# Band pass filter bandwidth problem

I am trying to design a band pass filter that allows frequencies between 16,384Hz and 32,768Hz. Firstly I tried to make it using a passive RC band pass filter:

Using the formula fc = 1/2πRC, the filter should work as I expect, but the result is far from being what I want. This is the result after an AC analysis:

The cutoff frequencies are: 7.1KHz and 71KHz at -9dB, the peak value of the gain is -6dB so I presumed that at -9dB are the cutoff frequencies.

What is even stranger to me is the fact that if I divide the circuit in two filter, a high pass filter (left side of the circuit) and a low pass filter (right side of the circuit), it works perfectly fine, both frequencies under 16KHz and above 32KHz are rejected.

Is there any solution for this circuit or an alternative circuit such a filter with this bandwidth?

Thank you!

• You haven't accounted for the fact that the 2 'halves' of your filter interact with and 'load' each other. Insert a unity-gain buffer between them and you'll probably see results much closer to what you're expecting. Commented May 20, 2019 at 16:21
• ...or ensure that Rl is much greater than Rh, so you might neglect the interaction of the two stages... Commented May 20, 2019 at 16:33
• Increase R1 by 3:1, and reduce Cl by 3:1; this reduces the interaction. Commented May 20, 2019 at 16:56

The problem with passive filters is they are lossy, and can have attenuation lower than 0dB even in the passband.

There are a few ways to over come this with active elements:

laptop2d already said how you can fix the filter, but I'd like to explain what is wrong with your design.

There are two problems. Firstly, both filters are filtering a bit on the intended passband. In the middle of the passband both filters have 1.7 dB of attenuation, if you simulate them separately. Adding those together you get 3.4 dB attenuation.

Secondly, the second stage is loading the first stage. Output impedance of a passive filter is high, and the load connected to it must be much higher in order to not affect the filter. Now the second stage is the load for the first stage. Their impedances are in the same order of magnitude, thus the second stage affects the first stage. Increasing the impedance of the second stage mitigates this problem slightly.

I tried increasing the RI to 100k and reducing CI to 47.9 pF, which increases the impedance but keeps the frequency, and got exactly what is expected, -3.4dB at the middle of the passband. This doesn't fix the cut-off frequencies though.

The cut-off frequency of the high-pass filter is too low because attenuation of the low-pass filter is "fading away" at that frequency. And vice versa.