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.

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Thus, 1000 W is 60 dBm.

What is 500 W in dBM? The standard reference point for dBm is 0.001 W. This yields.

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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.

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1000 W is about 30 dBW.

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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.

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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.