For example, we have been dealing with second-order low pass filters and I just have a couple questions regarding this.

When asked to find the -3dB frequency I took the magnitude of the transfer function and set it equal to the low pass gain (A) divided by √2. When squaring all of this, expanding, and simplifying, this brings a quartic function that has to be solved with four roots. When I solve for these roots, I receive two complex conjugate frequencies, one positive frequency, and one negative frequency (equal in magnitude to the positive frequency).

**1. What do these complex and negative frequencies mean? Looking at the bode plot the rolloff is -40 dB/decade but how does this work? Shouldn't there be a double positive root (pole) frequency?**

**2. Also, at what value of Q does a function start peaking at the oscillation frequency?**

Thanks for the help,

JP