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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Concept explainers

Analog to Digital Converters

The analog-to-digital converter (ADC) allows circuits controlled by microprocessors, Arduinos, Raspberry Pi, and various reasonable digital circuits to be connected to the real world. In the real world, analog signals have a continuous stream of information from a variety of sources and sensors capable of measuring sound, light, temperature, or movement, in addition to the many digital systems that interact with their environment by measuring analog signals from those transducers.

Question

d - f only, thank you!

### Fourth Order Lowpass Filter Design

#### Transfer Function
The 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 Design
To 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) $.

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