Basic fundamentals of -3dB .........!

mishra87

Joined Jan 17, 2016
851
Can anybody let me understand the what is -3dB attenuation in electrical and electronics...!!!

MrChips

Joined Oct 2, 2009
21,671
A bel is the logarithm (base-10) of the power ratio.

1:1 power ratio is 0 bel.
1:10 power ratio is 1 bel.
1:100 power ratio is 2 bel.
1:1000 power ratio is 3 bel.

There are 10 decibels in 1 bel.

Hence,
1:1 power ratio is 0dB.
1:10 power ratio is 10dB.
1:100 power ratio is 20dB.
1:1000 power ratio is 30dB.

1:2 power ratio is 3dB.

How did we arrive at this?

$image=http://forum.allaboutcircuits.com/js/mimetex.cgi?log_{10}%20(2)%20=0.3010&hash=c924571e066b4e1868078877b1f07bdc$
which makes

$image=http://forum.allaboutcircuits.com/js/mimetex.cgi?10%20\times%20log_{10}%20(2)%20\;\approx\;3&hash=4c208ef53e29673cad77d2ed75734748$
and

$image=http://forum.allaboutcircuits.com/js/mimetex.cgi?10%20\times%20log_{10}%20\left%20(%20\frac{1}{2}\right)\;\approx\;-3&hash=5525d22f5254b6ff2ec321f571bc10d4$

(with thanks to Papabravo, post #5)

In filter circuits, one wishes to identify the roll-off (cut-off, corner or knee point) frequency in the frequency response curve. When the power is reduced to 50% this is the -3dB point, i.e. the gain is -3dB (i.e. the signal is attenuated by 3dB).

For a voltage V into a load resistor R, the power into the load is calculated as

$$P = \frac{V^2}{R}$$

Hence the voltage drop at the cut-off frequency is 1/√2 = 0.707 or 70%

When the voltage drops to 50% this represents a power gain of -6dB.

(Note that we need to be careful with our choice of words. When someone says "-3dB attenuation" we know what they mean, i.e. a loss of 3dB. Semantically, "-3dB attenuation" means a "gain of 3dB". The person really means to say "3dB attenuation" or "-3dB gain".)

shteii01

Joined Feb 19, 2010
4,644
One of the things I was missing for the longest time is the fact that you are looking for a point that is reduced by 3dB.

Take MrChips graph. The highest point is 0, this is maximum power. The point where signal is at half power is 0dB-3dB=-3dB. However, if you have signal that has maximum power at 5dB, then the point where signal has half power is at 5-3=2dB. Another example, you have signal that has maximum power at -7dB, then the signal will have half its power at -7dB-3dB=-10dB.

Papabravo

Joined Feb 24, 2006
14,252
I think your basic question was why is 3 dB so special?
Well it is because:

$$log_{10} (2) =0.3010$$ which makes

$$10 \times log_{10} (2) \;\approx\;3$$ and

$$10 \times log_{10} \left ( \frac{1}{2}\right)\;\approx\;-3$$

MrChips

Joined Oct 2, 2009
21,671
I think your basic question was why is 3 dB so special?
Well it is because:

$$log_{10} (2) =0.3010$$ which makes

$$10 \times log_{10} (2) \;\approx\;3$$ and

$$10 \times log_{10} \left ( \frac{1}{2}\right)\;\approx\;-3$$
I was just about to add that to my post #3. Papabravo beats me to it.

crutschow

Joined Mar 14, 2008
25,269
-3dB is the point where a signal is reduced to 1/2 the power (1/√2 of the voltage) of the base signal level.

It also happens to be the frequency that you calculate for a simple resistor and capacitor low/high pass filter from its RC time-constant (called the corner frequency or 1/2πRC) which happens to be the -3dB point in it's response curve.
By convention, most filters are characterized by this -3dB corner frequency point (among other characteristics).

Papabravo

Joined Feb 24, 2006
14,252
Continuing...
The reason it is called a "corner" frequency is because the ideal piecewise linear approximation of the typical lowpass response actually has a 'corner' at about the 3 dB point. (I'm not sure it is exact, but if not it is close.)

MrChips

Joined Oct 2, 2009
21,671
For a basic RC low-pass filter, the -3dB point has some significant characteristics.
The corner frequency occurs at ω = 1/RC

i.e. $$2 \pi f = \frac{1}{RC}$$

At this point the reactance of C matches the reactance of R.
The resultant impedance

$$Z = \sqrt{R^2 + {X_c}^2}$$

$$V_{out} = V_{in} \frac{X_c}{Z}$$

From this you can see where the 70% voltage drop appears.

The phase shift is -45° at the -3dB point.

Reference: http://www.electronics-tutorials.ws/filter/filter_2.html

mishra87

Joined Jan 17, 2016
851
Hello,

A lot of information on decibels can be found in the links of this page of the EDUCYPEDIA:

Bertus
A bel is the logarithm (base-10) of the power ratio.

1:1 power ratio is 0 bel.
1:10 power ratio is 1 bel.
1:100 power ratio is 2 bel.
1:1000 power ratio is 3 bel.

There are 10 decibels in 1 bel.

Hence,
1:1 power ratio is 0dB.
1:10 power ratio is 10dB.
1:100 power ratio is 20dB.
1:1000 power ratio is 30dB.

1:2 power ratio is 3dB.

How did we arrive at this?

$image=http://forum.allaboutcircuits.com/js/mimetex.cgi?log_{10}%20(2)%20=0.3010&hash=c924571e066b4e1868078877b1f07bdc$
which makes

$image=http://forum.allaboutcircuits.com/js/mimetex.cgi?10%20\times%20log_{10}%20(2)%20\;\approx\;3&hash=4c208ef53e29673cad77d2ed75734748$
and

$image=http://forum.allaboutcircuits.com/js/mimetex.cgi?10%20\times%20log_{10}%20\left%20(%20\frac{1}{2}\right)\;\approx\;-3&hash=5525d22f5254b6ff2ec321f571bc10d4$

(with thanks to Papabravo, post #5)

In filter circuits, one wishes to identify the roll-off (cut-off, corner or knee point) frequency in the frequency response curve. When the power is reduced to 50% this is the -3dB point, i.e. the gain is -3dB (i.e. the signal is attenuated by 3dB).

View attachment 105993

For a voltage V into a load resistor R, the power into the load is calculated as

$$P = \frac{V^2}{R}$$

Hence the voltage drop at the cut-off frequency is 1/√2 = 0.707 or 70%

When the voltage drops to 50% this represents a power gain of -6dB.

(Note that we need to be careful with our choice of words. When someone says "-3dB attenuation" we know what they mean, i.e. a loss of 3dB. Semantically, "-3dB attenuation" means a "gain of 3dB". The person really means to say "3dB attenuation" or "-3dB gain".)
I did not understand
(Note that we need to be careful with our choice of words. When someone says "-3dB attenuation" we know what they mean, i.e. a loss of 3dB. Semantically, "-3dB attenuation" means a "gain of 3dB". The person really means to say "3dB attenuation" or "-3dB gain".)

In either cases it is written " -3db attenuation " but different meaning in terms of loss and gain. ..!!!

MrChips

Joined Oct 2, 2009
21,671
We know what the writer means when they say "-3dB attenuation" but this is incorrect.
Two negatives make a positive. "-3dB attenuation" is literally translated to "3dB gain" but this is not what the writer is trying to express.

The writer should have said "-3dB gain" or "3dB attenuation".

johnmariow

Joined May 4, 2016
20

mishra87

Joined Jan 17, 2016
851
For a basic RC low-pass filter, the -3dB point has some significant characteristics.
The corner frequency occurs at ω = 1/RC

i.e. $$2 \pi f = \frac{1}{RC}$$

At this point the impedance of C matches the impedance of R.
The resultant impedance

$$Z = \sqrt{R^2 + {X_c}^2}$$

$$V_{out} = V_{in} \frac{X_c}{Z}$$

From this you can see where the 70% voltage drop appears.

The phase shift is -45° at the -3dB point.

View attachment 106004

Reference: http://www.electronics-tutorials.ws/filter/filter_2.html
Thanks for your valuable time and information.

I wanted to understand of -3db because it's frequently used term in electronics.
We know what the writer means when they say "-3dB attenuation" but this is incorrect.
Two negatives make a positive. "-3dB attenuation" is literally translated to "3dB gain" but this is not what the writer is trying to express.

The writer should have said "-3dB gain" or "3dB attenuation".
actually I was totally blank about this term 3db and it's meaning . I wanted to understand the complete theory of 3db whether it's in terms of gain or loss. I have frequently seen in explain it's Always written -3db that's why I wrote the same.

wayneh

Joined Sep 9, 2010
16,399
I have no problem understanding the relative meaning of decibels, but I always struggle with the absolute. For instance my home theater receiver dutifully reports the volume setting in decibels. If the wife is out, I can watch a movie at -20dB and have it be gloriously loud. The AV gear heads talk about 0dB being "reference level". What the heck does that mean?

MrChips

Joined Oct 2, 2009
21,671
I have no problem understanding the relative meaning of decibels, but I always struggle with the absolute. For instance my home theater receiver dutifully reports the volume setting in decibels. If the wife is out, I can watch a movie at -20dB and have it be gloriously loud. The AV gear heads talk about 0dB being "reference level". What the heck does that mean?
Aha! That is a darn good question.
In the telephony, recording and broadcasting industry there is a standard reference level of 1mW into 600Ω.
VU meters are calibrated so that the needle shows 0dB when 1mW into 600Ω is applied. This is equivalent to a voltage input of 0.775V into 600Ω.

Lestraveled

Joined May 19, 2014
1,946
The dB system is a relatitive system and has no absolute value unless referenced to something else. For instance dBm is dB referenced to 1 milliwatt. dBV is db referenced to 1 volt.

MrChips

Joined Oct 2, 2009
21,671
owwwww!

105dB_SPL is loud!

You may want to set your volume control to maybe -60dB.

wayneh

Joined Sep 9, 2010
16,399
Well I think the idea is that 105dB is the loudest peaks. Most content would be 20dB below that, or 85dB. Since I'm usually 25 below that, I guess I'm at 60dB.