Asecond order low pass filter is generally characterized by the following transfer function: �(��) = �' ( (� �)( + � + �' � - + �' ( = 1 (� �)( �' ( + � + 1 ��' - + 1 analyze the relation between the input and output voltage for the circuit in figure 2a (sallen-key second order low-pass filter), and prove that the transfer function, resonant frequency and the quality factor are given by �(��) = 1 1 + ���((�1 + �() − �(�1�(�1�( �' = 1 2�6�1�(�1�( � = 6�1�(�1�( �((�1 + �() design a low pass active filter with 1 khz resonant frequency and a q = 1. because there are multiple parameters for this design, it is good practice to fix the resistor values, and set the capacitors to be integer multiples of one another. for example, let �1 = �( = � and c2 = n c1 where n is an integer, and solve for the value of n that satisfies the q-value. let c1 = 50uf and choose the value of r that satisfy the resonant frequency f0. for the designed filter, draw the absolute of the transfer function |h(ω)| verses frequency.