the Bessel filter transfer function is defined via bessel polynomials. If we consider for example a 2nd order filter, the transfer function is: $$ H(s) = \frac{3}{s^2+3*s+3} $$ I wanted to build a simulation for such a filter with a Sallen-Key-Architecture. Therefore I consulted this design guide by TI. They define the transfer function of a 2nd order low pass as:
Ao is 1 since I want the gain to be unity. I looked at the table below in order to correctly calculate the C- and R-values.
Hence the transfer function becomes: $$ H(s) = \frac{1}{0.618*s^2+1.3617*s+1} $$
I ran the simulation and looked at the bode plot. It showed the desired result (the -3db cutoff frequency was as calculated).
However I do not understand why the transfer function looks so differently. Its definetely not a Bessel polynomial. I checked the step response and observed an overshoot of 0.4% as one would expect for a Bessel filter. Therefor I have 3 Questions:
- How come that the transfer function in the ti design guide is not a bessel polynomial.
- Should the pole location of a 2nd order Bessel filter be the same for any filter with a certain cutoff frequency?
- Can a second order bessel low pass have a different Q factor than 0.5773?
Thanks!