a) Write the transfer function for the prototype low-pass Butterworth filter obtained in P...

a) Write the transfer function for the prototype low-pass Butterworth filter obtained in Problem 1 (a).

b) Write the transfer function for the scaled filter in (a) (see Problem 2).

c) Check the expression derived in part (b) by using it to calculate the gain (in decibels) at 7000 Hz. Compare your result with that found in Problem 3.

Problem 1

a) Determine the order of a low-pass Butterworth filter that has a cutoff frequency of 2000 Hz and a gain of no more than − 30 dB at 7000 Hz.

Problem 2

The circuit in Fig. 15.21 has the transfer function given by Eq. 15.34. Show that if the circuit in Fig. 1 is scaled in both magnitude and frequency. the transfer function of the scaled circuit is

Figure 1

Problem 3

b) What is the actual gain, in decibels, at 7000 Hz?