Appendix F: Quality Factor of RLC Circuits
by Ahmad Hemami
Electricity and Electronics for Renewable Energy Technology
- Cover
- Half Title
- Title
- Copyright
- Dedication
- Contents
- Preface
- Acknowledgments
- Author
- 1 Energy and Electricity
- 2 Basic Mathematics and Systems of Measurement Units
- 2.1 Introduction
- 2.2 Ratio and Percentage
- 2.3 Area and Volume Ratios
- 2.4 Angles, Triangles, and Trigonometric Relationships
- 2.5 Principal Measurement Entities and Systems of Measurement
- 2.6 Other Measurement Entities and Their Derivation
- 2.7 Conversion between Systems of Measurement Units
- 2.8 Formulas, Relationships, and Equations
- 2.9 Chapter Summary
- 3 Atomic Structure of Materials
- 3.1 Introduction
- 3.2 Material Properties
- 3.3 Atom and Molecule
- 3.4 Atomic Structure of Materials
- 3.5 Differences between Materials
- 3.6 Similarities between Materials Based on Valence Electrons
- 3.7 Categorization of Materials: Conductors and Insulators
- 3.8 Electric Charge and Energy in Electrons
- 3.9 Chapter Summary
- 4 DC and AC Electricity
- 5 Voltage, Current, and Power
- 5.1 Introduction
- 5.2 Electric Current
- 5.3 Electric Voltage
- 5.4 Ohm’s Law: Relationship between Voltage, Current, and Load Resistance
- 5.5 Measuring Electric Current
- 5.6 Measuring Electric Voltage
- 5.7 Multimeter
- 5.8 Measuring Resistance
- 5.9 Electric Power
- 5.10 Measuring Electric Power and Energy
- 5.11 Chapter Summary
- 6 DC Circuits Relationships
- 6.1 Introduction
- 6.2 Series Circuit
- 6.3 Resistors in Series
- 6.4 Parallel Circuit
- 6.5 Resistors in Parallel
- 6.6 Combined Series and Parallel Resistors
- 6.7 Rule of Series Circuits
- 6.8 Rule of Parallel Circuits
- 6.9 Examples of Combined Circuits
- 6.10 Voltage Divider
- 6.11 Capacitors in DC Circuits
- 6.12 Inductors in DC Circuits
- 6.13 Power in DC Circuits
- 6.14 Chapter Summary
- 7 DC Motors and Generators
- 8 AC Circuits Relationships
- 8.1 Introduction
- 8.2 Vectors
- 8.3 AC Circuit Measurements and Values
- 8.4 Resistors in AC Circuits
- 8.5 Inductors in AC Circuits
- 8.6 Capacitors in AC Circuits
- 8.7 Power in Inductors and Capacitors
- 8.8 Phase Difference
- 8.9 Power in AC
- 8.10 Series RLC Circuits
- 8.11 Parallel RLC Circuits
- 8.12 Voltage Divider in AC Circuits
- 8.13 Resonance
- 8.14 Power Factor Correction
- 8.15 Chapter Summary
- Advanced Learning: AC Problem Solving Using Complex Numbers
- 9 Three-Phase Systems
- 9.1 Introduction
- 9.2 Three-Phase Electricity
- 9.3 Properties of a Three-Phase System
- 9.4 Load Connection in Three-Phase Systems
- 9.5 Three-Phase Loads
- 9.6 Use of Vectors in Three-Phase Electricity
- 9.7 Unbalanced Loads
- 9.8 Chapter Summary
- Advanced Learning: Mathematical Representation of Three-Phase Systems
- 10 Transformers
- 10.1 Introduction
- 10.2 An Illustrative Example
- 10.3 Single-Phase Transformer
- 10.4 Ideal Transformer
- 10.5 Autotransformer and Isolation Transformer
- 10.6 Transformer Mounting
- 10.7 Three-Phase Transformers
- 10.8 Transformer Applications and Power Rating
- 10.9 Transformer Efficiency
- 10.10 Transformer Circuits
- 10.11 Chapter Summary
- Advanced Learning: Real Transformer Circuit Analysis
- 11 AC Motors and Generators
- 12 Electric Power Transmission and Distribution
- 12.1 Introduction
- 12.2 Power Transmission and Distribution
- 12.3 Electric Cables
- 12.4 Fault Detection and Protective Measures
- 12.5 Transmission Lines
- 12.6 Rules for Network Problems
- 12.7 High Voltage Direct Current Transmission
- 12.8 Chapter Summary
- Advanced Learning: Positive, Negative, and Zero Sequence for Fault Analysis
- 13 Electronic Components, Functions, and Devices
- 14 Diode
- 15 Regulating Diodes and Applications
- 16 Diode Rectifiers and Filters
- 17 Transistor
- 17.1 Introduction
- 17.2 Junction Transistor
- 17.3 Transistor Size and Packaging
- 17.4 Transistors Connection and Biasing Configuration
- 17.5 Modes of Operation
- 17.6 How a Transistor Works
- 17.7 Transistor Properties
- 17.8 Transistor Main Functions
- 17.9 Transistor as a Switch
- 17.10 Transistor Amplifier
- 17.11 Biasing a Transistor
- 17.12 Chapter Summary
- 18 Transistor Circuits
- 18.1 Introduction
- 18.2 Transistor Characteristic Curves
- 18.3 Common-Emitter Amplifier
- 18.4 Common-Base Amplifier
- 18.5 Common-Collector Amplifier
- 18.6 Current Gain, Voltage Gain, and Power Gain in Amplifiers
- 18.7 Amplifier Classes
- 18.8 Input and Output Impedance
- 18.9 Coupling and Impedance Matching
- 18.10 Testing Transistors
- 18.11 Chapter Summary
- 19 Switchable Diodes and Gated Transistors
- 20 Power Converters
- 21 Electronic Power Converters in Wind Turbines and Solar Photovoltaic Systems
- 22 Digital Electronics
- 23 Logic Circuits and Applications
- 24 Encoders and Decoders
- Glossary
- Appendix A: Internal Resistance of Batteries and Battery Aging
- Appendix B: Switches
- Appendix C: Special Transformers
- Appendix D: Mil and Circular Mil
- Appendix E: Standard Resistors
- Appendix F: Quality Factor of RLC Circuits
- Appendix G: Structure of Logic Gates
- Index
Appendix F: Quality Factor of RLC Circuits
This appendix is added for those readers who might need it for other application than electric circuits, such as in communications. For parallel and series circuits a quality factor Q can be defined using the values of the three components. Q is a ratio; so it is a number without any unit. Here R is the resistance of a resistor that is part of the RLC and must not be confused with the internal resistance of a coil as an inductor.
For a parallel RLC circuit the quality is
| (F.1) |
At the resonance frequency, for which XC = XL, C can be substituted in terms of L and Equation F.1 assumes the form
| (F.2) |
Because XC = XL, Q can also be written as Q =
For a series RLC the quality is XC
| (F.3) |
and for the resonance frequency (XC = XL) substituting for C in terms of L leads to
| (F.4) |
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