a) Using 0.1 µF capacitors, design an active broad band first-order bandpass filter that h...

a) Using 0.1 µF capacitors, design an active broad band first-order bandpass filter that has a lower cutoff frequency of 1000 Hz, an upper cutoff frequency of 5000 Hz, and a passband gain of 0 dB,  Use prototype versions of the low pass and high-pass filters in the design process (see Problems 1 and 2).

b) Write the transfer function for the scaled filter.

c) Use the transfer function derived in part (b) to find H(jωo), where ωo is the center frequency of the filter.

d) What is the passband gain (in decibels) of the filler at ωo?

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

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 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.