The dBm unit is decibels relative to 1 milliwatt. To obtain a dBm value from a value of power in milliwatts, use the following equation:

(A.1)

To obtain power in watts from a power level specified in dBm, use the following equation:

(A.2)

The dBW unit is decibels relative to 1 watt. To obtain a dBW value from a value of power in watts, use the following equation:

(A.3)

Note that (A.1), (A.2), and (A.3) are independent of characteristic impedance ( Z ₀), hence, they will work for any impedance.

If P _w, is broken down into its constituents, then

(A.4)

Placing (A.4) into (A.2), we arrive at the relationship between voltage and dBm. Note that it is dependent on Z ₀ :

(A.5)

Often, for cable TV applications an impedance-dependent unit called V _dBmV is used. It is defined as

(A.6)

The argument of the log ₁₀( ) function is actually a voltage ratio, but the decibel concept was originally defined for power. Because power is defined as V ²/ R, the V ² term gives rise to the logarithmic multiplier of 20: 10 log( X ²) = 20 log( X).

Also,

(A.7)

Substituting (A.5) into (A.6), the following relationship is found:

(A.8)

For a 50- ? device or circuit,

(A.9)

For a 75- ? device or circuit,

(A.10)

Tables A.1 and A.2 are a means to demonstrate the relationships of the various power and voltage...