Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013
57
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You can illustrate this rule of thumb with two specific wattage levels for example 1000 W and
500 W. First, convert watts to dBm. Table 4.3 gives the reference point for the definitions of
dBm, dBW, dBV, an dBu. The table shows that dBM uses 0.001 W as the reference point,
which means that it is in the denominator inside the log.
( )
Thus, 1000 W is 60 dBm.
What is 500 W in dBM? The standard reference point for dBm is 0.001 W. This yields.
( *
We see that 500 W is about 57 dBm, confirming that doubling the wattage results in a 3 dB
increase, just as we predicted. We get the same result if we compute the increase in decibels
based on dBW. dBW uses a reference point of 1 W in the denominator.
( )
1000 W is about 30 dBW.
( *
500 W is about 27 dBW. Again, doubling the wattage results in a 3 dB increase, as predicted.
Continuing with Table 4.5, we can show that if we multiply power by 10, we have a 10
dB increase in power.
If we divide the power by 10, we get a 10 dB decrease in power.
( *
For voltage, we use the formula
(
), as shown in Table 4.3. From this we can
show that if we double the voltage, we have a 6 dB increase.
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