Converting mW to dB
Date: 06/14/2001 at 21:45:44 From: Jeff Carson Subject: Conversion of mW to dB I this equation during a radio receiver discussion. 4x10-12mW = -114dBm How does it equate? What is the math that performs this conversion?
Date: 06/15/2001 at 12:04:22 From: Doctor Peterson Subject: Re: Conversion of mW to dB Hi, Jeff. According to my favorite source on units, How Many? A Dictionary of Units of Measurement, by Russ Rowlett: http://www.unc.edu/~rowlett/units/ dB m, dB W logarithmic units of power used in electronics. These units measure power in decibels above the reference level of 1 milliwatt in the case of dB m and 1 watt in the case of dB W. A power of n watts equals 10 log n dB W; conversely, a power of p dB W equals 10^(p/10) watts. The same formulas link dB m to milliwatts. An increase of 10 dB m or 10 dB W represents a 10-fold increase in power. Since 1 watt = 1000 milliwatts, 0 dB W = 30 dB m. (Look up decibel and bel there, too.) Another source I found, a column by Ron Hranac in the April 2000 issue of Communications Technology: Broadband DBmV: Power in Terms of Voltage http://www.cabletoday.com/ct2/archives/0400/0400col1.htm says that dBm is read as "decimal milliwatt," and gives the same formula: dBm = 10log(P/1 mW), where P is a power level in milliwatts Note that a bel is the base-ten logarithm of any ratio; in this case the ratio is that of the given power to a 1 mW output. A decibel is 1/10 of a bel, accounting for the factor of ten. So in your example, with P = 4x10^-12 mW, we get 10 log(4x10^-12) = 10 (log(4) - 12) = -113.98 which agrees with what you read, rounded appropriately. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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