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1.11 or 1.22? Noise Bandwidth Ratios for 2rd Order Low-Pass Filters

Nicole Han
Intellectual 2230 points

 

When doing deduction of AC Noise Bandwidth Ratio for first and second Order Low-Pass Filters, my result matches well with 1.57 for the 1st LPF, while differs  for 2rd LPF, it’s 1.11, while in most reference it is 1.22. But in the book of “Design with Operational Amplifier and Analog Integrated Circuits”, it is also 1.11.  the following is from the Chinese version of this book, Page 297.

  • 0
    TI__Expert 3555 points

    Nicole,

    There is additional noise gain at the corner frequency of the low pass filter. The amount of additional noise gain is proportional to the Q of the filter. The Q value for 2nd order Bessel, Butterworth, Chebyshev, etc. is different. You are using a Q value of 0.707 in your calculation. This value is correct for a Butterworth filter. Do you know what Q value that most reference material uses?

    I need to know what kind of filter that you are evaluating. Additionally for your information, the total noise of the filter depends on the amplifier and the topology of the filter (Sallen-Key, MFB, etc.).