# dB Tables

Just some lookup tables. More info on Decibel on Wikipedia.

## dB

**Relative** amplitude and power; dB above or below '1';

Ampl | Power | dB |
---|---|---|

10.0 | 100 | 20 |

7.94 | 63.1 | 18 |

5.62 | 31.6 | 15 |

3.98 | 15.9 | 12 |

3.16 | 10.0 | 10 |

2.82 | 7.94 | 9 |

2.51 | 6.31 | 8 |

2.24 | 5.01 | 7 |

2.00 | 3.98 | 6 |

1.78 | 3.16 | 5 |

1.58 | 2.51 | 4 |

1.41 | 2.00 | 3 |

1.26 | 1.58 | 2 |

1.12 | 1.26 | 1 |

1.00 | 1.00 | 0 |

0.89 | 0.79 | -1 |

0.79 | 0.63 | -2 |

0.71 | 0.50 | -3 |

0.63 | 0.40 | -4 |

0.56 | 0.32 | -5 |

0.50 | 0.25 | -6 |

0.45 | 0.20 | -7 |

0.40 | 0.16 | -8 |

0.35 | 0.13 | -9 |

0.32 | 0.10 | -10 |

0.25 | 0.06 | -12 |

0.18 | 0.03 | -15 |

0.13 | 0.02 | -18 |

0.10 | 0.01 | -20 |

The numbers in the above table are **relative** numbers, not volts or
watts;

If you reduce the volume by 3 dB you do get about 71% of the previous
amplitude and 50% of the previous power.

## dBs and camera stops

The relative amplitudes of the 3 dB steps (-6, -3, 0, ...) almost but
not quite correspond with camera
f-numbers;

F-numbers are (rounded) multiples of √2. 3 dB steps are close
approximations thereof;

Stop | Ratio | dB |
---|---|---|

22 | 16 √2 | 27.09 |

16 | 16 | 24.08 |

11 | 8 √2 | 21.07 |

8 | 8 | 18.06 |

5.6 | 4 √2 | 15.05 |

4 | 4 | 12.04 |

2.8 | 2 √2 | 9.03 |

2 | 2 | 6.02 |

1.4 | √2 | 3.01 |

1 | 1 | 0 |

0.7 | 1/√2 | ‒3.01 |

0.5 | 1/2 | ‒6.02 |

The difference between the two (3 vs 3.01 dB) is about 0.12%.

## dBm

The table below is based on 0 dB is 1 mW in 600 Ω (744.59667 mV).

dBm | mV |
---|---|

0 | 775 |

-1 | 690 |

-2 | 615 |

-3 | 548 |

-4 | 489 |

-5 | 436 |

-6 | 388 |

-7 | 346 |

-8 | 308 |

-9 | 275 |

-10 | 245 |

-11 | 218 |

-12 | 195 |

-13 | 173 |

-14 | 155 |

-15 | 138 |

-18 | 97.5 |

-20 | 77.5 |

The telephone audio signal level is -9 dBm or 275 mV.
DTMF
tones are -7 dBm or 346 mV.

Dial- and other tones are different in each country. Often used values are
-12 dBm for dial tones and -20 dBm for busy- and ring-back tones.

## dB below clip level

The peek level in this table corresponds with 32767 (the largest possible value of a 16‑bit signed integer).

Peek dB | Max val |
---|---|

0 | 32767 |

-1 | 29203 |

-2 | 26027 |

-3 | 23197 |

-4 | 20674 |

-5 | 18426 |

-6 | 16422 |

-7 | 14636 |

-8 | 13044 |

-9 | 11626 |

-10 | 10361 |

-11 | 9234 |

-12 | 8230 |

-13 | 7335 |

-14 | 6537 |

-15 | 5826 |

-18 | 4125 |

-20 | 3276 |

The dB values in the above table are accurate for a square wave only.
For a pure **sine wave** the RMS dB values are 3 dB lower
(3.01 dB to be exact).

Sine RMS dB | Max val |
---|---|

-3 | 32767 |

-4 | 29238 |

-5 | 26058 |

-6 | 23224 |

-7 | 20699 |

-8 | 18448 |

-9 | 16441 |

-10 | 14653 |

-11 | 13060 |

-12 | 11639 |

-13 | 10374 |

-14 | 9245 |

-15 | 8240 |

-16 | 7344 |

-17 | 6545 |

-18 | 5833 |

-19 | 5199 |

-20 | 4633 |

## dBm and bits

On the Wikipedia page
Digital
milliwatt is a description of 1 kHz 0 dBm
Alaw and µlaw test
signals. Below a translation to 16‑bit signed integers;

Of course, the actual analogue signal isn't this 'clunky'. Below a
more realistic signal;

It's supposed to be a pure sine wave, but does in fact have some
3^{rd} harmonic distortion.

Note that the 8‑bit values below are hex and the 16‑bit values decimal;

### Alaw

Degr | 8-bit | 16-bit |
---|---|---|

202.5 | 34 | -8960 |

247.5 | 21 | -20992 |

292.5 | 21 | -20992 |

337.5 | 34 | -8960 |

22.5 | b4 | 8960 |

67.5 | a1 | 20992 |

112.5 | a1 | 20992 |

157.5 | b4 | 8960 |

Note: The highest value which a Alaw to
16‑bit conversion can produce is 32256 which is 0.14 dB (peek)
below 32767.

For a 500 Hz sine of the same amplitude the 0° to 180° values are;

Degr | 16-bit |
---|---|

0 | 8 |

22.5 | 8960 |

45 | 16128 |

67.5 | 20992 |

90 | 23040 |

112.5 | 20992 |

135 | 16128 |

157.5 | 8960 |

180 | 8 |

Note: There is no '0' in Alaw. It's either 8 or -8.

Note: This signal is 0.02 dB (RMS) stronger than the 1 kHz signal.

### μlaw

Degr | 8-bit | 16-bit |
---|---|---|

202.5 | 1e | -8828 |

247.5 | 0b | -20860 |

292.5 | 0b | -20860 |

337.5 | 1e | -8828 |

22.5 | 9e | 8828 |

67.5 | 8b | 20860 |

112.5 | 8b | 20860 |

157.5 | 9e | 8828 |

Note: The highest value which a μlaw to
16‑bit conversion can produce is 32124 which is 0.17 dB (peek)
below 32767.

For a 500 Hz sine of the same amplitude the 0° to 180° values are;

Degr | 16-bit |
---|---|

0 | 0 |

22.5 | 8828 |

45 | 15996 |

67.5 | 20860 |

90 | 22908 |

112.5 | 20860 |

135 | 15996 |

157.5 | 8828 |

180 | 0 |

Note: This signal is 0.02 dB (RMS) stronger than the 1 kHz
signal.

Note: Some documents may mention a 14‑bit value of 5768 for 90° and
5329 for 67.5°. These correspond to 16‑bit values of 23072 and 21316.
However, if you convert these to µlaw and back you end up with 22908 and
20860.

### dB Conversion table

For Alaw the 90° value is 23040, for μlaw 22908. These are 3.06 resp
3.11 dB below 32767.

So the **peek** level is about 3 dB below clip level. Therefore the
RMS value of a **sine** wave is about 6 dB below clip level.

Note: As long as the signal doesn't clip, it's the RMS value that counts!

Below a litte conversion table;

dB below clip level | dBm | |
---|---|---|

Peek | RMS | |

0 | -3 | 3 |

-3 | -6 | 0 |

-6 | -9 | -3 |

-9 | -12 | -6 |

-12 | -15 | -9 |

-15 | -18 | -12 |

Note that the RMS values in this table apply to pure **sinusoidal**
signals!

You can check the volume of a file with 'sox [File Format] File_Name -n stats';

~$ sox -t raw -r 8000 -e signed-integer -b 16 -c 1 File_Name.sln -n stats DC offset 0.000010 Min level -0.462158 Max level 0.505310Pk lev dB -5.93RMS lev dB -27.92RMS Pk dB -14.87RMS Tr dB -90.69 Crest factor 12.58 Flat factor 0.00 Pk count 2 Bit-depth 15/16 Num samples 2.86M Length s 357.440 Scale max 1.000000 Window s 0.050

Note that the '-n stats' bit goes **after** the file name.