Help converting microwatts,milliwatts into dBm and vice versa
Becky Riggenbach
Would appreciate any assistance as I am a novice at converting
microwatts, milliwatts, watts and kilowatts and watts into dBm, dBW. Any
assistance with proper use of scientific calc would also be greatly
appreciated. Thanks so much!
David Rahardja
First, some definitions and terminology:
1 microwatt = 10^-6 watts
1 milliwatt = 10^-3 watts
1 kilowatt = 10^3 watts
0 dBm = Voltage corresponding to 1mW into a resistive load
0 dBW = Voltage corresponding to 1W into a resistive load
Remember that dBm and dBW refer to VOLTAGE comparisons, not power.
If you recall, power P = V * V(conjugate) / R. So a doubling in
voltage results in a squaring of power.
The decibel signifies a ratio of two quantities, defined as:
V2/V1 in decibels = 20 * log (V2/V1)
Using the power formula, and taking V1 and V2 to be the magnitudes
of the voltage,
(V2/V1)^2 in decibels = 20 * log(P2/P1)
or
V2/V1 in decibels = 10 * log(P2/P1)
So, if a known voltage produces 1mW into a resistive load, we can
calculate the voltage needed to produce any other amount of power with
the same load:
Power needed Voltage ratio
1 mW 0 dBm
1 uW -30 dBm
1 W 30 dBm
1 kW 60 dBm
Or if you use 0 dBW as the reference:
Power needed Voltage ratio
1 W 0 dBW
1 kW 30 dBW
1 mW -30 dBW
1 uW -60 dBW
Hope that helps.
-----------------------
David Rahardja - dav...@pobox.com
Electrical / Computer Engineering Major
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-----------------------
Robert H. Penoyer
dav...@pobox.com (David Rahardja) wrote:
>On Tue, 05 Aug 1997 15:41:52 -0700, Becky Riggenbach
><rri...@Emory.Edu> wrote:
>
>>Would appreciate any assistance as I am a novice at converting
>>microwatts, milliwatts, watts and kilowatts and watts into dBm, dBW. Any
>>assistance with proper use of scientific calc would also be greatly
>>appreciated. Thanks so much!
>
> First, some definitions and terminology:
>
> 1 microwatt = 10^-6 watts
> 1 milliwatt = 10^-3 watts
> 1 kilowatt = 10^3 watts
>
> 0 dBm = Voltage corresponding to 1mW into a resistive load
> 0 dBW = Voltage corresponding to 1W into a resistive load
>
> Remember that dBm and dBW refer to VOLTAGE comparisons, not power.
Nonsense! the "m" in dBm and the "W" in dBW refer to milliWATT and
WATT, respectively. There's no need to refer to voltage.
>If you recall, power P = V * V(conjugate) / R. So a doubling in
>voltage results in a squaring of power.
Nope. A doubling in voltage results in a quadrupling of power.
dBm = 10 log(P / 10^-3 W), so:
1 microwatt = 10 log(10^-6 / 10^-3) = -30 dBm
1 milliwatt = 10 log(10^-3 / 10^-3) = 0 dBm
1 watt = 10 log( 1 / 10^-3) = +30 dBm
1 kilowatt = 10 log(10^+3 / 10^-3) = +60 dBm
dBW = 10 log(P / 1 W), so:
1 microwatt = 10 log(10^-6) = -60 dBW
1 milliwatt = 10 log(10^-3) = -30 dBW
1 watt = 10 log( 1) = 0 dBW
1 kilowatt = 10 log(10^+3) = +30 dBW
David Rahardja
>dav...@pobox.com (David Rahardja) wrote:
>
>>On Tue, 05 Aug 1997 15:41:52 -0700, Becky Riggenbach
>><rri...@Emory.Edu> wrote:
>>
>>>Would appreciate any assistance as I am a novice at converting
>>>microwatts, milliwatts, watts and kilowatts and watts into dBm, dBW. Any
>>>assistance with proper use of scientific calc would also be greatly
>>>appreciated. Thanks so much!
>>
>> First, some definitions and terminology:
>>
>> 1 microwatt = 10^-6 watts
>> 1 milliwatt = 10^-3 watts
>> 1 kilowatt = 10^3 watts
>>
>> 0 dBm = Voltage corresponding to 1mW into a resistive load
>> 0 dBW = Voltage corresponding to 1W into a resistive load
>>
>> Remember that dBm and dBW refer to VOLTAGE comparisons, not power.
>
>Nonsense! the "m" in dBm and the "W" in dBW refer to milliWATT and
>WATT, respectively. There's no need to refer to voltage.
Hmmm... please refer to Horowitz & Hill's "Art of Electronics" p.17.
You'll find that I practically lifted the definition from there.
>>If you recall, power P = V * V(conjugate) / R. So a doubling in
>>voltage results in a squaring of power.
>
>Nope. A doubling in voltage results in a quadrupling of power.
Oops. You're right. I stand corrected.
>dBm = 10 log(P / 10^-3 W), so:
>
>1 microwatt = 10 log(10^-6 / 10^-3) = -30 dBm
>1 milliwatt = 10 log(10^-3 / 10^-3) = 0 dBm
>1 watt = 10 log( 1 / 10^-3) = +30 dBm
>1 kilowatt = 10 log(10^+3 / 10^-3) = +60 dBm
>
>dBW = 10 log(P / 1 W), so:
>
>1 microwatt = 10 log(10^-6) = -60 dBW
>1 milliwatt = 10 log(10^-3) = -30 dBW
>1 watt = 10 log( 1) = 0 dBW
>1 kilowatt = 10 log(10^+3) = +30 dBW
The problem is that dBm and dBW are not used to denote the amount of
power being delivered. The units refer to VOLTAGE levels into some
standard load... in radio, it's 50 ohms, in the audio business, it's
600 ohms. When I have a 30dBm audio signal entering my audio mixer,
for example, I'm not receiving 1W of power, but rather a voltage level
that would deliver 1W into an IMAGINARY load of 600 ohms. That is,
30dBm = 24.5Vrms. The actual power delivered may be fractions of a
milliwatt, but it is called 30dBm nevertheless.
So in all practicality, dBm and dBW do refer to VOLTAGE (not even
current), not power. It is an unfortunate choice of symbols, but it
should not be misunderstood.
Roy McCammon
David Rahardja wrote:
>
> On Sat, 09 Aug 1997 02:35:32 GMT, rpen...@pacbell.net (Robert H.
> Penoyer) wrote:
>
> >dav...@pobox.com (David Rahardja) wrote:
> >
> >>On Tue, 05 Aug 1997 15:41:52 -0700, Becky Riggenbach
> >><rri...@Emory.Edu> wrote:
> >>
> >>>Would appreciate any assistance as I am a novice at converting
> >>>microwatts, milliwatts, watts and kilowatts and watts into dBm, dBW. Any
> >>>assistance with proper use of scientific calc would also be greatly
> >>>appreciated. Thanks so much!
> >>
> >> First, some definitions and terminology:
> >>
> >> 1 microwatt = 10^-6 watts
> >> 1 milliwatt = 10^-3 watts
> >> 1 kilowatt = 10^3 watts
> >>
> >> 0 dBm = Voltage corresponding to 1mW into a resistive load
> >> 0 dBW = Voltage corresponding to 1W into a resistive load
> >>
> >> Remember that dBm and dBW refer to VOLTAGE comparisons, not power.
> >
> >Nonsense! the "m" in dBm and the "W" in dBW refer to milliWATT and
> >WATT, respectively. There's no need to refer to voltage.
>
> Hmmm... please refer to Horowitz & Hill's "Art of Electronics" p.17.
> You'll find that I practically lifted the definition from there.
Yes, God Fathers H&H did say something like that. On the same page
they also said dB = 10 log (P2/P1) where P2 and P1 are power levels
and said you can use the voltage form only in the special case that
the waveforms are the same, but other wise the power ratio form
is required. Power ratio is more general in this sense.
Otherwise the entire section is about computing dB's from voltage
ratio's and they mention certain "standard amplitudes" designated
dBV (refered to 1 volt) and dBm (the voltage producing 1 mW into
an understood resistence). Remember, they are talking about how you
compute dB's from voltage ratio's. they didn't say dBm means a voltage
or that dBm refers to voltage comparison. They just said that if
you are comparing voltages then dBm means a certain understood
voltage in that context.
One of the advantages of thinking about dB in terms of power, is
that you get consistent results when there is more than one impedence
in the system.
For example, if you have a 600 ohm source and 600 ohm load and the
source is adjusted so that it delivers 0 dBm into a 600 ohm load,
we all know that the load recieves 1 mW and the voltage is
sqrt(.6) = .775 volts. If we connect the source to a 600 ohm
20 dB attenuator and then to the 600 ohm load, we get -20dBm,
10 microwatts and 0.0775 volts. Fine.
Now connect the 600 ohm source to the 900 ohm load. Well, the
voltage is 2*(.775)*(900)/(900+600) = .930V and the load receives
0.96 mW. But do we refer it to 600 ohms (.775 V) giving +1.584 dB
or to 900 ohms (.949V) giving -.177 dB? If we stick to power
transmitted
though, we know that 10*log( .96) = -.177 dBm.
Another reason to use power is that I can always use an ideal
transformer to change the impedence and voltages at various points
but that won't (ideally) change the power. Thus if I have a source
delivers 1 milliwatt (0dBm), I can transform it as needed to
match the load and know that I still have 0dBm, regardless of
the "reference" impedences.
And, in some sense, power is more fundamental that voltage. Power
lifts stuff and makes thing hot. Voltage is a concept (power
per amp). If I have a 1 Megawatt power plant, I can heat
a certein number of homes, lift a certain amount of water, etc,
regardless of what voltage is coming out of the power plant.
>
Opinions expressed herein are my own and may not represent those of my employer.