Audio Engineering

Measurement 39

2.3 Expressing Power as an Audio Level ......................................................................

The reference power is 0.001 W (1 mW). When expressed as a level, this power is called
0 dBm (0 dB referenced to 1 mW).

Thus to express a power level we need two powers—fi rst the measured power W 1 and
second the reference power W 2. This can be written as a power change in dB:

W

W

E

E

R

R

1

2

1

2

2

2

1

2

1

1

^1

1

⎛

⎝

⎜⎜

⎜⎜

⎜⎜

⎜⎜

⎜

⎞

⎠

⎟⎟

⎟⎟

⎟⎟

⎟⎟

⎟⎟

⎛

⎝

⎜⎜

⎜⎜

⎜⎜

⎜⎜

⎜⎜

⎞

⎠

⎟⎟

⎟⎟⎟

⎟⎟

⎟⎟

⎟⎟

⎟

⎛

⎝

⎜⎜

⎜⎜

⎞

⎠

⎟⎟

⎟⎟

⎛

⎝

⎜⎜

⎜⎜

⎞

⎠

⎟⎟

 ⎟⎟

E

E

R

R

1

2

2

2 1

2. (2.10)

This can be written as a power level:

10 1

2

2

2

2

1

log

E

E

R

R

power cha

⎛

⎝

⎜⎜

⎜⎜

⎞

⎠

⎟⎟

⎟⎟

⎛

⎝

⎜⎜

⎜⎜

⎞

⎠

⎟⎟

⎟⎟

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

 nnge in dB (2.11)

o r

20 1 10

2

2

1

log log

E

E

R

R

power change in dB. (2.12)

2.3.1 Special Circumstance

When R 1  R 2 and only then:

Power level in dB

E

E

 20 1

2

log (2.13)

where E 2 is the voltage associated with the reference power.