What does the -6db/octave mean?

[retracell]

I understand that pass and band filters are not really described by their gain but by their slope. Apparently for a low pass filter it is -6db/octave? I think an octave means a doubling of the angular frequency but I'm not too sure.

And also the equation for a integrator with feedback resistance:

$$\frac{V_o}{V_i}=-\frac{\frac{R_f}{R_i}}{1+sR_fC_f}$$

What does this calculate since you end up with a imaginary number?
And when one says you measure pass voltage at some frequency. Does it mean the f frequency or the omega angular frequency?

 

[MisterX]

In this context, the word octave indicates the frequency interval to double the frequency (doesn't have to be angular).

The equation you posted is a transfer function in the Laplace domain. The equation describes the Laplace transform of an output voltage divided by the Laplace transform of an input voltage.

 

[NascentOxygen]

What does this calculate since you end up with a imaginary number?

If s=0, it's DC, and the denominator here evaluates to 1.
If jwRC=j1 the denominator evaluates to a magnitude of sqrt(2) and this defines the -3dB corner frequency of the low-pass filter. For frequencies much above this, every time you double the frequency, the output of the filter falls by another 6dB.

 

[sophiecentaur]

It's just a bit of Engineers' jargon. Helpful and elegant to some but confusing to the uninitiated. Like so much of Engineering. Life's too short to do without such convenient shorthand.

 

[psparky]

For example...A guitar has several different "E" notes...all at different octaves.

If you play two different "E" notes...they are in perfect tune with each other...but their frequencies are clearly different. One note is higher, the other lower. Not an expert on this subject...but just throwing some things out.

Typically, low pass frequency filters fall at 20db per decade. For example...if break frequency is 100 hz...it drops 20 db until 1,000hz. It drops another 20 db at 10,000 hz...etc.

Now, that's if you have only one pole in the denominator. If you have two poles, it falls at 40 db per deca...if three poles then 60 db per deca...etc.

I can't explain your question exactly, but hopefully I spurred some brainstorming.

 

[psparky]

Also, what nascentoxygen is saying...is half true.

It does fall at -3db at the break frequency (1/ square root of 2 = .7) ( 20 LOG . 7 = -3 db)...but I don't think this equates to -6 db per deca.

If it does...prove it.

 

[Averagesupernova]

6 db per octave means that every time the frequency is doubled/halved the output VOLTAGE is doubled/halved.

 

[NascentOxygen]

Also, what nascentoxygen is saying...is half true.

It does fall at -3db at the break frequency (1/ square root of 2 = .7) ( 20 LOG . 7 = -3 db)...but I don't think this equates to -6 db per deca.

If it does...prove it.

We clearly agree on one thing--that you're wrong on all counts.

Whatever is deca?

 

[psparky]

Deca...decade...whatever. To Nascentoxygen, prove your 6 db theory with some math or something. Don't just make a statement. Prove it or just say your not sure.

To averagesupernova...your explanation is interesting...but now you need to prove it so the rest of us can learn.

Expand upon your explanation and use some math. Or give an example...or something.

Further more...can we step back and have someone clearly define an "octave"?

 

[sophiecentaur]

What is the point in faffing around having disagreements about something that you can find in a thousand textbooks and all over the internet? It's yer hormones talking here, I think. There is clearly a mis-match between the way the OP wants to be told things and the way that people are able or prepared to tell him them.
Rather than complaining, why not go down the road and look it up. It may involve visiting a number of different books or websites before you find the information in a digestible form but it seems you are only managing to have arguments this way.

Forums are much more suited to giving opinions and sometimes work very well at helping people - who are being receptive.

There is no point cross-questioning and demanding proofs of things that are so readily available all over the place. A bit of self help can be very rewarding.

 

[psparky]

Good point. Let's not discuss anything on here and look everything up on the internet.

Sorry physics forum, you are no longer needed. Please remove your site from the internet.

 

[sophiecentaur]

No need to throw all you toys out of the pram. You were not "discussing". You were just arguing where no argument is needed. What is the point? Just look up the proper answer and you're sorted.
This stuff was all sorted out and the terminology was written down long before even I was born. You could "discuss" whether the terms are appropriate but they are written in stone, by now.

 

[psparky]

Fine, I'll prove it myself.

Take a simple low pass filter like 10/(s+1)

Or say 10/(JW+1)

If the original angular frequency (W) is 10...you get a gain of @ 1

If I double W...10/(20J + 1)...you get a gain of @ .5 which makes sense because you expect a low pass filter to drop in gain as frequency rises.

If I cut the original frequency of 10 in half...I have 10/(5J+1) which equals approximately 2.

Hmmm...things are making sense now.

Now where does this 6 db per octave come from?

Since we are saying we double the output...that means multiplying by 2.

20 log 2 = 6 db...

And if we are saying we get half the output...that means multiplying by .5

20 log .5 = -6db...fascinating indeed.

How's that for self help?

 

[jim hardy]

"can we step back and have someone clearly define an "octave"? "

it was interesting to google "octave etymology"
middle Latin, eighth day after a festival.. (hangovers lasted that long back then?)
eighth day after is same day of following week
so the root thought is same location in next iteration of a repeating pattern

it was also interesting to google "octave define"
http://en.wikipedia.org/wiki/Octave
there's something in our hearing neurology that attunes us to harmonics in sound
even rats and monkeys recognize them
so doubtless musical notes were recognized as being an iterative, repeating pattern long before the advent of frequency counters.

so, in our context an octave is a frequency ratio of 2 or 1/2 not eight like the name implies.

6db/octave is 20db/decade - i remember a test question(over forty years ago) was to prove that.
but it's the order of the filter that sets the slope. one pole gives 6, 2 poles give 12, etc.

Thanks guys, i learned something - and that's my daily goal.
yesterday's epiphany was 65 Chevy carburetor idle circuit.

old jim

 

[sophiecentaur]

Did I say you were wrong?
Of course, you're right; I should hope so, too- a bright lad like you. But why get so ratty about it?
If NascentOxygen doesn't recognise what you are saying as true then he only needs to check it against another source.
But, to be honest, "six dB per octave" is only a description - like saying 30mph. It sometimes applies and sometimes doesn't. Many filters are much sharper than that. The meaning of Six dB per Octave is absolutely clear as long as one knows what a dB is and what an Octave is. Both are very lookupable.

 

[psparky]

Thanks Jim...

Now the thread can essentially be put to rest.

Also, in my proof above, you will notice the phase shift that occurs from the "J" in the denominator. This can be seen on your bodi plots from school...and the phase shift can be calculated at every single frequency and will produce a nice smooth line if you go thru the trouble to do it.

See Sophie, proofs can be useful. I am 100% satisfied on this subject and learned something as well.

 

[sophiecentaur]

"can we step back and have someone clearly define an "octave"? "

it was interesting to google "octave etymology"
middle Latin, eighth day after a festival.. (hangovers lasted that long back then?)
eighth day after is same day of following week
so the root thought is same location in next iteration of a repeating pattern

it was also interesting to google "octave define"
http://en.wikipedia.org/wiki/Octave
there's something in our hearing neurology that attunes us to harmonics in sound
even rats and monkeys recognize them
so doubtless the notes were recognized as being an iterative, repeating pattern long before the advent of frequency counters.

so, in our context an octave is a frequency ratio of 2 or 1/2 not eight like the name implies.

6db/octave is 20db/decade - i remember a test question(over forty years ago) was to prove that.
but it's the order of the filter that sets the slope. one pole gives 6, 2 poles give 12, etc.

Thanks guys, i learned something - and that's my daily goal.
yesterday's epiphany was 65 Chevy carburetor idle circuit.

old jim

Doesn't "octave" (in music) just relate to the eight intervals in a normal scale, before it repeats?
Decade,on the other hand, relates to a ratio of ten.
Both are in very common use.

 

[sophiecentaur]

See Sophie, proofs can be useful. I am 100% satisfied on this subject and learned something as well.

Excellent use of time - compared with just getting aerated and cross.

 

[psparky]

Yes, I can see if I have a double pole or a triple pole...the fall off will clearly be "sharper".

 

[jim hardy]

""Doesn't "octave" (in music) just relate to the eight intervals in a normal scale, before it repeats? ""

it could very well, sophi... i don't have any music knowledge
i do understand that we use twelfth root of two as ratio between adjacent notes(?right term?) in Bach's even tempered scale so i figured maybe there's twelve intervals - i don't know.

That's why i googled 'octave entymology' , to see why an 'octave' isn't instead called a doubling or a twelv-ing, and found to my surprise it goes back to Latin and days of the week. I think math of vibrating strings (frequency) wasn't figured out until Newton's time but i could be wrong.

so i put out what i'd read, figuring i'd likely get enlightened further by somebody with knowledge of music science.
"when the student is ready a teacher will appear"

i always like to look up etymology of terms.
it helps cement in a feeling for what the originators were thinking.

Now that I'm retired have more time for such adventures. In between carburetors and household maintenance, that is.
Had a rough week recently, a "revolt of the machines'. Dishwasher motor burned up, washiing machine door froze up, and microwave put on a pyrotechnic display complete with yellow belching flames.
Got 'em all repaired !

old jim

 

[MisterX]

""Doesn't "octave" (in music) just relate to the eight intervals in a normal scale, before it repeats? ""

it could very well, sophi... i don't have any music knowledge
i do understand that we use twelfth root of two as ratio between adjacent notes(?right term?) in Bach's even tempered scale so i figured maybe there's twelve intervals - i don't know.

There's 11 notes in the chromatic scale, and with equal temperament, the frequency of a note is $\sqrt[12]{2}$ times the frequency of the adjacent "lower" note. These intervals are known as "half steps".

$\left(\sqrt[12]{2}\right)^{12} = 2$

Which means 12 half steps "up" would result in a note double the frequency of the starting note.

Seven notes of the 11 are involved in various other scales, such as major and minor scales. Use of these "heptatonic" scales is very common, which relates to why an interval over which the frequency is doubled/halved is called an octave.

 

[jim hardy]

"""These notes may have some notable harmonic properties. Anyway, use of these "heptatonic" scales is very common, which relates to why an interval over which the frequency is doubled/halved is called an octave. ""

So Sophi is right, with seven notes the eighth one would be an octave away?
That would sure explain the name "octave".
hmmm i wonder how they decided to have seven notes...
And i just googled "piano keyboard octave". Wikipedia shows 12 keys per octave on a Steinway Grand - i guess that's standard?

i do recall once, when those Hewlett Packard calculators were new, comparing-twelfth-root-of-two frequencies to other music scale frequency integer ratios like 6::5, 7::6, etc and seeing that they could indeed be mighty close.

My mentor 'Charlie' told me that Bach was "The Mathematician of Music" who figured that out.
Bach reckoned that if you tuned a harpischord even tempered you could play in different keys without re-tuning it, wrote a piece of music to demonstrate that, performed it and brought roars of approval from the crowd.
That crowd was certainly more sophisticated than i am.

Charlie claimed you could tune a piano with one tuning fork and the 12th root of 2 by counting the beat frequencies to get your first octave.


so much science, so little time...

as i said, i learn from most everybody i meet.

Thank you, Sophie and Mr X !


old jim

 

[sophiecentaur]

The whole system of musical scales is a bit of a bodge, actually. The major scale (the 7 white notes on a piano) didn't start off using the twelth root of 2. That's the even tempered scale and allowed a 'near enough' playing in all musical keys. The original scale came from what could be played on an open pipe, like a bugle. There is aw fndamental

 

[sophiecentaur]

The whole system of musical scales is a bit of a bodge, actually. The major scale (the 7 white notes on a piano) didn't start off using the twelth root of 2. That's the even tempered scale and allowed a 'near enough' playing in all musical keys. The original scale came from what could be played on an open pipe, like a bugle. There is aw fndamental

 

[psparky]

We've stated earlier that an octave higher or lower... is twice the frequency or half the frequency.

So if middle C is at 261...then a higher C occurs at 522 hz and a lower C occurs at 130.5 hz...etc.

If a guitar string is equally struck between these three C's...I'm going to assume that the 6 db rule is going to be in effect. Just an assumption...

 

[retracell]

Wow I haven't been checking on my question for a while. I think the most basic understandable answer was that as you double the frequency, the dB rises by 6. I'm currently studying sophomore computer engineering so anything more fancy is not necessary... yet. Oh and I really got mixed up with the equation and forgot that a filter simply has the gain of an inverting amplifier at pass band.

Actually I'm quite honored that my question has sparked a meaningful discussion amongst the people here. It has helped me realize how much engineering application is involved in everything.

Thanks a lot for the help and insight.

 

[psparky]

Wow I haven't been checking on my question for a while. I think the most basic understandable answer was that as you double the frequency, the dB rises by 6. I'm currently studying sophomore computer engineering so anything more fancy is not necessary... yet. Oh and I really got mixed up with the equation and forgot that a filter simply has the gain of an inverting amplifier at pass band.

Actually I'm quite honored that my question has sparked a meaningful discussion amongst the people here. It has helped me realize how much engineering application is involved in everything.

Thanks a lot for the help and insight.

As engineers and scientists...we like to know WHY things happen. Saying that... when you double the frequency that the db rises 6 didn't mean much to me until I proved it mathematically and saw it on a graph. But that's how I roll.