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First and Second Order Circuits and Equations E-Book

Robert O'Rourke

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Herausgeber: John Wiley & Sons
Kategorie: Wissenschaft und neue Technologien
Sprache: Englisch

Beschreibung

First and second order electric and electronic circuits contain energy storage elements, capacitors and inductors, fundamental to both time and frequency domain circuit response behavior, including exponential decay, overshoot, ringing, and frequency domain resonance.

First and Second Order Circuits and Equations provides an insightful and detailed learning and reference resource for circuit theory and its many perspectives and duals, such as voltage and current, inductance and capacitance, and serial and parallel. Organized and presented to make each information topic immediately accessible, First and Second Order Circuits and Equations offers readers the opportunity to learn circuit theory faster and with greater understanding.

First and Second Order Circuits and Equations readers will also find:

Root locus charts of second order characteristic equation roots both in terms of damping factor ζ as well as damping constant α.
Detailed treatment of quality factor Q and its relationship to bandwidth and damping in both frequency and time domains.
Inductor and capacitor branch relationship step response insights in terms of calculus intuition.
Derivations of voltage divider and current divider formulae in terms of Kirchhoff’s laws.

First and Second Order Circuits and Equations is an essential tool for electronic industry professionals learning circuits on the job, as well as for electrical engineering, mechanical engineering, and physics students learning circuits and their related differential equations.

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Veröffentlichungsjahr: 2024

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Leseprobe

Cover

Table of Contents

Title Page

Dedication

About the Author

Acknowledgments

Part 1: Circuit Elements and Resistive Circuits

1 Ohm's Law, Branch Relationships, and Sources

1.1 Chapter Summary and Polarity Reference

1.2 Branch Relationships and

–

Characteristics

1.3 Ohm's Law, Resistance, and Resistors

1.4 Current, Voltage, and Sources Overview

1.5 Voltage Sources

1.6 Current and Current Sources

Note

2 Kirchhoff's Laws and Resistive Dividers

2.1 Kirchhoff's Laws and Dividers Comparison Summary

2.2 Kirchhoff's Laws Physical Analogies

2.3 Source Polarity in KVL – Time and Frequency Domains

2.4 Formulae Summary for Resistors in Series and Parallel

2.5 Resistors in Series

2.6 Voltage Dividers

2.7 Parallel Circuit Element Formulae

2.8 Current Dividers

2.9 Current and Voltage Intuitions

3 Opamp Models and Resistive Circuits

3.1 Introduction and Ideal Opamp Model Results Overview

3.2 Ideal Opamp Resistive Amplifier Circuits

4 Reactive Circuit Elements

4.1 Capacitor and Inductor Comparison Summary

4.2 Capacitors

4.3 Inductors

Part 2: First‐Order Circuits

5 First‐Order RC and RL Circuits Introduction

5.1 What are First‐Order Circuits?

5.2 Intuitive First‐Order Circuit Frequency Domain Examples

5.3 First‐Order Natural and Step Response Overview

6 First‐Order Frequency Domain Response

6.1 First‐Order Frequency Response Overview

6.2 Series RC High‐pass Filter Frequency Response

6.3 Series RL Low‐pass Filter Frequency Response

6.4 Series RC Low‐pass Filter Frequency Response

6.5 Series RL High‐pass Filter Frequency Response

6.6 Parallel RL Low‐pass Filter Frequency Response

6.7 Parallel RC High‐pass Filter Frequency Response

7 Discharging and Charging First‐Order RC and RL Circuits

7.1 Discharging RC and RL Circuits – Natural Response

7.2 Charging RC and RL Circuits – Step Response

7.3 The Exponential Time Constant

(Tau)

7.4 Pulse Train Time Constants Simulation Example

8 Natural Response of RC and RL Circuits

8.1 RC and RL Circuits Natural Response Summary

8.2 RC and RL Natural Response Derivation

8.3 RC Natural Response (ZIR) Time Constants and Initial Current

8.4 Natural Response of Series RL with Voltage Source

8.5 First‐Order RC and RL Natural Response Summary

9 First‐Order Step Response of RC and RL Circuits

9.1 First‐Order Step Response Summary Overview

9.2 Intuitive Analysis of RC and RL Step Response

9.3 Series RC Step Response Solution Using a Particular Solution

9.4 Series RL Step Response Solution Using a Particular Solution

9.5 Series RL Step Response with Voltage Source

9.6 First‐Order Step Response Summary

10 Complete Response of First‐Order RC and RL Circuits

10.1 First‐Order Complete Response Summary Overview

10.2 Series RC Complete Response Examples

10.3 RL Complete Response Example and Intuitive Analysis

10.4 Complete Response with Switches

10.5 Complete Response General Derivation and Formulae

Notes

11 First‐Order Opamp Integrator and Differentiator Circuits

11.1 RC Integrator Circuit Step Response

11.2 Opamp Integrator Circuit

11.3 Opamp Inverting Differentiator Circuit

Part 3: Second‐Order Circuits

12 Second‐Order RLC Circuits Overview

12.1 What are Second‐Order Circuits?

12.2 Resonance in the Frequency Domain

12.3 Second‐Order RLC Transfer Functions and

12.4 Two Time Domain Responses

13 Second‐Order RLC Frequency Response

13.1 Series and Parallel RLC Impedance

13.2 Second‐Order RLC Frequency Response

13.3 Second‐Order RLC Bandwidth and Quality Factor

14 Second‐Order RLC Circuit Natural Response

14.1 Second‐Order Natural Response Introduction

14.2 Second‐order Natural Response in Terms of

, and

14.3 Second‐order Damping Variables

and

14.4 Second‐order Damping Ratio

– Zeta

Note

15 Second‐Order RLC Step and Complete Response

15.1 RLC Step Response Intuitive Overview

15.2 RLC Step Response Detailed Analyses

15.3 Parallel RLC Intuitive Step Response Example

15.4 Complete RLC Time Domain Response

Part 4: Technical Background Topics

16 Complex Numbers, Exponentials, and Phasors

16.1 Imaginary and Complex Numbers

16.2 Exponentials, Complex Numbers, and Trigonometry

16.3 Phasors and Sinusoidal Steady State

Index

End User License Agreement

List of Tables

Chapter 6

Table 6.1 Common first‐order circuit topologies and the shapes of their fre...

Chapter 9

Table 9.1 The shapes and orientations of voltage and current time domain re...

Chapter 12

Table 12.1 Three response cases in terms of quality factor Q.

Chapter 14

Table 14.1 Simulated series RLC currents for the four damping cases in term...

List of Illustrations

Chapter 1

Figure 1.1a Current source driving a resistor.

Figure 1.1b Voltage source across a resistor.

Figure 1.2 Resistor schematic symbol with passive sign convention.

Figure 1.3 Passive sign convention on a generic fictitious schematic symbol....

Figure 1.4a 1 volt DC voltage source across a 5 ohm resistor.

Figure 1.4b 200 mA DC current source driving a 5 ohm resistor.

Figure 1.5 Circuit simulation schematic with avoltage source and a resistor....

Figure 1.6 Circuit simulation schematic with a current source and a resistor...

Figure 1.7 Circuit simulation schematic with a DC current source, pointed do...

Figure 1.8 Schematic with a current source, pointed up, and a resistor.

Figure 1.9 Resistor schematic diagram and ohm's law expressions where curren...

Figure 1.10 Table showing schematic symbols and branch relationships for res...

Figure 1.11a Fictitious generic circuit schematic symbol.

Figure 1.11b Fictitious generic circuit schematic symbol.

Figure 1.12 Fictitious generic circuit schematic symbol.

Figure 1.13 Resistor schematic symbol, marked with passive sign convention, ...

Figure 1.14 Diode schematic symbol and nonlinear

characteristic.

Figure 1.15 Resistor circuit element visual summary including the resistor s...

Figure 1.16 Examples of common circuit element schematic symbols.

Figure 1.17 Resistor schematic symbol.

Figure 1.18 Resistor schematic symbol labeled with passive sign convention f...

Figure 1.19 Resistor schematic symbol labeled with passive sign convention f...

Figure 1.20 Generic circuit element schematic symbol labeled in terms of sin...

Figure 1.21 Generic circuit element schematic symbol labeled in terms of Lap...

Figure 1.22 Block of resistive material labeled with current for visualizing...

Figure 1.23 Block of resistive material for resistivity discussion.

Figure 1.24 Two adjacent blocks of resistive material.

Figure 1.25 Two blocks of resistive material connected end-to-end.

Figure 1.26a Ideal current source schematic symbol.

Figure 1.26b Ideal voltage source schematic symbol.

Figure 1.27a

characteristic showing the branch relationship of an ideal c...

Figure 1.27b

characteristic showing the branch relationship of an ideal v...

Figure 1.28 Independent ideal voltage source schematic symbol.

Figure 1.29 Schematic with voltage source across a resistor.

Figure 1.30 Independent ideal voltage source schematic symbol.

Figure 1.31 Independent ideal AC voltage source schematic symbol.

Figure 1.32 Independent ideal DC voltage source schematic symbol.

Figure 1.33 Independent ideal voltage source schematic symbol, labeled with ...

Figure 1.34

–

characteristic curve for independent voltage source with vol...

Figure 1.35 Short-circuited voltage source with dashed X to indicate that it...

Figure 1.36 Voltage source embellished with separated charge to visualize vo...

Figure 1.37 Drawing of a voltage source in parallel with a capacitor showing...

Figure 1.38 Conductive block, labeled with positive charges and current dire...

Figure 1.39 Independent current source schematic symbol.

Figure 1.40 Circuit schematic with current source and resistor.

Figure 1.41 An alternative circuit schematic symbol sometimes used for curre...

Figure 1.42 Resistive circuit schematic with a current source disconnected a...

Figure 1.43 Independent current source labeled with reference polarity.

Figure 1.44

characteristic and branch relationship of an ideal constant c...

Figure 1.45 Independent current source labeled with reference polarity.

Figure 1.46 Independent current source labeled with reference polarity.

Figure 1.47

–

characteristic for an independent current source of value

Chapter 2

Figure 2.1a Voltage divider circuit marked with voltage polarities correspon...

Figure 2.1b Junction of three wires with two currents marked as entering the...

Figure 2.2a Two resistors in series.

Figure 2.2b Two resistors in parallel.

Figure 2.3a Resistive voltage divider circuit.

Figure 2.3b Resistive current divider circuit.

Figure 2.4 Got skipped in numbering.

Figure 2.5 Two‐resistor circuit for visualizing voltage loops.

Figure 2.6 Junction of three wires with currents marked as entering the node...

Figure 2.7 Water pump and pipe loop diagram for comparison to current flow....

Figure 2.8 Current source and ideal wire for demonstrating current flow only...

Figure 2.9 Voltage divider circuit marked with voltage polarities correspond...

Figure 2.10 Voltage divider circuit marked with voltage polarities correspon...

Figure 2.11 Current source and resistor schematic labeled with voltage refer...

Figure 2.12 Circuit simulation result from current square wave circuit showi...

Figure 2.13 Circuit simulation schematic with current source and current met...

Figure 2.14 Circuit simulation result voltage plot showing voltage polarity....

Figure 2.15 Circuit simulation result current plot showing current polarity....

Figure 2.16 Voltage and resistor schematic labeled with voltage reference po...

Figure 2.17 Circuit simulation result voltage showing voltage polarity.

Figure 2.18 Circuit simulation schematic with voltage source, resistor, and ...

Figure 2.19 Circuit simulation result showing voltage source polarity.

Figure 2.20 Circuit simulation result showing current polarity according to ...

Figure 2.21 Circuit simulation result showing current polarity through the v...

Figure 2.22 Current source and resistor schematic showing voltage polarity....

Figure 2.23 Circuit simulation schematic with current source and current met...

Figure 2.24 Circuit simulation result showing positive‐node voltage.

Figure 2.25 Circuit simulation result showing positive current in clockwise ...

Figure 2.26 Circuit simulation result showing zero‐phase change.

Figure 2.27 Circuit simulation result showing no phase shift.

Figure 2.28 Schematic showing voltage polarity.

Figure 2.29 Circuit simulation schematic with alternating current voltage so...

Figure 2.30 Circuit simulation result showing positive current through the v...

Figure 2.31 Circuit simulation result showing zero‐phase shift across the vo...

Figure 2.32 Circuit simulation result showing positive voltage across the re...

Figure 2.33 Circuit simulation result showing positive value of current in t...

Figure 2.34a Circuit simulation result showing 180 ° phase shift in current....

Figure 2.34b Circuit simulation result showing 180 ° phase shift in voltage....

Figure 2.35a Two resistors in series.

Figure 2.35b Two resistors in parallel.

Figure 2.36a

resistors in series.

Figure 2.36b

resistors in parallel.

Figure 2.37a Two purely resistive impedances in series.

Figure 2.37b Two purely resistive impedances in parallel.

Figure 2.38a

purely resistive impedances in series.

Figure 2.38b

purely resistive impedances in parallel.

Figure 2.39a Two resistors in series.

Figure 2.39b

resistors in series.

Figure 2.40 Voltage divider circuit with two resistors.

Figure 2.41 Circuit schematic with voltage source across n resistors in seri...

Figure 2.42 Two conductances in series.

Figure 2.43

conductances in series.

Figure 2.44 Two conductances in series.

Figure 2.45 Two conductances in series.

Figure 2.46 Two resistive impedances in series.

Figure 2.47

resistive impedances in series.

Figure 2.48 Resistive voltage divider circuit.

Figure 2.49 Resistive impedance voltage divider circuit.

Figure 2.50 Two resistors in parallel.

Figure 2.51

resistors in parallel.

Figure 2.52 Two resistors and a voltage source in parallel.

Figure 2.53

resistors in parallel.

Figure 2.54 Two conductances in parallel.

Figure 2.55 Two resistive impedances in parallel.

Figure 2.56

resistive impedances in parallel.

Figure 2.57 Current divider circuit.

Figure 2.58 Current divider circuit.

Figure 2.59 Voltage divider circuit.

Figure 2.60 Current divider circuit.

Chapter 3

Figure 3.1 Inverting amplifier schematic.

Figure 3.2 Non‐inverting amplifier schematic.

Figure 3.3 Standard opamp model with finite input resistance and finite outp...

Figure 3.4 Opamp model showing controlled source modeling approach.

Figure 3.5 Voltage‐controlled voltage source.

Figure 3.6 Ideal opamp model with vanishing input voltage and gain approachi...

Figure 3.7 Inverting amplifier schematic.

Figure 3.8 Voltage divider around opamp negative input terminal.

Figure 3.9 Inverting amplifier schematic showing no input current into opamp...

Figure 3.10 Non‐inverting amplifier schematic drawn with negative terminal u...

Figure 3.11 Non‐inverting amplifier drawn with negative terminal down.

Figure 3.12 Non‐inverting amplifier schematic with resistors drawn to indica...

Chapter 4

Figure 4.1a Capacitor schematic symbol with passive sign convention polarity...

Figure 4.1b Inductor schematic symbol with passive sign convention polarity ...

Figure 4.2a Capacitor voltage and current phasors.

Figure 4.2b Inductor voltage and current phasors.

Figure 4.3a

capacitors in parallel.

Figure 4.3b

inductors in series.

Figure 4.4 Capacitor schematic symbol with passive sign convention polarity ...

Figure 4.5 Parallel‐plate capacitor drawing driven by lumped element voltage...

Figure 4.6 Two capacitors in parallel.

Figure 4.7

capacitors in parallel.

Figure 4.8 Capacitor schematic symbol dotted line visualization of plate siz...

Figure 4.9 Two capacitors in series.

Figure 4.10

capacitors in series.

Figure 4.11 Capacitor voltage sinusoid lagging current sinusoid in phase.

Figure 4.12 Capacitor phasor diagram with capacitor voltage as reference.

Figure 4.13 Capacitor phasor diagram with current as reference.

Figure 4.14 Inductor schematic symbol with passive sign convention polarity ...

Figure 4.15 Inductor diagram with coil and fields and driven by a lumped ele...

Figure 4.16 Two inductors in series.

Figure 4.17

inductors in series.

Figure 4.18 Inductor symbol joining to visualize inductance adding in series...

Figure 4.19 Two inductors in parallel.

Figure 4.20

inductors in parallel.

Figure 4.21 Inductor voltage sinusoid leading current sinusoid in phase.

Figure 4.22 Inductor phasor diagram with inductor current as reference.

Figure 4.23 Inductor phasor diagram with inductor voltage as reference.

Chapter 5

Figure 5.1a Series RC circuit driven by AC voltage.

Figure 5.1b Parallel RL circuit driven by AC current.

Figure 5.2a RC low-pass filter response.

Figure 5.2b RL high-pass filter response.

Figure 5.3a Series RC circuit driven by voltage step.

Figure 5.3b Parallel RL circuit driven by current step.

Figure 5.4a Voltage step input function.

Figure 5.4b Current step input function.

Figure 5.5a RC circuit step voltage responses.

Figure 5.5b RL circuit step current responses.

Figure 5.6 Capacitor schematic symbol marked with reference polarity.

Figure 5.7 Inductor schematic symbol marked with reference polarity.

Figure 5.8a RC high-pass filter schematic.

Figure 5.8b RC high-pass filter frequency response.

Figure 5.9a RL low-pass filter schematic.

Figure 5.9b RL low-pass filter frequency response.

Figure 5.10a RC low-pass filter schematic.

Figure 5.10b RC low-pass filter frequency response.

Figure 5.11a RL high-pass filter schematic.

Figure 5.11b RL low-pass filter frequency response.

Figure 5.12a RL high-pass filter schematic.

Figure 5.12b RL high-pass filter frequency response.

Figure 5.13a RC low-pass filter schematic.

Figure 5.13b RC low-pass filter frequency response.

Figure 5.14a Parallel RL schematic driven by AC current source.

Figure 5.14b Series RL schematic driven by AC voltage source.

Figure 5.15a Parallel RC circuit schematic.

Figure 5.15b Parallel RL circuit schematic.

Figure 5.16a RC natural response voltage.

Figure 5.16b RL natural response current.

Figure 5.17 Series RC circuit with voltage step input.

Figure 5.18 Series RC circuit step response resistor voltage.

Figure 5.19 Series RC circuit step response loop current.

Figure 5.20 Series RL circuit with voltage step input.

Figure 5.21 Series RL circuit step response resistor voltage.

Figure 5.22 Series RL circuit step response loop current.

Chapter 6

Figure 6.1 Example Bode magnitude plot of first‐order high‐pass filter.

Figure 6.2 Example Bode phase plot.

Figure 6.3a Example Bode plot of first‐order low‐pass filter.

Figure 6.3b Example Bode plot of first‐order high‐pass filter.

Figure 6.4a Bode plot of first‐order low‐pass filter with −3 dB point marked...

Figure 6.4b Bode plot of first‐order high‐pass filter with −3 dB point marke...

Figure 6.5 Series RC high‐pass circuit driven by sinusoidal voltage source....

Figure 6.6 High‐pass filter Bode magnitude plot.

Figure 6.7 Series RC high‐pass filter Bode phase plot.

Figure 6.8 Series RC circuit simulation schematic driven by sinusoidal volta...

Figure 6.9 Series RC frequency domain simulation of output voltage magnitude...

Figure 6.10 Series RC simulation of capacitor voltage frequency response.

Figure 6.11 Series RC simulation of loop current over frequency.

Figure 6.12 Series RC frequency domain simulation of output voltage phase.

Figure 6.13 Series RC high‐pass filter circuit driven by sinusoidal voltage ...

Figure 6.14 Series RC high‐pass filter circuit driven by sinusoidal voltage ...

Figure 6.15 Series RC high‐pass filter circuit driven by sinusoidal voltage ...

Figure 6.16 Series RC high‐pass filter Bode magnitude plot.

Figure 6.17 Series RC Bode magnitude plot high‐frequency asymptote.

Figure 6.18 Series RC Bode magnitude plot low‐frequency asymptote.

Figure 6.19 Series RC Bode magnitude plot corner frequency.

Figure 6.20 Series RC high‐pass filter finished Bode magnitude plot.

Figure 6.21 Series RC high‐pass filter circuit driven by sinusoidal voltage ...

Figure 6.22 Series RC Bode phase plot construction.

Figure 6.23 Series RC Bode phase plot finished.

Figure 6.24 Series RC high‐pass filter circuit driven by sinusoidal voltage ...

Figure 6.25 Series RC high‐pass filter current phasor diagram.

Figure 6.26 Series RC resistor and capacitor voltages phasor diagram.

Figure 6.27 Series RC phasor diagram calculating source phasor.

Figure 6.28 Series RC phasor diagram with opposite orientation of source pha...

Figure 6.29 Series RC phasor diagram with source phasor at −45°.

Figure 6.30 Series RC phasor diagram with source phasor on real axis.

Figure 6.31 Series RL low‐pass filter circuit driven by sinusoidal voltage s...

Figure 6.32 example Bode magnitude plot of first‐order low‐pass filter.

Figure 6.33 Series RL Bode phase plot.

Figure 6.34 Series RL circuit simulation schematic driven by sinusoidal volt...

Figure 6.35 Series RL frequency domain simulation of output voltage magnitud...

Figure 6.36 Series RL simulation of inductor voltage frequency response.

Figure 6.37 Series RL low‐pass filter simulation of current.

Figure 6.38 Series RL simulation of output voltage phase response.

Figure 6.39 Series RL low‐pass filter circuit driven by sinusoidal voltage s...

Figure 6.40 Series RL low‐pass filter circuit driven by sinusoidal voltage s...

Figure 6.41 Series RL simulation of output voltage phase response.

Figure 6.42 Series RL low‐pass filter circuit driven by sinusoidal voltage s...

Figure 6.43 Series RL low‐pass filter current phasor diagram.

Figure 6.44 Series RL resistor and inductor voltages phasor diagram.

Figure 6.45 Series RL phasor diagram calculating source phasor.

Figure 6.46 Series RL phasor diagram with opposite orientation of source pha...

Figure 6.47 Series RL phasor diagram with source phasor at plus 45°.

Figure 6.48 Series RL phasor diagram with source phasor on real axis.

Figure 6.49 Series RL low‐pass filter circuit driven by sinusoidal voltage s...

Figure 6.50 Series RL low‐pass filter circuit driven by sinusoidal voltage s...

Figure 6.51 Series RL low‐pass filter Bode magnitude plot.

Figure 6.52 Series RL Bode magnitude plot high‐frequency asymptote.

Figure 6.53 Series RL Bode magnitude plot low‐frequency asymptote.

Figure 6.54 Series RL Bode magnitude plot corner frequency.

Figure 6.55 Series RL low‐pass filter finished Bode magnitude plot.

Figure 6.56 Series RL low‐pass filter circuit driven by sinusoidal voltage s...

Figure 6.57 Series RL circuit output voltage phase response.

Figure 6.58 Series RL circuit output voltage phase response construction.

Figure 6.59 Series RL circuit output voltage phase response construction fin...

Figure 6.60 Series RC low‐pass circuit driven by sinusoidal voltage source....

Figure 6.61 Low‐pass filter Bode magnitude plot.

Figure 6.62 Series RC low‐pass filter Bode phase plot.

Figure 6.63 Series RC circuit simulation schematic driven by sinusoidal volt...

Figure 6.64 Series RC frequency domain simulation of output voltage magnitud...

Figure 6.65 Series RC simulation of resistor voltage frequency response.

Figure 6.66 Series RC simulation of loop current over frequency.

Figure 6.67 Series RC frequency domain simulation of output voltage phase.

Figure 6.68 Series RC low‐pass filter circuit driven by sinusoidal voltage s...

Figure 6.69 Series RC low‐pass filter Bode magnitude plot.

Figure 6.70 Series RC low‐pass filter circuit driven by sinusoidal voltage s...

Figure 6.71 Series RC low‐pass filter Bode magnitude plot.

Figure 6.72 Series RC low‐pass filter circuit driven by sinusoidal voltage s...

Figure 6.73 Series RC low‐pass filter current phasor diagram.

Figure 6.74 Series RC resistor and capacitor voltages phasor diagram.

Figure 6.75 Series RC phasor diagram calculating source phasor.

Figure 6.76 Series RC phasor diagram with opposite orientation of source pha...

Figure 6.77 Series RC phasor diagram with source phasor at −45°.

Figure 6.78 Series RC phasor diagram with source phasor on real axis.

Figure 6.79 Sinusoids showing capacitor voltage lagging capacitor current.

Figure 6.80 Series RL circuit schematic driven by sinusoidal voltage source....

Figure 6.81 Series RL output voltage high‐pass frequency response magnitude....

Figure 6.82 Series RL high‐pass filter output voltage phase response.

Figure 6.83 Series RL circuit simulation schematic driven by sinusoidal volt...

Figure 6.84 Series RL simulation of output voltage magnitude frequency respo...

Figure 6.85 Series RL simulation of resistor output magnitude response.

Figure 6.86 Series RL high‐pass filter simulation of current.

Figure 6.87 Series RL simulation of inductor output voltage phase response....

Figure 6.88 Series RL circuit schematic driven by sinusoidal voltage source....

Figure 6.89 Series RL circuit schematic driven by sinusoidal voltage source....

Figure 6.90 Series RL high‐pass filter Bode magnitude plot.

Figure 6.91 Series RL circuit schematic driven by sinusoidal voltage source....

Figure 6.92 Series RL high‐pass filter Bode phase plot.

Figure 6.93 Series RL circuit schematic driven by sinusoidal voltage source....

Figure 6.94 Phasor diagram showing voltage leading current for an inductor....

Figure 6.95 Phasor diagram of inductive impedance showing 90° phase angle.

Figure 6.96 Phasor diagram of resistive impedance plotted on real axis.

Figure 6.97 Phasor diagram of current on real axis as a reference.

Figure 6.98 Series RL phasor diagram calculating source voltage phasor.

Figure 6.99 Series RL phasor diagram with opposite orientation of source pha...

Figure 6.100 Series RL phasor diagram with source phasor at plus 45°.

Figure 6.101 Series RL phasor diagram with inductor voltage phasor on imagin...

Figure 6.102 Series RL phasor diagram showing source voltage phasor on real ...

Figure 6.103 Parallel RL circuit schematic driven by sinusoidal current sour...

Figure 6.104 Parallel RL output current low‐pass frequency response magnitud...

Figure 6.105 Parallel RL low‐pass filter voltage phase response.

Figure 6.106 Parallel RL circuit simulation schematic driven by sinusoidal c...

Figure 6.107 Parallel RL simulation of voltage magnitude frequency response....

Figure 6.108 Parallel RL simulation of inductor output current frequency res...

Figure 6.109 Parallel RL simulation of inductor output current phase respons...

Figure 6.110 Parallel RL circuit simulation of transfer impedance magnitude ...

Figure 6.111 Parallel RL circuit simulation of transfer impedance phase resp...

Figure 6.112 Parallel RL circuit schematic driven by sinusoidal current sour...

Figure 6.113 Parallel RL circuit Bode magnitude plot of current transfer fun...

Figure 6.114 Parallel RL circuit schematic driven by sinusoidal current sour...

Figure 6.115 Parallel RL circuit schematic driven by sinusoidal current sour...

Figure 6.116 Parallel RL circuit current transfer function output phase.

Figure 6.117 Parallel RL circuit schematic driven by sinusoidal current sour...

Figure 6.118 Parallel RL circuit transfer impedance magnitude frequency resp...

Figure 6.119 Parallel RL circuit schematic driven by sinusoidal current sour...

Figure 6.120 Parallel RL circuit current transfer function output phase.

Figure 6.121 Parallel RL phasor diagram of voltage on real axis as a referen...

Figure 6.122 Parallel RL phasor diagram of inductor and resistor currents.

Figure 6.123 Parallel RL phasor diagram calculating source current phasor.

Figure 6.124 Parallel RL phasor diagram with opposite orientation of source ...

Figure 6.125 Parallel RL phasor diagram with current source phasor at −45°....

Figure 6.126 Parallel RL phasor diagram with current source phasor on real a...

Figure 6.127 Parallel RC circuit schematic driven by sinusoidal current sour...

Figure 6.128 Parallel RC circuit Bode magnitude plot of current transfer fun...

Figure 6.129 Parallel RC circuit current transfer function output phase.

Figure 6.130 Parallel RC circuit simulation schematic driven by current sour...

Figure 6.131 Parallel RC circuit Bode magnitude plot of current transfer fun...

Figure 6.132 Parallel RC simulation of capacitor output current frequency re...

Figure 6.133 Parallel RC simulation of current transfer function phase respo...

Figure 6.134 Parallel RC simulation of impedance transfer function magnitude...

Figure 6.135 Parallel RC simulation of impedance transfer function phase res...

Figure 6.136 Parallel RC circuit schematic driven by sinusoidal current sour...

Figure 6.137 Parallel RC circuit Bode magnitude plot of current transfer fun...

Figure 6.138 Parallel RC input impedance schematic diagram.

Figure 6.139 Parallel RC circuit schematic driven by sinusoidal current sour...

Figure 6.140 Parallel RC circuit transfer impedance phase response.

Figure 6.141 Parallel RC circuit schematic driven by sinusoidal current sour...

Figure 6.142 Parallel RC phasor diagram of source voltage phasor on real axi...

Figure 6.143 Parallel RC phasor diagram of capacitor and resistor current ph...

Figure 6.144 Parallel RC phasor diagram calculating source current phasor.

Figure 6.145 Parallel RL phasor diagram with opposite orientation of source ...

Figure 6.146 Parallel RL phasor diagram with current source phasor at 45°.

Figure 6.147 Parallel RL phasor diagram with current source phasor on real a...

Chapter 7

Figure 7.1a RC circuit switching to show natural response discharging.

Figure 7.1b RL circuit switching to show natural response discharging.

Figure 7.2a RC natural response capacitor voltage.

Figure 7.2b RL natural response inductor current.

Figure 7.3a RC natural response capacitor current.

Figure 7.3b RL natural response inductor voltage.

Figure 7.4a RC schematic switched to charge the capacitor voltage initial co...

Figure 7.4b RL schematic switched to set up the inductor current initial con...

Figure 7.5a RC schematic, without switches, showing charging by voltage sour...

Figure 7.5b RL schematic, without switches, showing charging by voltage sour...

Figure 7.6a RC schematic switched for natural response discharging

Figure 7.6b RL schematic switched for natural response discharging.

Figure 7.7a RC natural response circuit with switch not included.

Figure 7.7b RL natural response circuit with switch not included.

Figure 7.8a RC natural response capacitor current discharging.

Figure 7.8b RL natural response inductor voltage decaying.

Figure 7.9a RC natural response decaying capacitor voltage.

Figure 7.9b RL natural response decaying inductor current.

Figure 7.10a RC circuit with step response switch for charging.

Figure 7.10b RL circuit with step response switch for charging.

Figure 7.11a RC circuit with closed switch for step response charging.

Figure 7.11b RL circuit with closed switch for step response charging.

Figure 7.12a RC circuit step response capacitor voltage charging.

Figure 7.12b RL circuit step response inductor voltage charging.

Figure 7.13a RC circuit step response capacitor current decaying.

Figure 7.13b RL circuit step response inductor voltage decaying.

Figure 7.14a RC circuit step response resistor voltage decaying.

Figure 7.14b RL circuit step response resistor current increasing.

Figure 7.15a RC natural response decaying capacitor voltage.

Figure 7.15b RL natural response decaying inductor current.

Figure 7.16 Graph of exponential function decay marked in units of time cons...

Figure 7.17 RC circuit QUCS simulation schematic with pulse train voltage in...

Figure 7.18 RC circuit pulse train simulation voltage response with 1 micro‐...

Figure 7.19 RC circuit pulse train simulation voltage response with 3 micro‐...

Figure 7.20 RC circuit pulse train simulation voltage response with 12 micro...

Chapter 8

Figure 8.1a Parallel RC circuit with initial capacitor voltage.

Figure 8.1b Parallel RL circuit with initial inductor current.

Figure 8.2a RC natural response capacitor voltage decaying from initial cond...

Figure 8.2b RL natural response inductor current decaying from initial condi...

Figure 8.3a Parallel RC circuit schematic with switches to model natural res...

Figure 8.3b Parallel RL circuit schematic with switches to model natural res...

Figure 8.4a Parallel RC circuit marked with

(

) corresponding to natural re...

Figure 8.4b Parallel RL circuit marked with

(

) corresponding to

(

) in F...

Figure 8.5a Parallel RC circuit marked with

(

) corresponding to natural re...

Figure 8.5b Parallel RL circuit marked with

(

) corresponding to

(

) in F...

Figure 8.6a RC natural response capacitor voltage decaying from initial cond...

Figure 8.6b RL natural response inductor current decaying from initial condi...

Figure 8.7a RC natural response capacitor current.

Figure 8.7b RL natural response inductor voltage.

Figure 8.8a Parallel RC circuit marked with

(

) corresponding to natural re...

Figure 8.8b Parallel RL circuit marked with

(

) corresponding to

(

) in F...

Figure 8.9 Parallel RC circuit marked with an initial condition capacitor vo...

Figure 8.10 RC natural response decaying exponential curve with the horizont...

Figure 8.11 Parallel RC circuit marked with v‐sub‐c of t corresponding to th...

Figure 8.12 Relation between the common slope intercept formula and the spec...

Figure 8.13a Series RL circuit with voltage source being removed to visualiz...

Figure 8.13b Parallel RL circuit with initial condition current

from the ...

Figure 8.14 Series RL circuit schematic with switch to model initial conditi...

Figure 8.15 Parallel RL circuit showing reference polarity current direction...

Figure 8.16 Parallel RL circuit with initial condition inductor current

....

Figure 8.17a RL natural response inductor current

(

) decaying from initial...

Figure 8.17b RL natural response inductor voltage

(

) decaying.

Figure 8.18 Series RC circuit with one switch to model the initial condition...

Chapter 9

Figure 9.1 Unit step function signal versus time.

Figure 9.2a Series RC circuit driven by voltage step function.

Figure 9.2b Parallel RL circuit driven by current step function.

Figure 9.3a Graph of voltage step function

(

) with amplitude

Figure 9.3b Graph of current step function

(

) with amplitude

Figure 9.4a Series RC circuit voltage responses to voltage step function.

Figure 9.4b Parallel RL circuit current responses to current step function....

Figure 9.5a Series RC circuit current response to voltage step function.

Figure 9.5b Parallel RL circuit voltage response to current step function.

Figure 9.6a Series RL circuit driven by voltage step function

(

Figure 9.6b Series RL circuit with DC voltage

and switch modeling step fu...

Figure 9.7 Graph of input step function

(

) with amplitude

Figure 9.8 Series RL inductor voltage response to voltage step function inpu...

Figure 9.9 Series RL current response to voltage step function input.

Figure 9.10a Series RC circuit driven by voltage step function.

Figure 9.10b Parallel RL circuit driven by current step function.

Figure 9.11a Graph of voltage step function

(

) with amplitude

Figure 9.11b Graph of current step function

(

) with amplitude

Figure 9.12a Series RC circuit driven by DC voltage

Figure 9.12b Parallel RL circuit driven by DC current

Figure 9.13a Series RC circuit driven by DC voltage

Figure 9.13b Parallel RL circuit driven by DC current

Figure 9.14a Series RC circuit current response to voltage step function.

Figure 9.14b Parallel RL circuit voltage response to current step function....

Figure 9.15a Series RC circuit resistor voltage response to voltage step fun...

Figure 9.15b Parallel RL circuit resistor current response to current step f...

Figure 9.16a Series RC circuit capacitor voltage response to voltage step fu...

Figure 9.16b Parallel RL circuit inductor current response to current step f...

Figure 9.17a Parallel RL circuit driven by current step function.

Figure 9.17b Series RL circuit driven by voltage step function.

Figure 9.18 Series RC circuit driven by voltage step function.

Figure 9.19 Unit step function signal versus time.

Figure 9.20 Parallel RC circuit for natural response.

Figure 9.21 Series RC circuit capacitor output voltage response to voltage s...

Figure 9.22 Series RC circuit current response to voltage step function.

Figure 9.23 Series RL circuit driven by voltage step function

(

Figure 9.24 Graph of voltage step function

(

) with amplitude

Figure 9.25 Parallel RL circuit for natural response.

Figure 9.26 Series RL circuit current response to voltage step function.

Figure 9.27 Series RL circuit inductor output voltage response to voltage st...

Figure 9.28a Series RL circuit driven by voltage step function

(

Figure 9.28b Series RL circuit with DC voltage

and switch modeling step f...

Figure 9.29 Series RL circuit current response to voltage step function.

Chapter 10

Figure 10.1a Parallel RC circuit with initial condition capacitor voltage

Figure 10.1b Parallel RL circuit with initial condition inductor current

....

Figure 10.2a Series RC circuit driven by voltage step function.

Figure 10.2b Series RL circuit driven by voltage step function.

Figure 10.3 Series RC circuit simulation schematic with no initial condition...

Figure 10.4 Series RC step response simulation plot of capacitor voltage.

Figure 10.5 Series RC step response simulation plot of currents.

Figure 10.6 Series RC circuit simulation schematic with 0.5 V initial condit...

Figure 10.7 RC step response simulation plot of capacitor voltage with 0.5 V...

Figure 10.8 RC step response simulation plot of capacitor current with 0.5 V...

Figure 10.9 Series RC circuit simulation schematic with −0.5 V initial condi...

Figure 10.10 Series RC step response simulation plot of capacitor voltage.

Figure 10.11 Series RC step response simulation plot of capacitor current.

Figure 10.12 Series RL circuit simulation schematic with no initial conditio...

Figure 10.13 Series RL step response simulation plot of voltages with no ini...

Figure 10.14 Series RL step response simulation plot of currents with no ini...

Figure 10.15 Series RL circuit simulation schematic with −25 mA initial cond...

Figure 10.16 RL step response simulation plot of voltages with −25 mA initia...

Figure 10.17 RL step response simulation plot of currents with −25 mA initia...

Figure 10.18 Series RL circuit simulation schematic with 25 mA initial condi...

Figure 10.19 RL step response simulation plot of voltages with 25 mA initial...

Figure 10.20 RL step response simulation plot of current with 25 mA initial ...

Figure 10.21a RC circuit schematic with switches to model complete response....

Figure 10.21b RL circuit schematic with switches to model complete response....

Figure 10.22 RC parallel circuit schematic driven by current source.

Figure 10.23 RL circuit schematic with switches to model complete response....

Figure 10.24 RL series circuit schematic driven by voltage source.

Figure 10.25a RC circuit schematic with switches to model complete response....

Figure 10.25b RL circuit schematic with switches to model complete response....

Chapter 11

Figure 11.1 RC series circuit schematic driven by current step function

(

Figure 11.2 Graph of voltage

(

) across the capacitor and the resistor.

Figure 11.3 Current step function

(

) with steady‐state value

Figure 11.4 Graph of constant voltage across the resistor and growing capaci...

Figure 11.5 Opamp integrator circuit with accumulating charge marked on the ...

Figure 11.6 RC opamp integrator circuit schematic.

Figure 11.7 RC opamp differentiator circuit schematic.

Chapter 12

Figure 12.1a Series RLC circuit schematic driven by a voltage source.

Figure 12.1b Parallel RLC circuit schematic driven by a voltage source.

Figure 12.2a Series RLC circuit schematic driven by sinusoidal voltage.

Figure 12.2b Parallel‐series RLC circuit schematic driven by sinusoidal volt...

Figure 12.3a Series RLC band pass simulated frequency response voltage in dB...

Figure 12.3b RLC band stop filter simulated frequency response voltage in dB...

Figure 12.4a Series RLC undriven circuit schematic.

Figure 12.4b Parallel RLC undriven circuit schematic.

Figure 12.5 Generic second‐order underdamped step response plot.

Figure 12.6a Series RLC circuit impedance schematic.

Figure 12.6b Parallel RLC circuit impedance schematic.

Figure 12.7a Series RLC simulated impedance plot magnitude and phase.

Figure 12.7b Parallel RLC simulated impedance plot magnitude and phase.

Figure 12.8a Series RLC circuit schematic driven by sinusoidal voltage.

Figure 12.8b Parallel RLC circuit schematic driven by sinusoidal current.

Figure 12.9 Plot of series RLC step response capacitor voltage for three cas...

Figure 12.10 Series RLC circuit schematic driven by voltage step function.

Chapter 13

Figure 13.1a Series RLC schematic.

Figure 13.1b Parallel RLC schematic.

Figure 13.2a Series RLC simulation results graph of impedance.

Figure 13.2b Parallel RLC simulation results graph of impedance.

Figure 13.3a Series RLC impedance schematic.

Figure 13.3b Parallel RLC impedance schematic.

Figure 13.4a Series RLC circuit schematic driven by sinusoidal voltage.

Figure 13.4b Parallel RLC circuit schematic driven by sinusoidal current.

Figure 13.5 Series RLC schematic elements.

Figure 13.6 Series RLC impedance schematic.

Figure 13.7a Series RLC circuit schematic driven by sinusoidal voltage.

Figure 13.7b Sinusoidal voltage source across resistor modeling resonance.

Figure 13.8 Series RLC impedance schematic.

Figure 13.9 Series RLC simulation schematic with sinusoidal voltage source....

Figure 13.10 Series RLC simulation results graph of impedance.

Figure 13.11 Series RLC simulation results graph of capacitor and inductor i...

Figure 13.12 Parallel RLC schematic.

Figure 13.13

resistive impedances in parallel.

Figure 13.14 Parallel RLC impedance schematic.

Figure 13.15 Parallel RLC schematic.

Figure 13.16 Parallel RLC impedance simulation results.

Figure 13.17a Parallel RLC circuit schematic driven by sinusoidal current.

Figure 13.17b Parallel current source and resistor with LC seemingly disconn...

Figure 13.18 Series RLC schematic with sinusoidal voltage source.

Figure 13.19 Series RLC schematic with sinusoidal voltage source.

Figure 13.20 Series RLC simulation schematic with sinusoidal voltage source....

Figure 13.21 Series RLC simulation results graph of voltage transfer functio...

Figure 13.22 Series RLC simulation results graph of voltage transfer functio...

Figure 13.23 Parallel RLC circuit schematic driven by sinusoidal current.

Figure 13.24 Parallel RLC circuit schematic driven by sinusoidal current.

Figure 13.25 Parallel RLC simulation schematic driven by sinusoidal current....

Figure 13.26 Parallel RLC simulation results plot of current transfer functi...

Figure 13.27 Parallel RLC simulation results plot of current transfer functi...

Figure 13.28 Series RLC circuit schematic driven by sinusoidal voltage.

Figure 13.29 Series RLC simulation schematic with sinusoidal voltage source....

Figure 13.30 Series RLC simulation of voltage transfer function magnitude wi...

Figure 13.31 Series RLC simulation of voltage transfer function magnitude in...

Figure 13.32 Series RLC simulation of voltage transfer function magnitude zo...

Figure 13.33 Series RLC 10 Ω simulation of voltage transfer function magnitu...

Figure 13.34 Parallel RLC circuit schematic driven by sinusoidal current.

Figure 13.35 Parallel RLC simulation schematic driven by sinusoidal current....

Figure 13.36 Parallel RLC 10 Ω simulation of current transfer function magni...

Figure 13.37 Parallel RLC 10 Ω simulation of current transfer function magni...

Figure 13.38 Parallel RLC 10 Ω simulation of current transfer function magni...

Figure 13.39 Parallel RLC 10 Ω simulation of voltage magnitude in dB.

Figure 13.40 Parallel RLC 3 Ω simulation of current transfer function magnit...

Figure 13.41 Series RLC circuit schematic driven by sinusoidal voltage.

Figure 13.42 Parallel RLC circuit schematic driven by sinusoidal current.

Chapter 14

Figure 14.1a Series RLC circuit with two initial conditions.

Figure 14.1b Parallel RLC circuit with two initial conditions.

Figure 14.2a Series RLC circuit with one initial condition.

Figure 14.2b Parallel RLC circuit with one initial condition.

Figure 14.3a Series RLC circuit with one initial condition.

Figure 14.3b Parallel RLC circuit with one initial condition.

Figure 14.4 Parallel RLC circuit schematic.

Figure 14.5a Series RLC circuit with two initial conditions.

Figure 14.5b Parallel RLC circuit with two initial conditions.

Figure 14.6a Overdamped series RLC simulated loop current.

Figure 14.6b Overdamped parallel RLC simulated voltage.

Figure 14.7a Critically damped series RLC simulated loop current.

Figure 14.7b Critically damped parallel RLC simulated voltage.

Figure 14.8a Underdamped series RLC simulated loop current.

Figure 14.8b Underdamped parallel RLC simulated voltage.

Figure 14.9a Lossless oscillatory series RLC simulated current.

Figure 14.9b Lossless oscillatory parallel RLC simulated voltage.

Figure 14.10 Series RLC simulation schematic with initial capacitor voltage....

Figure 14.11 Series RLC critically damped simulated current and capacitor vo...

Figure 14.12 Parallel RLC simulation schematic with initial inductor current...

Figure 14.13 Parallel RLC critically damped simulated voltage and inductor c...

Figure 14.14a Series RLC circuit with two initial conditions.

Figure 14.14b Parallel RLC circuit with two initial conditions.

Figure 14.15a Series RLC circuit with one initial condition.

Figure 14.15b Parallel RLC circuit with one initial condition.

Figure 14.16 Series RLC circuit with one initial condition.

Figure 14.17 Parallel RLC circuit with two initial conditions.

Figure 14.18 Series RLC circuit with one initial condition.

Figure 14.19 Parallel RLC circuit with two initial conditions.

Figure 14.20a Series RLC circuit with one initial condition.

Figure 14.20b Parallel RLC circuit with one initial condition.

Figure 14.21 Series RLC circuit with two initial conditions.

Figure 14.22 Parallel RLC circuit with two initial conditions.

Figure 14.23a Series RLC circuit with one initial condition.

Figure 14.23b Parallel RLC circuit with one initial condition.

Figure 14.24 Series RLC overdamped natural response current.

Figure 14.25 Series RLC overdamped root locations in the complex plane.

Figure 14.26 Series RLC critically damped natural response current.

Figure 14.27 Series RLC critically damped root locations in the complex plan...

Figure 14.28 Series RLC underdamped natural response current.

Figure 14.29 Series RLC underdamped root locations in the complex plane.

Figure 14.30 Series RLC lossless oscillatory natural response current.

Figure 14.31 Series RLC lossless oscillatory root locations in the complex p...

Figure 14.32 RLC natural response root locus locations in the complex plane....

Figure 14.33 RLC natural response overdamped and critically damped root loca...

Figure 14.34a Series RLC undriven circuit schematic.

Figure 14.34b Parallel RLC undriven circuit schematic.

Figure 14.35 Series RLC overdamped natural response current.

Figure 14.36 Series RLC critically damped natural response current.

Figure 14.37 Series RLC underdamped natural response current.

Figure 14.38 Series RLC lossless oscillatory natural response current.

Figure 14.39 RLC natural response root locus locations in the complex plane....

Chapter 15

Figure 15.1 RLC circuit driven by a voltage source step function with magnit...

Figure 15.2 Step function graph versus time with DC amplitude of

Figure 15.3 Series RLC simulation schematic driven by step voltage.

Figure 15.4 Series RLC circuit schematic driven by step voltage.

Figure 15.5 Series RLC simulated inductor and input voltages.

Figure 15.6 Series RLC simulated capacitor, resistor, and input voltages.

Figure 15.7 Series RLC simulated capacitor voltages for various dampings.

Figure 15.8 Step function graph.

Figure 15.9 Series RLC schematic driven by step voltage.

Figure 15.10 Parallel RLC simulation schematic driven by step current.

Figure 15.11 Parallel RLC circuit schematic driven by step current.

Figure 15.12 Parallel RLC simulated voltage and input current.

Figure 15.13 Parallel RLC simulated inductor and capacitor currents.

Figure 15.14 Parallel RLC simulated inductor currents for various dampings....

Figure 15.15 Parallel RLC simulation schematic with initial condition induct...

Figure 15.16 Parallel RLC simulated complete response voltage and input curr...

Figure 15.17 Parallel RLC simulated complete response capacitor and inductor...

Chapter 16

Figure 16.1 Impedance equation and real and imaginary parts.

Figure 16.2 Impedance equation with resistance and reactance.

Figure 16.3 Admittance equation with conductance and susceptance.

Figure 16.4a Complex plane with rectangular expression of complex number.

Figure 16.4b Complex plane with polar expression of complex number.

Figure 16.5 Complex plane with unit circuit and labeled with

Figure 16.6 Sine and cosine in terms of sides of a triangle and unit circle....

Figure 16.7 Tangent in terms of unit circuit on the complex plane.

Figure 16.8 Complex plane showing two complex conjugate complex numbers.

Figure 16.9a Resistive voltage divider circuit.

Figure 16.9b RL voltage divider circuit in terms of phasors.

Figure 16.10 Graph of sine wave marked as extending to infinity.

Figure 16.11 Stepped sine wave.

Figure 16.12 Projections of sine on the imaginary axis and cosine on the rea...

Figure 16.13 Graph of sine and cosine versus time showing 90°phase shift.

Figure 16.14 Two graphs of example phasor

leading phasor

by 90°.

Guide

Cover

Table of Contents

Series Page

Title Page

Dedication

About the Author

Acknowledgments

Begin Reading

Index

End User License Agreement

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First and Second Order Circuits and Equations

Technical Background and Insights

Robert O'RourkeUSA

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Library of Congress Cataloging‐in‐Publication Data

Names: O'Rourke, Robert (Electronic engineer), author.

Title: First and second order circuits and equations : technical background and insights / Robert O'Rourke.

Description: Hoboken, New Jersey : Wiley, [2024] | Includes index.

Identifiers: LCCN 2024008985 (print) | LCCN 2024008986 (ebook) | ISBN 9781119913535 (hardback) | ISBN 9781119913542 (adobe pdf) | ISBN 9781119913559 (epub)

Subjects: LCSH: Electric circuits. | Electronic circuits. | Differential equations.

Classification: LCC TK454 .O75 2024 (print) | LCC TK454 (ebook) | DDC 621.381501/5153‐‐dc23/eng/20240314

LC record available at https://lccn.loc.gov/2024008985

LC ebook record available at https://lccn.loc.gov/2024008986

Cover Design: Wiley

Cover Image: Courtesy of Robert O'Rourke

To my wife Evelyn, whose loving support made this book possible.

About the Author

Robert O'Rourke has an electrical engineering degree from UC Berkeley, including coursework in circuit theory and electromagnetics. Robert has taught electronics and calculus at college level. Robert worked with circuit theory and circuit and system simulation at Analogy, now a part of Synopsys, Inc. During several positions in his career, Robert hired and managed electronic engineers in applications engineering roles that involved circuit theory. Robert has taught circuit and electromagnetic simulation training courses for multiple vendors. As part of Ansys, Robert also created circuit and electromagnetic simulation product training courses for the Ansys Learning Hub.

Acknowledgments

The simulations made for this book and the simulation schematics and graphs appearing in this book were made with the QUCS simulator, available from SourceForge.net.

The author would also like to thank Professor Alberto Sangiovanni‐Vincentelli, who first taught him circuit theory at UC Berkeley.

Part 1Circuit Elements and Resistive Circuits

1Ohm's Law, Branch Relationships, and Sources

1.1 Chapter Summary and Polarity Reference

1.1.1 Chapter Summary

Ohm's law describes the relationship between voltage, current, and resistance for resistive circuits. This chapter describes Ohm's law and the related circuit elements, resistors, current sources, and voltage sources. This chapter also covers the more general idea of branch relationships, the relation between the voltage across a circuit element and the current through a circuit element, for resistors, voltage sources, and current sources.

Current source and resistor

Voltage source and resistor

Figure 1.1a Current source driving a resistor.

Figure 1.1b Voltage source across a resistor.

Figure 1.1a

, the current source drives current through the resistor causing a voltage drop across the resistor.

Figure 1.1b

, the voltage source across the resistor causes current to flow through the resistor.

The ideal independent

current source

supplies a fixed amount of current

through the resistor

regardless of the amount of voltage across the source.

The ideal independent

voltage source

supplies a fixed amount of voltage

across the resistor

regardless of the amount of current through the source.

The resistor

resists the flow of current through it. The amount of voltage

, that develops across the resistor

, as a result of the current

flowing through the resistor

, is determined by Ohm's law,

equals

, shown in Equation

1.1a

The resistor

resists the flow of current through it. The amount of current, that flows through the resistor, as a result of the voltage

across the resistor

, is determined by Ohm's law,

equals

over

, shown in Equation

1.1b

1.1.1.1 Ohm's Law

Figure 1.2 Resistor schematic symbol with passive sign convention.

The voltage across a resistor, shown in Figure 1.2, equals the current through the resistor times the resistance of the resistor.

(1.1a)

The current through a resistor equals the voltage across the resistor divided by the resistance of the resistor.

(1.1b)

1.1.1.2 Branch Relationships

The branch relationship is the equation describing the relationship between current through a circuit element (in a branch of a circuit) and the voltage across the circuit element. For example, Ohm's law V = IR or I = V/R is the branch relationship of a resistor. Figure 1.3, with a simple square shape, is a generic, non‐specific circuit element.

Figure 1.3 Passive sign convention on a generic fictitious schematic symbol.

1.1.2 Polarity Reference

In Figure 1.4a, 1 V divided by 5 Ω equals 200 mA (0.2 A).

Figure 1.4a 1 volt DC voltage source across a 5 ohm resistor.

In each of these two direct current (DC) examples, Figures 1.4a and 1.4b, the current in the loop is 200 mA DC, going down through the resistor from + to −, and the voltage across the 5 Ω resistor is 1 V DC.

Figure 1.4b 200 mA DC current source driving a 5 ohm resistor.

In Figure 1.4b, 0.2 A multiplied by 5 Ω equals 1 V.

1.1.2.1 DC Voltage Source Polarity Example

The voltage source in Figure 1.4a applies voltage across the resistor, and the + (plus) and − (minus) signs on the resistor indicate the polarity of the voltage.

Figure 1.5 shows a circuit simulation schematic corresponding to the circuit in Figure 1.4a. The voltage source symbol in Figure 1.5 is specific to DC voltage sources.

Figure 1.5 Circuit simulation schematic with avoltage source and a resistor.

There is a current meter in the right‐hand leg of the circuit, just below the resistor. The downward arrow in the current meter symbol indicates a reference direction pointing down; the current meter considers clockwise flow of current in the circuit to be positive.

For the DC circuit simulation, there is a table of results in Figure 1.5. VR, measured at the top of the circuit, is positive 1 V, and the current Pr1.I, measured by the current meter, is 200 mA, verifying that current flows downward through the resistor.

1.1.2.2 DC Current Source Polarity Example

The arrow, pointing up in the current source in Figure 1.4b, indicates the direction of a positive current from the source. Applying Ohm's law, multiplying the current times the resistance, tells us the voltage across the resistor, both the amount and the polarity of the voltage. The + (plus) and − (minus) signs on the resistor indicate the polarity of the voltage.

Figure 1.6 shows a circuit simulation schematic corresponding to the circuit in Figure 1.4b. The downward arrow in the current meter symbol indicates a reference direction pointing down; the current meter considers clockwise flow of current in the circuit to be positive.

Figure 1.6 Circuit simulation schematic with a current source and a resistor.

In Figure 1.6, the current source arrow points up, telling us that current flows up and out of the current source, and then down through the resistor. As expected from Ohm's law, 200 mA multiplied by 5 Ω yields 1 mV across the resistor. This 1 V result appears in the table under V1.V. The current direction of the current source and the current meter are the same, and the measured current, under Pr1.I, is positive 200 mA.

At the top of the schematic in Figure 1.6

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