# Notch filter transfer function

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?

• As you can see, the first function approaches a value of 1/2 for w=0 (at DC) - where as the 2nd function is unity at w=0. That is the only difference - a constant scaling factor. – LvW Dec 6 '14 at 16:27

If $\omega_0$ equals $\dfrac{1}{RC\sqrt2}$ then what's the problem?
This would make Q = $\dfrac{1}{\sqrt2}$.
I think that the constant 1/2 factor doesn't matter as much as the first order term at the denominator, $\dfrac{1}{R_1C_1}s$. Depending on the requirements, that might violate them.