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

#### Andrew Hodson

Joined May 26, 2016
5
Can anybody let me understand the what is -3dB attenuation in electrical and electronics...!!!

#### Papabravo

Joined Feb 24, 2006
14,252
$$-3\;\approx\;-3.010\;...\;=\;10 \times log\left( \frac{1}{2} \right)$$
This is the relationship for Power

If we are talking about Voltage or Current, then
$$-3\;\approx\;-3.010\;...\;=\;20 \times log\left( \frac{1}{\sqrt{2}} \right)$$

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#### MrAl

Joined Jun 17, 2014
7,759
Hello there,

The -3db amplitude is an important measurement standard in filters and other electronics. It's widely used almost like the "rise time" and "fall time" of a pulse signal often being measured at 10 percent and 90 percent of the full height of the pulse.

The -3db amplitude is often quoted as being "3db down" because the amplitude measurement is lower than the reference amplitude by 3db. In filters it is used to describe the bandwidth limits. For example, if we have a filter response that starts out low like -10db at 1Hz, then rises to -3db at 900Hz then peaks at 0db at 1000Hz and then falls back down to -3db at 1100Hz, we say that the "bandwidth" is 200Hz, because the span of frequency between the -3db points is 200Hz, and that would be a bandpass filter. For a lowpass filter, there is usually only one -3db point and that is at the frequency where the signal is down by 3db from the gain in the passband. So if the passband gain was 0db and at 300Hz the signal was 3db down, we could say the bandwidth was 300Hz.
This is a very important measurement for many different components used in electronics like filters and op amps.

#### AnalogKid

Joined Aug 1, 2013
8,540
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.
In broadcast television in the 70's, VU meters were calibrated to read 0 dB at an input level of +8 dBm. An attenuator pad lets you terminate line in 600 ohms while terminating the meter in 3600 ohms (?) for the correct ballistics without messing up the reference indication. Radio calibrates at +4 dBm. According to Wiki, most of TV land has moved to this calibration level.

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#### mishra87

Joined Jan 17, 2016
851
Dear all

I have tried to design a low pass filter.
Please find the attached schematic and simulation results..
I have done here AC sweep analysis .

could anybody elaborate me-

1. V1 and V2 in plot.
2. Where is -3db or +3db point
3. How do calculate start point in plot.
4. What is the phase degree.
5. Is this right way for circuit analysis.
6. How one can analyse this circuit.

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#### MrAl

Joined Jun 17, 2014
7,759
Dear all

I have tried to design a low pass filter.
Please find the attached schematic and simulation results..
I have done here AC sweep analysis .

could anybody elaborate me-

1. V1 and V2 in plot.
2. Where is -3db or +3db point
3. How do calculate start point in plot.
4. What is the phase degree.
5. Is this right way for circuit analysis.
6. How one can analyse this circuit.

Hi,

Can you post a jpg or gif file of your circuit instead? Thanks.

#### bertus

Joined Apr 5, 2008
20,661
Hello,

@MrAl ,

I have extracted the images from the doc file:

Bertus

#### mishra87

Joined Jan 17, 2016
851

#### MrAl

Joined Jun 17, 2014
7,759
I

I think ,
It's now clearly visible. .
Can any explain my questions.
Thanks Bertus for posting the picture itself.

Hello,

Yes you just look at where the signal magnitude starts out, then drop down by -3, draw a horizontal line, and where the line intersects the response line (the curve) draw a vertical line down through the x axis and the intersection of that line and the x axis shows you the -3db frequency. This works only when the magnitude is plotted in db, which your plot is.

The start point (reference point) depends on the type of response. This is low pass so it would normally be taken from the response where the frequency is 0 Hz, but in more complicated response curves you have to look for the 'passband' which can be anywhere between 0Hz and the -3db point. In your case the response is flat so you can take 0Hz as the starting point, and the response is 0db there so you can take 0db as the reference magnitude.

Once you find the -3db frequency you can find the phase at that frequency simply by looking at the phase plot. If you found say 720Hz, then you would look at the phase plot at a frequency of 720Hz and that would tell you the phase.

This analysis seems appropriate for this circuit, yes, if it is to be used as a filter.

To analyze the circuit you should know complex numbers. The circuit is basically a voltage divider but instead of two resistors it uses one resistor and one cap. The resistor impedance is just R1, but the cap impedance is 1/(j*w*C), and the output is:
Vout=Vin*(1/jwC)/(R1+1/jwC)
where jwC=j*w*C for short, and w=2*pi*f, and j is the imaginary operator.

A resistive voltage divider is:
Vout=Vin*R2/(R1+R2)

so you might notice that all we had to do was replace R2 with 1/jwC.

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