Power and Voltage ratios in DECIBELS
The decibel notation is basically a method of expressing power ratio,
the number of decibels (N dB) being given by

where P 1 and P2 are the two power levels under consideration.
On the assumption of constant impedance the notation is also used for voltage ratio, giving

where V1 and V2 are the two voltage levels.
In the above expressions the denominator (P1 or V1) is the reference level,
so that a power or voltage may be expressed as "NdB with respect to X watts or volts"
This is often contracted to dB μV (to mean decibels with respect to 1 μV).
dBm (with respect to 1 mW),
dB W (with respect to 1 watt), etc.

Table I
Ratio Down Ratio Up
Voltage Power Decibels Voltage Power
1.0 1.0 0 1.0 1.0
.9886 .9772 .1 1.012 1.023
.9661 .9333 .3 1.035 1.072
.9550 .9120 .4 1.047 1.096
.9441 .8913 .5 1.059 1.122
.9333 .8710 .6 1.072 1.148
.9226 .8511 .7 1.084 1.175
.9120 .8318 .8 1.096 1.202
.9016 .8128 .9 1.109 1.230
.8913 .7943 1.0 1.122 1.259
.8710 .7586 1.2 1.148 1.318
.8511 .7244 1.4 1.175 1.380
.8318 .6918 1.6 1.202 1.445
.8128 .6607 1.8 1.230 1.514
.7943 .6310 2.0 1.259 1.585
.7762 .6026 2.2 1.288 1.660
.7586 .5754 2.4 1.318 1.738
.7413 .5495 2.6 1.349 1.820
.7244 .5248 2.8 1.380 1.905
.7079 .5012 3.0 1.413 1.995
.6683 .4467 3.5 1.496 2.239
.6310 .3981 4.0 1.585 2.512
.5957 .3548 4.5 1.679 2.818
.5623 .3162 5.0 1.778 3.162
.5309 .2818 5.5 1.884 3.548
.5012 .2512 6 1.995 3.981
.4467 .1995 7 2.239 5.012
.3981 .1585 8 2.515 6.310
.3548 .1259 9 2.818 7.943
.3162 .1 10 3.162 10.00
.2818 .07943 11 3.548 12.59
.2512 .06310 12 3.981 15.85
.2239 .05012 13 4.467 19.95
.1995 .03981 14 5.012 25.12
.1778 .03162 15 5.623 31.62
.1585 .02512 16 6.310 39.81
.1413 .01995 17 7.079 50.12
.1259 .01585 18 7.943 63.10
.1122 .01259 19 8.913 79.43
.1000 .01000 20 10.000 100.00





Where the numerator of the ratio is less than the denominator N becomes negative;
this may be expressed as "-N dB" or "N dB down",
positive values on N being regarded as "N dB up" by analogy.

Tables I and II facilitate rapid conversion between decibels and voltage or power ratios.
To convert decibels to voltage or power ratios use Table I;
to convert voltage or power ratio to decibels use Table II.
Table I covers dB ratios up to 20dB only.
For values of N greater than 20 proceed as follows.
Let X be the whole number of times that 20 can be divided into N,
to leave a remainder that falls within the range of the table.
Look up the voltage or power ratio corrseponding to this remainder on the appropriate side of the table.
For voltage ratio "up" multiply by 10 x
For power ratio "down" divide by 10 x
For power ratio multiply or divide, as appropriate, by 10 2x

Table II
Voltage
or
Power
ratio
dB
Voltage
dB
Power
1.0 0.0 0.0
1.1 0.83 0.41
1.2 1.58 0.79
1.3 2.28 1.14
1.4 2.92 1.46
1.5 3.52 1.76
1.75 4.86 2.43
2.0 6.02 3.01
2.5 7.96 3.98
3.0 9.54 4.77
3.5 10.88 5.44
4.0 12.04 6.02
4.5 13.06 6.53
5.0 13.98 6.94
5.5 14.81 7.40
6.0 15.56 7.78
6.5 16.26 8.13
7.0 16.90 8.45
7.5 17.5 8.75
8.0 18.06 9.03
8.5 18.58 9.29
9.0 19.08 9.54
9.25 19.32 9.16
9.5 19.55 9.27
9.6 19.65 9.32
9.7 19.74 9.87
9.8 19.83 9.91
9.9 19.91 9.95
10.0 20.0 10.0





Table II covers voltage and power ratios from 1 to 10.
For power ratios outside this range move the decimal point to the left or right
to bring the figure within the range,
then add 10 dB for each position that it is moved to the left,
or subtract 10 dB for each position that it is moved to the right.
For voltage ratios use the same procedure,
but add or subtract 20 dB instead of 10 dB.
Ratios close to 1 and to 10 are given in smaller increments
than the rest of the table for convenience of conversion
when errors are to be expressed in decibels.







Click to enlarge

Reference: Marconi Electronics Instrumentation Catalogue 79/80