# Question 3 (15 marks) The circuit in figure 3 illustrates a Sallen-Key high-pass filter R Rz Figure

Question 3 (15 marks) The circuit in figure 3 illustrates a Sallen-Key high-pass filter R Rz Figure 3 awhere s=ja is given by Vi(s) (a) Show that the transfer function of H(s) H (s) R RC [7 marks] (b) Show that a second order Butterworth filter satisfies the following requirements: Cut-off frequency, fe Pass-band gain, Gpass = 0 dB Stop-band gain, Gstop -20 dB atf 1.5 kHz =6 kHz 12 marks (c) Select the individual components of the circuit in figure 2 to meet the specifications in part (c). Use C 1nF. The Butterworth polynomial for a normalised second-order filter is given by D(s) s2+ v2s + 1. [6 marks] Page 5 of 9