Logarithms
Logarithms are used to simplify math. Multiplication and division can be accomplished through addition and subtraction.
log(1) = 0
log(number greater than 1) = positive
log(number less than 1) = negative
log(A•B) = log(A) + log(B)
log(A/B) = log(A) - log(B)
log(A)n = n•log(A)
Power
ratio expressed in dB
dB stands for decibel (1/10 of a Bel). The dB is a way of expressing the ratio between two power levels logarithmically.
P(dB) = Numerical power ratio expressed in dB
P1 = Power 1 (input)
P2 = Power 2 (output)
Decibels can be added and subtracted to determine the total gain of a system.
Pout = 10dBm + 5dB - 10dB + 20dB = 25dBm
|
P(dB) = 10 log10 (P2/P1) |
Ratio |
V(dB) = 20 log10 (V2/V1) |
|
120 |
1.00E+12 |
240 |
|
90 |
1.00E+09 |
180 |
|
60 |
1.00E+06 |
120 |
|
50 |
1.00E+05 |
100 |
|
40 |
1.00E+04 |
80 |
|
30 |
1000 |
60 |
|
20 |
100 |
40 |
|
10 |
10 |
20 |
|
9.5 |
9 |
19.1 |
|
9.0 |
8 |
18.1 |
|
8.5 |
7 |
16.9 |
|
7.8 |
6 |
15.6 |
|
7.0 |
5 |
14.0 |
|
6.0 |
4 |
12.0 |
|
4.8 |
3 |
9.5 |
|
3.0 |
2 |
6.0 |
|
0 |
1 |
0 |
|
-0.5 |
0.9 |
-0.9 |
|
-1.0 |
0.8 |
-1.9 |
|
-1.5 |
0.7 |
-3.1 |
|
-2.2 |
0.6 |
-4.4 |
|
-3.0 |
0.5 |
-6.0 |
|
-4.0 |
0.4 |
-8.0 |
|
-5.2 |
0.3 |
-10.5 |
|
-7.0 |
0.2 |
-14.0 |
|
-10 |
0.1 |
-20 |
|
-20 |
0.01 |
-40 |
|
-30 |
0.001 |
-60 |
|
-40 |
1.00E-04 |
-80 |
|
-50 |
1.00E-05 |
-100 |
|
-60 |
1.00E-06 |
-120 |
|
-90 |
1.00E-09 |
-180 |
|
-120 |
1.00E-12 |
-240 |
Power
expressed in dBm
Most of the time, power is expressed in dBm in RF applications. dBm is power relative to one milliwatt.
Voltage
ratio expressed in dB
As long as you use a consistent resistance you can express voltage as a logarithmic ratio as follows:
and 
When R1 = R2 the second term goes to 0.
V(dB) = Numerical voltage ratio expressed in dB
V1 = Voltage 1 (input)
V2 = Voltage 2 (output)
end