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

MrChips

Joined Oct 2, 2009
19,724
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?

which makes

and



(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).

250hz_low_pass.png

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
4,647
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
12,682
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
19,724
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
23,722
-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
12,682
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
19,724
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.

RC Low Pass Filter response.gif

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

Thread Starter

mishra87

Joined Jan 17, 2016
576
Hello,

A lot of information on decibels can be found in the links of this page of the EDUCYPEDIA:
http://educypedia.karadimov.info/electronics/decibels.htm

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?

which makes

and



(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
19,724
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".
 

Thread Starter

mishra87

Joined Jan 17, 2016
576
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
16,124
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
19,724
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.
 

wayneh

Joined Sep 9, 2010
16,124
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.
 

Thread Starter

mishra87

Joined Jan 17, 2016
576
Thank you all for your comment !!!
Let me go through all the comment and links given by you people and try to understand ..!!!!!!!!!
 
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