a) Show that if the low-pass filter circuit illustrated in Fig. 1 is scaled in both magnit...

a) Show that if the low-pass filter circuit illustrated in Fig. 1 is scaled in both magnitude and frequency, the transfer function of the scaled circuit is the same as Eq. 15.1 with s replaced by s/kf, where kf is the frequency scale factor.

b) In the prototype version of the low-pass filter circuit in Fig. 1, ωc = 1 rad/s, C = 1F, R2 = 1 n, and R1 = 1/K ohms. What is the transfer function of the prototype circuit?

c) Using the result obtained in (a), derive the transfer function of the scaled filter.

Figure 1