Handbook for Sound Engineers

Fundamentals of Audio and Acoustics 25

unit. Relative levels are useful for live work. Absolute

levels are useful for equipment specifications and cali-

bration. Fig. 2-4 lists some references used for deter-

mining absolute levels.

The decibel was originally used in imped-

ance-matched interfaces and always with a power refer-

ence. Power requires knowledge of the resistance that a

voltage is developed across. If the resistance value is

fixed, changes in applied voltage can be expressed in

dB, since the power developed will be directly propor-

tional to the applied voltage. In modern sound systems,

few device interfaces are impedance matched. They are

actually mismatched to optimize the voltage transfer

between components. While the same impedance does

not exist at each device interface, the same impedance

condition may. If a minimum 1:10 ratio exists between

the output impedance and input impedance, then the

voltage transfer is essentially independent of the actual

output or input impedance values. Such an interface is

termed constant voltage, and the signal source is said to

be operating open circuit or un-terminated. In constant

voltage interfaces, open circuit conditions are assumed

when using the decibel. This means that the level

change at the output of the system is caused by

changing the voltage somewhere in the processing chain

and is dependent on the voltage change only, not the

resistance that it is developed across or the power

transfer. Since open-circuit conditions exist almost

universally in modern analog systems, the practice of

using the decibel with a voltage reference is widespread

and well-accepted.

One of the major utilities of the decibel is that it

provides a common denominator when considering

level changes that occur due to voltage changes at

various points in the signal chain. By using the decibel,

changes in sound level at a listener position can be

determined from changes in the output voltage of any

device ahead of the loudspeaker. For instance, a

doubling of the microphone output voltage produces a

6 dB increase in output level from the microphone,

mixer, signal processor, power amplifier, and ultimately

the sound level at the listener. This relationship assumes

linear operating conditions in each device. The 6 dB

increase in level from the microphone could be caused

by the talker speaking 6 dB louder or by simply

reducing the miking distance by one-half (a 2:1 distance

ratio). The level controls on audio devices are normally

calibrated in relative dB. Moving a fader by 6 dB causes

the output voltage of the device (and system) to increase

by a factor of 2 and the output power from the device

(and system) to be increased by a factor of four.

Absolute levels are useful for rating audio equip-

ment. A power amplifier that can produce 100 watts of

continuous power is rated at

(2-2)

Subjective Change Voltage,

Distance,

Pressure

Ratio

% of

Original

PowerRatio dB

Change

20log 10log

Barely perceptible 1.12:1 89 1.26:1 1 dB

1.26: 179 1.58:12 dB

Noticeable to most 1.41:1 71 2:1 3 dB

1.58: 163 2.51:14 dB

1.78: 156 3.16:15 dB

Goal for system

changes

2:1 50 4:1 6 dB

2.24: 145 5 :17 dB

2.51: 140 6.3:18 dB

2.8: 136 8 :19 dB

Twice as loud or

soft

3.16:1 32 10:1 10 dB

10 : 110 100 :1 20 dB
31.6:1 3 1000 :1 30 dB
Limits of audibility 100:1 1 10,000:1 40 dB
316 : 1 0.3 100,000:1 50 dB
1000 : 1 0.1 1,000,000:1 60 dB
Figure 2-3. Some important decibel changes and the ratios
of power, voltage, pressure, and distance that produce
them. Courtesy Syn-Aud-Con.

Electrical Power

dBW 1 Watt

dBm 0.001 Watt

Acoustical Power

dB-PWL or Lw 10 ^12 Wa t t

Electrical Voltage

dBV 1 Volt

dBu 0.775 Volts

Acoustical Pressure

dB SPL or Lp 0.00002 Pascals

Figure 2-4. Some common decibel references used by the

audio industry.

Lout= 10 logW

= 10 log 100

=20 dBW