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**Review of Basic Electrical and Magnetic Circuit Concepts**

Chapter 3 Review of Basic Electrical and Magnetic Circuit Concepts Electric Circuits Phasors Power, Power Factor Fourier Analysis Inductors and Capacitors Magnetic Circuits Transformers Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**AVERAGE POWER AND RMS CURRENT**

Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Sinusoidal Steady State**

Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Phasor Representation**

Z jL R Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Power, Reactive Power, Power Factor**

Complex power S Real power is Reactive power is Power Factor Ideally power factor should be 1.0 Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Chapter 3 Basic Electrical and Magnetic Circuit Concepts**

Example An inductive load connected to a 120V, 60Hz ac source draws 1 kW at a power factor of 0.8. Calculate the capacitance required in parallel with the load in order to bring the power factor to 0.95. Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Chapter 3 Basic Electrical and Magnetic Circuit Concepts**

Example (end) Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Non-sinusoidal waveforms in steady state**

Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Non-sinusoidal waveforms in steady state (cont.)**

current drawn from power electronic equipment is highly distorted However In steady state waveforms repeat with period T=1/f f is the fundamental frequency (f1) The current signal has many harmonics (multiples) of the fundamental The harmonics can be calculated by Fourier Analysis Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Chapter 3 Basic Electrical and Magnetic Circuit Concepts**

Fourier Analysis -a non sinusoidal waveform f(t) repeating with angular frequency can be expressed as Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Chapter 3 Basic Electrical and Magnetic Circuit Concepts**

Fourier Analysis Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Distortion in the Input Current**

Voltage is assumed to be sinusoidal Subscript “1” refers to the fundamental The phase 1 is between the voltage and the current fundamental Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Line-Current Distortion(1)**

Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Total Harmonic Distortion -THD**

Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Chapter 3 Basic Electrical and Magnetic Circuit Concepts**

POWER FACTOR - PF -starting with the definition of average power Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Inductor and Capacitor Phasors (1)**

Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Inductor and Capacitor Phasors (2)**

Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Phasor Representation**

Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**** Inductor and Capacitor Response**

Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Chapter 3 Basic Electrical and Magnetic Circuit Concepts**

Response of L and C Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Average vL and iC in steady state**

-steady-state condition implies that voltage and current waveforms repeat with a time period T: Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Inductor Voltage and Current in Steady State**

Volt-seconds over T equal zero. Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Capacitor Voltage and Current in Steady State**

Amp-seconds over T equal zero. Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Chapter 3 Basic Electrical and Magnetic Circuit Concepts**

Ampere’s Law Direction of magnetic field due to currents Ampere’s Law: Magnetic field along a path Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Chapter 3 Basic Electrical and Magnetic Circuit Concepts**

Ampere’s Law Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Direction of Magnetic Field**

Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Chapter 3 Basic Electrical and Magnetic Circuit Concepts**

Flux Lines Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Chapter 3 Basic Electrical and Magnetic Circuit Concepts**

Magnetic Flux Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Concept of Magnetic Reluctance**

Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Chapter 3 Basic Electrical and Magnetic Circuit Concepts**

Faraday’s Law Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Definition of Self-inductance L**

Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Chapter 3 Basic Electrical and Magnetic Circuit Concepts**

Inductance L A l Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Analysis of a Transformer (1)**

Very simple case: Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Analysis of a Transformer (2)**

Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Analysis of a Transformer (3)**

Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Transformer Equivalent Circuit**

Lm N2/N1 Lm Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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**Chapter 3 Basic Electrical and Magnetic Circuit Concepts**

Ideal Transformers R1=R2=0 Ll1=Ll2=0 Core permeability = Electrónica de Potência © 2008 José Bastos Chapter 3 Basic Electrical and Magnetic Circuit Concepts

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