Fundamentals of Electrical Engineering 1 Grundlagen der Elektrotechnik 1

Größe: px
Ab Seite anzeigen:

Download "Fundamentals of Electrical Engineering 1 Grundlagen der Elektrotechnik 1"

Transkript

1 Fundamentals of Electrical Engineering 1 Grundlagen der Elektrotechnik 1 Chapter: Operational Amplifiers / Operationsverstärker Michael E. Auer Source of figures: Alexander/Sadiku: Fundamentals of Electric Circuits, McGraw-Hill

2 Course Content Basic Concepts / Grundlagen Basic Laws / Grundgesetze Circuit Theorems / Zweipoltheorie Common Methods of Network Analysis / Allgemeine Netzwerkanalyse Operational Amplifiers / Operationsverstärker Capacitors and Inductors / Kapazitäten und Induktivitäten Basic C and L Circuits Switching / Einfache Schaltvorgänge

3 Chapter Content Basics of Op Amps / OV Grundlagen Ideal Op Amp / Idealer OV Inverting Amplifier / Invertierender Verstärker Noninverting Amplifier / Nichtinvertierender Verstärker Summing Amplifier / Summierer Verstärker Difference Amplifier / Differenzverstärker Cascaded Op Amp Circuits / Zusammenschaltung von OVs Summary / Zusammenfassung

4 Chapter Content Basics of Op Amps / OV Grundlagen Ideal Op Amp / Idealer OV Inverting Amplifier / Invertierender Verstärker Noninverting Amplifier / Nichtinvertierender Verstärker Summing Amplifier / Summierer Verstärker Difference Amplifier / Differenzverstärker Cascaded Op Amp Circuits / Zusammenschaltung von OVs Summary / Zusammenfassung

5 OpAmp Basics (1) It is an electronic unit that behaves like a voltage-controlled voltage source. It is an active circuit element designed to perform amplification and mathematical operations of addition, subtraction, multiplication, division, differentiation and integration.

6 OpAmp Basics (2) A typical op amp: (a) pin configuration, (b) circuit symbol, (b) device (c)

7 OpAmp Basics (3) The equivalent circuit Of the non-ideal op amp Op Amp output: v o as a function of V d A Open Loop Voltage Gain v d = v 2 v 1 v o = A v d = A(v 2 v 1 )

8 OpAmp Basics (4) Typical ranges for op amp parameters Parameter Typical range Ideal values Open-loop gain, A 10 5 to 10 8 Ω Input resistance, i 10 5 to Ω Ω Output resistance, o 10 to 100 Ω 0 Ω Supply voltage, V CC 5 to 24 V

9 OpAmp Example Circuit Simulation model

10 Chapter Content Basics of Op Amps / OV Grundlagen Ideal Op Amp / Idealer OV Inverting Amplifier / Invertierender Verstärker Noninverting Amplifier / Nichtinvertierender Verstärker Summing Amplifier / Summierer Verstärker Difference Amplifier / Differenzverstärker Cascaded Op Amp Circuits / Zusammenschaltung von OVs Summary / Zusammenfassung

11 Definition of the Ideal OpAmp An ideal op amp has the following characteristics: Infinite open-loop gain, A V d = 0 Infinite input resistance, i i 1 = i 2 = 0 Zero output resistance, o 0 Ideal Voltage source

12 Chapter Content Basics of Op Amps / OV Grundlagen Ideal Op Amp / Idealer OV Inverting Amplifier / Invertierender Verstärker Noninverting Amplifier / Nichtinvertierender Verstärker Summing Amplifier / Summierer Verstärker Difference Amplifier / Differenzverstärker Cascaded Op Amp Circuits / Zusammenschaltung von OVs Summary / Zusammenfassung

13 Inverting Amplifier Basic Circuit Inverting amplifier reverses the polarity of the input signal while amplifying it v o = f 1 v i A V = f 1 Voltage gain in out = 1 = 0

14 Inverting Amplifier Equivalent Circuit Polarity!

15 Inverting Amplifier Example (1) efer to the op amp below. If v i = 0.5V, calculate: (a) The voltage gain, (b) the output voltage, v o and (c) the current in the 10kΩ resistor. Answer: (a) 2.5; (b) -1.25V; (c) 50μA

16 Inverting Amplifier Example (2) Determine the voltage v o in the circuit below. Answer: v o = 3 v a 12 = -6V

17 Chapter Content Basics of Op Amps / OV Grundlagen Ideal Op Amp / Idealer OV Inverting Amplifier / Invertierender Verstärker Noninverting Amplifier / Nichtinv. Verstärker Summing Amplifier / Summierer Verstärker Difference Amplifier / Differenzverstärker Cascaded Op Amp Circuits / Zusammenschaltung von OVs Summary / Zusammenfassung

18 Noninverting Amplifier Basic Circuit Non-inverting amplifier is designed to produce positive voltage gain v o f = v i in out AV = 1+ = =0 f 1 positive!

19 Noninverting Amplifier Example Calculate the voltage v o in the circuit below. Answer: v o = 7V

20 Unity Gain Amplifier (Voltage Follower) Special noninverting amplifier with: f = 0 ; 1 = Voltage follower Application as buffer amplifier to isolate one circuit from another

21 Chapter Content Basics of Op Amps / OV Grundlagen Ideal Op Amp / Idealer OV Inverting Amplifier / Invertierender Verstärker Noninverting Amplifier / Nichtinvertierender Verstärker Summing Amplifier / Summierer Verstärker Difference Amplifier / Differenzverstärker Cascaded Op Amp Circuits / Zusammenschaltung von OVs Summary / Zusammenfassung

22 Summing Amplifier Basic Circuit Summing Amplifier is an op amp circuit that combines several inputs and produces an output that is the weighted sum of the inputs. + + = v v v v f f f o ( ) : if v v v v v v v v f o f f f o + + = + + = = =

23 Summing Amplifier Example Calculate the voltage v o and the current i o. Answer: v o = -8V; i o = - 4.8mA

24 Chapter Content Basics of Op Amps / OV Grundlagen Ideal Op Amp / Idealer OV Inverting Amplifier / Invertierender Verstärker Noninverting Amplifier / Nichtinvertierender Verstärker Summing Amplifier / Summierer Verstärker Difference Amplifier / Differenzverstärker Cascaded Op Amp Circuits / Zusammenschaltung von OVs Summary / Zusammenfassung

25 Difference Amplifier Basic Circuit Difference amplifier is a device that amplifies the difference between two inputs but rejects any signals common to the two inputs. v o = (1 + (1 + / / ) v ) v v o if = v v = = 1

26 Instrumentation Amplifier

27 Chapter Content Basics of Op Amps / OV Grundlagen Ideal Op Amp / Idealer OV Inverting Amplifier / Invertierender Verstärker Noninverting Amplifier / Nichtinvertierender Verstärker Summing Amplifier / Summierer Verstärker Difference Amplifier / Differenzverstärker Cascaded Op Amp Circuits / Zusammenschaltung von OVs Summary / Zusammenfassung

28 Cascaded OpAmps It is an arrangement of two or more op amp circuits such that the output to one is the input of the next.

29 Two-stage Amplifier Example Determine 1 to 5 so that v o = -5v 1 +3v 2 and in = 10kΩ Answer: 1 = 3 = 10kΩ 4 = 30kΩ 2 = 5 = 50kΩ

30 Cascaded OpAmps Example Find v o and i o in the circuit shown below. Ans: 350mV, 25μA

31 Application: DAC Digital-to Analog Converter (DAC) : it is a device which transforms digital signals into analog form. Four-bit DCA: (a) block diagram (b) binary weighted ladder type V f f f f 0 = V1 + V2 + V3 + V where V 1 MSB, V 4 LSB V 1 to V 4 are either 0 or 1 V

32 Chapter Content Basics of Op Amps / OV Grundlagen Ideal Op Amp / Idealer OV Inverting Amplifier / Invertierender Verstärker Noninverting Amplifier / Nichtinvertierender Verstärker Summing Amplifier / Summierer Verstärker Difference Amplifier / Differenzverstärker Cascaded Op Amp Circuits / Zusammenschaltung von OVs Summary / Zusammenfassung

33 Summary The OpAmp is a high gain amplifier that has high input resistance and low output resistance. An ideal OpAmp has an infinite input resistance, a zero output resistance, and an infinite gain. For an ideal OpAmp, the current into each of its two input terminals is zero, and the voltage across its input terminals is negligibly small. In an inverting amplifier, the output is a negative multiple of the input. In a noninverting amplifier, the output is a positive multiple of the input. In a voltage follower, the output follows the input. In a summing amplifier, the output is the weighted sum of the inputs. In a difference amplifier, the output is proportional to the difference of the two inputs. OpAmp circuits may be cascaded without changing their input-output relationships. Typical applications of the OpAmp considered in this chapter include the DAC and the instrumentation amplifier.

a) Name and draw three typical input signals used in control technique.

a) Name and draw three typical input signals used in control technique. 12 minutes Page 1 LAST NAME FIRST NAME MATRIKEL-NO. Problem 1 (2 points each) a) Name and draw three typical input signals used in control technique. b) What is a weight function? c) Define the eigen value

Mehr

Computational Models

Computational Models - University of Applied Sciences - Computational Models - CSCI 331 - Friedhelm Seutter Institut für Angewandte Informatik Part I Automata and Languages 0. Introduction, Alphabets, Strings, and Languages

Mehr

FEM Isoparametric Concept

FEM Isoparametric Concept FEM Isoparametric Concept home/lehre/vl-mhs--e/folien/vorlesung/4_fem_isopara/cover_sheet.tex page of 25. p./25 Table of contents. Interpolation Functions for the Finite Elements 2. Finite Element Types

Mehr

Overview thermostat/ temperature controller

Overview thermostat/ temperature controller Thermostat TR-238 The Thermostat TR-238 is a electronic two-level controller for controlling of and in climate control units and vehicles. Voltage range (12V): Voltage range (24V): Control range: Hystereses:

Mehr

Datasheet. Page 1 of 7

Datasheet. Page 1 of 7 Features 20 Encoder Positions 4-way Joystick LED-Illumination high quality signal processing Benefits Tactile multi purpose application premium design Hall Effect technology Applications Multiple switch

Mehr

Electrical testing of Bosch common rail Injectors

Electrical testing of Bosch common rail Injectors Electrical testing of Bosch common rail Injectors Contents: 1. Adapter cable for Hybridtester FSA 050 (article number 0 684 010 050 / 1 687 023 571) 2. Electrical testing of Bosch common rail solenoid

Mehr

FEM Isoparametric Concept

FEM Isoparametric Concept FEM Isoparametric Concept home/lehre/vl-mhs--e/cover_sheet.tex. p./26 Table of contents. Interpolation Functions for the Finite Elements 2. Finite Element Types 3. Geometry 4. Interpolation Approach Function

Mehr

Asynchronous Generators

Asynchronous Generators Asynchronous Generators Source: ABB 1/21 2. Asynchronous Generators 1. Induction generator with squirrel cage rotor 2. Induction generator with woed rotor Source: electricaleasy.com 2/21 2.1. Induction

Mehr

Electrical testing of Bosch common rail piezo injectors

Electrical testing of Bosch common rail piezo injectors Applies to generation CRI 3: Bosch 10-position order number 0 445 115 = CRI 3-16 (CRI 3.0) 1600 bar 0 445 116 = CRI 3-18 (CRI 3.2) 1800 bar 0 445 117 = CRI 3-20 (CRI 3.3) 2000 bar Tools required: Hybrid

Mehr

PATENT SPECIFICATION. (D Priority: 25.03.83 US 47861 1 Proprietor: FAIRCHILD CAMERA & INSTRUMENT CORPORATION

PATENT SPECIFICATION. (D Priority: 25.03.83 US 47861 1 Proprietor: FAIRCHILD CAMERA & INSTRUMENT CORPORATION Europaisches Patentamt J ) European Patent Office Publication number: 0123 5 8 6 Office europeen des brevets B1 EUROPEAN PATENT SPECIFICATION Date of publication of patent specification: 01.06.88 Application

Mehr

Eingebettete Taktübertragung auf Speicherbussen

Eingebettete Taktübertragung auf Speicherbussen Eingebettete Taktübertragung auf Speicherbussen Johannes Reichart Workshop Hochgeschwindigkeitsschnittstellen Stuttgart, 07.11.2008 Unterstützt durch: Qimonda AG, München Institut für Prof. Elektrische

Mehr

Attention: Give your answers to problem 1 and problem 2 directly below the questions in the exam question sheet. ,and C = [ ].

Attention: Give your answers to problem 1 and problem 2 directly below the questions in the exam question sheet. ,and C = [ ]. Page 1 LAST NAME FIRST NAME MATRIKEL-NO. Attention: Give your answers to problem 1 and problem 2 directly below the questions in the exam question sheet. Problem 1 (15 points) a) (1 point) A system description

Mehr

Certificate of conformity Generating unit, NS-protection

Certificate of conformity Generating unit, NS-protection Applicant: Product: Certificate of conformity Generating unit, NS-protection Schneider Electric Solar Inverters USA, Inc. 250 South Vasco Road Livermore, California 94551 USA Photovoltaic Inverter with

Mehr

Installationsanleitung / installation manual - DIMMbox

Installationsanleitung / installation manual - DIMMbox Inhalt / Content Funktionsbeschreibung... 2 Anschlusskonfigurationen... 3 Konstantspannung... 3 Konstantstrom... 3 Art der Steuerung... 4 Analogeingang... 4 Digital Addressable Lighting Interface (DALI):...

Mehr

Übung 3: VHDL Darstellungen (Blockdiagramme)

Übung 3: VHDL Darstellungen (Blockdiagramme) Übung 3: VHDL Darstellungen (Blockdiagramme) Aufgabe 1 Multiplexer in VHDL. (a) Analysieren Sie den VHDL Code und zeichnen Sie den entsprechenden Schaltplan (mit Multiplexer). (b) Beschreiben Sie zwei

Mehr

DPM_flowcharts.doc Page F-1 of 9 Rüdiger Siol :28

DPM_flowcharts.doc Page F-1 of 9 Rüdiger Siol :28 Contents F TOOLS TO SUPPORT THE DOCUMENTATION... F-2 F.1 GRAPHIC SYMBOLS AND THEIR APPLICATION (DIN 66 001)... F-2 F.1.1 Flow of control... F-3 F.1.2 Terminators and connectors... F-4 F.1.3 Lines, arrows

Mehr

Bayesian Networks. Syntax Semantics Parametrized Distributions Inference in Bayesian Networks. Exact Inference. Approximate Inference

Bayesian Networks. Syntax Semantics Parametrized Distributions Inference in Bayesian Networks. Exact Inference. Approximate Inference Syntax Semantics Parametrized Distributions Inference in Exact Inference Approximate Inference enumeration variable elimination stochastic simulation Markov Chain Monte Carlo (MCMC) 1 Includes many slides

Mehr

auf differentiellen Leitungen

auf differentiellen Leitungen Eingebettete Taktübertragung auf differentiellen Leitungen Johannes Reichart Kleinheubacher Tagung Miltenberg, 28.09.2009 Institut für Prof. Elektrische Dr.-Ing. und Optische Manfred Nachrichtentechnik

Mehr

Keysight Technologies Using InfiniiMax Probes with Test Equipment other than Infiniium Oscilloscopes

Keysight Technologies Using InfiniiMax Probes with Test Equipment other than Infiniium Oscilloscopes Ihr Spezialist für Mess- und Prüfgeräte Keysight Technologies Using InfiniiMax Probes with Test Equipment other than Infiniium Oscilloscopes Configuration Guide Introduction The benefits of the Keysight

Mehr

Certificate of conformity Generating unit, NS-protection

Certificate of conformity Generating unit, NS-protection Certificate of conformity Generating unit, NS-protection Applicant: Product: Schneider Electric Solar Inverters USA, Inc. 250 South Vasco Road Livermore, California 94551 USA Photovoltaic Inverter with

Mehr

AU-D2. Coaxial/Optical Audio Converter OPERATION MANUAL

AU-D2. Coaxial/Optical Audio Converter OPERATION MANUAL AU-D2 Coaxial/Optical Audio Converter OPERATION MANUAL Table of Contents 1. Introduction 1 2. Features 1 3. Operation Controls and Functions 2 3.1 Input Panel Diagram 2 3.2 Output Panel Diagram 2 3.3 Switcher

Mehr

Finite Difference Method (FDM)

Finite Difference Method (FDM) Finite Difference Method (FDM) home/lehre/vl-mhs-1-e/folien/vorlesung/2a_fdm/cover_sheet.tex page 1 of 15. p.1/15 Table of contents 1. Problem 2. Governing Equation 3. Finite Difference-Approximation 4.

Mehr

Mock Exam Behavioral Finance

Mock Exam Behavioral Finance Mock Exam Behavioral Finance For the following 4 questions you have 60 minutes. You may receive up to 60 points, i.e. on average you should spend about 1 minute per point. Please note: You may use a pocket

Mehr

PELTIER-HOCHLEISTUNGSMODULE

PELTIER-HOCHLEISTUNGSMODULE Wolfgang Knap Gesellschaft m.b.h. & Co.KG A-113 Wien Lilienberggasse 13 Tel.: +43-1-43 8 12 Fax: +43-1-48 72 13 e-mail: info@knap.at http://www.knap.at PELTIER-HOCHLEISTUNGSMODULE Die Hochleistungsmodule

Mehr

Unit 1. Motivation and Basics of Classical Logic. Fuzzy Logic I 6

Unit 1. Motivation and Basics of Classical Logic. Fuzzy Logic I 6 Unit 1 Motivation and Basics of Classical Logic Fuzzy Logic I 6 Motivation In our everyday life, we use vague, qualitative, imprecise linguistic terms like small, hot, around two o clock Even very complex

Mehr

MU-307 A SAFETY INSTRUCTIONS SICHERHEITSHINWEISE FEATURES MERKMALE

MU-307 A SAFETY INSTRUCTIONS SICHERHEITSHINWEISE FEATURES MERKMALE SAFETY INSTRUCTIONS Read all safety instruction before operating the amplifiers. 1. Install equipment as follow condition: - Install at flat place, not bending curved. - Do not install near the water and

Mehr

Field-Circuit Coupling for Mechatronic Systems: Some Trends and Techniques

Field-Circuit Coupling for Mechatronic Systems: Some Trends and Techniques Field-Circuit Coupling for Mechatronic Systems: Some Trends and Techniques Stefan Kurz Robert Bosch GmbH, Stuttgart Now with the University of the German Federal Armed Forces, Hamburg stefan.kurz@unibw-hamburg.de

Mehr

Schalten einer kapazitiven Last mit einem Transistor

Schalten einer kapazitiven Last mit einem Transistor . Schalten einer kapazitiven Last mit einem Transistor In allgemeinen technischen Anwendungen ist das Schalten einer kapazitiven Last eher von untergeordneter Bedeutung. In Rechnersystemen (Computernetzwerken)

Mehr

Betriebsanleitung. Finhol Natural Tube Series - Booster. Technische Daten

Betriebsanleitung. Finhol Natural Tube Series - Booster. Technische Daten Betriebsanleitung Natural Tube Series - Booster Aluminium Druckguss Gehäuse Gewicht ca. 300 gr. Masse: 145 x 95 x 50 mm Regler: Level Fussschalter Output/Input-Buchse 6,3 mm unsymmetrisch DC-Buchse: für

Mehr

Digital-Analog-Konverter (DAC)

Digital-Analog-Konverter (DAC) . Digital-Analog-Konverter (DAC) Problem: geringe Abweichung der Übertragungselemente von der Idealität führt durch Fehlerfortpflanzung zu großem Fehler analoge Technik: Minimierung der Fehler digitale

Mehr

Weather forecast in Accra

Weather forecast in Accra Weather forecast in Accra Thursday Friday Saturday Sunday 30 C 31 C 29 C 28 C f = 9 5 c + 32 Temperature in Fahrenheit Temperature in Celsius 2 Converting Celsius to Fahrenheit f = 9 5 c + 32 tempc = 21

Mehr

Aufgabe 1. Aufgabe 2 U A. (t) (t) (t) U U E. (t) R 2 R 1 U IN U OUT

Aufgabe 1. Aufgabe 2 U A. (t) (t) (t) U U E. (t) R 2 R 1 U IN U OUT Aufgabe 1 Die gegebene Operationsverstärkerschaltung soll als Eingangsverstärker für einen A/D-Umsetzer mit einem Eingangsspannungsbereich von 0 bis 10 V verwendet werden. Die Spannung U IN liegt im Bereich

Mehr

Introduction to Python. Introduction. First Steps in Python. pseudo random numbers. May 2016

Introduction to Python. Introduction. First Steps in Python. pseudo random numbers. May 2016 to to May 2016 to What is Programming? All computers are stupid. All computers are deterministic. You have to tell the computer what to do. You can tell the computer in any (programming) language) you

Mehr

Algorithm Theory 3 Fast Fourier Transformation Christian Schindelhauer

Algorithm Theory 3 Fast Fourier Transformation Christian Schindelhauer Algorithm Theory 3 Fast Fourier Transformation Institut für Informatik Wintersemester 2007/08 Chapter 3 Fast Fourier Transformation 2 Polynomials Polynomials p over real numbers with a variable x p(x)

Mehr

Ein Stern in dunkler Nacht Die schoensten Weihnachtsgeschichten. Click here if your download doesn"t start automatically

Ein Stern in dunkler Nacht Die schoensten Weihnachtsgeschichten. Click here if your download doesnt start automatically Ein Stern in dunkler Nacht Die schoensten Weihnachtsgeschichten Click here if your download doesn"t start automatically Ein Stern in dunkler Nacht Die schoensten Weihnachtsgeschichten Ein Stern in dunkler

Mehr

Electrical testing of Bosch common rail solenoid valve (MV) injectors

Electrical testing of Bosch common rail solenoid valve (MV) injectors Applies to MV injector, generation: -CRI 1.0 / 2.0 / 2.1 / 2.2 -CRIN 1 / 2 / 3, with K oder AK plug Bosch 10-position order number Bosch-Bestellnummer CRI: 0 445 110 xxx Bosch-Bestellnummer CRIN: 0 445

Mehr

Betriebsarten-Umschalter Common mode / Differential mode switch

Betriebsarten-Umschalter Common mode / Differential mode switch Betriebsarten-Umschalter Common mode / Differential mode switch Beschreibung: Der Betriebsarten-Umschalter CMDM 87 erweitert die Messmöglichkeiten zweier V-Netznachbildungen um die einer T- und Delta-Netznachbildung.

Mehr

rot red braun brown rot red RS-8 rot red braun brown R S V~

rot red braun brown rot red RS-8 rot red braun brown R S V~ Kleiner Ring 9 /Germany Phone: 0049 4122 / 977 381 Fax: 0049 4122 / 977 382 Sample connections: Feedback module with integrated detection of occupied tracks for the RS-feedback bus (Lenz Digital plus)

Mehr

MultiPortSwitch. VGA Umschalter. Version 1.0 As of April 19 th 2004 Subject to change!

MultiPortSwitch. VGA Umschalter. Version 1.0 As of April 19 th 2004 Subject to change! MultiPortSwitch VGA Umschalter Version 1.0 As of April 19 th 2004 Subject to change! Document version: Version Date Name Comment 1.00 29.03.2004 J. Klein Compiled Distributed by: idata industrielle Datensysteme

Mehr

Analogtechnik 2, Semestertest Technique analogique 2, Test de semestre

Analogtechnik 2, Semestertest Technique analogique 2, Test de semestre Analogtechnik 2, Semestertest Technique analogique 2, Dr. Theo Kluter 05. 06. 2011 Name/Nom : Vorname/Prénom : Klasse/Classe : Aufgabe/ Punkte maximal/ Punkte erreicht/ Problème : Points maximaux : Points

Mehr

PROFIBUS-DP Repeater 1 to 1 and 1 to 5 with optional level converter module

PROFIBUS-DP Repeater 1 to 1 and 1 to 5 with optional level converter module LSS PROFIBUS-DP Repeater 1 to 1 and 1 to 5 with optional level converter module The LSS PROFIBUS-DP repeaters 1 to 1 and 1 to 5 are used for coupling up to six PROFIBUS bus segments in RS 485 bus technology.

Mehr

Spezifikation für Freigabe / specification for release

Spezifikation für Freigabe / specification for release 74272722 STAR-FIX LFS mit Sicherheitsverschluß STAR-FIX LFS with Safety Lock DATUM / DATE : 2010-10-07 a 31,0 typ. mm b 35,1 typ. mm c 28,0 typ. mm für Kabeldurchmesser / for cable diameter Ø 8,5-12,5

Mehr

1. THÉVENIN/NORTON EQUIVALENCE

1. THÉVENIN/NORTON EQUIVALENCE 1. THÉVENN/NORTON EQUVALENCE Aufgabe: Benutzen Sie die Netzumwandlung zur Berechnung des Stromes 4. Lösung: 2A. VOLTAGE DVDER (SPANNUNGSTELER) Any serial combination of impedances acts as a voltage divider

Mehr

Harry gefangen in der Zeit Begleitmaterialien

Harry gefangen in der Zeit Begleitmaterialien Episode 011 Grammar 1. Plural forms of nouns Most nouns can be either singular or plural. The plural indicates that you're talking about several units of the same thing. Ist das Bett zu hart? Sind die

Mehr

Electrical tests on Bosch unit injectors

Electrical tests on Bosch unit injectors Valid for Bosch unit injectors with order numbers 0 414 700 / 0 414 701 / 0 414 702 Parts Kit Magnet*: - F00H.N37.925 - F00H.N37.933 - F00H.N37.934 * For allocation to the 10-place Bosch order number,

Mehr

Tube Analyzer LogViewer 2.3

Tube Analyzer LogViewer 2.3 Tube Analyzer LogViewer 2.3 User Manual Stand: 25.9.2015 Seite 1 von 11 Name Company Date Designed by WKS 28.02.2013 1 st Checker 2 nd Checker Version history Version Author Changes Date 1.0 Created 19.06.2015

Mehr

D-BAUG Informatik I. Exercise session: week 1 HS 2018

D-BAUG Informatik I. Exercise session: week 1 HS 2018 1 D-BAUG Informatik I Exercise session: week 1 HS 2018 Java Tutorials 2 Questions? expert.ethz.ch 3 Common questions and issues. expert.ethz.ch 4 Need help with expert? Mixed expressions Type Conversions

Mehr

Newest Generation of the BS2 Corrosion/Warning and Measurement System

Newest Generation of the BS2 Corrosion/Warning and Measurement System Newest Generation of the BS2 Corrosion/Warning and Measurement System BS2 System Description: BS2 CorroDec 2G is a cable and energyless system module range for detecting corrosion, humidity and prevailing

Mehr

Statistics, Data Analysis, and Simulation SS 2015

Statistics, Data Analysis, and Simulation SS 2015 Mainz, June 11, 2015 Statistics, Data Analysis, and Simulation SS 2015 08.128.730 Statistik, Datenanalyse und Simulation Dr. Michael O. Distler Dr. Michael O. Distler

Mehr

Algebraische Spezifikation von Software und Hardware II

Algebraische Spezifikation von Software und Hardware II Algebraische Spezifikation von Software und Hardware II Markus Roggenbach Mai 2008 3. Signaturen 3. Signaturen 2 Grundlegende Frage Wie lassen sich Interfaces beschreiben? Signaturen = Sammlung aller bekannten

Mehr

Mixed tenses revision: German

Mixed tenses revision: German Mixed tenses revision: Gman Teaching notes This is a whole class game in wh one team (the red team) has to try to win hexagons in a row across the PowPoint grid from left to right, while the oth team (the

Mehr

R&R. Ges. für Rationalisierung und Rechentechnik mbh. R&R RR-P-508 / ST106-EX1 motor-control unit

R&R. Ges. für Rationalisierung und Rechentechnik mbh. R&R RR-P-508 / ST106-EX1 motor-control unit R&R R&R RR-P-08 / ST06-EX motor-control unit housing wxhxd weight application power supply aluminum anodized approx. 6 x 8 x 8 mm housing similar to ST0 drawing DNR967 approx. 80 g motor desk control unit

Mehr

Hazards and measures against hazards by implementation of safe pneumatic circuits

Hazards and measures against hazards by implementation of safe pneumatic circuits Application of EN ISO 13849-1 in electro-pneumatic control systems Hazards and measures against hazards by implementation of safe pneumatic circuits These examples of switching circuits are offered free

Mehr

Dienstleistungsmanagement Übung 5

Dienstleistungsmanagement Übung 5 Dienstleistungsmanagement Übung 5 Univ.-Prof. Dr.-Ing. Wolfgang Maass Chair in Economics Information and Service Systems (ISS) Saarland University, Saarbrücken, Germany Besprechung Übungsblatt 4 Slide

Mehr

Accelerating Information Technology Innovation

Accelerating Information Technology Innovation Accelerating Information Technology Innovation http://aiti.mit.edu Ghana Summer 2011 Lecture 05 Functions Weather forecast in Accra Thursday Friday Saturday Sunday 30 C 31 C 29 C 28 C f = 9 5 c + 32 Temperature

Mehr

IR-Empfänger für Fernbedienungen IR-Receiver for Remote Control Systems SFH 5110 SFH 5111

IR-Empfänger für Fernbedienungen IR-Receiver for Remote Control Systems SFH 5110 SFH 5111 IR-Empfänger für Fernbedienungen IR-Receiver for Remote Control Systems SFH 5 SFH 5 Beschreibung SFH 5 und SFH 5 sind Infrarot-Empfänger für die Erkennung von Signalen aus Infrarot-Fernbedienungssystemen

Mehr

Sample connections and application for feedback module RS-16-Opto!

Sample connections and application for feedback module RS-16-Opto! Kleiner Ring /Germany Phone: 00 / Fax: 00 / Sample connections and application for feedback module RS--Opto!. Connect the feedback module to the Digital plus System. Connect the feedback module to the

Mehr

Introduction FEM, 1D-Example

Introduction FEM, 1D-Example Introduction FEM, 1D-Example home/lehre/vl-mhs-1-e/folien/vorlesung/3_fem_intro/cover_sheet.tex page 1 of 25. p.1/25 Table of contents 1D Example - Finite Element Method 1. 1D Setup Geometry 2. Governing

Mehr

Ein- und Ausgangsspannung 220-240V / Leistung: 800 VA / Abmessungen: 203 x 147 x 445mm / Gewicht: 20kg / Normenzertifikate: EN 60950, EN 60601-1

Ein- und Ausgangsspannung 220-240V / Leistung: 800 VA / Abmessungen: 203 x 147 x 445mm / Gewicht: 20kg / Normenzertifikate: EN 60950, EN 60601-1 Produktinformationen Powervar ABCE800-22IEC USV POWERVAR Unterbrechungsfreier Strommanager Der neue Security One USM oder unterbrechungsfreier Strommanager, hat viele neue Funktionen zu bieten. Sie können

Mehr

CABLE TESTER. Manual DN-14003

CABLE TESTER. Manual DN-14003 CABLE TESTER Manual DN-14003 Note: Please read and learn safety instructions before use or maintain the equipment This cable tester can t test any electrified product. 9V reduplicated battery is used in

Mehr

Technische Universität Kaiserslautern Lehrstuhl für Virtuelle Produktentwicklung

Technische Universität Kaiserslautern Lehrstuhl für Virtuelle Produktentwicklung functions in SysML 2.0 La Jolla, 22.05.2014 12/10/2015 Technische Universität Kaiserslautern Lehrstuhl für Virtuelle Produktentwicklung Dipl. Wirtsch.-Ing. Christian Muggeo Dipl. Wirtsch.-Ing. Michael

Mehr

asled3000 Dimmbarer High Power LED-Treiber

asled3000 Dimmbarer High Power LED-Treiber asled3000 Dimmbarer High Power LED-Treiber A1.20 01/07 Leistungsmerkmale asled3000 ist ein dimmbares Treibermodul zur Versorgung von Hochleistungs-LEDs beliebiger Lichtfarbe. Es kann bis zu 6 LEDs mit

Mehr

Dynamic Hybrid Simulation

Dynamic Hybrid Simulation Dynamic Hybrid Simulation Comparison of different approaches in HEV-modeling GT-SUITE Conference 12. September 2012, Frankfurt/Main Institut für Verbrennungsmotoren und Kraftfahrwesen Universität Stuttgart

Mehr

D/A-Converts. Jian-Jia Chen (slides are based on Peter Marwedel) Informatik 12 TU Dortmund Germany

D/A-Converts. Jian-Jia Chen (slides are based on Peter Marwedel) Informatik 12 TU Dortmund Germany 12 D/A-Converts Jian-Jia Chen (slides are based on Peter Marwedel) Informatik 12 TU Dortmund Germany Springer, 2010 2016 年 12 月 06 日 These slides use Microsoft clip arts. Microsoft copyright restrictions

Mehr

D/A-Converts. Jian-Jia Chen (slides are based on Peter Marwedel) Informatik 12 TU Dortmund Germany

D/A-Converts. Jian-Jia Chen (slides are based on Peter Marwedel) Informatik 12 TU Dortmund Germany 12 D/A-Converts Jian-Jia Chen (slides are based on Peter Marwedel) Informatik 12 TU Dortmund Germany Springer, 2010 2015 年 11 月 24 日 These slides use Microsoft clip arts. Microsoft copyright restrictions

Mehr

HIR Method & Tools for Fit Gap analysis

HIR Method & Tools for Fit Gap analysis HIR Method & Tools for Fit Gap analysis Based on a Powermax APML example 1 Base for all: The Processes HIR-Method for Template Checks, Fit Gap-Analysis, Change-, Quality- & Risk- Management etc. Main processes

Mehr

v+s Output Quelle: Schotter, Microeconomics, , S. 412f

v+s Output Quelle: Schotter, Microeconomics, , S. 412f The marginal cost function for a capacity-constrained firm At output levels that are lower than the firm s installed capacity of K, the marginal cost is merely the variable marginal cost of v. At higher

Mehr

IR-Empfänger für Fernbedienungen IR-Receiver for Remote Control Systems SFH 5110 SFH 5111

IR-Empfänger für Fernbedienungen IR-Receiver for Remote Control Systems SFH 5110 SFH 5111 IR-Empfänger für Fernbedienungen IR-Receiver for Remote Control Systems SFH 5 SFH 5 Beschreibung SFH 5 und SFH 5 sind Infrarot-Empfänger für die Erkennung von Signalen aus Infrarot-Fernbedienungssystemen

Mehr

Unit 4. The Extension Principle. Fuzzy Logic I 123

Unit 4. The Extension Principle. Fuzzy Logic I 123 Unit 4 The Extension Principle Fuzzy Logic I 123 Images and Preimages of Functions Let f : X Y be a function and A be a subset of X. Then the image of A w.r.t. f is defined as follows: f(a) = {y Y there

Mehr

Unit 6. Fuzzy Inference. Fuzzy Logic I 159

Unit 6. Fuzzy Inference. Fuzzy Logic I 159 Unit 6 Fuzzy Inference Fuzzy Logic I 159 Motivation Our ultimate goal is to be able to proceed IF-THEN rules involving vague linguistic expressions which are modeled by fuzzy sets. Question: What is still

Mehr

[[ [ [ [[ Natur, Technik, Systeme. Test, Dezember Erstes Semester WI10. PV Panel und Kondensator

[[ [ [ [[ Natur, Technik, Systeme. Test, Dezember Erstes Semester WI10. PV Panel und Kondensator Natur, Technik, Systeme Test, Dezember 00 Erstes Semester WI0 Erlaubte Hilfsmittel: Bücher und persönlich verfasste Zusammenfassung. Rechen- und Schreibzeugs. Antworten müssen begründet und nachvollziehbar

Mehr

Data Structures and Algorithm Design

Data Structures and Algorithm Design - University of Applied Sciences - Data Structures and Algorithm Design - CSCI 340 - Friedhelm Seutter Institut für Angewandte Informatik Contents 1 Analyzing Algorithms and Problems 2 Data Abstraction

Mehr

Komponenten / Components

Komponenten / Components INTERFACE / TERMINALS TERMINAL IHT 7260-1-100 Panel Mounting / 100363 Bediengerät für die Bedienung und Konfiguration für das M 4000 PCS und TWIN. Zum Einbau in die Schalttafel. Operator interface and

Mehr

Produktinformation Access-Gateway. Product information Access gateway AGW 670-0

Produktinformation Access-Gateway. Product information Access gateway AGW 670-0 Produktinformation Access-Gateway Product information Access gateway AGW 670-0 1 2 3 4 2 Deutsch Anwendung Access-Gateway zur physikalischen Trennung von 2 Netzwerken an einem Access-Server. Durch den

Mehr

p^db=`oj===pìééçêíáåñçêã~íáçå=

p^db=`oj===pìééçêíáåñçêã~íáçå= p^db=`oj===pìééçêíáåñçêã~íáçå= How to Disable User Account Control (UAC) in Windows Vista You are attempting to install or uninstall ACT! when Windows does not allow you access to needed files or folders.

Mehr

Magic Figures. We note that in the example magic square the numbers 1 9 are used. All three rows (columns) have equal sum, called the magic number.

Magic Figures. We note that in the example magic square the numbers 1 9 are used. All three rows (columns) have equal sum, called the magic number. Magic Figures Introduction: This lesson builds on ideas from Magic Squares. Students are introduced to a wider collection of Magic Figures and consider constraints on the Magic Number associated with such

Mehr

Einbauanleitung Komfort CAN Bus Interface 62240

Einbauanleitung Komfort CAN Bus Interface 62240 Einbauanleitung Komfort CAN Bus Interface 62240 Wichtiger Hinweis vor dem Einbau: Bitte beachten Sie generell beim Einbau von elektronischen Baugruppen in Fahrzeugen die Einbaurichtlinien und Garantiebestimmungen

Mehr

Aktivelektronik VP 150

Aktivelektronik VP 150 Leistungsmerkmale der VP 150 Die VP 150 ist eine Einplatinenlösung, die aufgrund des Platinendesigns für den Einsatz als Subwoofer Aktiv-Modul gedacht ist. Verstärkerelektronik inkl. Aktivweiche zum Betrieb

Mehr

Surface not flat ø = GEX Maße in mm, wenn nicht anders angegeben/dimensions in mm, unless otherwise specified.

Surface not flat ø = GEX Maße in mm, wenn nicht anders angegeben/dimensions in mm, unless otherwise specified. SFH 56 IR-mpfänger/Demodulator-Baustein IR-Receiver/Demodulator Device SFH 56 X.3 9.7 6.3 5.9.9. 9. 3. 3..5 max. V OUT V S GND Surface not flat.3 B.65.5.5 ø.5 B.54 X.5.54 = 7.6.7. 3x R.75 4.3 3.7 6. 5.5

Mehr

ICL Series Rail-Mount Hydraulic Magnetic Circuit Breaker

ICL Series Rail-Mount Hydraulic Magnetic Circuit Breaker Ihr autorisierter Distributor: Neumüller Elektronik GmbH info@hq-schutzschalter.de ICL Series Rail-Mount Hydraulic Magnetic Circuit Breaker Introduction 133 Configurations 134 Operating Characteristics

Mehr

CAN-Bus-Systems. Microprocessor-controlled Can-Bus-node with digital and analog signal in- and outputs.

CAN-Bus-Systems. Microprocessor-controlled Can-Bus-node with digital and analog signal in- and outputs. CAN-BUS-node 1362 3 digital inputs, active high 8 analog inputs for resistor sensor 10 digital outputs 24V/200mA short-circuit-proof 2 digital outputs 24V/2A short-circuit-proof 5 digital outputs 24V/5A

Mehr

ZU Endlagenschalter, elektrisch für WA 131 / 131 H Limit Switch, Electrical, for WA 131 / 131 H.

ZU Endlagenschalter, elektrisch für WA 131 / 131 H Limit Switch, Electrical, for WA 131 / 131 H. ZU 0859 Endlagenschalter, elektrisch für WA 131 / 131 H Limit Switch, Electrical, for WA 131 / 131 H www.knick.de Bauart und Funktion Der Endlagenschalter ZU 0859 wandelt die pneumatischen Endlagen signale,

Mehr

DYNAMISCHE GEOMETRIE

DYNAMISCHE GEOMETRIE DYNAMISCHE GEOMETRIE ÄHNLICHKEITSGEOMETRIE & MODELLIERUNG PAUL LIBBRECHT PH WEINGARTEN WS 2014-2015 CC-BY VON STAUDT KONSTRUKTIONEN Menü Erinnerung: Strahlensatz Längen, Frame Zielartikel Addition, Subtraktion

Mehr

Monitor VIS 3xx Kurzanleitung

Monitor VIS 3xx Kurzanleitung Monitor VIS 3xx Kurzanleitung 19.08.08 Art. Nr. 22261 Inhalt: 1. Spezifikationen...2 2. Tastenfunktionen...2 3. Menüführung und Einstellungen...3 Technik nach Maß Wöhler Monitor VIS 3xx 1. Spezifikationen

Mehr

H o c h s c h u l e D e g g e n d o r f H o c h s c h u l e f ü r a n g e w a n d t e W i s s e n s c h a f t e n

H o c h s c h u l e D e g g e n d o r f H o c h s c h u l e f ü r a n g e w a n d t e W i s s e n s c h a f t e n Time Aware Shaper Christian Boiger christian.boiger@hdu-deggendorf.de IEEE 802 Plenary September 2012 Santa Cruz, California D E G G E N D O R F U N I V E R S I T Y O F A P P L I E D S C I E N C E S Time

Mehr

1. Hardware Configuration Hardware-Konfiguration Software-Konfiguration Software Configuration...4

1. Hardware Configuration Hardware-Konfiguration Software-Konfiguration Software Configuration...4 Einzel- und Verbundkonfiguration Stand-alone and Multi-unit Configuration Inhaltsverzeichnis 1. Hardware-Konfiguration... 2 1.1 Netzwerkadressen...2 1.2 Verkabelung...2 Contents 1. Hardware Configuration...2

Mehr

Snap-in switch for switches PSE, MSM and MCS 30

Snap-in switch for switches PSE, MSM and MCS 30 Product manual Snap-in switch for switches PSE, MSM and MCS 30 CONTENTS 1. PRODUCT DESCRIPTION 2. DATA AND DIMENSIONAL DRAWINGS 2.1. Technical Data 2.2. Dimensions of PSE with a Mounting Diameter 19 mm

Mehr

VLT. Instruction/Instruktion. VLT Series V TTL / Linedriver -> 24 V DC option. Encodersignalwandler. Converter for encoder inputs *MI50I151*

VLT. Instruction/Instruktion. VLT Series V TTL / Linedriver -> 24 V DC option. Encodersignalwandler. Converter for encoder inputs *MI50I151* VLT Instruction/Instruktion Drives and Controls VLT Series 5000 5V TTL / Linedriver -> 24 V DC option Encodersignalwandler Converter for encoder inputs MI.50.I1.51 VLT is a registered Danfoss trademark

Mehr

Lehrstuhl für Allgemeine BWL Strategisches und Internationales Management Prof. Dr. Mike Geppert Carl-Zeiß-Str. 3 07743 Jena

Lehrstuhl für Allgemeine BWL Strategisches und Internationales Management Prof. Dr. Mike Geppert Carl-Zeiß-Str. 3 07743 Jena Lehrstuhl für Allgemeine BWL Strategisches und Internationales Management Prof. Dr. Mike Geppert Carl-Zeiß-Str. 3 07743 Jena http://www.im.uni-jena.de Contents I. Learning Objectives II. III. IV. Recap

Mehr

Introduction to Python. Introduction. First Steps in Python. pseudo random numbers. May 2018

Introduction to Python. Introduction. First Steps in Python. pseudo random numbers. May 2018 to to May 2018 to What is Programming? All computers are stupid. All computers are deterministic. You have to tell the computer what to do. You can tell the computer in any (programming) language) you

Mehr

Multicriterial Design Decision Making regarding interdependent Objectives in DfX

Multicriterial Design Decision Making regarding interdependent Objectives in DfX Overview Multicriterial Design Decision Making regarding interdependent Objectives in DfX S. Bauer The Design Process Support of the Design Process with Design for X Visualization of Decision Problems

Mehr

Spezifikation für Freigabe / specification for release

Spezifikation für Freigabe / specification for release @@FRM 1@@ Spezifikation für Freigabe / specification for release : A Mechanische Abmessungen / dimensions: Größe / size 1008 A 2,5 ± 0,2 mm B 2,0 ± 0,2 mm C 1,0 (max.) mm D 0,5 ± 0,3 mm B Elektrische Eigenschaften

Mehr

VGM. VGM information. HAMBURG SÜD VGM WEB PORTAL USER GUIDE June 2016

VGM. VGM information. HAMBURG SÜD VGM WEB PORTAL USER GUIDE June 2016 Overview The Hamburg Süd VGM Web portal is an application that enables you to submit VGM information directly to Hamburg Süd via our e-portal Web page. You can choose to enter VGM information directly,

Mehr

Mitglied der Leibniz-Gemeinschaft

Mitglied der Leibniz-Gemeinschaft Methods of research into dictionary use: online questionnaires Annette Klosa (Institut für Deutsche Sprache, Mannheim) 5. Arbeitstreffen Netzwerk Internetlexikografie, Leiden, 25./26. März 2013 Content

Mehr

Schachaufgabe 05: Ma-Übung Chess Problem 05: Mate training

Schachaufgabe 05: Ma-Übung Chess Problem 05: Mate training Schachaufgabe 05: Ma-Übung Chess Problem 05: Mate training In dieser Aufgabe ist kein Zug zu finden. Vielmehr sollst du herausfinden, wieviel weiße Figuren mindestens nö"g sind, um den schwarzen König

Mehr

Mathematics (M4) (English version) ORIENTIERUNGSARBEIT (OA 11) Gymnasium. Code-Nr.:

Mathematics (M4) (English version) ORIENTIERUNGSARBEIT (OA 11) Gymnasium. Code-Nr.: Gymnasium 2. Klassen MAR Code-Nr.: Schuljahr 2005/2006 Datum der Durchführung Donnerstag, 6.4.2006 ORIENTIERUNGSARBEIT (OA 11) Gymnasium Mathematics (M4) (English version) Lesen Sie zuerst Anleitung und

Mehr

VGM. VGM information. HAMBURG SÜD VGM WEB PORTAL - USER GUIDE June 2016

VGM. VGM information. HAMBURG SÜD VGM WEB PORTAL - USER GUIDE June 2016 Overview The Hamburg Süd VGM-Portal is an application which enables to submit VGM information directly to Hamburg Süd via our e-portal web page. You can choose to insert VGM information directly, or download

Mehr

Information Flow. Basics. Overview. Bell-LaPadula Model embodies information flow policy. Variables x, y assigned compartments x, y as well as values

Information Flow. Basics. Overview. Bell-LaPadula Model embodies information flow policy. Variables x, y assigned compartments x, y as well as values Information Flow Overview Basics and background Compiler-based mechanisms Execution-based mechanisms 1 Basics Bell-LaPadula Model embodies information flow policy Given compartments A, B, info can flow

Mehr