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?

[IconicPCB]

No per unit is a linear quantity designed to make life simpler much as the logarithmic Bell and deciBell are.
As I said .. an engineer thing.

[electrolust]

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.

Oh ^really?

[RogerRowland]

Oh ^really?

+¹ 

[DimitriP]

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?

Why do you need to work it out? Haven't you heard  of forums ?  ( I can resist all, but tempation )

[TimFox]

When you need to convert a ratio of monetary values to dB, remember to use the factor x10, not x20, since money is power.

[Simon]

decibels were devised for audible sound and out ears are logaritmic in response, so we hear a 30dB sound as three times as load as 10dB but the sound power is 100x stronger.

the scale was found to be very convinient for electronics as well particularly when dealing with representations of sound. As others have said it makes it much easier to deal with amplification and attenuation because being a log scale subtractions can be used instead of divisions and additions instead of multiplication. The principle has been widely used in other areas of maths and was discovered long before electronics.

[fivefish]

When you need to convert a ratio of monetary values to dB, remember to use the factor x10, not x20, since money is power.

Hahaha... good one.

decibels were devised for audible sound and out ears are logaritmic in response,

No. The Bel was originally used for power measurement in telephony (named after Alexander Graham Bell).
decibel is one-tenth of a Bel. 

[IanB]

No. The Bel was originally used for power measurement in telephony (named after Alexander Graham Bell).
decibel is one-tenth of a Bel.

We use the decibel because the bel was too big for normal use. I guess that's because A.G. Bell was a bighead... 

[Simon]

No. The Bel was originally used for power measurement in telephony (named after Alexander Graham Bell).
decibel is one-tenth of a Bel.

We use the decibel because the bel was too big for normal use. I guess that's because A.G. Bell was a bighead... 

ok but isn't 1dB 1/10th of a Bell ?, as soon as we talk 10, 20 dB we might as well say 1B, 2B, but i suppose it also makes sense to keep it all in the same unit and use 1dB not 0.1B

[T3sl4co1l]

If you round down your decibels to the nearest multiple of 10, and express the rounding error as a linear (rather than logarithmic) factor, you have precisely the scientific notation.

Alternately, if you absorb the linear factor of scientific notation into the exponent, so that all numbers are represented as 1.0 x 10^p, you have exactly the decibel notation -- well, bels anyway, plus a few superfluous characters (we don't need the "1.0 x 10^" part, putting a dB at the end to remind us of the difference).

Tim

[IanB]

And rather curiously, even the "linear" part of a floating point number, the mantissa, is not actually linear.

For instance, suppose decimal numbers are to be represented to a precision of 2 significant figures. Then the range of values that can be represented to full two digit precision is from 1.0 x 10ⁿ to 9.9 x 10ⁿ.

However, a one digit change from 1.0 to 1.1 represents a difference of 10% [= (1.1 - 1.0) / 1.1], whereas a one digit change from 9.8 to 9.9 is only 1% [= (9.9 - 9.8 ) / 9.8]. The scale is quite non-linear.

Sure, you can add more digits, but the general non-linearity remains. For instance, 1.00000 to 1.00001 is 0.001%, whereas 9.99998 to 9.99999 is 0.0001%. It is still ten times more precise.

This is actually a good reason why computers should work in binary. For instance, going from 100000 to 100001 in binary is 3.1%, and going from 111110 to 111111 is 1.6%. The difference in representational precision only varies by a factor of 2 rather than a factor of 10. This means that binary values can cover the range of possible values for a given precision with a more even distribution.

[TimFox]

No, the mantissa is linear.  If your code gives constant ratios (such as 10%) for a given increment, then that code is geometric or exponential (same thing).  If the code gives constant increments for a given increment in the code, then that is linear.

[IanB]

No, the mantissa is linear.  If your code gives constant ratios (such as 10%) for a given increment, then that code is geometric or exponential (same thing).  If the code gives constant increments for a given increment in the code, then that is linear.

But it doesn't give constant increments in value for a constant increment in the code.

If I increment 9.9e01 by 1, I get 1.0e02, an increment of 1. If I increment 1.0e02 by 1, I get 1.0e02, an increment of 0. The smallest increment I can now make is 10, in going to 1.1e02.

Floating point representation is a quasi-geometric scale, but floating point binary is closer to truly geometric than floating point decimal.

So yes, linear is the wrong way to describe it, but in terms of even distribution of numbers there remains an advantage to binary.

[T3sl4co1l]

What you are talking about has nothing to do with the representational system and all to do with the distinction between arithmetic and geometric operations.  A geometric (proportional) operation has a scale-dependent arithmetic difference, and vice versa.  It doesn't matter what writing system is used to express numbers for either operation.

Tim

[dom0]

No, the mantissa is linear.  If your code gives constant ratios (such as 10%) for a given increment, then that code is geometric or exponential (same thing).  If the code gives constant increments for a given increment in the code, then that is linear.

But it doesn't give constant increments in value for a constant increment in the code.

If I increment 9.9e01 by 1, I get 1.0e02, an increment of 1. If I increment 1.0e02 by 1, I get 1.0e02, an increment of 0. The smallest increment I can now make is 10, in going to 1.1e02.

Floating point representation is a quasi-geometric scale, but floating point binary is closer to truly geometric than floating point decimal.

So yes, linear is the wrong way to describe it, but in terms of even distribution of numbers there remains an advantage to binary.

The mantissa is linear, but obviously the absolute step size depends on the exponent.

[electrolust]

This is actually a good reason why computers should work in binary. For instance, going from 100000 to 100001 in binary is 3.1%, and going from 111110 to 111111 is 1.6%. The difference in representational precision only varies by a factor of 2 rather than a factor of 10. This means that binary values can cover the range of possible values for a given precision with a more even distribution.

The difference from 01 to 10 is 100% though!!!

Representational precision?

I hope by now you understand the silliness of what you have said.

[IanB]

The difference from 01 to 10 is 100% though!!!

Representational precision?

I hope by now you understand the silliness of what you have said.

What I'm talking about is floating point wobble. It is addressed in computer science in relation to the possible error when values are represented as floating point quantities in machine computation. It can be found referenced, for example, in the IEEE-754 standard.

There is nothing silly about it at all.

This article gives a more technical and detailed explanation:

https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

[electrolust]

Ah, well indeed that's exactly right.  Arbitrary precision requires arbitrary space, so tradeoffs are made.

It has nothing to do with the number base.

[GNU_Ninja]

I bet if dBs didn't exist we would have ...

invented 'em