# Finding the 3dB point of a transfer function.

**URL:** https://boards.straightdope.com/t/finding-the-3db-point-of-a-transfer-function/138872
**Category:** Factual Questions
**Created:** [November 26, 2002, 12:42pm UTC](https://boards.straightdope.com/t/finding-the-3db-point-of-a-transfer-function/138872 "2002-11-26T12:42:36Z")
**Posts on this page:** 4
**Page:** 1

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### Author: ![Cubsfan](https://avatars.discourse-cdn.com/v4/letter/c/f4b2a3/32.png) [@Cubsfan](https://boards.straightdope.com/u/Cubsfan)
#### Post date: [November 26, 2002, 12:42pm UTC](https://boards.straightdope.com/t/finding-the-3db-point-of-a-transfer-function/138872/1 "2002-11-26T12:42:36Z")

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I am trying to figure out how to find the -3dB point for the transfer function 8(1+2s) and for some reason I am having a brain fart. I did this a million times the first 2 years of school but haven’t done it in a long time so I have forgotten.

I know it is when the power is 1\2 so I am thinking that I find when the Tf= 1/2 ? Then 10log of that? I think I am wrong here. Can someone starighten me out?

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### Author: ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)
#### Post date: [November 26, 2002, 1:07pm UTC](https://boards.straightdope.com/t/finding-the-3db-point-of-a-transfer-function/138872/2 "2002-11-26T13:07:59Z")

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0.5=8/(1+2s)  
s=?  
duh?

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### Author: ![andy\_fl](https://avatars.discourse-cdn.com/v4/letter/a/49beb7/32.png) [@andy\_fl](https://boards.straightdope.com/u/andy_fl)
#### Post date: [November 26, 2002, 1:09pm UTC](https://boards.straightdope.com/t/finding-the-3db-point-of-a-transfer-function/138872/3 "2002-11-26T13:09:42Z")

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Make the bode plot in Matlab:

Draw a horizontal line from the y axis parallel to the x axis starting from 0.7 (-3dB) till you reach your amplitude curve, from there drop vertically down and read off the value from the x-axis. Thats you bandwidth.

Alternatively, replace s by j w (w = omega), then solve the equation :

.7 = Magnitude(8/1+2jw)

Hope that helps.

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### Author: ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)
#### Post date: [November 26, 2002, 1:22pm UTC](https://boards.straightdope.com/t/finding-the-3db-point-of-a-transfer-function/138872/4 "2002-11-26T13:22:09Z")

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Yes, **andy\_fl** is right, but it requires knowledge of whether the questions was phrased in voltages or powers.

I should have said:

either

0.5 = 8/(1+ 2s)

or

0.707 = 8/1 + 2s)

s=?  
duh?