Adding dBm to dB: A Guide from Rappaport's Wireless Comm.

[tensorbundle]

How does it become valid to add a dB with dB_m? I found in a book that the author did like the following:
60dB_m - 155 dB = - 95 dB_m

Isn't it necessary to convert 155 dB into dB_m or vice versa and then doing the algebra?
The book is wireless communication by Theodre Rappaport.

 

[Dickfore]

The conversion is this:

$$\begin{array}{l} L(\mathrm{dB}_{m}) = 10 \cdot \log_{10}{\left(\frac{P}{1 \, \mathrm{mW}}\right)} = 10 \cdot \log_{10}{\left(\frac{P}{1 \, \mathrm{W}} \, \frac{1 \, \mathrm{W}}{1 \, \mathrm{mW}}}\right)} \\ \\ = 10 \cdot \log_{10}{\left(10^{3} \, \frac{P}{1 \, \mathrm{W}}\right)} = 10 \cdot \left(3 + \log_{10}{\left(\frac{P}{1 \, \mathrm{W}}\right)}\right) \\ \\ = 30 + 10 \cdot \log_{10}{\left(\frac{P}{1 \, \mathrm{W}}\right)} = 30 + L(\mathrm{dB}) \end{array}$$

So, it is a simple shift. This does not alter the final result.

 

[tensorbundle]

Thanks. Your explanation clarified the thing very well.

 

[davenn]

Isn't it necessary to convert 155 dB into dB_m or vice versa and then doing the algebra?

No and that's the truly wonderful thing about it :)

In my RF electronics work and my hobby as an amateur radio operator I do a lot of work in the microwave bands. and being able to just add up all the gains and losses in dB makes it so easy to do link budgets etc. no messing around with trying to correlate mW 's or W 's with dB 's of gain and loss


Dave
VK2TDN

 

[sophiecentaur]

The fact is that dB is a ratio.
dBmW is just the ratio wrt 1milliwatt. If you wrote -115dB relative to a mW it would just take more space but would mean the same thing.

 

[davenn]

The fact is that dB is a ratio.

True ... and it seems to take a lot of effort for some I have taught over the years to come to that understanding :)
the number of times I still see some one saying " an antenna has 15dB gain" to which I respond 15dB gain compared to what?, a wet piece of string ??
in antenna gain for example the gain is usually related to one of two options

You can use dBi gain relative to an isotropic radiator or
You can use dBd gain relative to an dipole radiator

for power levels the 2 more common ones are

dBm -- power relative to 1mW = 0dBm (10mW = 10dBm, 100mW = 20dBm) or
dBW -- power relative to 1W


cheers
Dave
VK2TDN

 

[sophiecentaur]

And how about the other one: "Is that dB volts or dB power?" ?

 

[Averagesupernova]

True ... and it seems to take a lot of effort for some I have taught over the years to come to that understanding :)
the number of times I still see some one saying " an antenna has 15dB gain" to which I respond 15dB gain compared to what?, a wet piece of string ??
in antenna gain for example the gain is usually related to one of two options

You can use dBi gain relative to an isotropic radiator or
You can use dBd gain relative to an dipole radiator

for power levels the 2 more common ones are

dBm -- power relative to 1mW = 0dBm (10mW = 10dBm, 100mW = 20dBm) or
dBW -- power relative to 1W


cheers
Dave
VK2TDN

The antenna case is a bit of an exception because the input is a voltage driving a specified impedance, the output is not. You would not be able to ask about a preamp in a receive antenna transmission line having 15 dB of gain compared to what. The input is a voltage driving a specific impedance and so is the output.

 

[davenn]

The antenna case is a bit of an exception because the input is a voltage driving a specified impedance, the output is not. You would not be able to ask about a preamp in a receive antenna transmission line having 15 dB of gain compared to what. The input is a voltage driving a specific impedance and so is the output.

yes that's true, a preamp or power amp a ratio of the output Vs input levels be that measured in mW, W, uV or Volts ... whatever.
And as with a pathloss, its just that a pathloss of say 165dB

sophiecentaur ...And how about the other one: "Is that dB volts or dB power?" ?

dBuV is another very common one... and for some reason that I have yet to discover (not my field of interest), the cable TV industry likes to use it rather than dBm.

cheers
Dave

 

[sophiecentaur]

Using dB when discussing Voltage can be fraught because dB is undeniably a power ratio. If you are not careful you can find yourself saying that a transformer can have 20dB gain! That would be daft. The expression 20dBuV has to be accompanied by the assumption that it's 50 Ohms (or whatever) throughout.

Using Voltages (with or without a log scale) for describing the performance of an antanna pre-amp can, of course, also be very misleading - particularly for low signal levels where noise is relevant. Matching an antenna + feeder into an amplifier so as to optimise niose performance can be a difficult problem because it relates to the way specific amplifying devices perform. In the end, all you can do for a link budget is to work with a required signal level (power) 'into 50 Ohms'.

 

[Ouabache]

The book is wireless communication by Theodre Rappaport.

I know Ted, we were students together at Purdue. Not only is he quite
intelligent but very witty as well. He would fit right in, here on PF. His
amateur call is N9NB.

 

[dlgoff]

I know Ted, we were students together at Purdue. Not only is he quite
intelligent but very witty as well. He would fit right in, here on PF. His
amateur call is N9NB.

Give him a call. We would love to have him as a member.

 

[Averagesupernova]

dB is NOT always undeniably a power ratio. One could technically say that a transformer with a winding ratio of 10:1 has a voltage ratio of 20 dB. Stereo separation is spec'd in dB and it is a voltage ratio.

 

[vk6kro]

dB is NOT always undeniably a power ratio. One could technically say that a transformer with a winding ratio of 10:1 has a voltage ratio of 20 dB. Stereo separation is spec'd in dB and it is a voltage ratio.

dB are defined in terms of power comparisons.
10 times the power is 10 dB. 100 times the power is 20 dB.

You can measure power with a voltmeter if you know the resistance involved.
Power = Voltage squared / R
This is why you use the 20 log... formula for voltages and 10 log ... for power. The 20 takes care of the squaring for you.

A dB meter does just that. The impedance is constant, so it measures power by measuring the voltage. You can't have a "voltage ratio of 20dB" because dB is a measurement of power ratios.

A perfect transformer would have a ratio of output power to input power of ZERO dB regardless of the turns ratio of the transformer. This is because the impedance involved is changing as well as the voltage and the power would stay the same.

Take an example:
You have a 10 ohm resistor and you put 50 volts across it, then 100 volts.
By how many dB has the power changed?

Power = E^2 / R
= 50 * 50 / 10 = 250 watts first
then 100 * 100 / 10 = 1000 watts
power ratio = 10 log (1000 / 250) = 6.02 dB

Now, work it out with just the voltages.
= 20 log (100 / 50)
= 6.02 dB

Same result, because these are just different ways of getting the same thing.

In the voltage case, you have to know the resistance stays the same, but this isn't true if you know the powers. Power is power, regardless of resistance.

Decibels cause a lot of confusion and lots of people believe there are different types of dB for power, voltage and even current. There are not. The dB is for measuring power and the other units can be used to achieve this if you understand the need for constant resistance.

 

[Dickfore]

In acoustics, it is used to measure intensity, which is power per unit area.

 

[sophiecentaur]

dB is NOT always undeniably a power ratio. One could technically say that a transformer with a winding ratio of 10:1 has a voltage ratio of 20 dB. Stereo separation is spec'd in dB and it is a voltage ratio.

I think you are mis-using the word "technically", here. The dB is often used very mis-leadingly to describe voltage ratios and is a trap for the unwary. Best not to use it that way without the appropriate caveats. After all, the Bell was introduced as a measure of sound level ratios (power per unit area).

It is, of course, quite acceptable to say things like "A 20dB increase of power into the load corresponds to a voltage increase of 10 times."

 

[Averagesupernova]

Straight out of Electronic Principles Third Edition by Malvino. Chapter 14 section 14-7:
-
"Voltage measurements are more common than power measurements. Therefore, it is not surprising that decibels are also used to specify voltage gain. Decibel voltage gain is defined as A' = 20 log A where A' = voltage gain in decibels, A = voltage gain. For example, if A is 40, then A' = 20 Log 40 = 32 dB."
-
Impedance is nowhere mentioned. Therefore, power is irrelevant. VK6KRO, I realize what you are saying, but to say dB is only used for power is quite simply wrong. I used to work for a company that built cable TV signal level meters, video generators, stereo and receiver performance testers, oscilloscopes, and other test equipment. I am quite familiar with dB.
-
BTW sophie, its Bel, and not Bell.

 

[vk6kro]

You can do whatever calculations you like, but please don't call them decibels unless you know the impedances are the same.

If you use the 20 log (V1/V2) formula for two different voltage levels, you are getting the power ratio indirectly by assuming the impedance is going to be the same. That is what dB comparisons are all about. They are only about power.

I know dB calculations are misused in the way you describe, but that doesn't make them correct and it has led to a lot of the confusion that exists.

If you want to dispute this, you can choose from some formidable opponents.
For example, Wikipedia says this:
Similarly, in electrical circuits, dissipated power is typically proportional to the square of voltage or current when the impedance is held constant. Taking voltage as an example, this leads to the equation:

where V1 is the voltage being measured, V0 is a specified reference voltage, and GdB is the power gain expressed in decibels. A similar formula holds for current.

 

[Averagesupernova]

Similarly, in electrical circuits, dissipated power is typically proportional to the square of voltage or current when the impedance is held constant. Taking voltage as an example, this leads to the equation:

If they are talking about power of course impedance will have to be considered. That is not what is argued. Call it confusion, misused, I don't really care. The fact remains that a lot of signals outputs in the industry from reputable companies are spec'd with a dB ratio concerning voltage and NOT power where a constant load impedance is not required nor spec'd.

 

[vk6kro]

As long as we agree that it is wrong.

Why else would you compare the squares of voltages except to compare powers?

If an amplifier has a voltage gain of 43, say it has a voltage gain of 43.
Using dB's just to impress the customers isn't going to impress anyone who knows the real meaning of dB's.

 

[Averagesupernova]

The reason the industry uses dB is to keep a wide dynamic range in a relatively easy to understand smallish number. A CD player with channel separation of 100 dB is much simpler to spec this way than the alternative. Also, you might want to read on wiki about dBu. The u stands for UNLOADED. It seems to be an industry standard.
-
I would say you compare the squares in order to keep everything in check when we ARE working with fixed impedances and switching between power and voltage. For instance: In the cable TV industry, 0 dBmV is one millivolt into a specific impedance usually 75 ohms. 0 dBmV is a target carrier level to be injected into the TV tuner. If we hook a signal level meter such as what I used to work on to a signal generator that has it's output spec'd in dBm, any change in the output of the generator will track in the same increase or decrease on the reading of the meter (in decibels), even though the meter is reading out in dBmV. When I first started working on this equipment over 20 years ago I thought to myself, "Why are we working in these hard to understand units?" They weren't easy for me at first. When you start to realize the dynamic range a spectrum analyzer is capable of showing you soon realize why. Consider a carrier that has a spurious product 60 dB below it yet is causing a problem in the picture of a TV receiver, you then realize why a log scale on a spectrum analyzer is advantageous compared to the scale being linear. The log scale (db) will show both signals at the same time whereas a linear scale would not begin to be able to do this. This is only the start of why we use dB. Comparing the squares as you put it is a small price to pay.
-
Edit: One more thing, I would assume the reason the cable TV industry uses dBmV (voltage reference) is because most receivers are spec'd in volts concerning their sensitivity. We generally don't think of injecting power into a receiver, even though technically we do since a well designed receiver will have a specific impedance and in the case of television it is 75 ohms.

 

[sophiecentaur]

If I design an amplifier and describe it as having a gain of 100, the description is useless because I haven't described the quantities involved. If I say that it has a gain of 20dB, very few people (informed users of such amplifiers) will interpret that wrongly - they will correctly assume that I mean a power gain of 100 or they may make a point of asking for clarification.
If I slip a transformer inside the box and it produces 10 times more volts at the output than at the input then people will want their money back, despite the fact that I can say 'hand on heart' there's a voltage gain of 20dB.
TV is a great example where you can 'get away with' using dBs without many problems because considerations about frequency response and echos force you to work at a standard impedance. When building an amplifier for lower frequencies, a range of input and output impedances are used and it would be futile not to involve the impedances in a description of the amplifier performance. 1V across a 10kΩ input producing 10V into a 4Ω load does not represent, in anyone's book of useful measurements, a gain of 20dB.

Quoting from one textbook may be useful but it can't be conclusive evidence - if a single 'expert witness' were used in a court case then at least one of the parties would not be satisfied. It is always good to go back to original definitions and the Bel (spelling corrected :-) ) is /was defined as a power ratio.

'Industry' uses a lot of systems for measuring and specifying performance which are not always helpful - how many audio amplifier manufacturers will tell you, for instance, what amplitude of 50Hz sinwave the amplifier will sustain at full gain into a 4Ω load? Loudness / peak music power and many others are used for commercial reasons and because people are just plain sloppy or ignorant and they can make things look better than they really are.

The very fact that this thread keeps going is because there is a lot of confusion around the topic. Of course the Logarithmic Scale is useful / essential in voltage measurements but the loose use of dBs still generates a great deal of confusion (and disappointment). If you know what you're doing then there need be no problem but very many users of dBs don't know the full implications of their use.

There is a parallel here with the use of the 'water analogy' in electrical circuits (think of the interminable threads we've on that topic). People seem prepared to fight to the death to justify it when all that is needed is that people should be aware of the caveats that must be applied. They are both traps for the unwary and, unfortunately, the unwary don't know they are the unwary.