage expressed in units of micro-volts, then to convert to volts we calculate

(5) E = Eµ X 10-6

Substituting into (4) we get

(6) dBm = 20 LOG (Eµ X 10-6) - 10 LOG (R) + 30

Now simplifying we get

(7) dBm = 20 LOG Eµ - 20 LOG (10-6) - 10 LOG (R) + 30

(8) dBm = 20 LOG Eµ -10 LOG (R) - 90

For the common situation where R=50, this simplifies to

(9) dBm = 20 LOG Eµ - 107

To convert the other way we find

(10) (dBm + 107)/20 = LOG Eµ

(11) Eµ = 10(dBm + 107)/20

DISCLAIMER: This information is believed to be accurate but there is no guarantee. We do our best!

Copyright © 2005 by James W. Hebert. Unauthorized reproduction prohibited!

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Author: James W. Hebert
This article first appeared January 8, 2005.