Frequency response. Chapter Introduction
|
|
- Emory Parks
- 8 years ago
- Views:
Transcription
1 Chapter Frequency response. Introduction The frequency response of a system is a frequency dependent function which expresses how a sinusoidal signal of a given frequency on the system input is transferred through the system. Time-varying signals at least periodical signals which excite systems, as the reference(setpoint) signal or a disturbance in a control system or measurement signals which are inputssignalstosignalfilters,canberegardedasconsistingofasumof frequency components. Each frequency component is a sinusoidal signal having a certain amplitude and a certain frequency. (The Fourier series expansion or the Fourier transform can be used to express these frequency components quantitatively.) The frequency response expresses how each of these frequency components is transferred through the system. Some components may be amplified, others may be attenuated, and there will be some phase lag through the system. The frequency response is an important tool for analysis and design of signal filters(as lowpass filters and highpass filters), and for analysis, and to some extent, design, of control systems. Both signal filtering and control systems applications are described(briefly) later in this chapter. Thedefinitionofthefrequencyresponse whichwillbegiveninthenext section appliesonlytolinearmodels,butthislinearmodelmayverywell be the local linear model about some operating point of a non-linear model. The frequency response can found experimentally or from a transfer function model. It can be presented graphically or as a mathematical function.
2 CHAPTER. FREQUENCY RESPONSE 2 Frequency t t Frequency 2 u(t) Excitation System y(t) Response t t Figure.: Sinusoidal signals in the input and the resulting responses on the output for two different frequencies.2 How to calculate frequency response from sinusoidal input and output Wecanfindthefrequencyresponseofasystembyexcitingthesystem with a sinusoidal signal of amplitude A and frequency ω[rad/s] and observingtheresponseintheoutputvariableofthesystem. Mathematically, we set the input signal to u(t)=usinωt (.) See Figure.. This input signal will give a transient response(which will die,eventually)andasteady-state response,y s (t),intheoutputvariable: y s (t) = Y sin(ωt+φ) (.2) = }{{} UAsin(ωt+φ) (.3) Y HereAisthe(amplitude)gain,andφ(phi)isthephaselag inradians. The frequencyofy s (t)willbethesameasinu(t). Figure.2showsindetail u(t)andy(t)forasimulatedsystem. Thesystemwhichissimulatedis y(s)= u(s) (.4) s+ The correspondance between a given frequency ω in rad/s and the same same frequencyf inhzisω=2πf.
3 CHAPTER. FREQUENCY RESPONSE 3 Figure.2: The input signal u(t) and the resulting(sinusoidal) response y(t) forasimulatedsystem. u(t)hasfrequencyω=3rad/sandamplitudeu =. Thesystemisgivenby(.4). (afirstordersystemwithgainandtime-constant). Theinputsignal u(t)hasfrequencyω=3rad/sandamplitudeu =. Aistheratiobetweentheamplitudesoftheoutputsignalandtheinput signal(in steady-state): ForthesignalsshowninFigure.2, A= Y U (.5) A= Y U =.32 =.32 (.6) φcanbecalculatedbyfirstmeasuringthetime-lag tbetweenu(t)and y s (t)andthencalculatingφasfollows: φ= ω t [rad] (.7)
4 CHAPTER. FREQUENCY RESPONSE 4 InFigure.2wefind t=.4sec,whichgives φ= ω t= 3.4=.23rad (.8) ThegainAandthephase-lagφarefunctionsofthefrequency. Wecanuse the following terminology: A(ω) is the gain function, and φ(ω) is the phase shift function (or more simply: phase function). We say that A(ω) and φ(ω) expresses the frequency response of the system. Bode diagram ItiscommontopresentA(ω)andφ(ω)graphicallyinaBodediagram, whichconsistsoftwosubdiagrams,onefora(ω)andoneforφ(ω),where the phase values are usually plotted in degrees(not radians). Figure.3 showsabodediagramofthefrequencyresponseofthesystemgivenby (.4). ThecurvesmaystemfromanumberofA-valuesandφ-valuesfound in experiments(or simulations) with an sinusoidal input signal of various frequencies. The curves may also stem from the transfer function of the system, as described in Section.3. The frequency axes usually show the -logarithmofthefrequencyinrad/sorinhz. Actually,thesystem(.4)isusedtogenerateu(t)andy(t)shownin Figure.2. WehaveearlierinthischaptercalculatedA(3)=.32=.2 db(thedb-unitisdescribedbelow)andphaselagφ(3)=.23rad= 72degrees. ThisgainvalueandphaselagvalueareindicatedintheBode diagram in Figure.3. The A(ω)-axis is usually drawn with decibel(db) as unit. The decibel valueofanumberxiscalculatedas Table. shows some examples of db-values. x[db]=2log x (.9).3 How to calculate frequency response from transfer functions InSection.2wesawhowtofindthefrequencyresponsefromexperiments onthesystem. Nomodelwasassumed. However,ifweknowatransfer function model of the system, we can calculate the frequency response from the transfer function, as explained below.
5 CHAPTER. FREQUENCY RESPONSE 5 Figure.3: The frequency response of the system given by(.4) presented in a Bode diagram SupposethatsystemhasthetransferfunctionH(s)frominpututo outputy,thatis, y(s) = H(s)u(s) (.) By setting s=jω (.) (j istheimaginaryunit)intoh(s),wegetthecomplexquantityh(jω), which is the frequency response (function). The gain function is A(ω) = H(jω) (.2) andthephaseshiftfunction istheangleorargumentofh(jω): φ(ω) = arg H(jω) (.3) Theformulas(.2)and(.3)willnotbederivedhere. 2 2 Aderivation ispresented inthetext-bookdynamiske systemer byf.haugen,tapir Forlag.
6 CHAPTER. FREQUENCY RESPONSE 6 = db. = 4dB. = 2dB.2 = 4dB.25 = 2dB.5 = 6dB 2 = 3dB = db 2 = 3dB 2 = 6dB = db 4 = 2dB 5 = 4dB = 2dB = 4dB Table.: Some db-values Example. Frequency response calculated from a transfer function We will find the frequency response for the transfer function The frequency response becomes H(jω)= H(s) s=jω = whichwewriteonpolarform: H(jω) = = H(s)= K Ts+ K Tjω+ = }{{} Re K 2 +(Tω) 2 e jarctan(tω ) K +jtω }{{} Im +(Tω) 2 e j[ arctan(tω)] (.4) (.5) (.6) (.7) Thus, the gain function is = H(jω) e jargh(jω) (.8) H(jω) = K +(Tω) 2 (.9)
7 CHAPTER. FREQUENCY RESPONSE 7 and the phase function is argh(jω)= arctan(tω) [rad] (.2) Figure.4showsthecurvesof H(jω) andargh(jω)drawninabode diagram. ThenumericalvaluesalongtheaxesassumeK=andT =. (The asymptotes indicated in the figure are not explained in this document.) Figure.4: Bode diagram for the frequency response of the first ordens system (.4). The asymptotes are not explained in this document. Toillustratetheuseof(.9)and(.2),letuscalculatethegainand phaselagvaluesforthefrequencyω=3rad/s. WeassumethatK=and T =. (.9)gives H(j3) = = ( =.36= 2log +3 2 )=.db (.2)
8 CHAPTER. FREQUENCY RESPONSE 8 (.2) gives argh(j3)= arctan(3)=.25rad= 7.6degrees (.22) [End of Example.] Thenextexampleshowshowthefrequencyresponsecanbefoundofa transfer function which consists of several factors in the numerator and/or the denominator. Example.2 Frequency response of a (more complicated) transfer function Given the transfer function H(s)=K T s+ (T 2 s+)s e τs (.23) (Theterme τs representsatime-delayofτ sec.) Wesets=jωinH(s) and then sets the individual factors on polar form. Finally, we combine thesefactorssothatweendupwithapolarformofh(jω): H(jω) = K T jω+ (T 2 jω+)jω e τjω (.24) ( ) 2 +(T ω) 2 e jarctan T ω = K[ = K ( 2 +(T 2 ω) 2 e jarctan T2 ω +(T ω) 2 +(T 2 ω) 2 ω } {{ } H(jω) e )] [ ]e τjω (.25) 2 +ω 2 e jπ 2 j [arctan(t ω) arctan(t 2 ω) π ] 2 τω } {{ } arg H(jω) (.26) So, the amplitude gain function is A(ω)= H(jω) = K +(T ω) 2 +(T 2 ω) 2 ω and the phase shift function is (.27) φ(ω)=argh(jω)=arctan(t ω) arctan(t 2 ω) π 2 τω (.28) [End of Example.2]
9 CHAPTER. FREQUENCY RESPONSE 9.4 Application of frequency response: Signal filters.4. Introduction Asignalfilter orjustfilter isusedtoattenuate(ideally: remove)a certain frequency interval of frequency components from a signal. These frequency components are typically noise. For example, a lowpass filter is used to attenuate high-frequent components(low-frequent components passes). Knowledge about filtering functions is crucial in signal processing, but it is useful also in control engineering because control systems can be regarded asfiltersinthesensethatthecontrolledprocessvariablecanfollowonlya certain range or interval of frequency components in the reference (setpoint) signal, and it will be only a certain frequency range of process disturbances that the control system can compensate for effectively. Furthermore, knowledge about filters can be useful in the analysis and design of physical processes. For example, a stirred tank in a process line can act as a lowpass filter since it attentuates low-frequent components in theinflowtothetank. In this section we will particularly study lowpass filters, which is the most commonly used filtering function, but we will also take a look at highpass filters, bandpass filters and bandstop filters. Figure.5 shows the gain function for ideal filtering functions and for practical filters(the phase lag functions are not shown). The passband is the frequency interval where the gain function has value, ideally(thus, frequency components in this frequency interval passes through the filter, unchanged). The stopband is the frequency interval where the gain function has value, ideally(thus, frequency components in this frequency intervalarestoppedthroughthefilter). 3 It can be shown that transfer functions for ideal filtering functions will have infinitely large order. Therefore, ideal filters can not be realized, neither with analog electronics nor with a filtering algorithm in a computer program. 3 Itisapitythatlowpassfilterswerenotcalledhighstopfiltersinsteadsincethemain purpose of a lowpass filter is to stop high-frequency components. Similarly, highpass filters shouldhavebeencalledlowstopfilters,butitistoolatenow...
10 CHAPTER. FREQUENCY RESPONSE Amplitude gain Lowpass: PB PB = passband SB = stopband Ideal Practical SB Frequency Highpass: SB PB Bandstop: PB SB PB Bandpass: SB PB SB Figure.5: The gain functions for ideal filters and for practical filters of various types..4.2 First order lowpass filters Themostcommonlyusedsignalfilteristhefirstorderlowpassfilter. As an example, it is the standard measurement filter in a feedback control system. The transfer function of a first order lowpass filter with input variable u and output variable y is usually written as H(s)= s + (.29) where [rad/s]isthebandwidth ofthefilter. Thisisafirstordertransfer
11 CHAPTER. FREQUENCY RESPONSE functionwithgaink=andtime-constantt =/. Thefrequency response is H(jω) = = jω + (ω (.3) = ) 2+e jarctan ω j (ω ) e 2+ ( arctan ω ωb ) (.3) The gain function is andthephaselagfunctionis H(jω) = (ω ) 2+ (.32) argh(jω)= arctan ω (.33) Figure.4 shows exact and asymptotic curves of H(jω) and arg H(jω) drawninabodediagram. Inthefigure,K=and =ω c. Thebandwidthdefinestheupperlimitofthepassband. Itiscommonto saythatthebandwidthisthefrequencywherethefiltergainis / 2=.7 3dB(abovethebandwidththegainislessthan/ 2). This bandwidth is therefore referred to as the 3 db-bandwidth. Now, whatisthe 3dB-bandwidthofafirstorderlowpassfilter? Itisthe ω-solution of the equation H(jω) = (ω ) 2+ = 2 (.34) Thesolutionisω=. Therefore, [rad/s]givenin(.29)isthe 3 db-bandwidth in rad/s. In Hertz the bandwidth is f b = 2π (.35) Figure.6showsthefrontpanelofasimulatorofafirstorderfilterwhere theinputsignalconsistsofasumoftwosinusoidsorfrequency components of frequency less than and greater than, respectively, the bandwidth. The simulation shows that the low frequent component(.5 Hz)passesalmostunchanged(itisinthepassbandofthefilter),whilethe high-frequent component(8 Hz) is attenuated(it lies in the stopband).
12 CHAPTER. FREQUENCY RESPONSE 2 Figure.6: Simulator for a first order lowpass filter where the input signal consists of a sum of two frequency componens Example.3 The RC-circuit as a lowpass filter Figure.7 shows an RC-circuit(the circuit contains the resistor R and the capacitor C). The RC-circuit is frequently used as an analogue lowpass filter: Signals of low frequencies passes approximately unchanged through the filter, while signals of high frequencies are approximately filtered out (stopped). v isthesignalsourceorinputvoltagetobefiltered,whilev 2 is the resulting filtered output voltage. Wewillnowfindamathematicalmodelrelatingv 2 tov. Firstweapply the Kirchhoff s voltage law in the circuit which consists the input voltage terminals, the resistor, and the capacitor(we consider the voltage drops to
13 CHAPTER. FREQUENCY RESPONSE 3 + i [A] v R [V] _ + i 2 + Input v [V] _ C [F] i C v 2 [V] _ Output Figure.7: RC-circuit be positive clockwise direction): v +v R +v 2 = (.36) (v 2 equalsthevoltagedropoverthecapacitor.) In(.36)v R isgivenby v R =Ri (.37) We assume that there is no current going through the output terminals. (This is a common assumption, and not unrealistic, since it it typical that the output terminals are connected to a subsequent circuit which has approximately infinite input impedance, causing the current into it to be approximately zero. An operational amplifier is an example of such a load-circuit.) Therefore, i=i C =C v 2 (.38) Thefinalmodelisachievedbyusingiasgivenby(.38)in(.37)andthen usingv R asgivenby(.37)forv R in(.36). Themodelbecomes RC v 2 (t)=v (t) v 2 (t) (.39) Thetransferfunctionfromtheinputvoltagev totheoutputvoltagev 2 becomes H v2,v (s)= RCs+ = s (.4) + Thus, the RC-circuit is a first order lowpass filter with bandwidth = RC rad/s (.4) IfforexampleR=kΩandC=µF,thebandwidthis =/RC= rad/s. (.4)canbeusedtodesigntheRC-circuit(calculatetheR-and C-values). [End of Example.3]
CIRCUITS LABORATORY EXPERIMENT 3. AC Circuit Analysis
CIRCUITS LABORATORY EXPERIMENT 3 AC Circuit Analysis 3.1 Introduction The steady-state behavior of circuits energized by sinusoidal sources is an important area of study for several reasons. First, the
More informationCHAPTER 6 Frequency Response, Bode Plots, and Resonance
ELECTRICAL CHAPTER 6 Frequency Response, Bode Plots, and Resonance 1. State the fundamental concepts of Fourier analysis. 2. Determine the output of a filter for a given input consisting of sinusoidal
More informationFrequency Response of Filters
School of Engineering Department of Electrical and Computer Engineering 332:224 Principles of Electrical Engineering II Laboratory Experiment 2 Frequency Response of Filters 1 Introduction Objectives To
More information2.161 Signal Processing: Continuous and Discrete Fall 2008
MT OpenCourseWare http://ocw.mit.edu.6 Signal Processing: Continuous and Discrete Fall 00 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MASSACHUSETTS
More informationchapter Introduction to Digital Signal Processing and Digital Filtering 1.1 Introduction 1.2 Historical Perspective
Introduction to Digital Signal Processing and Digital Filtering chapter 1 Introduction to Digital Signal Processing and Digital Filtering 1.1 Introduction Digital signal processing (DSP) refers to anything
More informationController Design in Frequency Domain
ECSE 4440 Control System Engineering Fall 2001 Project 3 Controller Design in Frequency Domain TA 1. Abstract 2. Introduction 3. Controller design in Frequency domain 4. Experiment 5. Colclusion 1. Abstract
More informationSophomore Physics Laboratory (PH005/105)
CALIFORNIA INSTITUTE OF TECHNOLOGY PHYSICS MATHEMATICS AND ASTRONOMY DIVISION Sophomore Physics Laboratory (PH5/15) Analog Electronics Active Filters Copyright c Virgínio de Oliveira Sannibale, 23 (Revision
More informationS-DOMAIN ANALYSIS: POLES, ZEROS, AND BODE PLOTS
S-DOMAIN ANAYSIS: POES, ZEROS, AND BODE POTS The main objectiveis to find amplifier voltage gain as a transfer function of the complex frequency s. In this s-domain analysis a capacitance С is replaced
More informationA Basic Introduction to Filters Active Passive and Switched-Capacitor
A Basic Introduction to Filters Active Passive and Switched-Capacitor 1 0 INTRODUCTION Filters of some sort are essential to the operation of most electronic circuits It is therefore in the interest of
More informationHow to Design 10 khz filter. (Using Butterworth filter design) Application notes. By Vadim Kim
How to Design 10 khz filter. (Using Butterworth filter design) Application notes. By Vadim Kim This application note describes how to build a 5 th order low pass, high pass Butterworth filter for 10 khz
More informationLAB 12: ACTIVE FILTERS
A. INTRODUCTION LAB 12: ACTIVE FILTERS After last week s encounter with op- amps we will use them to build active filters. B. ABOUT FILTERS An electric filter is a frequency-selecting circuit designed
More informationAnalog signals are those which are naturally occurring. Any analog signal can be converted to a digital signal.
3.3 Analog to Digital Conversion (ADC) Analog signals are those which are naturally occurring. Any analog signal can be converted to a digital signal. 1 3.3 Analog to Digital Conversion (ADC) WCB/McGraw-Hill
More informationLaboratory #5: RF Filter Design
EEE 194 RF Laboratory Exercise 5 1 Laboratory #5: RF Filter Design I. OBJECTIVES A. Design a third order low-pass Chebyshev filter with a cutoff frequency of 330 MHz and 3 db ripple with equal terminations
More informationLaboratory 4: Feedback and Compensation
Laboratory 4: Feedback and Compensation To be performed during Week 9 (Oct. 20-24) and Week 10 (Oct. 27-31) Due Week 11 (Nov. 3-7) 1 Pre-Lab This Pre-Lab should be completed before attending your regular
More informationLM833,LMF100,MF10. Application Note 779 A Basic Introduction to Filters - Active, Passive,and. Switched Capacitor. Literature Number: SNOA224A
LM833,LMF100,MF10 Application Note 779 A Basic Introduction to Filters - Active, Passive,and Switched Capacitor Literature Number: SNOA224A A Basic Introduction to Filters Active, Passive, and Switched-Capacitor
More informationNAPIER University School of Engineering. Electronic Systems Module : SE32102 Analogue Filters Design And Simulation. 4 th order Butterworth response
NAPIER University School of Engineering Electronic Systems Module : SE32102 Analogue Filters Design And Simulation. 4 th order Butterworth response In R1 R2 C2 C1 + Opamp A - R1 R2 C2 C1 + Opamp B - Out
More informationChapter 12: The Operational Amplifier
Chapter 12: The Operational Amplifier 12.1: Introduction to Operational Amplifier (Op-Amp) Operational amplifiers (op-amps) are very high gain dc coupled amplifiers with differential inputs; they are used
More informationLab #9: AC Steady State Analysis
Theory & Introduction Lab #9: AC Steady State Analysis Goals for Lab #9 The main goal for lab 9 is to make the students familar with AC steady state analysis, db scale and the NI ELVIS frequency analyzer.
More informationAN-837 APPLICATION NOTE
APPLICATION NOTE One Technology Way P.O. Box 916 Norwood, MA 262-916, U.S.A. Tel: 781.329.47 Fax: 781.461.3113 www.analog.com DDS-Based Clock Jitter Performance vs. DAC Reconstruction Filter Performance
More informationPIEZO FILTERS INTRODUCTION
For more than two decades, ceramic filter technology has been instrumental in the proliferation of solid state electronics. A view of the future reveals that even greater expectations will be placed on
More informationε: Voltage output of Signal Generator (also called the Source voltage or Applied
Experiment #10: LR & RC Circuits Frequency Response EQUIPMENT NEEDED Science Workshop Interface Power Amplifier (2) Voltage Sensor graph paper (optional) (3) Patch Cords Decade resistor, capacitor, and
More informationPID Control. Chapter 10
Chapter PID Control Based on a survey of over eleven thousand controllers in the refining, chemicals and pulp and paper industries, 97% of regulatory controllers utilize PID feedback. Desborough Honeywell,
More informationTime series analysis Matlab tutorial. Joachim Gross
Time series analysis Matlab tutorial Joachim Gross Outline Terminology Sampling theorem Plotting Baseline correction Detrending Smoothing Filtering Decimation Remarks Focus on practical aspects, exercises,
More informationEngineering Sciences 22 Systems Summer 2004
Engineering Sciences 22 Systems Summer 24 BODE PLOTS A Bode plot is a standard format for plotting frequency response of LTI systems. Becoming familiar with this format is useful because: 1. It is a standard
More informationAnalog and Digital Filters Anthony Garvert November 13, 2015
Analog and Digital Filters Anthony Garvert November 13, 2015 Abstract In circuit analysis and performance, a signal transmits some form of information, such as a voltage or current. However, over a range
More informationAnalog Signal Conditioning
Analog Signal Conditioning Analog and Digital Electronics Electronics Digital Electronics Analog Electronics 2 Analog Electronics Analog Electronics Operational Amplifiers Transistors TRIAC 741 LF351 TL084
More informationPHYSICS 360 - LAB #2 Passive Low-pass and High-pass Filter Circuits and Integrator and Differentiator Circuits
PHYSICS 360 - LAB #2 Passie Low-pass and High-pass Filter Circuits and Integrator and Differentiator Circuits Objectie: Study the behaior of low-pass and high-pass filters. Study the differentiator and
More informationChapter 9: Controller design
Chapter 9. Controller Design 9.1. Introduction 9.2. Effect of negative feedback on the network transfer functions 9.2.1. Feedback reduces the transfer function from disturbances to the output 9.2.2. Feedback
More informationAnalog Filters. A common instrumentation filter application is the attenuation of high frequencies to avoid frequency aliasing in the sampled data.
Analog Filters Filters can be used to attenuate unwanted signals such as interference or noise or to isolate desired signals from unwanted. They use the frequency response of a measuring system to alter
More informationVCO Phase noise. Characterizing Phase Noise
VCO Phase noise Characterizing Phase Noise The term phase noise is widely used for describing short term random frequency fluctuations of a signal. Frequency stability is a measure of the degree to which
More informationUNIVERSITY OF CALIFORNIA AT BERKELEY College of Engineering Department of Electrical Engineering and Computer Sciences. EE105 Lab Experiments
UNIVERSITY OF CALIFORNIA AT BERKELEY College of Engineering Department of Electrical Engineering and Computer Sciences EE15 Lab Experiments Bode Plot Tutorial Contents 1 Introduction 1 2 Bode Plots Basics
More informationPositive Feedback and Oscillators
Physics 3330 Experiment #6 Fall 1999 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 informationUniversity of Rochester Department of Electrical and Computer Engineering ECE113 Lab. #7 Higher-order filter & amplifier designs March, 2012
University of Rochester Department of Electrical and Computer Engineering ECE113 Lab. #7 Higherorder filter & amplifier designs March, 2012 Writeups, due one week after the lab is performed, should provide
More informationLock - in Amplifier and Applications
Lock - in Amplifier and Applications What is a Lock in Amplifier? In a nut shell, what a lock-in amplifier does is measure the amplitude V o of a sinusoidal voltage, V in (t) = V o cos(ω o t) where ω o
More informationLecture 1-6: Noise and Filters
Lecture 1-6: Noise and Filters Overview 1. Periodic and Aperiodic Signals Review: by periodic signals, we mean signals that have a waveform shape that repeats. The time taken for the waveform to repeat
More informationBasic Op Amp Circuits
Basic Op Amp ircuits Manuel Toledo INEL 5205 Instrumentation August 3, 2008 Introduction The operational amplifier (op amp or OA for short) is perhaps the most important building block for the design of
More informationVer 3537 E1.1 Analysis of Circuits (2014) E1.1 Circuit Analysis. Problem Sheet 1 (Lectures 1 & 2)
Ver 3537 E. Analysis of Circuits () Key: [A]= easy... [E]=hard E. Circuit Analysis Problem Sheet (Lectures & ). [A] One of the following circuits is a series circuit and the other is a parallel circuit.
More informationKeysight Technologies Understanding the Fundamental Principles of Vector Network Analysis. Application Note
Keysight Technologies Understanding the Fundamental Principles of Vector Network Analysis Application Note Introduction Network analysis is the process by which designers and manufacturers measure the
More informationSUMMARY. Additional Digital/Software filters are included in Chart and filter the data after it has been sampled and recorded by the PowerLab.
This technique note was compiled by ADInstruments Pty Ltd. It includes figures and tables from S.S. Young (2001): Computerized data acquisition and analysis for the life sciences. For further information
More information30. Bode Plots. Introduction
0. Bode Plots Introduction Each of the circuits in this problem set is represented by a magnitude Bode plot. The network function provides a connection between the Bode plot and the circuit. To solve these
More informationFilter Comparison. Match #1: Analog vs. Digital Filters
CHAPTER 21 Filter Comparison Decisions, decisions, decisions! With all these filters to choose from, how do you know which to use? This chapter is a head-to-head competition between filters; we'll select
More informationWhat you will do. Build a 3-band equalizer. Connect to a music source (mp3 player) Low pass filter High pass filter Band pass filter
Audio Filters What you will do Build a 3-band equalizer Low pass filter High pass filter Band pass filter Connect to a music source (mp3 player) Adjust the strength of low, high, and middle frequencies
More informationCHAPTER 8 ANALOG FILTERS
ANALOG FILTERS CHAPTER 8 ANALOG FILTERS SECTION 8.: INTRODUCTION 8. SECTION 8.2: THE TRANSFER FUNCTION 8.5 THE SPLANE 8.5 F O and Q 8.7 HIGHPASS FILTER 8.8 BANDPASS FILTER 8.9 BANDREJECT (NOTCH) FILTER
More informationTCOM 370 NOTES 99-4 BANDWIDTH, FREQUENCY RESPONSE, AND CAPACITY OF COMMUNICATION LINKS
TCOM 370 NOTES 99-4 BANDWIDTH, FREQUENCY RESPONSE, AND CAPACITY OF COMMUNICATION LINKS 1. Bandwidth: The bandwidth of a communication link, or in general any system, was loosely defined as the width of
More informationSCHWEITZER ENGINEERING LABORATORIES, COMERCIAL LTDA.
Pocket book of Electrical Engineering Formulas Content 1. Elementary Algebra and Geometry 1. Fundamental Properties (real numbers) 1 2. Exponents 2 3. Fractional Exponents 2 4. Irrational Exponents 2 5.
More informationLow Pass Filter Rise Time vs Bandwidth
AN121 Dataforth Corporation Page 1 of 7 DID YOU KNOW? The number googol is ten raised to the hundredth power or 1 followed by 100 zeros. Edward Kasner (1878-1955) a noted mathematician is best remembered
More informationUnit2: Resistor/Capacitor-Filters
Unit2: Resistor/Capacitor-Filters Physics335 Student October 3, 27 Physics 335-Section Professor J. Hobbs Partner: Physics335 Student2 Abstract Basic RC-filters were constructed and properties such as
More informationFundamentals of Power Electronics. Robert W. Erickson University of Colorado, Boulder
Robert W. Erickson University of Colorado, Boulder 1 1.1. Introduction to power processing 1.2. Some applications of power electronics 1.3. Elements of power electronics Summary of the course 2 1.1 Introduction
More informationSee Horenstein 4.3 and 4.4
EE 462: Laboratory # 4 DC Power Supply Circuits Using Diodes by Drs. A.V. Radun and K.D. Donohue (2/14/07) Department of Electrical and Computer Engineering University of Kentucky Lexington, KY 40506 Updated
More informationChapter 29 Alternating-Current Circuits
hapter 9 Alternating-urrent ircuits onceptual Problems A coil in an ac generator rotates at 6 Hz. How much time elapses between successive emf values of the coil? Determine the oncept Successive s are
More informationisim ACTIVE FILTER DESIGNER NEW, VERY CAPABLE, MULTI-STAGE ACTIVE FILTER DESIGN TOOL
isim ACTIVE FILTER DESIGNER NEW, VERY CAPABLE, MULTI-STAGE ACTIVE FILTER DESIGN TOOL Michael Steffes Sr. Applications Manager 12/15/2010 SIMPLY SMARTER Introduction to the New Active Filter Designer Scope
More informationLABORATORY 2 THE DIFFERENTIAL AMPLIFIER
LABORATORY 2 THE DIFFERENTIAL AMPLIFIER OBJECTIVES 1. To understand how to amplify weak (small) signals in the presence of noise. 1. To understand how a differential amplifier rejects noise and common
More informationReview of Fourier series formulas. Representation of nonperiodic functions. ECE 3640 Lecture 5 Fourier Transforms and their properties
ECE 3640 Lecture 5 Fourier Transforms and their properties Objective: To learn about Fourier transforms, which are a representation of nonperiodic functions in terms of trigonometric functions. Also, to
More informationHomework Assignment 03
Question 1 (2 points each unless noted otherwise) Homework Assignment 03 1. A 9-V dc power supply generates 10 W in a resistor. What peak-to-peak amplitude should an ac source have to generate the same
More informationIntroduction to Digital Filters
CHAPTER 14 Introduction to Digital Filters Digital filters are used for two general purposes: (1) separation of signals that have been combined, and (2) restoration of signals that have been distorted
More informationLoop Bandwidth and Clock Data Recovery (CDR) in Oscilloscope Measurements. Application Note 1304-6
Loop Bandwidth and Clock Data Recovery (CDR) in Oscilloscope Measurements Application Note 1304-6 Abstract Time domain measurements are only as accurate as the trigger signal used to acquire them. Often
More informationBode Diagrams of Transfer Functions and Impedances ECEN 2260 Supplementary Notes R. W. Erickson
Bode Diagrams of Transfer Functions and Impedances ECEN 2260 Supplementary Notes. W. Erickson In the design of a signal processing network, control system, or other analog system, it is usually necessary
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 informationCTCSS REJECT HIGH PASS FILTERS IN FM RADIO COMMUNICATIONS AN EVALUATION. Virgil Leenerts WØINK 8 June 2008
CTCSS REJECT HIGH PASS FILTERS IN FM RADIO COMMUNICATIONS AN EVALUATION Virgil Leenerts WØINK 8 June 28 The response of the audio voice band high pass filter is evaluated in conjunction with the rejection
More informationLaboratory Manual. ELEN-325 Electronics
Laboratory Manual ELEN-325 Electronics Department of Electrical & Computer Engineering Texas A&M University Prepared by: Dr. Jose Silva-Martinez (jsilva@ece.tamu.edu) Rida Assaad (rida@ece.tamu.edu) Raghavendra
More informationUnderstanding the Fundamental Principles of Vector Network Analysis. Application Note 1287-1. Table of Contents. Page
Understanding the Fundamental Principles of Vector Network Analysis Application Note 1287-1 Table of Contents Page Introduction 2 Measurements in Communications Systems 2 Importance of Vector Measurements
More informationApplication Report SLOA024B
Application Report July 999 Revised September 2002 Mixed Signal Products SLOA024B IMPORTANT NOTICE Texas Instruments Incorporated and its subsidiaries (TI) reserve the right to make corrections, modifications,
More informationReading: HH Sections 4.11 4.13, 4.19 4.20 (pgs. 189-212, 222 224)
6 OP AMPS II 6 Op Amps II In the previous lab, you explored several applications of op amps. In this exercise, you will look at some of their limitations. You will also examine the op amp integrator and
More informationUnderstanding Power Impedance Supply for Optimum Decoupling
Introduction Noise in power supplies is not only caused by the power supply itself, but also the load s interaction with the power supply (i.e. dynamic loads, switching, etc.). To lower load induced noise,
More informationVCO K 0 /S K 0 is tho slope of the oscillator frequency to voltage characteristic in rads per sec. per volt.
Phase locked loop fundamentals The basic form of a phase locked loop (PLL) consists of a voltage controlled oscillator (VCO), a phase detector (PD), and a filter. In its more general form (Figure 1), the
More informationMotor Control. Suppose we wish to use a microprocessor to control a motor - (or to control the load attached to the motor!) Power supply.
Motor Control Suppose we wish to use a microprocessor to control a motor - (or to control the load attached to the motor!) Operator Input CPU digital? D/A, PWM analog voltage Power supply Amplifier linear,
More informationPID Control. 6.1 Introduction
6 PID Control 6. Introduction The PID controller is the most common form of feedback. It was an essential element of early governors and it became the standard tool when process control emerged in the
More informationPulse Width Modulation (PWM) LED Dimmer Circuit. Using a 555 Timer Chip
Pulse Width Modulation (PWM) LED Dimmer Circuit Using a 555 Timer Chip Goals of Experiment Demonstrate the operation of a simple PWM circuit that can be used to adjust the intensity of a green LED by varying
More informationSERIES-PARALLEL DC CIRCUITS
Name: Date: Course and Section: Instructor: EXPERIMENT 1 SERIES-PARALLEL DC CIRCUITS OBJECTIVES 1. Test the theoretical analysis of series-parallel networks through direct measurements. 2. Improve skills
More informationDigital to Analog Converter. Raghu Tumati
Digital to Analog Converter Raghu Tumati May 11, 2006 Contents 1) Introduction............................... 3 2) DAC types................................... 4 3) DAC Presented.............................
More informationDynamic Process Modeling. Process Dynamics and Control
Dynamic Process Modeling Process Dynamics and Control 1 Description of process dynamics Classes of models What do we need for control? Modeling for control Mechanical Systems Modeling Electrical circuits
More informationLecture 9. Poles, Zeros & Filters (Lathi 4.10) Effects of Poles & Zeros on Frequency Response (1) Effects of Poles & Zeros on Frequency Response (3)
Effects of Poles & Zeros on Frequency Response (1) Consider a general system transfer function: zeros at z1, z2,..., zn Lecture 9 Poles, Zeros & Filters (Lathi 4.10) The value of the transfer function
More informationChapter 16. Active Filter Design Techniques. Excerpted from Op Amps for Everyone. Literature Number SLOA088. Literature Number: SLOD006A
hapter 16 Active Filter Design Techniques Literature Number SLOA088 Excerpted from Op Amps for Everyone Literature Number: SLOD006A hapter 16 Active Filter Design Techniques Thomas Kugelstadt 16.1 Introduction
More informationFrequency response: Resonance, Bandwidth, Q factor
Frequency response: esonance, Bandwidth, Q factor esonance. Let s continue the exploration of the frequency response of circuits by investigating the series circuit shown on Figure. C + V - Figure The
More informationImpedance 50 (75 connectors via adapters)
VECTOR NETWORK ANALYZER PLANAR TR1300/1 DATA SHEET Frequency range: 300 khz to 1.3 GHz Measured parameters: S11, S21 Dynamic range of transmission measurement magnitude: 130 db Measurement time per point:
More informationAC 2012-3923: MEASUREMENT OF OP-AMP PARAMETERS USING VEC- TOR SIGNAL ANALYZERS IN UNDERGRADUATE LINEAR CIRCUITS LABORATORY
AC 212-3923: MEASUREMENT OF OP-AMP PARAMETERS USING VEC- TOR SIGNAL ANALYZERS IN UNDERGRADUATE LINEAR CIRCUITS LABORATORY Dr. Tooran Emami, U.S. Coast Guard Academy Tooran Emami received her M.S. and Ph.D.
More informationPHASOR DIAGRAMS HANDS-ON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER - BPA
PHASOR DIAGRAMS HANDS-ON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER - BPA What are phasors??? In normal practice, the phasor represents the rms maximum value of the positive half cycle of the sinusoid
More informationCancellation of Load-Regulation in Low Drop-Out Regulators
Cancellation of Load-Regulation in Low Drop-Out Regulators Rajeev K. Dokania, Student Member, IEE and Gabriel A. Rincόn-Mora, Senior Member, IEEE Georgia Tech Analog Consortium Georgia Institute of Technology
More informationChapter 10. RC Circuits ISU EE. C.Y. Lee
Chapter 10 RC Circuits Objectives Describe the relationship between current and voltage in an RC circuit Determine impedance and phase angle in a series RC circuit Analyze a series RC circuit Determine
More informationFig. 1 :Block diagram symbol of the operational amplifier. Characteristics ideal op-amp real op-amp
Experiment: General Description An operational amplifier (op-amp) is defined to be a high gain differential amplifier. When using the op-amp with other mainly passive elements, op-amp circuits with various
More informationExperiment #11: LRC Circuit (Power Amplifier, Voltage Sensor)
Experiment #11: LRC Circuit (Power Amplifier, Voltage Sensor) Concept: circuits Time: 30 m SW Interface: 750 Windows file: RLC.SWS EQUIPMENT NEEDED Science Workshop Interface Power Amplifier (2) Voltage
More informationApplication of network analyzer in measuring the performance functions of power supply
J Indian Inst Sci, July Aug 2006, 86, 315 325 Indian Institute of Science Application of network analyzer in measuring the performance functions of power supply B SWAMINATHAN* AND V RAMANARAYANAN Power
More informationDIGITAL-TO-ANALOGUE AND ANALOGUE-TO-DIGITAL CONVERSION
DIGITAL-TO-ANALOGUE AND ANALOGUE-TO-DIGITAL CONVERSION Introduction The outputs from sensors and communications receivers are analogue signals that have continuously varying amplitudes. In many systems
More informationDesign of a TL431-Based Controller for a Flyback Converter
Design of a TL431-Based Controller for a Flyback Converter Dr. John Schönberger Plexim GmbH Technoparkstrasse 1 8005 Zürich 1 Introduction The TL431 is a reference voltage source that is commonly used
More informationNetwork Analyzer Operation
Network Analyzer Operation 2004 ITTC Summer Lecture Series John Paden Purposes of a Network Analyzer Network analyzers are not about computer networks! Purposes of a Network Analyzer Measures S-parameters
More informationMATRIX TECHNICAL NOTES
200 WOOD AVENUE, MIDDLESEX, NJ 08846 PHONE (732) 469-9510 FAX (732) 469-0418 MATRIX TECHNICAL NOTES MTN-107 TEST SETUP FOR THE MEASUREMENT OF X-MOD, CTB, AND CSO USING A MEAN SQUARE CIRCUIT AS A DETECTOR
More information2006-1171: INCREASING PRODUCTIVITY AND AVOIDING CIRCUIT SIMULATION ERRORS IN MULTISIM
2006-1171: INCREASING PRODUCTIVITY AND AVOIDING CIRCUIT SIMULATION ERRORS IN MULTISIM John Hackworth, Old Dominion University John R. Hackworth is Program Director for the Electrical Engineering Technology
More informationECE 3510 Final given: Spring 11
ECE 50 Final given: Spring This part of the exam is Closed book, Closed notes, No Calculator.. ( pts) For each of the time-domain signals shown, draw the poles of the signal's Laplace transform on the
More informationThe Membrane Equation
The Membrane Equation Professor David Heeger September 5, 2000 RC Circuits Figure 1A shows an RC (resistor, capacitor) equivalent circuit model for a patch of passive neural membrane. The capacitor represents
More informationObjectives The purpose of this lab is build and analyze Differential amplifiers based on NPN transistors (or NMOS transistors).
1 Lab 03: Differential Amplifiers (BJT) (20 points) NOTE: 1) Please use the basic current mirror from Lab01 for the second part of the lab (Fig. 3). 2) You can use the same chip as the basic current mirror;
More informationAVR127: Understanding ADC Parameters. Introduction. Features. Atmel 8-bit and 32-bit Microcontrollers APPLICATION NOTE
Atmel 8-bit and 32-bit Microcontrollers AVR127: Understanding ADC Parameters APPLICATION NOTE Introduction This application note explains the basic concepts of analog-to-digital converter (ADC) and the
More informationUnderstanding Dynamic Range in Acceleration Measurement Systems. February 2013 By: Bruce Lent
in Acceleration Measurement Systems February 2013 By: Bruce Lent Topics to discuss Definition of dynamic range The effective range Making full use of the high level Using filters to improve dynamic range
More informationLaboratory Manual and Supplementary Notes. CoE 494: Communication Laboratory. Version 1.2
Laboratory Manual and Supplementary Notes CoE 494: Communication Laboratory Version 1.2 Dr. Joseph Frank Dr. Sol Rosenstark Department of Electrical and Computer Engineering New Jersey Institute of Technology
More informationChapter 8 - Power Density Spectrum
EE385 Class Notes 8/8/03 John Stensby Chapter 8 - Power Density Spectrum Let X(t) be a WSS random process. X(t) has an average power, given in watts, of E[X(t) ], a constant. his total average power is
More informationLR Phono Preamps. Pete Millett ETF.13. pmillett@hotmail.com
LR Phono Preamps Pete Millett ETF.13 pmillett@hotmail.com Agenda A bit about me Part 1: What is, and why use, RIAA? Grooves on records The RIAA standard Implementations of RIAA EQ networks and preamps
More informationA Simple Current-Sense Technique Eliminating a Sense Resistor
INFINITY Application Note AN-7 A Simple Current-Sense Technique Eliminating a Sense Resistor Copyright 998 A SIMPE CURRENT-SENSE TECHNIQUE EIMINATING A SENSE RESISTOR INTRODUCTION A sense resistor R S,
More informationThe Calculation of G rms
The Calculation of G rms QualMark Corp. Neill Doertenbach The metric of G rms is typically used to specify and compare the energy in repetitive shock vibration systems. However, the method of arriving
More informationMore Filter Design on a Budget
Application Report SLOA096 December 2001 More Filter Design on a Budget Bruce Carter High Performance Linear Products ABSTRACT This document describes filter design from the standpoint of cost. Filter
More informationElectronics. Discrete assembly of an operational amplifier as a transistor circuit. LD Physics Leaflets P4.2.1.1
Electronics Operational Amplifier Internal design of an operational amplifier LD Physics Leaflets Discrete assembly of an operational amplifier as a transistor circuit P4.2.1.1 Objects of the experiment
More informationAnalysis of Common-Collector Colpitts Oscillator
Analysis of Common-Collector Colpitts Oscillator H R Pota May 20, 2005 Introduction Murphy s rule when paraphrased for oscillators reads [], Amplifiers will oscillate but oscillators won t. As we all know,
More information