1. Electric Circuit
- 1.1. Circuit Elements
- - 1.1.1. Active Circuit Elements
  - 1.1.2. Passive Circuit Elements
- 1.2. Ohms Law
- 1.3. Open Circuits
- 1.4. Short Circuits
2. Resistance
- 2.1. Resistance of Circular Wires
- 2.2. Temperature Effect on Resistance
- 2.3. Resistor
- 2.4. Color coding and Standard Resistor Values
- 2.5. Metric Units of Resistance
3. Series DC Circuits
- 3.1. Series Circuit
- 3.2. Circuit Instrumentation
- 3.3. Series Circuit Power Distribution
- 3.4. Series Voltage Sources
- 3.5. Kirchhoffs Voltage Law
- 3.6. Voltage Division in a Series Circuit
- 3.7. Interchanging Series Elements
- 3.8. Circuit Analysis Notation
- - 3.8.1. Single and Double Subscript Notation
- 3.9. Internal Resistance of Voltage Sources
- 3.10. Voltage Regulation
- 3.11. Loading Effects of Instruments
4. Parallel DC Circuits
- 4.1. Parallel Circuits
- 4.2. Power Distribution
- 4.3. Kirchhoffs Current law
- 4.4. Current Divider Rule
- 4.5. Voltage Sources in Parallel
- 4.6. Voltmeter Loading Effect
- 4.7. Troubleshooting Techniques
- 4.8. Parallel DC Circuits Applications
5. Series Parallel Circuits
- 5.1. Reduce and Return Approach
- 5.2. Block Diagram Approach
- 5.3. Ladder Networks
- 5.4. Voltage Divider Supply
- 5.5. Potentiometer Loading
- 5.6. Iron Vane Movement
6. Methods of Analysis
- 6.1. Current Sources
- 6.2. Branch Current Analysis
- 6.3. Mesh Analysis
- 6.4. Mesh Analysis with Current Sources
- 6.5. Nodal Analysis
- 6.6. Nodal Analysis with Voltage Sources
- 6.7. Bridge Networks
- 6.8. Wye Delta Transformation
7. Network Theorems
- 7.1. Linearity Property
- 7.2. Superposition Theorem
- 7.3. Thevenins Theorem
- 7.4. Nortons Theorem
- 7.5. Maximum Power Transfer Theorem
- 7.6. Application of Maximum Power Transfer Method
- 7.7. Millmans Theorem
- 7.8. Substitution Theorem
- 7.9. Reciprocity Theorem
8. Capacitors
- 8.1. Capacitance
- 8.2. Types of capacitor
- 8.3. Initial Conditions of capacitor
- 8.4. Capacitor Charging Phase
- 8.5. Capacitor Discharging Phase
- 8.6. Instantaneous Values of Capacitor
- 8.7. Thevenin Equivalent Circuit of Capacitor
- 8.8. Current through capacitor
- 8.9. Capacitors in series and parallel
- 8.10. Energy Stored by a Capacitor
- 8.11. Stray Capacitance
9. Magnetic Circuits
- 9.1. Magnetic Flux Density
- 9.2. Permeability
- 9.3. Magnetic Reluctance
- 9.4. Ohms Law for Magnetic Circuits
- 9.5. Magnetizing Force
- 9.6. Hysteresis Curve
- 9.7. Domain Theory of Magnetism
- 9.8. Amperes Circuital Law
- 9.9. Series Magnetic Circuits
- 9.10. Magnetic Circuit Air Gaps
- 9.11. Series Parallel Magnetic Circuits
- 9.12. Application of Magnetic circuits
10. Inductors
- 10.1. Faradays Law of Induction
- 10.2. Lenz law
- 10.3. Self Inductance
- 10.4. Types of Inductors
- 10.5. Inductor values
- 10.6. Induced Voltage
- 10.7. RL Transients (storage cycle)
- 10.8. Initial Values
- 10.9. RL Transients (decay cycle)
- 10.10. Thevenin Equivalent Circuit of Inductor
- 10.11. Inductors in Series and Parallel
- 10.12. RL and RLC Circuits with DC Inputs
- 10.13. Energy Stored by an Inductor
- 10.14. Application of inductors
11. Sinusoidal Alternating Waveforms
- 11.1. Sinusoidal AC Voltage Generation
- 11.2. Sinusoidal AC Waveform Definitions
- 11.3. The Sine Wave
- 11.4. General Format for the Sinusoidal Voltage or Current
- 11.5. Sinusoidal Waveforms Phase Relations
- 11.6. Average Value
- 11.7. Effective or Root Mean Square (rms) Values
- 11.8. AC meters and Instruments
12. The Basic Elements and Phasors
- 12.1. The Derivative
- 12.2. Response of Resistor to a Sinusoidal Voltage
- 12.3. Response of Inductor to a Sinusoidal Voltage
- 12.4. Response of Capacitor to a Sinusoidal Voltage
- 12.5. Frequency Effects on L and C in DC Circuits
- 12.6. Frequency Response of the Basic Elements
- 12.7. Sinusoidal Voltage Average Power
- 12.8. AC Power Factor
- 12.9. Complex Numbers
- 12.10. Phasors
13. Series and Parallel ac Circuits
- 13.1. Impedance and the Phasor Diagram
- 13.2. AC Series Configuration
- 13.3. AC Circuits Voltage divider rule
- 13.4. Frequency Response of the RC Circuit
- 13.5. SUMMARY of Series ac Circuits
- 13.6. Admittance and Susceptance
- 13.7. Parallel ac Networks
- 13.8. AC Circuits Current Divider Rule
- 13.9. Frequency Response of the Parallel RL Network
- 13.10. Parallel ac Networks Summary
- 13.11. AC Equivalent Circuit
- 13.12. Phase Shift Measurement with Dual Trace Oscilloscope
- 13.13. Application of Series and Parallel ac Circuits
- - 13.13.1. Home Wiring
  - 13.13.2. Speaker Systems
14. Methods of Analysis of AC Network
- 14.1. Independent Versus Dependent Controlled Sources
- 14.2. Source Conversion of ac Circuits
- 14.3. Mesh Analysis for ac Circuits
- 14.4. Nodal Analysis for ac Circuits
- 14.5. AC Bridge Networks
- 14.6. Ac Wye Delta Transformation
15. AC Network Theorem
- 15.1. Superposition Theorem (ac)
- 15.2. Thevenins Theorem (ac)
- 15.3. Nortons Theorem (ac)
- 15.4. Maximum Power Transfer Theorem (ac)
16. Power (AC)
- 16.1. Resistive (AC) Circuit Power Calculation
- 16.2. Apparent Power
- 16.3. Inductive Circuit and Reactive Power
- 16.4. Capacitive Circuit
- 16.5. The Power Triangle
- 16.6. The Total P, Q and S
- 16.7. Power Factor Correction
- 16.8. Wattmeters and Power Factor Meters
- 16.9. Effective Resistance
17. Resonance
- 17.1. Series Resonant Circuit
- 17.2. The Quality Factor (Q)
- 17.3. Total Impedance Versus Frequency
- 17.4. Selectivity of Frequency
- 17.5. Magnitudes of Voltages across RLC versus Frequency
- 17.6. Examples of Series Resonance Circuits
- 17.7. Parallel Resonant Circuit
- - 17.7.1. Resonace Frequency of a Parallel Resonant Circuit
- 17.8. Selectivity Curve for Parallel Resonant Circuits
- 17.9. Effect of Quality Factor greater than or Equal to 10
- 17.10. Examples of Parallel Resonance
- 17.11. Applications of Resonance Circuits
18. Transformer
- 18.1. Mutual Inductance
- 18.2. The Iron Core Transformer
- 18.3. Reflected Impedance and Power
- - 18.3.1. Transformer as a Impedance Matching
  - 18.3.2. Transformer as an Isolation Device
- 18.4. Iron Core Transformer Equivalent Circuit
- 18.5. Transformer Frequency Considerations
- 18.6. Series Connection of Mutually Coupled Coils
- 18.7. Air Core Transformer
- 18.8. Transformer Nameplate Data
- 18.9. Types of Transformers
- 18.10. Tapped and Multiple Load Transformers
- 18.11. Networks with Magnetically Coupled Coils
- 18.12. Applications of Transformer
- - 18.12.1. Transformer for Low Voltage Compensation
  - 18.12.2. Ballast Transformer
19. Polyphase Systems
- 19.1. The Three Phase Generator
- 19.2. The Y Connected Generator
- - 19.2.1. Phase Sequence (Y CONNECTED GENERATOR)
  - 19.2.2. Y connected Generator connected to a Y connected load
- 19.3. The Y Delta System
- 19.4. The Delta Connected Generator
- 19.5. The Delta Delta, Delta Y Three Phase Systems
- 19.6. Power Calculation of Y Connected Balanced Load
- 19.7. Power Calculation of Delta Connected Balanced Load
- 19.8. The Three Wattmeter Method
- 19.9. The Two Wattmeter Method
- 19.10. Unbalanced Three phase Four wire, Y Connected Load
- 19.11. Unbalanced, Three phase, Three wire, Y Connected Load
20. Frequency Response
- 20.1. Logarithm
- 20.2. Decibels
- 20.3. Transfer Function
- 20.4. Filters
- 20.5. Bode Plots
- - 20.5.1. High Pass RC Filter
  - 20.5.2. Low Pass RC Filter
- 20.6. Sketching the Bode Response
- 20.7. Low Pass Filter with Limited Attenuation
- 20.8. High Pass Filter with Limited Attenuation
- 20.9. Crossover Networks
- 20.10. Application of Filters
- - 20.10.1. Attenuators
  - 20.10.2. Noise Filters
21. Pulse Waveform and the RC Response
- 21.1. Ideal versus Actual Pulse Waveform
- 21.2. Properties of a Pulse Waveform
- 21.3. Pulse Repetition Rate and Duty Cycle
- 21.4. Average Value of a Pulse Waveform
- 21.5. Transient in RC Network
- 21.6. RC Response to Square Wave Inputs
- 21.7. Oscilloscope Attenuator
- 21.8. Compensating Attenuator Probe
- 21.9. Application of Pulse Waveform
22. The Laplace Transform
- 22.1. Properties of The Laplace Transform
- 22.2. List of the Properties of The Laplace Transform
- 22.3. Examples of The Laplace Transform
- 22.4. The Inverse Laplace Transform
- 22.5. Examples of The Inverse Laplace Transform
- 22.6. Circuit Application of The Laplace Transform
- 22.7. Transfer Function of The Laplace Transform
- 22.8. The Convolution Integral
- 22.9. Application to Integrodifferential Equations
- 22.10. Application of The Laplace Transform to the Network Stability
- 22.11. Application of The Laplace Transform to the Network Synthesis
23. The Fourier Series
- 23.1. Trigonometric Fourier Series
- 23.2. Symmetry Considerations of The Fourier Series
- 23.3. Common Functions of The Fourier Series
- 23.4. Circuit Application of The Fourier Series
- 23.5. Average Power and RMS Values of The Fourier Series
- 23.6. Exponential Fourier Series
- 23.7. Application of the Fourier Series to Spectrum Analyzers
- 23.8. Application of the Fourier Series to Filters
24. Fourier Transform
- 24.1. Properties of the Fourier Transform
- 24.2. Examples of the Fourier Transform
- 24.3. Examples of the Inverse Fourier Transform
- 24.4. Circuit Application of the Fourier Transform
- 24.5. Parsevals Theorem
- 24.6. Comparing the Fourier and Laplace Transform
- 24.7. Application of the Fourier Transform to the Amplitude Modulation
- 24.8. Application of the Fourier Transform to the Sampling
25. Two Port Networks
- 25.1. Impedance Parameters
- 25.2. Admittance Parameters
- 25.3. Hybrid Parameters
- 25.4. Transmission Parameters
- 25.5. Relationships between Parameters
- 25.6. Interconnection of Networks
- 25.7. Application of the Two Port Networks to the Transistor Circuits
- 25.8. Application of the Two Port Networks to the Ladder Network Synthesis
26. Nonsinusoidal Circuits
- 26.1. Circuit Response to a Nonsinusoidal Input
- 26.2. Addition and Subtraction of Nonsinusoidal Waveforms

Properties of the Fourier Transform

Electrical Circuit Analysis > Fourier Transform

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We now develop some properties of the Fourier transform that are useful in finding the transforms of complicated functions from the transforms of simple functions. For each property, we will first state and derive it, and then illustrate it with some examples.

Linearity
Time Scaling
Time Shifting
Frequency Shifting (or Amplitude Modulation)
Time Differentiation
Time Integration
Reversal
Duality
Convolution

The Fourier Series

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Properties of the Fourier Transform

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