For some active filter circuit I have derived the following transfer function:
$$T(s) = \frac12\cdot{s^2+{1\over2R_1^2C_1^2}\over s^2+{1\over R_1C_1}s+{1\over2R_1^2C_1^2}}$$
I need to show that this circuit implements a notch filter, for which the transfer function is given in the following form:
$$T(s)_\text{NF}={s^2+\omega_0^2\over s^2+{\omega_0\over Q}s+\omega_0^2}$$
It is easy to see that my transfer functions almost corresponds to the given form except for the constant factor of \$\frac12\$ before the fraction. Should I be bothered by this factor, i.e, does it influence the derived TF to be not of a notch filter TF form?
Best Answer
If \$\omega_0\$ equals \$\dfrac{1}{RC\sqrt2}\$ then what's the problem?
This would make Q = \$\dfrac{1}{\sqrt2}\$.
It all sounds very reasonable to me. DC transfer function will be 0.5 as indicated by @LvW.