# Analysis and Simulation of Filters: How it works

Description| How it works| Low Pass Filter| Tuning a RadioThis app is mostly a combination of the Laplace to Time Domain Converter and Bode Plot Generator tools. See their "How it works" pages to learn about how these tools work.

There are some variations from the above tools. The defined formulae for obtaining the Bode plot have been modified to cater for the second order functions. For obtaining the time domain response of the first order filters, the second order ODE is used by adding a pole and a zero to the transfer function within the calculations. This way, the same solver can be used for both first and second order filters.

The calculations for the pole-zero plot are straightforward, the calculations for these are in the range AE11:AG14. The zero is obtained by setting the numerator to 0 and solving for the number w and the poles are obtained by the same process on the denominator. In this app, the first order filters do not have any zeros.