Audio Engineering

Measurement

Don Davis and Eugene Patronis

2.1 Concepts Underlying the Decibel and its Use in Sound Systems ...........................

Most system measurements of level start with a voltage amplitude. Relative level changes
at a given point can be observed on a voltmeter scale when it is realized that

10 1 10

2

22

1

2

log log

E

E

P

P

 (2.1)

which is only true if both values are measured at an identical point in their circuit. A common
usage has been to remove the exponent from the ratio and apply it to the multiplier.

210 1 20

2

1

2

    log log

E

E

E

E

(2.2)

Bear in mind that the decibel is always and only based on a power ratio. Any other kind
of ratio (i.e., voltage, current, or sound pressure) must fi rst be turned into a power ratio by
squaring and then converted into a power level in decibels.

2.1.1 Converting Voltage Ratios to Power Ratios

Many audio technicians are confused by the fact that doubling the voltage results in
a 6-dB increase while doubling the power only results in a 3-dB increase. Figure 2.1
demonstrates what happens if we simultaneously check both the voltage and the power in
a circuit where we double the voltage. Note that for a doubling of the voltage, the power
increases four times.

CHAPTER 2