9780199339136, Chapter 1, Problem 70P

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Chapter 1, Problem 70P Step-by-step solution Step of 5 Draw the circuit diagram using Laplace representation of the parameters as shown in Figure 1. 1 sC + + Vₛ(s) V₁ V₁(s) - Figure 1 Step Apply voltage division rule to determine the voltage V₁(s). sC sC sCR, 1 sCR, = (1) 1 Hence, the expression for is 1 Step 5 For substitute 0 for in equation (1). 0 1 0+ Therefore, the value is Step Recall equation (1) R, R1 1 1+ Substitute for R1 1+ = 1+0 Therefore, value of the R1 The value of gain is 0 at low or zero frequency (s=0) and maximum at high or infinite frequency Hence, the transfer function shows the characteristics of STC high-pass filter Step of 5 The expression for the 3-dB radian frequency is as follows: (2) Here, is the time constant The time constant is represented as follows: From Figure 1, and thus, Substitute for in equation (2) 1 = 1 Substitute 100 Hz for for and 5 for 1 100 2π(100)(25x10³) 63.66 nF Hence, the required value of the capacitance should be greater than the value 63.66 nF