Everything You Ever Wanted to Know about dB:

                Cynthia Furse      University of Utah

               

1)       Definition

 

Anything in dB = 10 * log10 (Anything in linear)

Voltage in dB = 10 * log10 (Voltage in Volts)

Power in dB = 10 * log10 (Power in Watts)

 

2) Relationship between Power and Voltage (Is it “10” or “20” ?)

 

Since Power = V2 / R

 

        Power in dB = 10 * log10 (Power in Watts)

                                 =10 * log10 (V2 / R)

         = 20 * log10 (Voltage / sqrt (R ) )

 

3) Other Flavors of dB:   dBW, dBm, dBμ

               

        Power (dB or dBW) = 10 * log10 (Power in Watts)

Power (dBm) = 10 * log10 (Power in milli (m)-Watts)

Power (dBμm) = 10 * log10 (Power in micro (μ)-Watts)

 

4) And dBd (for antennas)

 

dBd is used to represent GAIN (a ratio) relative to a dipole antenna:

Power (in maximum direction) of a dipole antenna = Pdip

Power (in maximum direction) of some other antenna = Pant

Gain of that antenna relative to a dipole = Pant / Pdip

 

Gain (dBd) = 10 * log10 (Pant / Pdip)

 

5) Common dB factors

 

                Linear Function                    dB Function

                1                                                              0 dB

* 2                                                           + 3 dB

                /   2                                                          - 3 dB

                * 10                                                         + 10 dB

                * 100                                                       + 20 dB

                / 10                                                          - 10 dB

                / 100                                                        - 20 dB

 

Example:

                1 Watt                                                    0 dB  

                2 Watt                                                    0 + 3 dB = 3 dB

                20 Watt                                  = 3 dB + 10 = 13 dB

 

6) dB Algebra

 

                PRX (linear) = PTX (linear) * Gain (linear)  / Loss (linear)

                PRX (dB) = PTX (dB) + Gain (dB) – Loss (dB)

                PRX (dBm) = PTX (dBm) + Gain (dB) – Loss (dB)

 

What ?!?  Why is there only one dBm on the right hand side of the equation?  Note that Gain and Loss factors are ratios, not powers.  The “flavor” of dB is determined by the power term, not the other ratios in the equation.