AC BEHAVIOR OF COMPONENTS
|
|
- Mavis Thomasina Lawrence
- 5 years ago
- Views:
Transcription
1 AC BEHAVIOR OF COMPONENTS
2 AC Behavior of Capacitor Consider a capacitor driven by a sine wave voltage: I(t) 2 1 U(t) ~ C The current: is shifted by 90 o (sin cos)! CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 2
3 Complex Impedance To simplify our calculations, we would like to extend the relation R= U/I to capacitors, using an impedance Z C. In order to get the phase right, we use complex quantities: for voltages and currents. By mixing complex and real parts, we can mix sin() and cos() components and therefore influence the phase. Note: Often j is used instead of i for the complex unit, because i is used as current symbol Often s is used for iω (or jω) CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 3
4 From Complex Values back to Real Quantities To find ( back ) the amplitude of such a complex signal, we calculate the length (magnitude) of the complex vector as Im z Re z * To get the phase, we use real and imaginary parts: z Im(z) Note: this simple formula works only in 2 quadrants. You may have to look at signs of Re(z) and Im(z) Re(z) CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 4
5 Hints for Mathematica Mathematica knows complex arithmetic Useful Functions are Abs[] and Arg[] Remember: Imaginary Unit is typed as ESC i i ESC If you want to simplify expression, M. has to know that expressions like ω, R, C, U are real. This can be done with Assumptions: Sometimes ComplexExpand[] can be used. It assumes all arguments are real (but not necessarily > 0): CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 5
6 Complex Impedance of the Capacitor We know that With we have Therefore Similar: The impedance of a capacitor becomes very small at high frequencies CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 6
7 Checking this for a Capacitor For an input voltage (sine wave of freq. ω) with phase = 0 we have The amplitude of I(t) is The phase is: We have dropped the time variant part and the constant U 0 CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 7
8 Simplifying even more As we have just seen, the propagates trivially to the output. We therefore drop this part and just use 1! CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 8
9 Recipe to Calculate Transfer Functions Replace all component by their complex impedances (1/(sC), sl, R) Assume a unit signal of 1 at the input (in reality it is ) Write down all node current equations or current equalities using Kirchhoff s Law (they depend on s) You need N equations for N unknowns Solve for the quantity you are interested in (most often V out ) Analyze the result (amplitude / phase / ) CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 9
10 Example: Low Pass Consider I R R v in C I C v out We have only one unknown: v out Current equality at node v out : Solve for v out : CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 10
11 Mathematica Hint Write down each node equation (here only 1): Solve them: v in R v out C Define a transfer function: CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 11
12 Low Pass as complex voltage divider R Z1 C Z2 This is an ac voltage divider with two impedances Z 1 = R and Z 2 = 1/sC Using the voltage divider formula, we get with ω 0 = 1/(RC), the corner frequency. CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 12
13 The HIGH Pass By exchanging R and C, low frequencies are blocked and high frequencies pass through. This is the High-Pass. C Z1 R Z2 We get CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 13
14 More Complicated Example R v 1 C v in R C vout We have now two unknowns: v 1, v out Eliminating v 1 gives: CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 14
15 Mathematica Steps Node equation (here 2): v in R v 1 C R v out Solve them: C Define a transfer function: CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 15
16 Mathematica Steps Replace s by i ω Calculate (squared) gain as absolute value To plot, convert to db (sqrt leads to factor 10 instead of 20) For phase, better use ArcTan[Re,Im] to get quadrant right CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 16
17 BODE PLOT
18 Transfer Function The transfer function of a linear, time invariant system visualizes how the amplitude and phase of a sine wave input signal of constant frequency ω appears at the output The frequency remains unchanged The transfer function H(ω) contains The phase change Φ(ω) The gain v(ω) = amp_in / amp_out (ω) in H(ω) out v(ω) Φ(ω) CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 18
19 Bode Diagram: Definition 20 db 0 db The Bode Plot shows gain (+ phase) of the transfer function The frequency (x-axis) is plotted logarithmically Gain is plotted (y-axis) logarithmically, often in decibel DB(x) = 20 log 10 (x): db db 2 6 db (not exactly!) 1 0 db / 2-6 db / 2-3 db -20 db -40 db dbs for multiplied quantities just add! CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 19
20 Bode Diagram: Properties Power functions are straight lines: Plot[x 2,{x,0,10}] LogPlot[x 2,{x,0,10}] LogLogPlot[x 2,{x,1,10}] LogLogPlot[Table[x N,{N,-1,3}],{x,1,10}] y=x 3 y=x 2 y=x y=x 0 = 1 y=x -1 CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 20
21 Bode Diagram: Properties 1/x function has slope -1: Multiplied functions are added in plot: 2 f1=2+x;f2=x -1 ; LogLogPlot[{f1, 5 f1},{x,0.01,100}] LogLogPlot[{f1, f2,f1 * f2},{x,0.01,100}] 5 f1 f1+f2 f1=2+x f1=2+x f2=1/x CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 21
22 THE LOW PASS FILTER
23 Analysis of the Low Pass Transfer Function Transfer Function: Magnitude: Phase: (rad or degree) CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 23
24 Bode Plot of LowPass (Amplitude) 0 db -3 db -6 db -20 db v ω 0 = 10 1/Sqrt(2) = dB point Factor 10 decrease in amplitude for factor 10 increase in frequency = -20 db / decade or -6 db / octave -26 db 1 / 10 (-20 db) -40 db ω x 10 (Decade) CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 24
25 The same in db -3 db -3 db point Approximation with straight lines CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 25
26 Bode Plot of LowPass (Phase) Phase ω 0 = 10 Lin-Log Plot! -45 degree -90 degree ω CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 26
27 Series Connection of two Low Pass Filters Consider two identical LP filters. A unit gain buffer makes sure that the second LP does not load the first one: R R C C From the properties of the LogLog Plot, the TF of the 2 nd order LP is just the sum of two 1 st order LPs: -6 db -3 db 1 LP 1 LP: -6 db / octave 2 LPs: -12 db / octave 2 LPs CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 27
28 Why bother so much about the low pass? All circuits behave like low-passes (at some frequency)! CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 28
29 Caveat! So far, frequency is expressed with ω, i.e. in radian / second We have: ω = 2 π ν Therefore, the frequencies in Hertz are 2π lower!!! db ω 0 = 1 / (RC) = 1 / (1n x 1M) = 1 / 1m = 1 khz ν = 1000 / 6.28 Hz = 160 Hz CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 29
30 Low Pass and High Pass CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 30
31 A More Complex Example Consider a (High Pass) filter with an inductor: C R v in L v out The transfer function is It is of second order (s has exponent of 2 in denominator) Magnitude: L=C=1 R=0.1,0.5,1,2 H(s) = (C L s 2 )/(1+C R s+c L s 2 ) Inductive peaking 12 db / octave = 40 db / decade CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 31
32 Phase Phase For fun: When is filter steep & flat? Zoom to corner frequency: L=C=1, R={1,Sqrt[2],2} CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 32
33 CIRCUIT SIMPLIFICATIONS
34 Large and Small Values To roughly understand behavior of circuits, only keep the dominant components: R Large R Large R Small R Small R Large R Small R Large R Small Eliminate larger or the smaller part (depending on circuit!) Error ~ ratio of components CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 34
35 The same for Capacitors C Large C Large C Small C Small C Large C Small C Large C Small CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 35
36 Resistors AND Capacitors Behavior depends on frequency ( Z C = 1/(2πν C) ) C Z C >> R ν << 1/(2π RC) Low frequency R Z C << R ν >> 1/(2π RC) High frequency Low frequency High frequency CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 36
37 Fourier Decomposition Maybe later Also: Step / Impulse response via inverse Laplace Transform Later CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 37
38 To Do S. 27: Bild: du/dt ~ W S. 31: Wieso U0 exp(iwt) weg? Show that Z C = Z R at the corner frequency Phasensprung bei LCR checken! CCS - Basics P. Fischer, ZITI, Uni Heidelberg, Seite 38
v(t) = V p sin(2π ft +φ) = V p cos(2π ft +φ + π 2 )
1 Let us revisit sine and cosine waves. A sine wave can be completely defined with three parameters Vp, the peak voltage (or amplitude), its frequency w in radians/second or f in cycles/second (Hz), and
More informationCHAPTER 6 Frequency Response, Bode. Plots, and Resonance
CHAPTER 6 Frequency Response, Bode Plots, and Resonance CHAPTER 6 Frequency Response, Bode Plots, and Resonance 1. State the fundamental concepts of Fourier analysis. 2. Determine the output of a filter
More informationExercise 4: (More) Filters
Exercise 4: (More) Filters Prof. Dr. P. Fischer Lehrstuhl für Schaltungstechnik und Simulation Uni Heidelberg CCS Exercise 4: Filters P. Fischer, ZITI, Uni Heidelberg Page1 Exercise 4.1 Analyze the following
More informationBode plot, named after Hendrik Wade Bode, is usually a combination of a Bode magnitude plot and Bode phase plot:
Bode plot From Wikipedia, the free encyclopedia A The Bode plot for a first-order (one-pole) lowpass filter Bode plot, named after Hendrik Wade Bode, is usually a combination of a Bode magnitude plot and
More informationEE233 Autumn 2016 Electrical Engineering University of Washington. EE233 HW7 Solution. Nov. 16 th. Due Date: Nov. 23 rd
EE233 HW7 Solution Nov. 16 th Due Date: Nov. 23 rd 1. Use a 500nF capacitor to design a low pass passive filter with a cutoff frequency of 50 krad/s. (a) Specify the cutoff frequency in hertz. fc c 50000
More informationBoise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab
Objectives Boise State University Department of Electrical and Computer Engineering ECE L Circuit Analysis and Design Lab Experiment #0: Frequency esponse Measurements The objectives of this laboratory
More informationBasic Circuits. Current Mirror, Gain stage, Source Follower, Cascode, Differential Pair,
Basic Circuits Current Mirror, Gain stage, Source Follower, Cascode, Differential Pair, CCS - Basic Circuits P. Fischer, ZITI, Uni Heidelberg, Seite 1 Reminder: Effect of Transistor Sizes Very crude classification:
More informationKent Bertilsson Muhammad Amir Yousaf
Today s topics Analog System (Rev) Frequency Domain Signals in Frequency domain Frequency analysis of signals and systems Transfer Function Basic elements: R, C, L Filters RC Filters jw method (Complex
More informationElectric Circuit Theory
Electric Circuit Theory Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 Chapter 15 Active Filter Circuits Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 Contents and Objectives 3 Chapter Contents 15.1 First-Order
More informationSECTION 7: FREQUENCY DOMAIN ANALYSIS. MAE 3401 Modeling and Simulation
SECTION 7: FREQUENCY DOMAIN ANALYSIS MAE 3401 Modeling and Simulation 2 Response to Sinusoidal Inputs Frequency Domain Analysis Introduction 3 We ve looked at system impulse and step responses Also interested
More informationCHAPTER 6 INTRODUCTION TO SYSTEM IDENTIFICATION
CHAPTER 6 INTRODUCTION TO SYSTEM IDENTIFICATION Broadly speaking, system identification is the art and science of using measurements obtained from a system to characterize the system. The characterization
More informationAdvanced Circuits Topics Part 2 by Dr. Colton (Fall 2017)
Part 2: Some Possibly New Things Advanced Circuits Topics Part 2 by Dr. Colton (Fall 2017) These are some topics that you may or may not have learned in Physics 220 and/or 145. This handout continues where
More informationωc ωc sin(wt 90o ) (for a capacitance) (4)
Physics'241'Signal'Processing:'Lab'3' Sinusoidal esponse of, L ircuits In the previous lab, we studied the behavior of series combinations of and L circuits with input square and triangular waveforms.
More informationExperiment 8 Frequency Response
Experiment 8 Frequency Response W.T. Yeung, R.A. Cortina, and R.T. Howe UC Berkeley EE 105 Spring 2005 1.0 Objective This lab will introduce the student to frequency response of circuits. The student will
More informationEK307 Passive Filters and Steady State Frequency Response
EK307 Passive Filters and Steady State Frequency Response Laboratory Goal: To explore the properties of passive signal-processing filters Learning Objectives: Passive filters, Frequency domain, Bode plots
More informationSimple AC Circuits. Introduction
Simple AC Circuits Introduction Each problem in this problem set involves the steady state response of a linear, time-invariant circuit to a single sinusoidal input. Such a response is known to be sinusoidal
More informationCHAPTER 9. Sinusoidal Steady-State Analysis
CHAPTER 9 Sinusoidal Steady-State Analysis 9.1 The Sinusoidal Source A sinusoidal voltage source (independent or dependent) produces a voltage that varies sinusoidally with time. A sinusoidal current source
More informationThe above figure represents a two stage circuit. Recall, the transfer function relates. Vout
LABORATORY 12: Bode plots/second Order Filters Material covered: Multistage circuits Bode plots Design problem Overview Notes: Two stage circuits: Vin1 H1(s) Vout1 Vin2 H2(s) Vout2 The above figure represents
More informationUNIVERSITY OF BABYLON BASIC OF ELECTRICAL ENGINEERING LECTURE NOTES. Resonance
Resonance The resonant(or tuned) circuit, in one of its many forms, allows us to select a desired radio or television signal from the vast number of signals that are around us at any time. Resonant electronic
More informationIE1206 Embedded Electronics
IE06 Embedded Electronics Le Le3 Le4 Le Ex Ex PIC-block Documentation, Seriecom Pulse sensors I,, R, P, serial and parallel KC LAB Pulse sensors, Menu program Start of programing task Kirchhoffs laws Node
More informationEK307 Active Filters and Steady State Frequency Response
EK307 Active Filters and Steady State Frequency Response Laboratory Goal: To explore the properties of active signal-processing filters Learning Objectives: Active Filters, Op-Amp Filters, Bode plots Suggested
More informationLab 9 Frequency Domain
Lab 9 Frequency Domain 1 Components Required Resistors Capacitors Function Generator Multimeter Oscilloscope 2 Filter Design Filters are electric components that allow applying different operations to
More informationFREQUENCY RESPONSE AND PASSIVE FILTERS LABORATORY
FREQUENCY RESPONSE AND PASSIVE FILTERS LABORATORY In this experiment we will analytically determine and measure the frequency response of networks containing resistors, AC source/sources, and energy storage
More informationEE Experiment 8 Bode Plots of Frequency Response
EE16:Exp8-1 EE 16 - Experiment 8 Bode Plots of Frequency Response Objectives: To illustrate the relationship between a system frequency response and the frequency response break frequencies, factor powers,
More informationPoles and Zeros of H(s), Analog Computers and Active Filters
Poles and Zeros of H(s), Analog Computers and Active Filters Physics116A, Draft10/28/09 D. Pellett LRC Filter Poles and Zeros Pole structure same for all three functions (two poles) HR has two poles and
More informationElectronics and Instrumentation ENGR-4300 Spring 2004 Section Experiment 5 Introduction to AC Steady State
Experiment 5 Introduction to C Steady State Purpose: This experiment addresses combinations of resistors, capacitors and inductors driven by sinusoidal voltage sources. In addition to the usual simulation
More informationECE 3155 Experiment I AC Circuits and Bode Plots Rev. lpt jan 2013
Signature Name (print, please) Lab section # Lab partner s name (if any) Date(s) lab was performed ECE 3155 Experiment I AC Circuits and Bode Plots Rev. lpt jan 2013 In this lab we will demonstrate basic
More informationFilter Notes. You may have memorized a formula for the voltage divider - if not, it is easily derived using Ohm's law, Vo Vi
Filter Notes You may have memorized a formula for the voltage divider - if not, it is easily derived using Ohm's law, Vo Vi R2 R+ R2 If you recall the formula for capacitive reactance, the divider formula
More informationLecture 16 Date: Frequency Response (Contd.)
Lecture 16 Date: 03.10.2017 Frequency Response (Contd.) Bode Plot (contd.) Bode Plot (contd.) Bode Plot (contd.) not every transfer function has all seven factors. To sketch the Bode plots for a generic
More informationVälkomna till TSRT15 Reglerteknik Föreläsning 5. Summary of lecture 4 Frequency response Bode plot
Välkomna till TSRT15 Reglerteknik Föreläsning 5 Summary of lecture 4 Frequency response Bode plot Summary of last lecture 2 Given a pole polynomial with a varying parameter P(s)+KQ(s)=0 We draw the location
More informationSTATION NUMBER: LAB SECTION: Filters. LAB 6: Filters ELECTRICAL ENGINEERING 43/100 INTRODUCTION TO MICROELECTRONIC CIRCUITS
Lab 6: Filters YOUR EE43/100 NAME: Spring 2013 YOUR PARTNER S NAME: YOUR SID: YOUR PARTNER S SID: STATION NUMBER: LAB SECTION: Filters LAB 6: Filters Pre- Lab GSI Sign- Off: Pre- Lab: /40 Lab: /60 Total:
More informationENG 100 Lab #2 Passive First-Order Filter Circuits
ENG 100 Lab #2 Passive First-Order Filter Circuits In Lab #2, you will construct simple 1 st -order RL and RC filter circuits and investigate their frequency responses (amplitude and phase responses).
More informationReadout Electronics. P. Fischer, Heidelberg University. Silicon Detectors - Readout Electronics P. Fischer, ziti, Uni Heidelberg, page 1
Readout Electronics P. Fischer, Heidelberg University Silicon Detectors - Readout Electronics P. Fischer, ziti, Uni Heidelberg, page 1 We will treat the following questions: 1. How is the sensor modeled?
More informationNH 67, Karur Trichy Highways, Puliyur C.F, Karur District DEPARTMENT OF INFORMATION TECHNOLOGY DIGITAL SIGNAL PROCESSING UNIT 3
NH 67, Karur Trichy Highways, Puliyur C.F, 639 114 Karur District DEPARTMENT OF INFORMATION TECHNOLOGY DIGITAL SIGNAL PROCESSING UNIT 3 IIR FILTER DESIGN Structure of IIR System design of Discrete time
More informationFrequency Response Analysis
Frequency Response Analysis Continuous Time * M. J. Roberts - All Rights Reserved 2 Frequency Response * M. J. Roberts - All Rights Reserved 3 Lowpass Filter H( s) = ω c s + ω c H( jω ) = ω c jω + ω c
More informationClass #16: Experiment Matlab and Data Analysis
Class #16: Experiment Matlab and Data Analysis Purpose: The objective of this experiment is to add to our Matlab skill set so that data can be easily plotted and analyzed with simple tools. Background:
More informationEECS40 RLC Lab guide
EECS40 RLC Lab guide Introduction Second-Order Circuits Second order circuits have both inductor and capacitor components, which produce one or more resonant frequencies, ω0. In general, a differential
More informationIE1206 Embedded Electronics
IE06 Embedded Electronics Le Le3 Le4 Le Ex Ex PI-block Documentation, Serial com Pulse sensors I,,, P, series and parallel K LAB Pulse sensors, Menu program Start of programing task Kirchhoffs laws Node
More informationEXPERIMENT 4: RC, RL and RD CIRCUITs
EXPERIMENT 4: RC, RL and RD CIRCUITs Equipment List An assortment of resistor, one each of (330, 1k,1.5k, 10k,100k,1000k) Function Generator Oscilloscope 0.F Ceramic Capacitor 100H Inductor LED and 1N4001
More informationExperiment Guide: RC/RLC Filters and LabVIEW
Description and ackground Experiment Guide: RC/RLC Filters and LabIEW In this lab you will (a) manipulate instruments manually to determine the input-output characteristics of an RC filter, and then (b)
More informationLab 6: Building a Function Generator
ECE 212 Spring 2010 Circuit Analysis II Names: Lab 6: Building a Function Generator Objectives In this lab exercise you will build a function generator capable of generating square, triangle, and sine
More informationPre-Lab. Introduction
Pre-Lab Read through this entire lab. Perform all of your calculations (calculated values) prior to making the required circuit measurements. You may need to measure circuit component values to obtain
More informationNon-ideal Behavior of Electronic Components at High Frequencies and Associated Measurement Problems
Nonideal Behavior of Electronic Components at High Frequencies and Associated Measurement Problems Matthew Beckler beck0778@umn.edu EE30 Lab Section 008 October 27, 2006 Abstract In the world of electronics,
More informationEE42: Running Checklist of Electronics Terms Dick White
EE42: Running Checklist of Electronics Terms 14.02.05 Dick White Terms are listed roughly in order of their introduction. Most definitions can be found in your text. Terms2 TERM Charge, current, voltage,
More informationEXPERIMENT 14 Variable-frequency networks
EXPEIMENT 14 Variable-frequency networks The objective of this experiment is to: Investigate networks excited with variable-frequency sinusoidal signals I. Introduction The ac steady-state behavior of
More informationLab 8 - INTRODUCTION TO AC CURRENTS AND VOLTAGES
08-1 Name Date Partners ab 8 - INTRODUCTION TO AC CURRENTS AND VOTAGES OBJECTIVES To understand the meanings of amplitude, frequency, phase, reactance, and impedance in AC circuits. To observe the behavior
More informationExperiment 2: Transients and Oscillations in RLC Circuits
Experiment 2: Transients and Oscillations in RLC Circuits Will Chemelewski Partner: Brian Enders TA: Nielsen See laboratory book #1 pages 5-7, data taken September 1, 2009 September 7, 2009 Abstract Transient
More informationTransmit filter designs for ADSL modems
EE 233 Laboratory-4 1. Objectives Transmit filter designs for ADSL modems Design a filter from a given topology and specifications. Analyze the characteristics of the designed filter. Use SPICE to verify
More informationLab #2: Electrical Measurements II AC Circuits and Capacitors, Inductors, Oscillators and Filters
Lab #2: Electrical Measurements II AC Circuits and Capacitors, Inductors, Oscillators and Filters Goal: In circuits with a time-varying voltage, the relationship between current and voltage is more complicated
More informationECE4902 Lab 5 Simulation. Simulation. Export data for use in other software tools (e.g. MATLAB or excel) to compare measured data with simulation
ECE4902 Lab 5 Simulation Simulation Export data for use in other software tools (e.g. MATLAB or excel) to compare measured data with simulation Be sure to have your lab data available from Lab 5, Common
More informationThe steeper the phase shift as a function of frequency φ(ω) the more stable the frequency of oscillation
It should be noted that the frequency of oscillation ω o is determined by the phase characteristics of the feedback loop. the loop oscillates at the frequency for which the phase is zero The steeper the
More informationOperational Amplifier BME 360 Lecture Notes Ying Sun
Operational Amplifier BME 360 Lecture Notes Ying Sun Characteristics of Op-Amp An operational amplifier (op-amp) is an analog integrated circuit that consists of several stages of transistor amplification
More informationDesigning Information Devices and Systems II Fall 2018 Elad Alon and Miki Lustig Homework 4
EECS 6B Designing Information Devices and Systems II Fall 208 Elad Alon and Miki Lustig Homework 4 This homework is solely for your own practice. However, everything on it is in scope for midterm, and
More informationUniversity of Illinois at Chicago Spring ECE 412 Introduction to Filter Synthesis Homework #2 Solutions. Problem 1
Problem 1 (a) Magnitude (impedance) scale the circuit so that all resistors are 1kΩ. Solution: Since all of the resistors in the circuit are 1Ω, we need to magnitude scale by k m = 1000; therefore, we
More informationLab #2: Electrical Measurements II AC Circuits and Capacitors, Inductors, Oscillators and Filters
Lab #2: Electrical Measurements II AC Circuits and Capacitors, Inductors, Oscillators and Filters Goal: In circuits with a time-varying voltage, the relationship between current and voltage is more complicated
More informationExercise 8: Frequency Response
Exercise 8: Frequency Response Introduction We can find the frequency response of a system by exciting the system with a sinusoidal signal of amplitude A and frequency ω [rad/s] (Note: ω = 2πf) and observing
More informationAnalog Filters D R. T A R E K T U T U N J I P H I L A D E L P H I A U N I V E R S I T Y, J O R D A N
Analog Filters D. T A E K T U T U N J I P H I L A D E L P H I A U N I V E S I T Y, J O D A N 2 0 4 Introduction Electrical filters are deigned to eliminate unwanted frequencies Filters can be classified
More informationPositive Feedback and Oscillators
Physics 3330 Experiment #5 Fall 2011 Positive Feedback and Oscillators Purpose In this experiment we will study how spontaneous oscillations may be caused by positive feedback. You will construct an active
More informationElectronics basics for MEMS and Microsensors course
Electronics basics for course, a.a. 2017/2018, M.Sc. in Electronics Engineering Transfer function 2 X(s) T(s) Y(s) T S = Y s X(s) The transfer function of a linear time-invariant (LTI) system is the function
More informationLab 6 rev 2.1-kdp Lab 6 Time and frequency domain analysis of LTI systems
Lab 6 Time and frequency domain analysis of LTI systems 1 I. GENERAL DISCUSSION In this lab and the next we will further investigate the connection between time and frequency domain responses. In this
More informationLow Pass Filter Introduction
Low Pass Filter Introduction Basically, an electrical filter is a circuit that can be designed to modify, reshape or reject all unwanted frequencies of an electrical signal and accept or pass only those
More informationBJT & FET Frequency Response
Chapter 4 BJT & FET Spring 2012 4 th Semester Mechatronics SZABIST, Karachi 2 Course Support humera.rafique@szabist.edu.pk Office: 100 Campus (404) Official: ZABdesk Subsidiary: https://sites.google.com/site/zabistmechatronics/home/spring-2012/ecd
More information(Refer Slide Time: 02:00-04:20) (Refer Slide Time: 04:27 09:06)
Digital Signal Processing Prof. S. C. Dutta Roy Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 25 Analog Filter Design (Contd.); Transformations This is the 25 th
More informationWelcome to your second Electronics Laboratory Session. In this session you will learn about how to use resistors, capacitors and inductors to make
Welcome to your second Electronics Laboratory Session. In this session you will learn about how to use resistors, capacitors and inductors to make simple circuits. You will find out how these circuits
More informationLRC Circuit PHYS 296 Your name Lab section
LRC Circuit PHYS 296 Your name Lab section PRE-LAB QUIZZES 1. What will we investigate in this lab? 2. Figure 1 on the following page shows an LRC circuit with the resistor of 1 Ω, the capacitor of 33
More informationMini Project 3 Multi-Transistor Amplifiers. ELEC 301 University of British Columbia
Mini Project 3 Multi-Transistor Amplifiers ELEC 30 University of British Columbia 4463854 November 0, 207 Contents 0 Introduction Part : Cascode Amplifier. A - DC Operating Point.......................................
More informationFilters and Tuned Amplifiers
CHAPTER 6 Filters and Tuned Amplifiers Introduction 55 6. Filter Transmission, Types, and Specification 56 6. The Filter Transfer Function 60 6.7 Second-Order Active Filters Based on the Two-Integrator-Loop
More informationNPTEL Online Course: Control Engineering
NPTEL Online Course: Control Engineering Dr. Ramkrishna Pasumarthy and Dr.Viswanath Assignment - 0 : s. A passive band pass filter with is one which: (a) Attenuates signals between the two cut-off frequencies
More informationAC CURRENTS, VOLTAGES, FILTERS, and RESONANCE
July 22, 2008 AC Currents, Voltages, Filters, Resonance 1 Name Date Partners AC CURRENTS, VOLTAGES, FILTERS, and RESONANCE V(volts) t(s) OBJECTIVES To understand the meanings of amplitude, frequency, phase,
More informationHomework Assignment 03 Solution
Homework Assignment 03 Solution Question 1 Determine the h 11 and h 21 parameters for the circuit. Be sure to supply the units and proper sign for each parameter. (8 points) Solution Setting v 2 = 0 h
More informationPhysics 303 Fall Module 4: The Operational Amplifier
Module 4: The Operational Amplifier Operational Amplifiers: General Introduction In the laboratory, analog signals (that is to say continuously variable, not discrete signals) often require amplification.
More informationStudy of Inductive and Capacitive Reactance and RLC Resonance
Objective Study of Inductive and Capacitive Reactance and RLC Resonance To understand how the reactance of inductors and capacitors change with frequency, and how the two can cancel each other to leave
More informationHomework Assignment 03
Homework Assignment 03 Question 1 (Short Takes), 2 points each unless otherwise noted. 1. Two 0.68 μf capacitors are connected in series across a 10 khz sine wave signal source. The total capacitive reactance
More informationπ Speakers Crossover Electronics 101
π Speakers Crossover Electronics 101 Overview 1. Resistors - Ohms Law Voltage Dividers and L-Pads 2. Reactive components - Inductors and Capacitors 3. Resonance 4. Peaking 5. Damping Formulas Ohm s Law
More informationChapter 4: Passive Analog Signal Processing
hapter 4: Passive Analog Signal Processing In this chapter we introduce filters and signal transmission theory. Filters are essential components of most analog circuits and are used to remove unwanted
More informationFilters And Waveform Shaping
Physics 3330 Experiment #3 Fall 2001 Purpose Filters And Waveform Shaping The aim of this experiment is to study the frequency filtering properties of passive (R, C, and L) circuits for sine waves, and
More informationDesigning Information Devices and Systems II Fall 2018 Elad Alon and Miki Lustig Homework 4
EECS 16B Designing Information Devices and Systems II Fall 2018 Elad Alon and Miki Lustig Homework 4 This homework is solely for your own practice. However, everything on it is in scope for midterm 1,
More informationExperiment 9 AC Circuits
Experiment 9 AC Circuits "Look for knowledge not in books but in things themselves." W. Gilbert (1540-1603) OBJECTIVES To study some circuit elements and a simple AC circuit. THEORY All useful circuits
More informationLaboratory 4: Amplification, Impedance, and Frequency Response
ES 3: Introduction to Electrical Systems Laboratory 4: Amplification, Impedance, and Frequency Response I. GOALS: In this laboratory, you will build an audio amplifier using an LM386 integrated circuit.
More informationSMS045 - DSP Systems in Practice. Lab 1 - Filter Design and Evaluation in MATLAB Due date: Thursday Nov 13, 2003
SMS045 - DSP Systems in Practice Lab 1 - Filter Design and Evaluation in MATLAB Due date: Thursday Nov 13, 2003 Lab Purpose This lab will introduce MATLAB as a tool for designing and evaluating digital
More informationApplication Note 4. Analog Audio Passive Crossover
Application Note 4 App Note Application Note 4 Highlights Importing Transducer Response Data Importing Transducer Impedance Data Conjugate Impedance Compensation Circuit Optimization n Design Objective
More informationClass #7: Experiment L & C Circuits: Filters and Energy Revisited
Class #7: Experiment L & C Circuits: Filters and Energy Revisited In this experiment you will revisit the voltage oscillations of a simple LC circuit. Then you will address circuits made by combining resistors
More informationENGR4300 Test 3A and 3B Fall 2003
Question 1 -- Astable Multivibrator R1 8 X1 18 1 1 2 U3 R2 TOPEN = 0 2 4 5 6 7 CC TRIGGER RESETOUTPUT CONTROL THRESHOLD DISCHARGE GND 555D R3 1Meg C1 C2 10uF.01uF 1 3 0 The circuit above has been simulated
More informationElectrochemical Impedance Spectroscopy
The Basics of Electrochemical Impedance Spectroscopy CORROSION COATINGS BATTERY TESTING PHOTOVOLTAICS C3 PROZESS- UND ANALYSENTECHNIK GmbH Peter-Henlein-Str. 20 D-85540 Haar b. München Telefon 089/45 60
More informationFrequency Response Properties of the Silicon Vertex Detector for BaBar
Frequency Response Properties of the Silicon Vertex Detector for BaBar Lawrence Lin Jeff Richman Sam Burke UCSB Summer 2001 Contents 1 Introduction 2 2 p-side of the Detector 3 3 n-side of the Detector
More informationE84 Lab 3: Transistor
E84 Lab 3: Transistor Cherie Ho and Siyi Hu April 18, 2016 Transistor Testing 1. Take screenshots of both the input and output characteristic plots observed on the semiconductor curve tracer with the following
More informationCourse materials and schedule are at. positron.hep.upenn.edu/p364
Physics 364, Fall 2014, Lab #4 Name: (RC circuits low-pass & high-pass filters, integrator, differentiator ) Wednesday, September 10 (section 401); Thursday, September 11 (section 402) Course materials
More informationClass XII Chapter 7 Alternating Current Physics
Question 7.1: A 100 Ω resistor is connected to a 220 V, 50 Hz ac supply. (a) What is the rms value of current in the circuit? (b) What is the net power consumed over a full cycle? Resistance of the resistor,
More informationExperiment 1 Alternating Current with Coil and Ohmic Resistors
Experiment Alternating Current with Coil and Ohmic esistors - Objects of the experiment - Determining the total impedance and the phase shift in a series connection of a coil and a resistor. - Determining
More informationWorksheet for Exploration 31.1: Amplitude, Frequency and Phase Shift
Worksheet for Exploration 31.1: Amplitude, Frequency and Phase Shift We characterize the voltage (or current) in AC circuits in terms of the amplitude, frequency (period) and phase. The sinusoidal voltage
More informationThe University of Texas at Austin Dept. of Electrical and Computer Engineering Final Exam
The University of Texas at Austin Dept. of Electrical and Computer Engineering Final Exam Date: December 18, 2017 Course: EE 313 Evans Name: Last, First The exam is scheduled to last three hours. Open
More informationDepartment of Electronic Engineering NED University of Engineering & Technology. LABORATORY WORKBOOK For the Course SIGNALS & SYSTEMS (TC-202)
Department of Electronic Engineering NED University of Engineering & Technology LABORATORY WORKBOOK For the Course SIGNALS & SYSTEMS (TC-202) Instructor Name: Student Name: Roll Number: Semester: Batch:
More information10. Introduction and Chapter Objectives
Real Analog - Circuits Chapter 0: Steady-state Sinusoidal Analysis 0. Introduction and Chapter Objectives We will now study dynamic systems which are subjected to sinusoidal forcing functions. Previously,
More informationCore Technology Group Application Note 6 AN-6
Characterization of an RLC Low pass Filter John F. Iannuzzi Introduction Inductor-capacitor low pass filters are utilized in systems such as audio amplifiers, speaker crossover circuits and switching power
More informationBasic Analog Circuits
Basic Analog Circuits Overview This tutorial is part of the National Instruments Measurement Fundamentals series. Each tutorial in this series, will teach you a specific topic of common measurement applications,
More informationEXPERIMENT 10: SINGLE-TRANSISTOR AMPLIFIERS 11/11/10
EXPERIMENT 10: SINGLE-TRANSISTOR AMPLIFIERS 11/11/10 In this experiment we will measure the characteristics of the standard common emitter amplifier. We will use the 2N3904 npn transistor. If you have
More informationSinusoids. Lecture #2 Chapter 2. BME 310 Biomedical Computing - J.Schesser
Sinusoids Lecture # Chapter BME 30 Biomedical Computing - 8 What Is this Course All About? To Gain an Appreciation of the Various Types of Signals and Systems To Analyze The Various Types of Systems To
More informationThe University of Texas at Austin Dept. of Electrical and Computer Engineering Midterm #2
The University of Texas at Austin Dept. of Electrical and Computer Engineering Midterm #2 Date: November 18, 2010 Course: EE 313 Evans Name: Last, First The exam is scheduled to last 75 minutes. Open books
More informationECE 231 Laboratory Exercise 6 Frequency / Time Response of RL and RC Circuits
ECE 231 Laboratory Exercise 6 Frequency / Time Response of RL and RC Circuits Laboratory Group (Names) OBJECTIVES Observe and calculate the response of first-order low pass and high pass filters. Gain
More informationEE202 Circuit Theory II , Spring
EE202 Circuit Theory II 2018-2019, Spring I. Introduction & Review of Circuit Theory I (3 Hrs.) Introduction II. Sinusoidal Steady-State Analysis (Chapter 9 of Nilsson - 9 Hrs.) (by Y.Kalkan) The Sinusoidal
More information