continuousWave --> Radio-->dBm to Microvolt Conversion

Conversion of Receiver Sensitivity
from micro-volts to dBm

by James W. Hebert

Conversion of signal levels from dBm measurement to voltage measurement is demonstrated.

Receiver Sensitivity Measurement

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 in micro-volts, then

(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 if voltage is in microvolts and resistance is 50-Ohm, 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!

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

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

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