# Power level

In electrical engineering, power levels indicate the electrical power in logarithmic form in order to be able to easily handle both very large and very small power specifications.

The power level is an absolute value that is given in decibels and refers to a defined power, typically 1 milliwatt (decibel milliwatt: dBm ), at high power also to 1 watt (decibel watt: dBW ).

## definition

The power level is often identified with the letters L P ( L = English level , P = English power ) and specified as a decibel value.

dB ( decibel ) is the unit of the power level L P , which describes the ratio of a power P compared to a reference power P 0 .

${\ displaystyle L_ {P} = 10 \, \ lg \ left ({\ frac {P} {P_ {0}}} \ right) \ operatorname {dB}}$

It is

${\ displaystyle P}$ the performance under consideration, the magnitude under consideration
${\ displaystyle P_ {0}}$ the reference power, reference value (reference)
${\ displaystyle \ lg}$ the logarithm to base 10

If the reference value is 1 mW (milliwatt), then the power level is given in the unit dBm .

The power levels in data transmission and on telephone lines are defined in V.2 of the V recommendations of the ITU-T standards (the V recommendations of the ITU relate to data transmission in telephone networks and contain general definitions, interface and modem specifications, broadband modems, the error display and data compression as well as the transmission quality).

## dB

dB ( decibel ) is the unit of the power level L P , which describes the ratio of a power P 1 in comparison to another power P 2 .

${\ displaystyle L_ {P} {(\ operatorname {dB})} = 10 \ log _ {10} \ left ({\ frac {P_ {1}} {P_ {2}}} \ right)}$
P 1 / P 2 dB description
0.001 −30 dB Weakening
0.010 −20 dB
0.100 −10 dB
1 000 0 dB 1: 1 transmission
10 000 10 dB Reinforcement
100 000 20 dB
1000 000 30 dB

In power measurement, a decibel (dB) is a unit for the logarithmic ratio of two power levels and thus a quantity in the dimension number for a power ratio . When using fixed reference services such as B. P 0 = 1 mW = 0.001 watts results in a size of the dimension number for a power , for which the dB is marked with an appendage m or W.

## dBm

dBm ( decibel milliwatt ) is the unit of the power level L P , which describes the ratio of a power P compared to the reference power of 1 mW ( milliwatt ).

${\ displaystyle L_ {P} {(\ operatorname {dBm})} = 10 \ log _ {10} \ left ({\ frac {P} {1 \, \ operatorname {mW}}} \ right)}$

and vice versa, when performance is sought:

${\ displaystyle P {(\ operatorname {mW})} = 10 ^ {^ {\ left ({\ frac {L_ {P} {(\ operatorname {dBm})}} {10}} \ right)}} \ cdot 1 \, \ operatorname {mW}}$

1 mW corresponds to 0 dBm, values ​​above 1 mW result in positive dBm values, values ​​below 1 mW negative.

The unit dBm is z. B. used for the transmission power or the RSSI value ( Received Signal Strength Indication ). With the latter, ASU ( Arbitrary Strength Unit ) can also be used in the unit instead of dBm .

## dBW

dBW ( decibel watt ) is the unit of the power level L P , which describes the ratio of a power P compared to the reference power of 1 W ( watt ).

${\ displaystyle L_ {P} {(\ operatorname {dBW})} = 10 \ log _ {10} \ left ({\ frac {P} {1 \, \ operatorname {W}}} \ right)}$

and vice versa, if the power is sought in watts (W)

${\ displaystyle P {(\ operatorname {W})} = 10 ^ {^ {\ left ({\ frac {L_ {P} {(\ operatorname {dBW})}} {10}} \ right)}} \ cdot 1 \, \ operatorname {W}}$

1 W corresponds to 0 dBW, values ​​above 1 W result in positive dBW values, values ​​below 1 W negative.

## conversion

Decibel milliwatt (dBm) and decibel watt (dBW) can be converted directly into each other, they differ by 30 dB (factor 1000).

${\ displaystyle L_ {P} {(\ operatorname {dBm})} = L_ {P} {(\ operatorname {dBW})} + 30dB}$
power dBm dBW
1 pW −90 dBm ...
1 nW −60 dBm ...
1 µW −30 dBm −60 dBW
10 µW −20 dBm −50 dBW
100 µW −10 dBm −40 dBW
1 mW 0 dBm −30 dBW
10 mW 10 dBm −20 dBW
100 mW 20 dBm −10 dBW
1 w 30 dBm 0 dBW
10 W 40 dBm 10 dBW
100 W 50 dBm 20 dBW
1 kW 60 dBm 30 dBW
1 MW 90 dBm 60 dBW
1 GW 120 dBm 90 dBW

When calculating with dBm (or dBW), please note the following:

dB ± dB = dB
dBm ± dB = dBm
dBm - dBm = dB
dBm + dBm: not defined

## literature

• Peter Bocker: data transfer . Volume I - Basics . Springer Verlag, Berlin / Heidelberg 1976, ISBN 978-3-662-06499-3 .
• Rudolf Nocker: Digital Communication Systems. 1. Volume, Basics of Baseband Transmission Technology, Friedrich Vieweg & Sohn Verlag, Wiesbaden 2004, ISBN 978-3-528-03976-9 .
• Ulrich Freyer: News transmission technology. Basics, components, processes and systems of telecommunications technology . 1st edition. Carl Hanser Verlag, Munich 2009, ISBN 978-3-446-41462-4 .
• Peter Welzel: Remote data transmission. Introductory basics for communication in open systems, Friedrich Vieweg & Sohn Verlag, Wiesbaden 1986, ISBN 978-3-663-00129-4 .
• Frieder Strauss: Basic course in high frequency technology. An introduction. 2nd Edition. Springer Verlag, Berlin / Heidelberg 2016, ISBN 978-3-658-11899-0 .