# Need comments on low noise band-pass filter design

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?

• This question lacks a question. – Peter Apr 7 '14 at 13:37
• What aspects of the design do you want comments on? Be very specific. – Scott Seidman Apr 7 '14 at 13:53
• The title of your question hints that you might have an issue with noise. What signal levels are you working with, and how much noise is "too much"? Be specific. – Dave Tweed Apr 7 '14 at 14:11
• 10 nVRMS seems like an awfully small input signal. Do you have a lot of gain in this filter? – horta Apr 7 '14 at 14:42

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.

• 36nV just from the 487 ohm resistor... – Spehro Pefhany Apr 7 '14 at 21:01
• @SpehroPefhany - that's the wideband noise I guess? – Andy aka Apr 7 '14 at 21:02
• Nope it's the in-band noise!!!! – Andy aka Apr 7 '14 at 21:04
• 160Hz BW, assuming 300K temperature! – Spehro Pefhany Apr 7 '14 at 21:04
• @SpehroPefhany yeah I just checked!!! Dear OP - here is a resistor noise calculator: sengpielaudio.com/calculator-noise.htm – Andy aka Apr 7 '14 at 21:05