d - f only, thank you! ### Fourth Order Lowpass Filter Design#### Transfer FunctionThe transfer function of the fourth order lowpass filter is given by:\[H(s) = \frac{1.4587 \times 10^7}{s^2 + 4868.2138s + 1.4587 \times 10^7} \times \frac{5.1506 \times 10^7}{s^2 + 2016.4802s + 5.1506 \times 10^7}\]#### Sallen-Key Lowpass Filter DesignTo design this filter, cascade two Sallen-Key second-order lowpass filters using the equal R, equal C method. The Sallen-Key second-order lowpass filter circuit is shown with components \( R_a \), \( R_b \), \( R_2 \), \( C_1 \), and \( C_2 \). \( R_a \) and \( R_b \) ensure the circuit has a gain of 1 at \( \omega = 0 \). The parameter \( k_m = 1000 \).##### Circuit Diagram Explained- **Input Source**: \( V_{in} \)- **Output**: \( V_o \)- **Operational Amplifier**: Indicated as "OPAMP" internally denoted by U1- **Components**: - Resistors: \( R_a \), \( R_b \), \( R_2 \), \( R_A \), \( R_B \) - Capacitors: \( C_1 \), \( C_2 \)#### Tasks(a) **Find \(\omega_{01}\) and \(Q_1\)** for the first second-order section with transfer function:\[ H_1(s) = \frac{1.4587 \times 10^7}{s^2 + 4868.2138s + 1.4587 \times 10^7} \](b) **Normalized Component Values**: Determine for the first second-order section as per \( H_1(s) \).This setup helps in creating a fourth-order lowpass filter with desired characteristics by efficiently pairing Sallen-Key filters using straightforward calculations and known configurations. (c) Find the scaled (both magnitude and frequency) component values for the first second-order section with transfer function \( H_1(s) \).(d) Find \(\omega_2\) and \(Q_2\) for the second second-order section with transfer function\[H_2(s) = \frac{5.1506 \times 10^7}{s^2 + 2016.4802s + 5.1506 \times 10^7}\](e) Find the normalized component values for the second second-order section with transfer function \( H_2(s) \).(f) Find the scaled (both magnitude and frequency) component values for the second second-order section with transfer function \( H_2(s) \).

Solution (d) - For the second second-order section,The transfer is given below,…

(d) Find wo2 and Q2 for the second second-order section with transfer function 5.1506 × 107 H2(s) s2 + 2016.4802s + 5.1506 × 107 (e) Find the normalized component values for the second second-order section with transfer function H2(s). (f) Find the scaled (both magnitude and frequency) component values for the second second- order section with transfer function H2(s).

(d) Find wo2 and Q2 for the second second-order section with transfer function 5.1506 × 107 H2(s) s2 + 2016.4802s + 5.1506 × 107 (e) Find the normalized component values for the second second-order section with transfer function H2(s). (f) Find the scaled (both magnitude and frequency) component values for the second second- order section with transfer function H2(s).

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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