Harmonic Formulas for Filtering Applications


 Tabitha Payne
 2 years ago
 Views:
Transcription
1 Harmonic Formulas for Filtering Applications Trigonometric Series Harmonic Analysis The history of the trigonometric series, for all practical purposes, came of age in 1822 with Joseph De Fourier s book that developed the concept. The basic idea of trigonometric series is to represent periodic functions by series of particular (trigonometric) period functions. Series of functions in which the general term is, with constant coefficients of a n b n, are called trigonometric series. Trigonometric series will converge in an interval of length, 2, since this is true the functions are periodic will converge for all x represents a periodic function. This function is not necessary continuous however. We only consider series that converges uniformly, then its sum in electrical systems. is continuous. This is what we have for harmonic analysis In our case a connection can be established between coefficients a n b n the sum function of. The multiplication of the series looks something like this Factors bounded by cos(px) or sin(px), where p is a positive integer allows us to calculate Integration of the series or for the integrals over the interval. When p these integrals have a value of 0. For p=n they are for n>0 for n=0
2 Because n=0 behaves like it does it is now conventional to write the trigonometric series as The EulerFourier formulae for n 0 looks like this Harmonic Analysis Formulas Let look back at basic circuits for a moment. We learned from Ohms law V = IR P=VI P=I 2 R. So the power delivered by an ac circuit at any given time is (1) Now we need the trigonometric identity we learned years ago (2) But the average power delivered by a ac source is the first term only, since the average value of a cosine wave is zero. It may have twice the frequency of the original input current waveform. Equating the average power of an ac generator to that delivered by a dc source: P av(ac) = P dc, leaves us with (3) So the effective values give us (4)
3 The effective value of any quantity plotted as a function of time can be found by using the following equation: or (5) This finally takes us to where we always wanted to go. By applying this equation to the following Fourier series we get (6) Then form (5) after performing the indicated operations we have the following: (7) but, since (8) Similarly, for (9) (10) (11) Looking what is called in mathematics as odd functions, this means x, x3, x5, x7 the like for which we have
4 Underst that even functions have nothing to do with even harmonics, nor odd functions with odd harmonics. An odd function is simply a function with odd powers of x an odd harmonic has an odd multiple of the fundamental frequency. This being state it is obvious that the sine wave is odd the cosine wave is even. Therefore, the sum of sine waves will be odd, a Fourier series containing only sine components represents an odd function. Just an aside when even odd functions are added the sum will be neither odd nor even. We will not get into that in this paper. Plotting three sine waves, 60 hertz as fundamental, the 5th 7th harmonic of 60 hertz. Using 360 degrees for the fundamental, we get 1800 degrees for the 5th 2520 degrees for the 7th. The individual sine waves look like this. We allowed the amplitude to 20 for the fundamental, 10 for the 5 th harmonic 5 for the 7 th harmonic. Adding these simultaneously we get the following distorted wave.
5 Assuming these are currents from (8), we get = amps This is known as the Total Harmonic Distortion Current or THDI. Series Resonant Circuit For the series RLC circuit resonance will occur when the total impedance is purely resistance. This occurs when X L = X C With this we can exp this
6 or where (1) (2) We already know, from earlier discussions, that we allow H to be a multiple of "f" we can force (2) to look like this then changing this to Reducing this we get (3) H will be the harmonic multiple to the fundamental From an earlier paper we showed the following:
7 From (3) we can come up with the systems harmonic resonance (4) Where: H = harmonic order MVA sc = = available short circuit at the capacitor bank. MVAR = capacitor bank size.
Fourier Series Analysis
School of Engineering Department of Electrical and Computer Engineering 332:224 Principles of Electrical Engineering II aboratory Experiment 6 Fourier Series Analysis 1 Introduction Objectives The aim
More informationCHAPTER 2 FOURIER SERIES
CHAPTER 2 FOURIER SERIES PERIODIC FUNCTIONS A function is said to have a period T if for all x,, where T is a positive constant. The least value of T>0 is called the period of. EXAMPLES We know that =
More informationFrequency response of a general purpose singlesided OpAmp amplifier
Frequency response of a general purpose singlesided OpAmp amplifier One configuration for a general purpose amplifier using an operational amplifier is the following. The circuit is characterized by:
More informationFourier Analysis. Nikki Truss. Abstract:
Fourier Analysis Nikki Truss 09369481 Abstract: The aim of this experiment was to investigate the Fourier transforms of periodic waveforms, and using harmonic analysis of Fourier transforms to gain information
More informationFig. 2 shows a simple step waveform in which switching time of power devices are not considered and assuming the switch is ideal.
CHAPTER 3: ANAYSIS OF THREEEE INERTER In this chapter an analysis of threelevel converter is presented by considering the output voltage waveform in order to determine the switching angle of power devices.
More informationLecture5. Fourier Series
Lecture5. Fourier Series In 1807 the French mathematician Joseph Fourier (17681830) submitted a paper to the Academy of Sciences in Paris. In it he presented a mathematical treatment of problems involving
More informationEðlisfræði 2, vor 2007
[ Assignment View ] [ Pri Eðlisfræði 2, vor 2007 31. Alternating Current Circuits Assignment is due at 2:00am on Wednesday, March 21, 2007 Credit for problems submitted late will decrease to 0% after the
More informationAdvanced Engineering Mathematics Prof. Jitendra Kumar Department of Mathematics Indian Institute of Technology, Kharagpur
Advanced Engineering Mathematics Prof. Jitendra Kumar Department of Mathematics Indian Institute of Technology, Kharagpur Lecture No. # 28 Fourier Series (Contd.) Welcome back to the lecture on Fourier
More informationIEEE519 SAYS. Harmonics are a function of the distribution system and the circuit configuration of the distorting load.
IEEE519 SAYS IEEE 519 1992 defines a harmonic as, "A sinusoidal component of a periodic wave or quantity having a frequency that is an integral multiple of the fundamental frequency. Harmonics are a function
More informationChapter 8. Introduction to Alternating Current and Voltage. Objectives
Chapter 8 Introduction to Alternating Current and Voltage Objectives Identify a sinusoidal waveform and measure its characteristics Describe how sine waves are generated Determine the various voltage and
More informationCoupled Electrical Oscillators Physics 3600 Advanced Physics Lab Summer 2010 Don Heiman, Northeastern University, 5/10/10
Coupled Electrical Oscillators Physics 3600 Advanced Physics Lab Summer 00 Don Heiman, Northeastern University, 5/0/0 I. Introduction The objectives of this experiment are: () explore the properties of
More informationContinuous Time Signals (Part  I) Fourier series
Continuous Time Signals (Part  I) Fourier series (a) Basics 1. Which of the following signals is/are periodic? (a) s(t) = cos t + cos 3t + cos 5t (b) s(t) = exp(j8 πt) (c) s(t) = exp( 7t) sin 1πt (d)
More informationME231 Measurements Laboratory Spring Fourier Series. Edmundo Corona c
ME23 Measurements Laboratory Spring 23 Fourier Series Edmundo Corona c If you listen to music you may have noticed that you can tell what instruments are used in a given song or symphony. In some cases,
More informationExperiment 08: RLC Circuits and Resonance Dr. Pezzaglia
Mar9 RLC Circuit Page Experiment 8: RLC Circuits and Resonance Dr. Pezzaglia Theory When a system at a stable equilibrium is displaced, it will tend to oscillate. An Inductor combined with Capacitor will
More informationBasic Electrical Theory
Basic Electrical Theory Impedance PJM State & Member Training Dept. PJM 2014 10/24/2013 Objectives Identify the components of Impedance in AC Circuits Calculate the total Impedance in AC Circuits Identify
More informationBASIC ELECTRONICS AC CIRCUIT ANALYSIS. December 2011
AM 5202 BASIC ELECTRONICS AC CIRCUIT ANALYSIS December 2011 DISTRIBUTION RESTRICTION: Approved for Pubic Release. Distribution is unlimited. DEPARTMENT OF THE ARMY MILITARY AUXILIARY RADIO SYSTEM FORT
More informationReactance and Impedance
Reactance and Impedance Capacitance in AC Circuits Professor Andrew H. Andersen 1 Objectives Describe capacitive ac circuits Analyze inductive ac circuits Describe the relationship between current and
More informationAn introduction to generalized vector spaces and Fourier analysis. by M. Croft
1 An introduction to generalized vector spaces and Fourier analysis. by M. Croft FOURIER ANALYSIS : Introduction Reading: Brophy p. 5863 This lab is u lab on Fourier analysis and consists of VI parts.
More informationAlternating Current. Asist. Prof. Dr. Aytaç Gören Asist. Prof. Dr. Levent Çetin
Asist. Prof. Dr. Aytaç Gören Asist. Prof. Dr. Levent Çetin 30.10.2012 Contents Alternating Voltage Phase Phasor Representation of AC Behaviors of Basic Circuit Components under AC Resistance, Reactance
More informationHarmonic Design Considerations
Harmonic Design Considerations Michael Leporace Specification Engineer, GE Consumer & Industrial ABSTRACT Power quality can be defined as the comparison of voltage and current waveforms to their fundamental
More informationMaths 361 Fourier Series Notes 2
Today s topics: Even and odd functions Real trigonometric Fourier series Section 1. : Odd and even functions Consider a function f : [, ] R. Maths 361 Fourier Series Notes f is odd if f( x) = f(x) for
More informationRightMark Audio Analyzer
RightMark Audio Analyzer Version 2.5 2001 http://audio.rightmark.org Tests description 1 Contents FREQUENCY RESPONSE TEST... 2 NOISE LEVEL TEST... 3 DYNAMIC RANGE TEST... 5 TOTAL HARMONIC DISTORTION TEST...
More informationPHASOR DIAGRAMS HANDSON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER  BPA
PHASOR DIAGRAMS HANDSON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER  BPA What are phasors??? In normal practice, the phasor represents the rms maximum value of the positive half cycle of the sinusoid
More informationR1 R2 R3. Figure1. Resistances in series V1 I. Figure 2. Equivalent circuit of figure 1 if RE= R1+R2+R3 VRE =V
Supplementary Notes for Unit 2  Part A (Unit 3 and 4 exams also includes the topics detailed in this note) Series circuits A series circuit is a circuit in which resistors are arranged in a chain, so
More informationSine and Cosine Series; Odd and Even Functions
Sine and Cosine Series; Odd and Even Functions A sine series on the interval [, ] is a trigonometric series of the form k = 1 b k sin πkx. All of the terms in a series of this type have values vanishing
More informationBasic AC Reactive Components IMPEDANCE
Basic AC Reactive Components Whenever inductive and capacitive components are used in an AC circuit, the calculation of their effects on the flow of current is important. EO 1.9 EO 1.10 EO 1.11 EO 1.12
More informationChapter 3. Simulation of NonIdeal Components in LTSpice
Chapter 3 Simulation of NonIdeal Components in LTSpice 27 CHAPTER 3. SIMULATION OF NONIDEAL COMPONENTS IN LTSPICE 3.1 PreLab The answers to the following questions are due at the beginning of the lab.
More informationFOURIER SERIES INSTRUCTOR: DR. GÜLDEN KÖKTÜRK
FOURIER SERIES INSTRUCTOR: DR. GÜLDEN KÖKTÜRK Contact Information Phone: 412 71 65 Email: gulden.kokturk@deu.edu.tr Web page: gulden.kokturk.com Office Hours for This Module April, 59: Wendesday 34,
More informationChapter 12. RL Circuits. Objectives
Chapter 12 RL Circuits Objectives Describe the relationship between current and voltage in an RL circuit Determine impedance and phase angle in a series RL circuit Analyze a series RL circuit Determine
More informationε: Voltage output of Signal Generator (also called the Source voltage or Applied
Experiment #10: LR & RC Circuits Frequency Response EQUIPMENT NEEDED Science Workshop Interface Power Amplifier (2) Voltage Sensor graph paper (optional) (3) Patch Cords Decade resistor, capacitor, and
More informationf x a 0 n 1 a 0 a 1 cos x a 2 cos 2x a 3 cos 3x b 1 sin x b 2 sin 2x b 3 sin 3x a n cos nx b n sin nx n 1 f x dx y
Fourier Series When the French mathematician Joseph Fourier (768 83) was tring to solve a problem in heat conduction, he needed to epress a function f as an infinite series of sine and cosine functions:
More informationExperiment 16 ANALOG FOURIER ANALYSIS. Experiment setup 4. Prelab problems 6. Experiment procedure 7. Appendix A: an effective highq filter A1
16i Experiment 16 ANALOG FOURIER ANALYI Introduction 1 Theory 1 Experiment setup 4 Prelab problems 6 Experiment procedure 7 Appendix A: an effective highq filter A1 16ii 161 1/31/14 INTRODUCTION In
More informationIntroduction to Complex Fourier Series
Introduction to Complex Fourier Series Nathan Pflueger 1 December 2014 Fourier series come in two flavors. What we have studied so far are called real Fourier series: these decompose a given periodic function
More informationφ 1, φ 2, φ 3 are the phase shifts of the respective sine wave components
Harmonic Currents Sources, Problems and Solutions Kevin Gaughan 5 November 005 Outline: Mathematical Background Source of Harmonic Currents Total Harmonic Distortion Problems caused by harmonic currents
More informationA complex number W consists of real and imaginary parts a and b respectively, and the imaginary constant j which is the square root of negative one.
eactance and Impedance A Voltage and urrent In a D circuit, we learned that the relationship between voltage and current was V=I, also known as Ohm's law. We need to find a similar law for A circuits,
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4  ALTERNATING CURRENT
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4  ALTERNATING CURRENT 4 Understand singlephase alternating current (ac) theory Single phase AC
More information2 Background: Fourier Series Analysis and Synthesis
GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGINEERING ECE 2025 Spring 2001 Lab #11: Design with Fourier Series Date: 3 6 April 2001 This is the official Lab #11 description. The
More informationHarmonics Made Simple
Harmonics Made Simple Just because harmonics is becoming a more prevalent problem, that doesn t mean the subject is getting any easier to understand Welding equipment is one of several sources of harmonics
More informationAC Circuits (CETT 1405) Credit: 4 semester credit hours (3 hours lecture, 4 hours lab) Prerequisite: CETT 1403
AC (CETT 1405) Credit: 4 semester credit hours (3 hours lecture, 4 hours lab) Prerequisite: CETT 1403 Course Description A study of the fundamentals of alternating current including series and parallel
More informationLesson 27. (1) Root Mean Square. The emf from an AC generator has the time dependence given by
Lesson 27 () Root Mean Square he emf from an AC generator has the time dependence given by ℇ = ℇ "#$% where ℇ is the peak emf, is the angular frequency. he period is he mean square value of the emf is
More informationEngineering Mathematics II
PSUT Engineering Mathematics II Fourier Series and Transforms Dr. Mohammad Sababheh 4/14/2009 11.1 Fourier Series 2 Fourier Series and Transforms Contents 11.1 Fourier Series... 3 Periodic Functions...
More informationTrigonometric Functions
Trigonometric Functions MATH 10, Precalculus J. Robert Buchanan Department of Mathematics Fall 011 Objectives In this lesson we will learn to: identify a unit circle and describe its relationship to real
More informationRESONANCE AND FILTERS
14221 RESONANCE AND FILTERS Experiment 1, Resonant Frequency and Circuit Impedance For more courses visit www.ciewc.edu OBJECTIVES 1. To verify experimentally our theoretical predictions concerning the
More informationBasic Electrical Theory
Basic Electrical Theory Power Principles and Phase Angle PJM State & Member Training Dept. PJM 2014 10/24/2013 Objectives At the end of this presentation the learner will be able to; Identify the characteristics
More informationRecap on Fourier series
Civil Engineering Mathematics Autumn 11 J. Mestel, M. Ottobre, A. Walton Recap on Fourier series A function f(x is called periodic if f(x = f(x + for all x. A continuous periodic function can be represented
More information4.6 GRAPHS OF OTHER TRIGONOMETRIC FUNCTIONS. Copyright Cengage Learning. All rights reserved.
4.6 GRAPHS OF OTHER TRIGONOMETRIC FUNCTIONS Copyright Cengage Learning. All rights reserved. What You Should Learn Sketch the graphs of tangent functions. Sketch the graphs of cotangent functions. Sketch
More informationDirect versus Alternating Current Things We Can Measure
Phil Sherrod W4PHS Direct versus Alternating Current Things We Can Measure Direct Current (DC) Alternating Current (AC) Voltage Voltage (peak, RMS) Current Current (peak, effective) Power True power, Apparent
More informationLecture VI. Review of even and odd functions Definition 1 A function f(x) is called an even function if. f( x) = f(x)
ecture VI Abstract Before learning to solve partial differential equations, it is necessary to know how to approximate arbitrary functions by infinite series, using special families of functions This process
More informationFourier Series. 1. Fullrange Fourier Series. ) + b n sin L. [ a n cos L )
Fourier Series These summary notes should be used in conjunction with, and should not be a replacement for, your lecture notes. You should be familiar with the following definitions. A function f is periodic
More informationEXPERIMENT 5: SERIES AND PARALLEL RLC RESONATOR CIRCUITS
EXPERIMENT 5: SERIES AND PARALLEL RLC RESONATOR CIRCUITS Equipment List S 1 BK Precision 4011 or 4011A 5 MHz Function Generator OS BK 2120B Dual Channel Oscilloscope V 1 BK 388B Multimeter L 1 Leeds &
More informationR f. V i. ET 438a Automatic Control Systems Technology Laboratory 4 Practical Differentiator Response
ET 438a Automatic Control Systems Technology Laboratory 4 Practical Differentiator Response Objective: Design a practical differentiator circuit using common OP AMP circuits. Test the frequency response
More informationPOWER SYSTEM HARMONICS. A Reference Guide to Causes, Effects and Corrective Measures AN ALLENBRADLEY SERIES OF ISSUES AND ANSWERS
A Reference Guide to Causes, Effects and Corrective Measures AN ALLENBRADLEY SERIES OF ISSUES AND ANSWERS By: Robert G. Ellis, P. Eng., Rockwell Automation Medium Voltage Business CONTENTS INTRODUCTION...
More informationE X P E R I M E N T 7
E X P E R I M E N T 7 The RC Circuit Produced by the Physics Staff at Collin College Copyright Collin College Physics Department. All Rights Reserved. University Physics II, Exp 7: The RC Circuit Page
More informationFourier Series Chapter 3 of Coleman
Fourier Series Chapter 3 of Coleman Dr. Doreen De eon Math 18, Spring 14 1 Introduction Section 3.1 of Coleman The Fourier series takes its name from Joseph Fourier (1768183), who made important contributions
More informationExperiment # (4) AM Demodulator
Islamic University of Gaza Faculty of Engineering Electrical Department Experiment # (4) AM Demodulator Communications Engineering I (Lab.) Prepared by: Eng. Omar A. Qarmout Eng. Mohammed K. Abu Foul Experiment
More informationInverse Circular Function and Trigonometric Equation
Inverse Circular Function and Trigonometric Equation 1 2 Caution The 1 in f 1 is not an exponent. 3 Inverse Sine Function 4 Inverse Cosine Function 5 Inverse Tangent Function 6 Domain and Range of Inverse
More informationFilters & Wave Shaping
Module 8 AC Theory Filters & Wave Shaping Passive Filters & Wave Shaping What you'll learn in Module 8. Module 8 Introduction Recognise passive filters with reference to their response curves. High pass,
More informationInductive and Capacitive Reactance
Inductive and Capacitive Reactance Course No: E04005 Credit: 4 PDH A. Bhatia Continuing Education and Development, Inc. 9 Greyridge Farm Court Stony Point, NY 10980 P: (877) 3225800 F: (877) 3224774
More informationM344  ADVANCED ENGINEERING MATHEMATICS Lecture 9: Orthogonal Functions and Trigonometric Fourier Series
M344  ADVANCED ENGINEERING MATHEMATICS ecture 9: Orthogonal Functions and Trigonometric Fourier Series Before learning to solve partial differential equations, it is necessary to know how to approximate
More informationElectrical Fundamentals  Reactance and Impedance
PDHonline Course E239 (4 PDH) Electrical Fundamentals  Reactance and Impedance Instructor: A. Bhatia, B.E. 2012 PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA 220306658 Phone & Fax: 7039880088
More informationIMPORTANCE OF SUPPLY SHORT CIRCUIT CAPACITY AND IEEE 519 STANDARD FOR UTILITIES AND POWER CONSUMERS
IMPORTANCE OF SUPPLY SHORT CIRCUIT CAPACITY AND IEEE 519 STANDARD FOR UTILITIES AND POWER CONSUMERS Dr. V. R. Kanetkar, Mr. K. E. Shinde and Mr. N. I. Dhang Shreem Electric Limited, Jaysingpur INTRODUCTION
More informationStep response of an RLC series circuit
School of Engineering Department of Electrical and Computer Engineering 332:224 Principles of Electrical Engineering II Laboratory Experiment 5 Step response of an RLC series circuit 1 Introduction Objectives
More informationNegative Feedback with Capacitors
Negative Feedback with Capacitors http://gaussmarkov.net January 8, 008 The web page OpAmps 4: Negative Feedback, describes several characteristics of the gain of a circuit like this one. This document
More informationINTRODUCTION TO ARBITRARY/FUNCTION GENERATOR
Page 1 of 7 INTRODUCTION TO ARBITRARY/FUNCTION GENERATOR BEFORE YOU BEGIN PREREQUISITE LABS Introduction to MATLAB Introduction to Oscilloscope EXPECTED KNOWLEDGE Ohm s law & Kirchhoff s laws Operation
More informationSection 64 Product Sum and Sum Product Identities
480 6 TRIGONOMETRIC IDENTITIES AND CONDITIONAL EQUATIONS Section 64 Product Sum and Sum Product Identities Product Sum Identities Sum Product Identities Our work with identities is concluded by developing
More informationCIRCUITS LABORATORY EXPERIMENT 3. AC Circuit Analysis
CIRCUITS LABORATORY EXPERIMENT 3 AC Circuit Analysis 3.1 Introduction The steadystate behavior of circuits energized by sinusoidal sources is an important area of study for several reasons. First, the
More informationApril 8. Physics 272. Spring Prof. Philip von Doetinchem
Physics 272 April 8 Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html Prof. Philip von Doetinchem philipvd@hawaii.edu Phys272  Spring 14  von Doetinchem  218 LC in parallel
More informationLABORATORY 10 TIME AVERAGES, RMS VALUES AND THE BRIDGE RECTIFIER. Bridge Rectifier
LABORATORY 10 TIME AVERAGES, RMS VALUES AND THE BRIDGE RECTIFIER Fullwave Rectification: Bridge Rectifier For many electronic circuits, DC supply voltages are required but only AC voltages are available.
More informationChapter 10. RC Circuits ISU EE. C.Y. Lee
Chapter 10 RC Circuits Objectives Describe the relationship between current and voltage in an RC circuit Determine impedance and phase angle in a series RC circuit Analyze a series RC circuit Determine
More informationNZQA registered unit standard 20431 version 2 Page 1 of 7. Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians
NZQA registered unit standard 0431 version Page 1 of 7 Title Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians Level 3 Credits 7 Purpose This unit standard covers
More informationHARMONICS  Understanding the Facts  Part 3 Richard P. Bingham
HARMONICS  Understanding the Facts  Part 3 Richard P. Bingham Abstract Understanding what is important to know about harmonics can be challenging for those without extensive electrical engineering backgrounds.
More informationExperiment # (7) FSK Modulator
Islamic University of Gaza Faculty of Engineering Electrical Department Experiment # (7) FSK Modulator Digital Communications Lab. Prepared by: Eng. Mohammed K. Abu Foul Experiment Objectives: 1. To understand
More informationElectrical Machines  I Prof. D. Kastha Department of Electrical Engineering Indian Institute of Technology, Kharagpur
Electrical Machines  I Prof. D. Kastha Department of Electrical Engineering Indian Institute of Technology, Kharagpur Lecture  9 Harmonics and Switching Transients in Single Phase Transformers So far
More informationAM Modulator. Experiment theory: Experiment # (3) Islamic University of Gaza Faculty of Engineering Electrical Department
Islamic University of Gaza Faculty of Engineering Electrical Department Experiment # (3) AM Modulator Communications Engineering I (Lab.) Prepared by: Eng. Omar A. Qarmout Eng. Mohammed K. Abu Foul Experiment
More informationName Date Day/Time of Lab Partner(s) Lab TA
Name Date Day/Time of Lab Partner(s) Lab TA Objectives LAB 7: AC CIRCUITS To understand the behavior of resistors, capacitors, and inductors in AC Circuits To understand the physical basis of frequencydependent
More information2 Rectifier Circuits HalfWave Rectifier Circuits FullWave Rectifier Circuits Linear SmallSignal Equivalent Circuits 7
Lecture Notes: 2304154 Physics and Electronics Lecture 5 (2 nd Half), Year: 2007 Physics Department, Faculty of Science, Chulalongkorn University 25/10/2007 Contents 1 IdealDiode Model 1 2 Rectifier Circuits
More informationFourier Series. 1. Introduction. 2. Square Wave
531 Fourier Series Tools Used in Lab 31 Fourier Series: Square Wave Fourier Series: Triangle Wave Fourier Series: Gibbs Effect Fourier Series: Coefficients How does a Fourier series converge to a function?
More informationApplication Guide. Power Factor Correction (PFC) Basics
Power Factor Correction (PFC) Basics Introduction Power Factor, in simple terms, is a number between zero and one that represents the ratio of the real power to apparent power. Real power (P), measured
More informationLRC Circuits. Purpose. Principles PHYS 2211L LAB 7
Purpose This experiment is an introduction to alternating current (AC) circuits. Using the oscilloscope, we will examine the voltage response of inductors, resistors and capacitors in series circuits driven
More informationFILTER DESIGN FOR PULSE WIDTH MODULATED INVERTERS
FILTER DESIGN FOR PULSE WIDTH MODULATED INVERTERS KAMARUDIN B.KHALID School of Electrical and Electronic Engineering Nanyang Technological University Nanyang Avenue, Singapore 639798 email: S7828122G@ntu.edu.sg
More informationLCR Series Circuits. AC Theory. Introduction to LCR Series Circuits. Module 9. What you'll learn in Module 9. Module 9 Introduction
Module 9 AC Theory LCR Series Circuits Introduction to LCR Series Circuits What you'll learn in Module 9. Module 9 Introduction Introduction to LCR Series Circuits. Section 9.1 LCR Series Circuits. Amazing
More informationChapter 22: Alternating current. What will we learn in this chapter?
Chapter 22: Alternating current What will we learn in this chapter? Contents: Phasors and alternating currents Resistance and reactance Series R L C circuit Power in accircuits Series resonance Parallel
More informationFourier cosine and sine series even odd
Fourier cosine and sine series Evaluation of the coefficients in the Fourier series of a function f is considerably simler is the function is even or odd. A function is even if f ( x) = f (x) Examle: x
More informationCurve Fitting. Next: Numerical Differentiation and Integration Up: Numerical Analysis for Chemical Previous: Optimization.
Next: Numerical Differentiation and Integration Up: Numerical Analysis for Chemical Previous: Optimization Subsections LeastSquares Regression Linear Regression General Linear LeastSquares Nonlinear
More informationPHYS 2426 Engineering Physics II (Revised July 7, 2011) AC CIRCUITS: RLC SERIES CIRCUIT
PHYS 2426 Engineering Physics II (Revised July 7, 2011) AC CIRCUITS: RLC SERIES CIRCUIT INTRODUCTION The objective of this experiment is to study the behavior of an RLC series circuit subject to an AC
More informationSimple Harmonic Motion: AC circuits: alternating current electricity
Simple Harmonic Motion: AC circuits: alternating current electricity Alternating current (AC) circuits explained using time and phasor animations. Impedance, phase relations, resonance and RMS quantities.
More informationL and C connected together. To be able: To analyse some basic circuits.
circuits: Sinusoidal Voltages and urrents Aims: To appreciate: Similarities between oscillation in circuit and mechanical pendulum. Role of energy loss mechanisms in damping. Why we study sinusoidal signals
More informationINTRODUCTION SELF INDUCTANCE. Introduction. Self inductance. Mutual inductance. Transformer. RLC circuits. AC circuits
Chapter 13 INDUCTANCE Introduction Self inductance Mutual inductance Transformer RLC circuits AC circuits Magnetic energy Summary INTRODUCTION Faraday s important contribution was his discovery that achangingmagneticflux
More informationExercise 4  Broadband transistor amplifier
ANALOG ELECTRONIC CIRCUITS Laboratory work Exercise 4  Broadband transistor amplifier Task 1: Design a broadband amplifier using a bipolar NPN transistor in a common emitter orientation. For input signal
More informationProduct Data Bulletin
Product Data Bulletin Power System Harmonics Causes and Effects of Variable Frequency Drives Relative to the IEEE 5191992 Standard Raleigh, NC, U.S.A. INTRODUCTION This document describes power system
More informationIntroduction to Fourier Series
Introduction to Fourier Series MA 16021 October 15, 2014 Even and odd functions Definition A function f(x) is said to be even if f( x) = f(x). The function f(x) is said to be odd if f( x) = f(x). Graphically,
More informationPower Factor Vs. Crest Factor: Critical Application Quantities Nicholas Piotrowski, Associated Power Technologies
Power Factor Vs. Crest Factor: Critical Application Quantities Nicholas Piotrowski, Associated Power Technologies Introduction Two critical quantities to specify when dealing with AC power sources are
More informationLecture  4 Diode Rectifier Circuits
Basic Electronics (Module 1 Semiconductor Diodes) Dr. Chitralekha Mahanta Department of Electronics and Communication Engineering Indian Institute of Technology, Guwahati Lecture  4 Diode Rectifier Circuits
More informationBASIC ELECTRONICS PROF. T.S. NATARAJAN DEPT OF PHYSICS IIT MADRAS LECTURE4 SOME USEFUL LAWS IN BASIC ELECTRONICS
BASIC ELECTRONICS PROF. T.S. NATARAJAN DEPT OF PHYSICS IIT MADRAS LECTURE4 SOME USEFUL LAWS IN BASIC ELECTRONICS Hello everybody! In a series of lecture on basic electronics, learning by doing, we now
More informationElectronics Prof. D.C. Dube Department of Physics Indian Institute of Technology, Delhi
Electronics Prof. D.C. Dube Department of Physics Indian Institute of Technology, Delhi Module No. #06 Power Amplifiers Lecture No. #01 Power Amplifiers (Refer Slide Time: 00:44) We now move to the next
More informationIntroduction to Fourier Series
Introduction to Fourier Series We ve seen one eample so far of series of functions. The Taylor Series of a function is a series of polynomials and can be used to approimate a function at a point. Another
More informationFourier Series & Fourier Transforms
Fourier Series & Fourier Transforms nicholas.harrison@imperial.ac.uk 19th October 003 Synopsis ecture 1 : Review of trigonometric identities Fourier Series Analysing the square wave ecture : The Fourier
More informationRectifier: It is a circuit which employs one or more diodes to convert ac voltage into pulsating dc voltage. We will consider the following circuits:
Rectifier: It is a circuit which employs one or more diodes to convert ac voltage into pulsating dc voltage. We will consider the following circuits: (i) Half wave rectifier. (ii) Full wave rectifier.
More informationANALYSIS AND APPLICATIONS OF LAPLACE /FOURIER TRANSFORMATIONS IN ELECTRIC CIRCUIT
www.arpapress.com/volumes/vol12issue2/ijrras_12_2_22.pdf ANALYSIS AND APPLICATIONS OF LAPLACE /FOURIER TRANSFORMATIONS IN ELECTRIC CIRCUIT M. C. Anumaka Department of Electrical Electronics Engineering,
More informationENGR 210 Lab 11 Frequency Response of Passive RC Filters
ENGR 210 Lab 11 Response of Passive RC Filters The objective of this lab is to introduce you to the frequencydependent nature of the impedance of a capacitor and the impact of that frequency dependence
More information