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Sec. 2–1 Properties of Signals and Noise 43
Because the signal power is 8s 2 2
(t)9/R = V and the noise power is 8n 2 rms signal /R
(t)9/R =
2
/R, this definition is equivalent to
V rms noise
(S>N) dB = 20 log a V rms signal
V rms noise
b
(2–21)
The decibel measure may also be used to indicate absolute levels of power with respect
to some reference level.
DEFINITION.
The decibel power level with respect to 1 mW is
actual power level (watts)
dBm = 10 log a
10 -3 b
= 30 + 10 log [actual power level (watts)]
(2–22)
where the “m” in the dBm denotes a milliwatt reference. Laboratory RF signal generators
are usually calibrated in terms of dBm.
Other decibel measures of absolute power levels are also used. When a 1-W reference
level is used, the decibel level is denoted dBW; when a 1-kW reference level is used, the decibel
level is denoted dBk. For example, a power of 5 W could be specified as 36.99 dBm, 6.99
dBW, or 23.0 dBk. The telephone industry uses a decibel measure with a “reference noise”
level of 1 picowatt (10 12 W) [Jordan, 1985]. This decibel measure is denoted dBrn. A level of
0 dBrn corresponds to -90 dBm. The cable television (CATV) industry uses a 1-millivolt
RMS level across a 75-Æ load as a reference. This decibel measure is denoted dBmV, and it is
defined as
dBmV = 20 log a V rms
(2–23)
10 -3 b
where 0 dBmV corresponds to -48.75 dBm.
It should be emphasized that the general expression for evaluating power is given
by Eq. (2–7). That is, Eq. (2–7) can be used to evaluate the average power for any type of
waveshape and load condition, whereas Eq. (2–12) is useful only for resistive loads. In other
books, especially in the power area, equations are given that are valid only for sinusoidal
waveshapes.
Phasors
Sinusoidal test signals occur so often in electrical engineering problems that a shorthand
notation called phasor notation is often used.
DEFINITION. A complex number c is said to be a phasor if it is used to represent a
sinusoidal waveform. That is,
w(t) = |c| cos[v 0 t + l c] = Re{ce jv 0t }
(2–24)