Electronic – How to know whether the bandpass filter is stable

amplifieranalogfilterstability

I am designing a bandpass filter using MFB. However, I do not know whether my filter is stable or not. Can anyone give me some criteria or methods to evaluate the stability of the filter design?(still using bode plot and applying the Barkhausen stability criterion?)

Here is the schematic in Multisim and the AC analysis plot:
enter image description here

enter image description here

Thank you very much

Best Answer

This is a second order biquadratic band pass filter (see HERE). The transfer function is $$ \frac{-sC_2R_2R_3}{s^2C_1C_2R_1R_2R_3 + s\left ( C_1+C_2 \right )R_1R_2 + \left ( R_1+R_2 \right )} $$

If the poles (those values of s for which the denominator equals zero) all lie in the left half of the s-plane (x-axis, reals; y-axis, imaginary), then the system is stable

>> denom=[C1*C2*R1*R2*R3 (C1+C2)*R1*R2 R1+R2]

denom =

   1.0e+04 *

    0.0000    0.0000    1.2474

>> roots(denom)

ans =

   1.0e+04 *

  -0.0535 + 1.2129i
  -0.0535 - 1.2129i

The real part of your roots are negative, thus all the poles lie in the left half of the s-plane, and your system is stable.

The Bode plot I get is: enter image description here

Your routine plotted the 270 degree phase lead as a 90 degree lag, but otherwise the bodes are close to matching. Your system is stable.

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