Audio Engineering

40 Chapter 2

2.4 Conventional Practice ..............................................................................................

When calculating power level in dBm, we commonly make E 2  0.775 V and R 2  600 Ω.
Note thatE 2 may be any voltage and R 2 any resistance so long as together they represent
0.001 W.

2.4.1 Levels in dB

1. 
   

   The term “ level ” is always used for a power expressed in decibels.

   
   


2. 
   

   10 1 10

   
   

2

2

2

1

2

log log

E

E

W

W



when R 1  R 2

210 20

10

1

2

1

2

1

2





log log

log.

E

E

E

E

W

W

3. Power defi nitions:

Apparent power  E I or E^2 ⁄ Z ,
The average real or absorbed power is (E^2 ⁄ Z )cosθ ,
The reactive power is ( E^2 ⁄ Z )sin θ ,
Power factor  cos θ.

4. The term “ gain ” or “ loss ” always means the power gain or power loss at the
   system’s output due to the device under test.

2.4.2 Practical Variations of the dBm Equations

When the reference is the audio standard, that is, 0.77459 V and 600 Ω , then

dB level to a reference

E

E

R

R

 10 1

2

2

2

2

1

log

⎛

⎝

⎜⎜

⎜⎜

⎞

⎠

⎟⎟

⎟⎟

⎛

⎝

⎜⎜

⎜⎜

⎞

⎠

⎟⎟

⎟⎟⎟

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

(2.14)

where E 2  0.77459 ... V, R 2  600 Ω. Then

R

R

2

1

 1000