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I'm not sure the relationship between transfer function from the 3dB point. The transfer function should give the gain, and I suppose when we put in the frequency at the 3dB point, the transfer function should be equal to a certain fraction?

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    \$\begingroup\$ The -3dB point does not uniquely determine the transfer function. If you know other information (e.g. that it's a low pass first order system) then you may be able to determine the transfer function. \$\endgroup\$ – Null Dec 8 '14 at 18:16
  • \$\begingroup\$ Only one point of a function does not determine the most simple function: A straight line. \$\endgroup\$ – LvW Dec 9 '14 at 9:17
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No, you cannot calculate the transfer function given one point on its bode plot namely the 3dB point. How would you know what it did at DC or HF - you don't know if it's a low pass, high pass or bandpass filter. You can't even tell how many orders the filter has.

Here are a low pass and a high pass filter having the same 3dB point as an example: -

enter image description here

If all you measured was the 3dB point you wouldn't know which filter it was. Here is a bandpass filter: -

enter image description here

Which 3dB point are you measuring or have knowledge of?

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