Why decibels and not scientific notation?

[ivan747]

I was just thinking this morning aobut decibels and how would I explain the need for them to a medicine student. Then it occured to me, well, why are we using decibels when scientific notation is capable of handling large orders of magnitude just as well?

[KJDS]

If I have a transmitter with an output power of 3x10^2 transmitting into a antenna with a gain of 23 over a path loss of 6.4x10-8 into a receiving antenna with a gain of 4.6 and the receiver needs an SNR of 18 in a 230kHz bandwidth to be able to demodulate the signal, what noise figure does it need?

Alternatively, if it's transmitting at +53dBm, through an antenna with a gain of 14dBi, over a path loss of 145dB into a receive antenna of . ...

Which would you rather work out?

[krivx]

You can add and subtract logarithmic ratios instead of multiplying and dividing...

[GNU_Ninja]

http://www.eevblog.com/2009/12/13/eevblog-49-decibels-dbs-for-engineers-a-tutorial/ 

dB are convenient

[coppice]

I was just thinking this morning aobut decibels and how would I explain the need for them to a medicine student. Then it occured to me, well, why are we using decibels when scientific notation is capable of handling large orders of magnitude just as well?

A medical student should have studied chemistry, and will be familiar with "p", as in pH and pK. Same kind of logarithmic scaling. Same reasons behind it.

[TimFox]

And you can write "dB" without klugey substitutes for superscripts in plain text.  "^2" is ugly, although required in the format used in these posts.

[vk6zgo]

I was just thinking this morning aobut decibels and how would I explain the need for them to a medicine student. Then it occured to me, well, why are we using decibels when scientific notation is capable of handling large orders of magnitude just as well?

A medical student should have studied chemistry, and will be familiar with "p", as in pH and pK. Same kind of logarithmic scaling. Same reasons behind it.

Another example is human hearing,which is why dBs became part of Electronics in the first place.

[suicidaleggroll]

Huge parts of this industry operate on a logarithmic scale, so why wouldn't you use a logarithmic unit to represent them?

[c4757p]

Most of you are missing the point of the question. The exponent in a scientific notation number follows the same sort of logarithmic scale as decibels.

[TimFox]

Yes, but one normally does not use a fractional exponent in scientific notation (such as 10^1.6).

[CatalinaWOW]

To expand on what TimFox is saying, the exponents are logarithmic, but the mantissas are not.  Therefore you can't multiply values by adding when you have numbers in scientific notation.  Fractional exponents could deal with the situation, but that is not what scientific notation is, and it would add its own complexities.

The simple answer to your medical student is that many problems in electronics and radio require multiplication.  Using a logarithm measure simplifies these calculations in a way that scientific notation does not.

[free_electron]

a solution invented out of necessity because all they had were paper tables and slide rules....

 we got computers that can deal with 5 million digit numbers. people kling on to old stuff

[KJDS]

a solution invented out of necessity because all they had were paper tables and slide rules....

 we got computers that can deal with 5 million digit numbers. people kling on to old stuff

Whilst that's true, I still prefer to get a rough idea in my head of what the answer should be before going near the computer.

It's still quicker to work out the gain of a complex system in my head in dB than it is otherwise with a calculator. A typical receiver architecture may have the following

roofing filter -1dB
LNA  15dB
Mixer  -6dB
IF filter -1dB
IF amp 15dB
mixer -6dB
IF filter -1dB
IF amp 15dB

total gain 30dB, simples. No calculator, no more than ten seconds of adding up.

[f5r5e5d]

yes, still have the human interface, human easier understanding, mental arithmetic limits

just "because computers" is if anything a reason to spend more time and effort in making easy human comprehension, use of results a priority

[c4757p]

Anyone who thinks computers solve this sort of problem is kidding himself. You still have to design the system, and to do that, you have to be able to juggle lots of possible candidate architectures in your head and have a mental feel for how they'll perform. That's how you decide how to arrange the parts in the first place. Somehow you have to know what circuit to draw into your computer before you can just ask it to spit out the answer for you

[fivefish]

I was just thinking this morning aobut decibels and how would I explain the need for them to a medicine student. Then it occured to me, well, why are we using decibels when scientific notation is capable of handling large orders of magnitude just as well?

It just doesn't represent a number... It represents the RATIO between 2 numbers. And a dB allows you to express a value whose ratio may be small (2x for example, or very large 10,000x) in an easy, "friendly", convenient format. 

(voltage gain dB for example)
2x is 6dB
100x is a 40dB increase.
1,000x is a 60dB increase.
2,000x is a 66dB increase.
10,000x is a 80dB increase.

So you need 2 values to have a RATIO, your number and a reference value. What's the reference value?
if 0.775Volts, then it's called dBu
if 1.0V then it's called dBV

[TimFox]

a solution invented out of necessity because all they had were paper tables and slide rules....

 we got computers that can deal with 5 million digit numbers. people kling on to old stuff

Very, very few practical problems (except for calculating the national debt) require huge numbers of digits.
Most electronic problems (especially, where 5% tolerance components are to be used) require only what we used to call "slide-rule accuracy".
When standing in front of the problem, not at your computer, being able to figure an approximate answer to see if the reading is "believable" before resorting to your computer of calculator is a huge advantage over those who cannot.

[Wim_L]

And you can write "dB" without klugey substitutes for superscripts in plain text.  "^2" is ugly, although required in the format used in these posts.

You can also use the E notation that is often used in programming languages, so 3.6x10^2 would be written as 3.6E2, which is a bit more compact.

[IconicPCB]

It's an engineer thing... not to be trifled with by uninitiated.

[retrolefty]

a solution invented out of necessity because all they had were paper tables and slide rules....

 we got computers that can deal with 5 million digit numbers. people kling on to old stuff

 A craftsman should not be judged on his tools, but rather the results of his work. 

[ivan747]

I showed the medicine student this thread and she got it. Thumbs up.

I also got it myself. It is a bit more intuitive yes, but you still have to think about dB to ratios conversion, so we are still relying on memory, tables and/or calculations.

I bet if dBs didn't exist we would have developed an intuition for multiplying scientific notation to reasonable accuracy just like we convert dB to ratios on our minds with reasonable accuracy. I don't know if it would be as easy, though.

[CatalinaWOW]

In many cases there is no need to convert the ratios.  Almost one converts dB to a signal to noise ratio before evaluating as good enough.  One just remembers the minimum acceptable dB, just as one would remember the minimum acceptable SNR.  Similarly, many spec sheets write the gain as dB, so no need to convert unless you are doing the rest of the calculation as a ratio. 

Many, many engineers do multiply numbers in scientific notation in their heads.  Rapidly and to slide rule or better accuracy.  But it is still more difficult as it requires multiplying two roughly two digit numbers (the mantissa) and adding two two or three digit numbers (the exponent) and at least part of the time adding a carry from the multiplication in the mantissa.  Doing the same thing in dB requires adding two numbers, which commonly only have two or three digits.

[fivefish]

Any EE would know the formula

dB = 10 log (Pout/Pin)

or expressing P in terms of Voltage and Impedance only (and assuming constant impedance so you can cancel it, leads to the equation):
dB = 20 log (Vout/Vin)

[IconicPCB]

dB in signal analysis is like one per unit in power generation and transmission.

[IanB]

dB in signal analysis is like one per unit in power generation and transmission.

Per unit is not a logarithmic scale though?