# Need comments on low noise band-pass filter design

analogfilter

I am a beginner in filter design. This is the bandpass filter and its central frequency is 2kHz. Would you please give me some comments on this design?

1st stage is a 1.9995 kHz bandpass filter using a standard multiple-feedback topology. It has a Q of about 20 and a gain of about 40 dB.

2nd stage is a 2.009 kHz BP filter with a Q of about 25 and a gain of about 40 dB.

Total gain of first stage is 40 dB which makes a 10nV 2 kHz signal into 1 microvolt.

Bandwidth of 1st stage is \$\dfrac{f_C}{Q}\$ = 100Hz and for the purposes of noise calculation you can assume the bandwidth is 1.6x greater at 160 Hz.

\$E_{NOISE}\$ from ADA4004 is 1.8nV /\$\sqrt{Hz}\$. This means noise in a 160 Hz bandwidth is 22.8 nV

This is bigger than your signal (10nV) therefore this isn't going to be a great design.

Even if you took into account the Q of the 2nd stage, the bandwidth would only be halved i.e. a half power point would become a quarter-power point. Noise voltage would be about 16 nV and still a significantly bigger value than your signal. This is made worse by the 2nd stage being 9.5 Hz different to the 1st stage.