Problem

Assume the circuit analyzed in Problem 1 is problem part a third-order low-pass Butterwort...

Assume the circuit analyzed in Problem 1 is problem part a third-order low-pass Butterworth filter having a passband gain of 4.

a) If C2 = 1 F in the prototype second-order section, what is the upper limit 011 C1
b) If the limiting value of C1 is chosen, what are the prototype values of R1,R2, and R3?
c) If the corner frequency of the filter is 2.5 kHz and C2 is chosen to be 10 nF, calculate the scaled values of C1, R1,R2, and R3.
d) Specify the scaled values of the resistors and the capacitor in the first-order section of the filter.
e) Construct a circuit diagram of the filter and label all the component values on the diagram.

Problem 1

The purpose of this problem is to guide you problem 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. 1.

a) Analyze the circuit qualitatively and convince yourself that the circuit is a low-pass filter with a passbahd gain of R2/R1.
b) Support your qualitative analysis by deriving the transfer function Vo/ Vi. To make the transfer function useful in terms of the entries in Table 15.1, put it in the form
c) Now observe that we have five circuit components − R1, R2,R3, C1, and C2 − and three transfer function constraints−K, b1, and bo. At 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 R2(G2) to be realizable. With this in mind, show that if C2− 1 F, the three conductances arc given by the expressions
For G2 to be realizable:
d) Based on the results obtained in (c), outline the design procedure for selecting the circuit components once K, bo, and b1 are known.