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3 dB bandwidth

Why do we measure the bandwidth of any amplifier as 3 dB down from the
gain value at DC? Why 3dB? Why not 2dB or 1dB?
I am not able to find a correct answer as to why did we choose this
standard.

Thank You
 
K

keith

Jan 1, 1970
0
Why do we measure the bandwidth of any amplifier as 3 dB down from the
gain value at DC? Why 3dB? Why not 2dB or 1dB?
I am not able to find a correct answer as to why did we choose this
standard.

3dB ~ half-power
 
T

Tom (at tomsweb.net)

Jan 1, 1970
0
Hi,
Why do we measure the bandwidth of any amplifier as 3 dB down from the
gain value at DC? Why 3dB? Why not 2dB or 1dB?
I am not able to find a correct answer as to why did we choose this
standard.

A voltage gain of -3dB is a voltage gain of 1/sqrt(2). Since power is
relative to the square of the voltage, this implies a power transfer
ratio of 1/2. So basically the -3dB point is the frequency where the
output power of the circuit is half of the power in the passband.

greetings,
Tom
 
L

Larry Brasfield

Jan 1, 1970
0
Why do we measure the bandwidth of any amplifier as 3 dB down from the
gain value at DC? Why 3dB? Why not 2dB or 1dB?
I am not able to find a correct answer as to why did we choose this
standard.

For a single pole low-pass filter, that drop (3.01 dB, actually)
occurs at the frequency where the straight-line projection of the
passband intersects the asymptote of the stopband. For a
series R/shunt C filter, it also where the magnitude of drop
across the R equals the magnitude on the C. So it is readily
calculated by hand, (as things were when that standard arose).
 
M

Michael Black

Jan 1, 1970
0
keith said:
Why not?


That would be 6bB. Choose it if you so desire.


Two is such a nice number. Besides, two is the loneliest number
since the number one and the 0db "point" doesn't tell us much.
And the issue isn't the measuring point, but that the point be consistent.
One can come up with really good filter specs, but it means nothing if it
turns out they were measuring at the 1.5dB point rather than the 3dB point.
Use an odd reference point, and at the very least you'd better be sure to
specify it. And even then, it can make for complicated comparisons with other
such units, and might even be considered outright misleading.

Michael
 
P

Phil Hobbs

Jan 1, 1970
0
Larry said:
For a single pole low-pass filter, that drop (3.01 dB, actually)
occurs at the frequency where the straight-line projection of the
passband intersects the asymptote of the stopband. For a
series R/shunt C filter, it also where the magnitude of drop
across the R equals the magnitude on the C. So it is readily
calculated by hand, (as things were when that standard arose).

And besides, if you're going to pick a single frequency as the boundary
between the passband and the stopband, it's natural to pick the point at
which half the power gets through.

Cheers,

Phil Hobbs
 
J

Joerg

Jan 1, 1970
0
Hello Keith,
That would be 6bB. Choose it if you so desire.

Actually that is done for many filters when they characterize the
roll-off at the 6dB and the 60dB points.
Two is such a nice number. Besides, two is the loneliest number
since the number one and the 0db "point" doesn't tell us much.

13 is more lonely...

Regards, Joerg
 
J

Joerg

Jan 1, 1970
0
Hello Larry,
... So it is readily calculated by hand,
(as things were when that standard arose).

Hey, they still are. I have one calculator in my drawer (HP11C) but
several slide rule calculators. No abacus though.

Thing is, if the power goes out I can keep going. A long time ago they
pestered me about it at a client's lab and one of the engineers bragged
about a new calculator with "continuous memory" that didn't fail when
the battery died. I told him my slide rule had continuous memory as
well. The slider...

Then one day a company came out with a slide rule calculator that had an
LCD and buttons. That almost made me sick.

Regards, Joerg
 
P

Pooh Bear

Jan 1, 1970
0
Why do we measure the bandwidth of any amplifier as 3 dB down from the
gain value at DC? Why 3dB? Why not 2dB or 1dB?

3dB down is half power. It's kinda 'traditional' to measure this.
I am not able to find a correct answer as to why did we choose this
standard.

In audio ( for one ) it's no longer the standard it was. Not least since
if you put say 10 devices in series, the signal will then be 30dB down at
the frequency in question !

With the higher performance available from modern circuit design and
components bandwidth in pro-audio is often now specced at -1dB or even
-0.5dB.

Graham
 
P

Pooh Bear

Jan 1, 1970
0
Larry said:
For a single pole low-pass filter, that drop (3.01 dB, actually)
occurs at the frequency where the straight-line projection of the
passband intersects the asymptote of the stopband. For a
series R/shunt C filter, it also where the magnitude of drop
across the R equals the magnitude on the C. So it is readily
calculated by hand, (as things were when that standard arose).

Nicely put.

Reactive and real component of the filter are equal. It's as good an
explanation as I need. ;-)

Graham
 
G

Guy Macon

Jan 1, 1970
0
Joerg said:
Hello Larry,


Hey, they still are. I have one calculator in my drawer (HP11C) but
several slide rule calculators. No abacus though.

Addiators work better for addition and subtraction, and are still
100% mechanical. There are usually a few on eBay cheap because
many were made and few people collect them. (Always contact the
seller and confirm that the slides move freely and that the numbers
are still readable).
Thing is, if the power goes out I can keep going. A long time ago they
pestered me about it at a client's lab and one of the engineers bragged
about a new calculator with "continuous memory" that didn't fail when
the battery died. I told him my slide rule had continuous memory as
well. The slider...

Then one day a company came out with a slide rule calculator that had an
LCD and buttons. That almost made me sick.

I remember that one. The calc only added and subtracted. There was a
sliderule with an addiator on the back too.

Back to the topic, 3DB is also the amount of drop you get when you
have the output impedence and the input impedence matched, which was
common in the days of transformer-balanced audio lines.
 
P

Pooh Bear

Jan 1, 1970
0
Guy said:
Addiators work better for addition and subtraction, and are still
100% mechanical. There are usually a few on eBay cheap because
many were made and few people collect them. (Always contact the
seller and confirm that the slides move freely and that the numbers
are still readable).


I remember that one. The calc only added and subtracted. There was a
sliderule with an addiator on the back too.

Back to the topic, 3DB is also the amount of drop you get when you
have the output impedence and the input impedence matched, which was
common in the days of transformer-balanced audio lines.

Nooooo ! That's a 6dB drop.

Thank God we got rid of so-called 'matched impedance working' and went for
'voltage matching' in audio a long long time ago.

I can recall seeing 600 ohm variable attenuators though in an antique studio
when I was a young 'un. I expect they'd cost around £1000 to make today. Just
to control the 'volume'. Wow !

Graham
 
R

Roger Lascelles

Jan 1, 1970
0
Larry Brasfield said:
For a single pole low-pass filter, that drop (3.01 dB, actually)
occurs at the frequency where the straight-line projection of the
passband intersects the asymptote of the stopband. For a
series R/shunt C filter, it also where the magnitude of drop
across the R equals the magnitude on the C. So it is readily
calculated by hand, (as things were when that standard arose).

A Larry said, the -3.01 db value falls out of the maths. For a single RC
combination, phase moves between 0 and 90 degrees : at -3.01 db the phase is
half way - 45 degrees.

Also, -3db frequency in radians per sec = 1/( C R )
{ farads, ohms )

When you sketch a Bode diagram, for example when checking the stability of a
feedback loop, you just draw straight lines to the -3db frequency asymptote
intersection points Larry mentioned, and you are close enough in engineering
terms.

So we got 70+ good years out of the -3db concept and that value still pops
out at me when I am writing the transfer function for some network on paper.
However, programs like Spice present a mass of result data and those special
frequencies are less special to us.

Engineering is all about getting a feel for the thing you work with, and
the -3db frequency is like this : its an *interesting* frequency for an
engineer. You generally know your circuit resistance- an estimate of your
capacitance and you calculate the "hot frequency" at -3db. At 3db changes
are happening : rolloff slopes are starting or finishing.

This was especially so in the valve/tube days where you would increase gain
by increasing load resistance, to the point where the -3db frequency was as
low as you could allow.

3 db was a nice fit with the audio world too, because tests on humans showed
that a 3 db change was just discernable to the ordinary listener. Of
course, many careful listeners can do better than that.

Roger Lascelles
 
K

keith

Jan 1, 1970
0
Hello Keith,


Actually that is done for many filters when they characterize the
roll-off at the 6dB and the 60dB points.

Sure, if those parameters are of particular interest. That was sorta my
point.
13 is more lonely...

Not according to Nilsson.
 
K

keith

Jan 1, 1970
0
Hello Larry,


Hey, they still are. I have one calculator in my drawer (HP11C) but
several slide rule calculators. No abacus though.

I have a slip-stic in my office and and HP45 around somewhere. The
batteries in the '45 have long gone to their maker though.
Thing is, if the power goes out I can keep going. A long time ago they
pestered me about it at a client's lab and one of the engineers bragged
about a new calculator with "continuous memory" that didn't fail when
the battery died. I told him my slide rule had continuous memory as
well. The slider...

Putting the slip-stic in its scabbard was tended to clear the memory.
Then one day a company came out with a slide rule calculator that had an
LCD and buttons. That almost made me sick.

I see it as someone with a sense of humor. I hope the PHB that
funded the development didn't expect to make much money on it though.
 
P

Pooh Bear

Jan 1, 1970
0
Roger said:
3 db was a nice fit with the audio world too, because tests on humans showed
that a 3 db change was just discernable to the ordinary listener. Of
course, many careful listeners can do better than that.

I have carefully 'lined up' audio tape recorders to an accuracy of better than
0.5dB 'by ear'.

3 dB is a dumbfuck 'standard'.


Graham
 
K

Kevin Aylward

Jan 1, 1970
0
Pooh said:
3dB down is half power. It's kinda 'traditional' to measure this.


In audio ( for one ) it's no longer the standard it was. Not least
since if you put say 10 devices in series, the signal will then be
30dB down at the frequency in question !

With the higher performance available from modern circuit design and
components bandwidth in pro-audio is often now specced at -1dB or even
-0.5dB.

Depends what you mean by "modern". -0.5dB performance was trivially and
cheaply achievable 25 years ago.


Kevin Aylward
[email protected]
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
 
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