The high-pass filter designed in Problem 15.41 is cascaded with the low-pass filter designed in Problem 15.42.

a) Describe the type of filter formed by this interconnection.

b) Specify the cutoff frequencies, the mid frequency, and the quality factor of the filter.

c) Use the results of Problems 15.35 and 15.40 to derive the scaled transfer function of the filter.

d) Check the derivation of (c) by using it to calculate is the mid frequency of the filter.

Problem 15.41

a) Using 8 kΩ resistors and ideal op amps, design a high-pass unity-gain Butterworth filter that has a cutoff frequency of 2.5 kHz and has a gain of no more than −55 dB at 500 Hz.

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

Problems 15.35

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

Problems 15.40

The circuit in Fig. 15.25 has the transfer function given by Eq. 15.47. Show that if the circuit is scaled in both magnitude and frequency, the transfer function of the scaled circuit is

Hence the transfer function of a scaled circuit is obtained from the transfer function of an un scaled circuit by simply replacing s in the un scaled transfer function by s/where is the frequency scaling factor.