a) Using 10 nF capacitors, design an active broad band first-order bandreject filter with...

a) Using 10 nF capacitors, design an active broad band first-order bandreject filter with a lower cuttoff frequency of 400 Hz, an upper cutoff frequency of 400Hz, and a passband gain of 0 dB. Use the prototype filter circuits introduced in Prolems 1 and 2 in the design process.

b) Draw the circuit diagram of the filter and label all the components.

c) What is the transfer function of the scaled filter?

d) Evaluate the transfer function derived in (c) at the center frequency of the filter.

e) What is the gain (in decibels) at the center frequency?

f) Using a computer program of your choice, make a Bode magnitude plot of the filter transfer function.

Problem 1

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 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

Problem 2

a) Show that if the high-pass filter illustrated in Fig. 15.4 is scaled in both magnitude and frequency, the transfer function is the same as Eq. 15.4 with s replaced by s/kf, where kf is the frequency scale factor.

b) In the prototype version of the high-pass filter circuit in Fig. 15.4, ω = 1 rad/s, R1= 1Ω, C = 1F, and R2 = K ohms. What is the transfer function of the prototype circuit?

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