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

(A.1)

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

(A.2)

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

(A.3)

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

If P _W is broken down to its constituents, then

(A.4)

Placing (A.4) into (A.3) arrives at the relationship between voltage and dBm. Note that it is dependent on impedance ( Z ₀):

(A.5)

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

(A.6)

Note the "20" multiplier. This is due to the fact that it is a voltage ratio and that the decibel concept has been originally defined for power. Since power is defined as V ² /R, the V ² term gives rise to the logarithmic "20" multiplier [10 log( X ²) = 20 log( X)].

(A.7)

Substituting (A.5) into (A.6) yields the following relationship:

(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 values. Note that the relationships between power...