Capacitors in Series and Parallel

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[...]... electronics in today’s modern world It is currently being offered in a large number of electrical engineering curricula in schools in the United States and throughout the world The number of schools offering an EMC course will no doubt continue to rapidly increase The reasons for EMC having grown in importance at such a rapid pace are due to (1) the increasing speeds and use of digital electronics in today’s... more critical in order to avoid unnecessary costs of EMC suppression measures that are added to bring the products into compliance Frequencies of use even in analog systems are escalating well into the GHz range, and it is difficult to find a product (including washing machines, automobiles, etc.) that doesn’t use digital electronics as a primary factor in that product’s performance These mandatory governmental... feels that this topic is one of the—if not the—most important topic in EMC, and this repositioning is intended to get the reader to begin thinking in terms of signal spectra early on Use of SPICE (simulation program with integrated circuit emphasis) [PSPICE (personal computer SPICE)] in computing signal spectra has now been included in that chapter Chapter 4, Transmission Lines and Signal Integrity, has... getting lost in detail Section 11.5, Diagnostic Tools, is new to the text and reflects the author’s view that it is virtually impossible to design a digital device to pass the regulatory requirements on the first testing It is crucially important in this age of low product cost and reduced development schedules to be able to determine the exact cause of the noncompliance and to determine how to bring... such courses in EMC that was introduced into an EE undergraduate curriculum was organized in the early 1980s at the University of Kentucky by the author It was taught as a senior technical elective and continues to be taught as an elective course there and at the author’s present institution, Mercer University The subject is rapidly increasing in importance, due in part to the increasing use and speeds... contains links to the latest revisions of the regulations But more importantly it contains numerous highly detailed and informative tutorial articles and other references on EMC The author also owes a significant debt of gratitude for this association with and insights gained from working with colleagues in the EMC group at IBM Information Products Division in Lexington, Kentucky (now Lexmark International)... The transition time of the pulse from off to on and vice versa is perhaps the most important factor in determining the spectral content of the pulse Fast (short) transition times generate a wider range of Introduction to Electromagnetic Compatibility, Second Edition, by Clayton R Paul Copyright # 2006 John Wiley & Sons, Inc 1 2 INTRODUCTION TO ELECTROMAGNETIC COMPATIBILITY (EMC) frequencies than do slower... implementing reduced susceptibility of a receptor to noise would be the use of error-correcting codes in a digital receptor Although undesired electromagnetic energy is incident on the receptor, the error-correcting codes may allow the receptor Capacitors in Series and Parallel Capacitors in Series and Parallel Bởi: OpenStaxCollege Several capacitors may be connected together in a variety of applications Multiple connections of capacitors act like a single equivalent capacitor The total capacitance of this equivalent single capacitor depends both on the individual capacitors and how they are connected There are two simple and common types of connections, called series and parallel, for which we can easily calculate the total capacitance Certain more complicated connections can also be related to combinations of series and parallel Capacitance in Series [link](a) shows a series connection of three capacitors with a voltage applied As for any Q capacitor, the capacitance of the combination is related to charge and voltage by C = V Note in [link] that opposite charges of magnitude Q flow to either side of the originally uncharged combination of capacitors when the voltage V is applied Conservation of charge requires that equal-magnitude charges be created on the plates of the individual capacitors, since charge is only being separated in these originally neutral devices The end result is that the combination resembles a single capacitor with an effective plate separation greater than that of the individual capacitors alone (See [link](b).) Larger plate separation means smaller capacitance It is a general feature of series connections of capacitors that the total capacitance is less than any of the individual capacitances 1/8 Capacitors in Series and Parallel (a) Capacitors connected in series The magnitude of the charge on each plate is Q (b) An equivalent capacitor has a larger plate separation d Series connections produce a total capacitance that is less than that of any of the individual capacitors We can find an expression for the total capacitance by considering the voltage across the Q Q individual capacitors shown in [link] Solving C = V for V gives V = C The voltages across the individual capacitors are thus V1 = Q C1 , V2 = Q C2 , and V3 = Q C3 The total voltage is the sum of the individual voltages: V = V1 + V2 + V3 Now, calling the total capacitance CS for series capacitance, consider that V= Q CS = V1 + V2 + V3 Entering the expressions for V1, V2, and V3, we get Q CS = Q C1 + Q C2 + Q C3 2/8 Capacitors in Series and Parallel Canceling the Qs, we obtain the equation for the total capacitance in series CS to be CS = C1 + C2 + C3 + , where “ ” indicates that the expression is valid for any number of capacitors connected in series An expression of this form always results in a total capacitance CS that is less than any of the individual capacitances C1, C2, , as the next example illustrates Total Capacitance in Series, Cs Total capacitance in series: CS C1 = C2 + + C3 + What Is the Series Capacitance? Find the total capacitance for three capacitors connected in series, given their individual capacitances are 1.000, 5.000, and 8.000 µF Strategy With the given information, the total capacitance can be found using the equation for capacitance in series Solution Entering the given capacitances into the expression for CS = 1.000 µF + 5.000 µF + 8.000 µF Inverting to find CS yields CS = = CS gives CS = C1 + C2 + C3 1.325 µF µF 1.325 = 0.755 µF Discussion The total series capacitance Cs is less than the smallest individual capacitance, as promised In series connections of capacitors, the sum is less than the parts In fact, it is less than any individual Note that it is sometimes possible, and more convenient, to solve an equation like the above by finding the least common denominator, which in this case (showing only whole-number calculations) is 40 Thus, CS = 40 40 µF + 40 µF + 40 µF = 53 40 µF , so that 3/8 Capacitors in Series and Parallel CS = 40 µF 53 = 0.755 µF Capacitors in Parallel [link](a) shows a parallel connection of three capacitors with a voltage applied Here the total capacitance is easier to find than in the series case To find the equivalent total capacitance Cp, we first note that the voltage across each capacitor is V, the same as that of the source, since they are connected directly to it through a conductor (Conductors are equipotentials, and so the voltage across the capacitors is the same as that across the voltage source.) Thus the capacitors have the same charges on them as they would have if connected individually to the voltage source The total charge Q is the sum of the individual charges: Q = Q1 + Q2 + Q3 (a) Capacitors in parallel Each is connected directly to the voltage source just as if it were all alone, and so the total capacitance in parallel is just the sum of the individual capacitances (b) The equivalent capacitor has a larger plate area and can therefore hold more charge than the individual capacitors Using the relationship Q = CV, we see that the total charge is Q = CpV, and the individual charges are Q1 = C1V, Q2 = C2V, and Q3 = C3V Entering these into the previous equation gives CpV = C1V + C2V + C3V ...TeAm YYePG Digitally signed by TeAm YYePG DN: cn=TeAm YYePG, c=US, o=TeAm YYePG, ou=TeAm YYePG, email=yyepg@msn.com Reason: I attest to the accuracy and integrity of this document Date: 2005.03.13 22:26:27 +08'00' QOS IN PACKET NETWORKS THE KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE QOS IN PACKET NETWORKS by Kun I. Park, Ph.D. The MITRE Corporation USA Springer eBook ISBN: 0-387-23390-3 Print ISBN: 0-387-23389-X Print ©2005 Springer Science + Business Media, Inc. All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Boston ©2005 Springer Science + Business Media, Inc. Visit Springer's eBookstore at: http://ebooks.kluweronline.com and the Springer Global Website Online at: http://www.springeronline.com Dedication For Meyeon and Kyunja. This page intentionally left blank Contents DEDICATION v PREFACE xiii CHAPTER 1 INTRODUCTION 1. 2. 3. NEED FOR QOS D EFINITION OF QOS ORGANIZATION OF THE BOOK 1 1 4 6 CHAPTER 2 BASIC MATHEMATICS FOR QOS 1. PROBABILITY THEORY 9 9 9 1.1 1.2 1.3 RANDOM EXPERIMENTS, OUTCOMES AND EVENTS DEFINITION OF PROBABILITY AXIOMATIC APPROACH TO PROBABILITY 2. RANDOM VARIABLES 10 12 17 17 19 22 24 25 25 25 26 27 30 2.1 2.2 2.3 2.4 2.5 DEFINITION CDF AND PDF MEAN AND VARIANCE THE NORMAL DISTRIBUTION THE POISSON DISTRIBUTION 3. S TOCHASTIC PROCESSES 3.1 3.2 3.3 3.4 DEFINITION OF A STOCHASTIC PROCESS CDF AND PDF OF STOCHASTIC PROCESS AUTOCORRELATION AND CROSS-CORRELATION THE NORMAL PROCESS viii QOS IN PACKET NETWORKS STATISTICAL CHARACTERIZATION OF A STOCHASTIC PROCESS STATIONARITY 3.5 3.6 30 33 33 36 37 37 40 40 41 41 42 43 44 44 48 49 51 52 52 53 57 57 58 3.6.1 3.6.2 STRICT SENSE STATIONARITY (SSS) W IDE SENSE STATIONARITY (WSS) 4. QUEUING THEORY BASICS 4.1 4.2 4.3 4.4 REAL-LIFE EXAMPLES OF QUEUING DEFINITION OF QUEUING SYSTEM BIRTH-DEATH PROCESS MODEL ARRIVAL RATE 4.4.1 4.4.2 4.4.3 4.4.4 4.4.5 4.4.6 DEFINITION EMPIRICAL DETERMINATION OF ARRIVAL RATE STATIONARITY ERGODICITY THE POISSON ARRIVAL MARKOV MODULATED POISSON PROCESS (MMPP) 4.5 4.6 4.7 SERVICE RATE UTILIZATION FACTOR QUEUING SYSTEM PERFORMANCE METRICS 4.7.1 LITTLE’S THEOREM 4.8 M/M/1 QUEUE 5. EXERCISES 5.1 5.2 PROBLEMS SOLUTIONS CHAPTER 3 QOS METRICS 1. NETWORK TYPES 1.1 1.2 CONNECTION-ORIENTED PACKET NETWORK SERVICES CONNECTIONLESS PACKET NETWORK SERVICES 61 61 61 63 63 63 64 67 69 69 70 71 72 74 75 76 77 77 79 2. DIGITAL COMMUNICATIONS SYSTEM 2.1 SOURCE CODING 2.1.1 2.1.2 WAVEFORM CODING LINEAR PREDICTIVE CODING (LPC) 2.2 PACKETIZATION 2.2.1 2.2.2 VOICE OVER ATM PACKETIZATION VOICE OVER IP PACKETIZATION 2.3 CHANNEL CODING 2.3.1 2.3.2 2.3.3 INTERLEAVING ERROR CORRECTION MODULATION 3. QOS OF REAL TIME SERVICES 3.1 QUANTIZATION NOISE 3.1.1 3.1.2 SOURCE OF QUANTIZATION NOISE EFFECT OF QUANTIZATION NOISE QOS IN PACKET NETWORKS ix 3.2 DELAY 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 3.2.8 3.2.9 FRAME DELAY PACKETIZATION DELAY INTERLEAVING DELAY ERROR CORRECTION CODING DELAY JITTER BUFFER DELAY PACKET QUEUING DELAY PROPAGATION DELAY EFFECT OF DELAY END-TO-END DELAY OBJECTIVES 3.3 DELAY VARIATION OR “JITTER” 3.4 3.5 SOURCE OF DELAY VARIATION 3.3.1 PACKET LOSS PROBABILITY SUBJECTIVE TESTING 80 80 82 83 84 84 84 86 87 87 BioMed Central Page 1 of 12 (page number not for citation purposes) Journal of Orthopaedic Surgery and Research Open Access Research article Fourier-transform infrared anisotropy in cross and parallel sections of tendon and articular cartilage Nagarajan Ramakrishnan, Yang Xia* and Aruna Bidthanapally Address: Department of Physics and Center for Biomedical Research, Oakland University, Rochester, MI 48309, USA Email: Nagarajan Ramakrishnan - ramakris@oakland.edu; Yang Xia* - xia@oakland.edu; Aruna Bidthanapally - bidthana@oakland.edu * Corresponding author Abstract Background: Fourier Transform Infrared Imaging (FTIRI) is used to investigate the amide anisotropies at different surfaces of a three-dimensional cartilage or tendon block. With the change in the polarization state of the incident infrared light, the resulting anisotropic behavior of the tissue structure is described here. Methods: Thin sections (6 μm thick) were obtained from three different surfaces of the canine tissue blocks and imaged at 6.25 μm pixel resolution. For each section, infrared imaging experiments were repeated thirteen times with the identical parameters except a 15° increment of the analyzer's angle in the 0° – 180° angular space. The anisotropies of amide I and amide II components were studied in order to probe the orientation of the collagen fibrils at different tissue surfaces. Results: For tendon, the anisotropy of amide I and amide II components in parallel sections is comparable to that of regular sections; and tendon's cross sections show distinct, but weak anisotropic behavior for both the amide components. For articular cartilage, parallel sections in the superficial zone have the expected infrared anisotropy that is consistent with that of regular sections. The parallel sections in the radial zone, however, have a nearly isotropic amide II absorption and a distinct amide I anisotropy. Conclusion: From the inconsistency in amide anisotropy between superficial to radial zone in parallel section results, a schematic model is used to explain the origins of these amide anisotropies in cartilage and tendon. Background Tendon is a soft connective tissue that lies in between bones and muscles in animal and human body to transfer the force experienced by muscle to the bone. Tendon therefore has the nature to resist mechanical tension. Depending upon the joint where it is placed, tendon can have different anatomic shapes [1]. Investigation on ten- don has been carried out in various aspects [2-6] such as understanding the shape, structure, mechanical proper- ties, tissue repair and structure-function relationship. Like tendon, articular cartilage is also a soft connective tissue, which covers the end surfaces of bones in synovial joints to distribute compressive loading. While type I collagen fibrils are commonly found in tendon as the highly organ- Published: 6 October 2008 Journal of Orthopaedic Surgery and Research 2008, 3:48 doi:10.1186/1749-799X-3-48 Received: 6 May 2008 Accepted: 6 October 2008 This article is available from: http://www.josr-online.com/content/3/1/48 © 2008 Ramakrishnan et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the SERIES AND PARALLEL CIRCUITS What are "series" and "parallel" circuits? Circuits consisting of just one battery and one load resistance are very simple to analyze, but they are not often found in practical applications. Usually, we find circuits where more than two components are connected together. There are two basic ways in which to connect more than two circuit components: series and parallel. First, an example of a series circuit: Here, we have three resistors (labeled R 1 , R 2 , and R 3 ), connected in a long chain from one terminal of the battery to the other. (It should be noted that the subscript labeling those little numbers to the lower-right of the letter "R" are unrelated to the resistor values in ohms. They serve only to identify one resistor from another.) The defining characteristic of a series circuit is that there is only one path for electrons to flow. In this circuit the electrons flow in a counter- clockwise direction, from point 4 to point 3 to point 2 to point 1 and back around to 4. Now, let's look at the other type of circuit, a parallel configuration: Again, we have three resistors, but this time they form more than one continuous path for electrons to flow. There's one path from 8 to 7 to 2 to 1 and back to 8 again. There's another from 8 to 7 to 6 to 3 to 2 to 1 and back to 8 again. And then there's a third path from 8 to 7 to 6 to 5 to 4 to 3 to 2 to 1 and back to 8 again. Each individual path (through R 1 , R 2 , and R 3 ) is called a branch. The defining characteristic of a parallel circuit is that all components are connected between the same set of electrically common points. Looking at the schematic diagram, we see that points 1, 2, 3, and 4 are all electrically common. So are points 8, 7, 6, and 5. Note that all resistors as well as the battery are connected between these two sets of points. And, of course, the complexity doesn't stop at simple series and parallel either! We can have circuits that are a combination of series and parallel, too: In this circuit, we have two loops for electrons to flow through: one from 6 to 5 to 2 to 1 and back to 6 again, and another from 6 to 5 to 4 to 3 to 2 to 1 and back to 6 again. Notice how both current paths go through R 1 (from point 2 to point 1). In this configuration, we'd say that R 2 and R 3 are in parallel with each other, while R 1 is in series with the parallel combination of R 2 and R 3 . This is just a preview of things to come. Don't worry! We'll explore all these circuit configurations in detail, one at a time! The basic idea of a "series" connection is that components are connected end-to-end in a line to form a single path for electrons to flow: The basic idea of a "parallel" connection, on the other hand, is that all components are connected across each other's leads. In a purely parallel circuit, there are never more than two sets of electrically common points, no matter how many components are connected. There are many paths for electrons to flow, but only one voltage across all components: Series and parallel resistor configurations have very different electrical properties. We'll explore the properties of each configuration in the sections to come. • REVIEW: • In a series circuit, all components are connected end-to-end, forming a single path for electrons to flow. • In a parallel circuit, all components are connected across each other, forming exactly two sets of electrically common points. • A "branch" in a parallel circuit is a path for electric current formed by one of the load components (such as a resistor). Simple series circuits Let's start with a series circuit consisting of three resistors and a single battery: The first principle to understand about series circuits is that the amount of current is the same through any component in the circuit. This is because there [...]... electronics in today’s modern world It is currently being offered in a large number of electrical engineering curricula in schools in the United States and throughout the world The number of schools offering an EMC course will no doubt continue to rapidly increase The reasons for EMC having grown in importance at such a rapid pace are due to (1) the increasing speeds and use of digital electronics in today’s... more critical in order to avoid unnecessary costs of EMC suppression measures that are added to bring the products into compliance Frequencies of use even in analog systems are escalating well into the GHz range, and it is difficult to find a product (including washing machines, automobiles, etc.) that doesn’t use digital electronics as a primary factor in that product’s performance These mandatory governmental... feels that this topic is one of the—if not the—most important topic in EMC, and this repositioning is intended to get the reader to begin thinking in terms of signal spectra early on Use of SPICE (simulation program with integrated circuit emphasis) [PSPICE (personal computer SPICE)] in computing signal spectra has now been included in that chapter Chapter 4, Transmission Lines and Signal Integrity, has... getting lost in detail Section 11.5, Diagnostic Tools, is new to the text and reflects the author’s view that it is virtually impossible to design a digital device to pass the regulatory requirements on the first testing It is crucially important in this age of low product cost and reduced development schedules to be able to determine the exact cause of the noncompliance and to determine how to bring... such courses in EMC that was introduced into an EE undergraduate curriculum was organized in the early 1980s at the University of Kentucky by the author It was taught as a senior technical elective and continues to be taught as an elective course there and at the author’s present institution, Mercer University The subject is rapidly increasing in importance, due in part to the increasing use and speeds... contains links to the latest revisions of the regulations But more importantly it contains numerous highly detailed and informative tutorial articles and other references on EMC The author also owes a significant debt of gratitude for this association with and insights gained from working with colleagues in the EMC group at IBM Information Products Division in Lexington, Kentucky (now Lexmark International)... The transition time of the pulse from off to on and vice versa is perhaps the most important factor in determining the spectral content of the pulse Fast (short) transition times generate a wider range of Introduction to Electromagnetic Compatibility, Second Edition, by Clayton R Paul Copyright # 2006 John Wiley & Sons, Inc 1 2 INTRODUCTION TO ELECTROMAGNETIC COMPATIBILITY (EMC) frequencies than do slower... implementing reduced susceptibility of a receptor to noise would be the use of error-correcting codes in a digital receptor Although undesired electromagnetic energy is incident on the receptor, the error-correcting codes may allow the receptor Resistors in Series and Parallel Resistors in Series and Parallel Bởi: OpenStaxCollege Most circuits have more than one component, called a resistor that limits the flow of charge in the circuit A measure of this limit on charge flow is called resistance The simplest combinations of resistors are the series and parallel connections illustrated in [link] ... which capacitors are in series and which are in parallel Capacitors C1 and C2 are in series Their combination, labeled CS in the figure, is in parallel with C3 Solution 5/8 Capacitors in Series and. .. capacitors shown in [link] 7/8 Capacitors in Series and Parallel A combination of series and parallel connections of capacitors Unreasonable Results (a) An 8.00 µF capacitor is connected in parallel. .. in a capacitor bank, would you connect capacitors in series or parallel? Explain Problems & Exercises Find the total capacitance of the combination of capacitors in [link] 6/8 Capacitors in Series