a) Use the circuits analyzed in Problems 15.50 and 15.52 to implement a broadband band reject filter having a pass band gain of 20 dB, a lower corner frequency of 1 kHz, an upper corner frequency of 8 kHz, and an attenuation of at least 24 dB at both 2 kHz and 4 kHz. Use 25 nF capacitors whenever possible.

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

Problems 15.50

The purpose of this problem is to guide you through the analysis necessary to establish a design procedure for determining the circuit components in a filter circuit. The circuit to be analyzed is shown in Fig. P15.50.

a) Analyze the circuit qualitatively and convince yourself that the circuit is a low-pass filter with a pass band gain of R₁/R₂

b) Support your qualitative analysis by deriving the transfer function

c) Now observe that we have five circuit components—

 

First glance, it appears we have two free choices among the five components. However, when we investigate the relationships between the circuit components and the transfer function constraints, we see that if C₂ is chosen, there is an upper limit on C₁ in order for  to be realizable. With this in mind, show that if  the three con-ductances are given by the expressions

d) Based on the results obtained in (c), outline the design procedure for selecting the circuit components once

Problems 15.52

Interchange the Rs and Cs in the circuit in Fig. P15.50; that is, replace

  

a) Describe the type of filter implemented as a result of the interchange

b) Confirm the filter type described in (a) by deriving the transfer function Write the transfer function in a form that makes it compatible with Table 15.1.

Table 15.1