Frequency response. Pavel Máša - XE31EO2. XE31EO2 Lecture11. Pavel Máša - XE31EO2 - Frequency response

Size: px
Start display at page:

Download "Frequency response. Pavel Máša - XE31EO2. XE31EO2 Lecture11. Pavel Máša - XE31EO2 - Frequency response"

Transcription

1 Frequency response XE3EO2 Lecture Pavel Máša - Frequency response

2 INTRODUCTION Frequency response describe frequency dependence of output to input voltage magnitude ratio and its phase shift as a function of frequency It can describe e.g.: Which frequencies pass filter Crossover in loudspeaker system Tuner in radio / TV, ADSL splitter Anti aliasing filter in CD player Which frequency range can be played with audio amplifier Affects maximum refresh frequency and screen resolution of analog monitor (it is related to frequency response of input amplifier) - Frequency response

3 TRANSFER FUNCTION AND ITS GRAPHICAL REPRESENTATION Consider linear 2 port Frequency dependence of output voltage may be qualified by transfer function Transfer function is a function of variable ω; graphical representation may be either:. In complex plane as Nyquist plot Im 0,5 ω 0,5 0 0,5 Re 0,5 ω=0 ω Following graphs represents frequency response of integrating RC circuit It s a curve in a complex plane, where to distinct points are assigned distinct values of frequency ω it is a path allocated by phasor endpoint, when frequency varies from zero to infinity The distance of selected point (related to distinct frequency ω) from origin defines the modulus of transfer function The angle between real axis and phasor is phase of the transfer function Nyquist plot of passive circuits with the exception of resonant circuit is situated inside unit circle It is important for examination of stability of circuits with feedback (Nyquist stability criterion) in practice it is simpler measure frequency response of the circuit than search for poles of (unknown) transfer function - Frequency response

4 2. Or separated into two parts as modulus and phase frequency response [db] [rad] Modulus frequency response is drawn as Both axes of modulus frequency response are logarithmic The unit is decibel [db] Phase frequency response is drawn as Frequency axis is logarithmic, phase axis is linear The unit is radian [rad] - Frequency response

5 BODE PLOT In the 930s Hendrik Wade Bode proposed simple, but accurate method for graphing modulus and phase responses By this method is possible draw accurate responses without use of computer Frequency response has information about time constants (in transients), quality factor of resonant circuit etc. Transfer function is generally P M k=0 P (p) = b kp k P N k=0 a kp = b 0 + b p + b 2 p b M p M k a 0 + a p + a 2 p a N p N Q M k= = K (p z k) Q N k (p p k) = b M (p z )(p z 2 ) (p z M ) a N (p p )(p p 2 ) (p p N ) z k p k roots of the polynomial in nominator zeros Roots of the polynomial in denominator poles here are hidden time constants of the transient By partial fraction decomposition of this transfer function we may find transient response The graph of this transfer function is spatial surface above p plane But we are interesting in the cut through the p plane, when ¾ =0 p = ¾ + j =0+j = j Then we get to sinusoidal steady state Variable is not frequencyω, but complex frequency jω - Frequency response

6 pole (tends to ) P(j) = P M k=0 b k(j) k P N k=0 a k(j) k = frequency response yellow cut is the modulus frequency response b 0 + b j + b 2 (j) b M (j) M a 0 + a (j)+a 2 (j) a N (j) N Q M k= = K (j z k) Q N k (j p k) = b M (j z )(j z 2 ) (j z M ) a N (j p )(j p 2 ) (j p N ) - Frequency response

7 The principle of the Bode plot are properties of logarithm, namely: Logarithm of the product is the sum of logarithms Logarithm of the quotient is the difference of logarithms log = 0 Considering last property is necessary normalize brackets in factorization: μ j z k = z k j + z k Then, if, log ³ j + 0 z k z k μ À, log ³ j + log z k z k z k Q M P 0 (j) = K 0 k= (j z k +) Q N k (j p k +) = b M( z )( z 2 ) ( z M ) a N ( p )( p 2 ) ( p N ) (j k= Graphically line with the slope 20 db / decade z M +) (j p +)(j p 2 +) (j p N +) z +)(j z 2 +) (j Modulus response: MX F db () =20log( P 0 (j) ) =20log(K 0 NX ))+ 20 log μ j + 20 log μ j + z k p k Phase response: '() =arg(p 0 (j)) = MX arg k= μ j + z k NX arg k= μ j + p k k= - Frequency response

8 Now we will investigate frequency response of RLC circuit the same, on which we studied 2 nd order transients P (p) =. R = 4 kω pc pl + R + pc P (p) = = L = H C = μf R = 4 kω, 2 kω a kω p 2 LC + prc + = LC p 2 + p R L + p p + P(j) = p ;2 = 2000 p = : = 3732: = 267:9 P 0 (j) = 3732: 267:9 (j 3732: +)(j LC (j) (j)+ 267:9 +) = (j (j) ;2 = 3732: = 267:9 3732: +)(j 267:9 +) - Frequency response

9 2. R = 2 kω P (p) = p p + P(j) = (j) (j)+ p ;2 = 000 p = 000 (j) ;2 = 000 P 0 (j) = 3. R = kω P (p) = (j = 000 +)2 (j 000 +)2 p p + P(j) = p ;2 = 500 p = j (j) (j)+ P 0 (j)= (j 000 )2 + j = (j 000 )2 + j (j) ;2 = j r Q - Frequency response

Designing Information Devices and Systems II Fall 2018 Elad Alon and Miki Lustig Discussion 5A

Designing Information Devices and Systems II Fall 2018 Elad Alon and Miki Lustig Discussion 5A EECS 6B Designing Information Devices and Systems II Fall 208 Elad Alon and Miki Lustig Discussion 5A Transfer Function When we write the transfer function of an arbitrary circuit, it always takes the

More information

8.1.6 Quadratic pole response: resonance

8.1.6 Quadratic pole response: resonance 8.1.6 Quadratic pole response: resonance Example G(s)= v (s) v 1 (s) = 1 1+s L R + s LC L + Second-order denominator, of the form 1+a 1 s + a s v 1 (s) + C R Two-pole low-pass filter example v (s) with

More information

CHAPTER 7 : BODE PLOTS AND GAIN ADJUSTMENTS COMPENSATION

CHAPTER 7 : BODE PLOTS AND GAIN ADJUSTMENTS COMPENSATION CHAPTER 7 : BODE PLOTS AND GAIN ADJUSTMENTS COMPENSATION Objectives Students should be able to: Draw the bode plots for first order and second order system. Determine the stability through the bode plots.

More information

Frequency Response. Re ve jφ e jωt ( ) where v is the amplitude and φ is the phase of the sinusoidal signal v(t). ve jφ

Frequency Response. Re ve jφ e jωt ( ) where v is the amplitude and φ is the phase of the sinusoidal signal v(t). ve jφ 27 Frequency Response Before starting, review phasor analysis, Bode plots... Key concept: small-signal models for amplifiers are linear and therefore, cosines and sines are solutions of the linear differential

More information

EE221 Circuits II. Chapter 14 Frequency Response

EE221 Circuits II. Chapter 14 Frequency Response EE22 Circuits II Chapter 4 Frequency Response Frequency Response Chapter 4 4. Introduction 4.2 Transfer Function 4.3 Bode Plots 4.4 Series Resonance 4.5 Parallel Resonance 4.6 Passive Filters 4.7 Active

More information

EE221 Circuits II. Chapter 14 Frequency Response

EE221 Circuits II. Chapter 14 Frequency Response EE22 Circuits II Chapter 4 Frequency Response Frequency Response Chapter 4 4. Introduction 4.2 Transfer Function 4.3 Bode Plots 4.4 Series Resonance 4.5 Parallel Resonance 4.6 Passive Filters 4.7 Active

More information

LECTURE 21: Butterworh & Chebeyshev BP Filters. Part 1: Series and Parallel RLC Circuits On NOT Again

LECTURE 21: Butterworh & Chebeyshev BP Filters. Part 1: Series and Parallel RLC Circuits On NOT Again LECTURE : Butterworh & Chebeyshev BP Filters Part : Series and Parallel RLC Circuits On NOT Again. RLC Admittance/Impedance Transfer Functions EXAMPLE : Series RLC. H(s) I out (s) V in (s) Y in (s) R Ls

More information

Chapter 8: Converter Transfer Functions

Chapter 8: Converter Transfer Functions Chapter 8. Converter Transfer Functions 8.1. Review of Bode plots 8.1.1. Single pole response 8.1.2. Single zero response 8.1.3. Right half-plane zero 8.1.4. Frequency inversion 8.1.5. Combinations 8.1.6.

More information

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder R. W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder 8.1. Review of Bode plots Decibels Table 8.1. Expressing magnitudes in decibels G db = 0 log 10

More information

Filters and Tuned Amplifiers

Filters and Tuned Amplifiers Filters and Tuned Amplifiers Essential building block in many systems, particularly in communication and instrumentation systems Typically implemented in one of three technologies: passive LC filters,

More information

Dynamic circuits: Frequency domain analysis

Dynamic circuits: Frequency domain analysis Electronic Circuits 1 Dynamic circuits: Contents Free oscillation and natural frequency Transfer functions Frequency response Bode plots 1 System behaviour: overview 2 System behaviour : review solution

More information

Refinements to Incremental Transistor Model

Refinements to Incremental Transistor Model Refinements to Incremental Transistor Model This section presents modifications to the incremental models that account for non-ideal transistor behavior Incremental output port resistance Incremental changes

More information

ELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 2010/2011 CONTROL ENGINEERING SHEET 5 Lead-Lag Compensation Techniques

ELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 2010/2011 CONTROL ENGINEERING SHEET 5 Lead-Lag Compensation Techniques CAIRO UNIVERSITY FACULTY OF ENGINEERING ELECTRONICS & COMMUNICATIONS DEP. 3rd YEAR, 00/0 CONTROL ENGINEERING SHEET 5 Lead-Lag Compensation Techniques [] For the following system, Design a compensator such

More information

Steady State Frequency Response Using Bode Plots

Steady State Frequency Response Using Bode Plots School of Engineering Department of Electrical and Computer Engineering 332:224 Principles of Electrical Engineering II Laboratory Experiment 3 Steady State Frequency Response Using Bode Plots 1 Introduction

More information

Homework 7 - Solutions

Homework 7 - Solutions Homework 7 - Solutions Note: This homework is worth a total of 48 points. 1. Compensators (9 points) For a unity feedback system given below, with G(s) = K s(s + 5)(s + 11) do the following: (c) Find the

More information

Frequency Dependent Aspects of Op-amps

Frequency Dependent Aspects of Op-amps Frequency Dependent Aspects of Op-amps Frequency dependent feedback circuits The arguments that lead to expressions describing the circuit gain of inverting and non-inverting amplifier circuits with resistive

More information

Definitions. Decade: A ten-to-one range of frequency. On a log scale, each 10X change in frequency requires the same distance on the scale.

Definitions. Decade: A ten-to-one range of frequency. On a log scale, each 10X change in frequency requires the same distance on the scale. Circuits II EECS 3220 Lecture notes on making Bode plots Definitions Network Transfer Function: The function H s Xout s X in s where X out represents the voltage or current response of the network to X

More information

Frequency domain analysis

Frequency domain analysis Automatic Control 2 Frequency domain analysis Prof. Alberto Bemporad University of Trento Academic year 2010-2011 Prof. Alberto Bemporad (University of Trento) Automatic Control 2 Academic year 2010-2011

More information

'XNH8QLYHUVLW\ (GPXQG73UDWW-U6FKRRORI(QJLQHHULQJ. EGR 224 Spring Test II. Michael R. Gustafson II

'XNH8QLYHUVLW\ (GPXQG73UDWW-U6FKRRORI(QJLQHHULQJ. EGR 224 Spring Test II. Michael R. Gustafson II 'XNH8QLYHUVLW\ (GPXQG73UDWW-U6FKRRORI(QJLQHHULQJ EGR 224 Spring 2018 Test II Michael R. Gustafson II Name (please print) In keeping with the Community Standard, I have neither provided nor received any

More information

Solution: K m = R 1 = 10. From the original circuit, Z L1 = jωl 1 = j10 Ω. For the scaled circuit, L 1 = jk m ωl 1 = j10 10 = j100 Ω, Z L

Solution: K m = R 1 = 10. From the original circuit, Z L1 = jωl 1 = j10 Ω. For the scaled circuit, L 1 = jk m ωl 1 = j10 10 = j100 Ω, Z L Problem 9.9 Circuit (b) in Fig. P9.9 is a scaled version of circuit (a). The scaling process may have involved magnitude or frequency scaling, or both simultaneously. If R = kω gets scaled to R = kω, supply

More information

Sinusoidal Steady-State Analysis

Sinusoidal Steady-State Analysis Chapter 4 Sinusoidal Steady-State Analysis In this unit, we consider circuits in which the sources are sinusoidal in nature. The review section of this unit covers most of section 9.1 9.9 of the text.

More information

ECE Circuit Theory. Final Examination. December 5, 2008

ECE Circuit Theory. Final Examination. December 5, 2008 ECE 212 H1F Pg 1 of 12 ECE 212 - Circuit Theory Final Examination December 5, 2008 1. Policy: closed book, calculators allowed. Show all work. 2. Work in the provided space. 3. The exam has 3 problems

More information

Frequency Response Analysis

Frequency Response Analysis Frequency Response Analysis Consider let the input be in the form Assume that the system is stable and the steady state response of the system to a sinusoidal inputdoes not depend on the initial conditions

More information

2nd-order filters. EE 230 second-order filters 1

2nd-order filters. EE 230 second-order filters 1 nd-order filters Second order filters: Have second order polynomials in the denominator of the transfer function, and can have zeroth-, first-, or second-order polyinomials in the numerator. Use two reactive

More information

MAS107 Control Theory Exam Solutions 2008

MAS107 Control Theory Exam Solutions 2008 MAS07 CONTROL THEORY. HOVLAND: EXAM SOLUTION 2008 MAS07 Control Theory Exam Solutions 2008 Geir Hovland, Mechatronics Group, Grimstad, Norway June 30, 2008 C. Repeat question B, but plot the phase curve

More information

Overview of Bode Plots Transfer function review Piece-wise linear approximations First-order terms Second-order terms (complex poles & zeros)

Overview of Bode Plots Transfer function review Piece-wise linear approximations First-order terms Second-order terms (complex poles & zeros) Overview of Bode Plots Transfer function review Piece-wise linear approximations First-order terms Second-order terms (complex poles & zeros) J. McNames Portland State University ECE 222 Bode Plots Ver.

More information

To find the step response of an RC circuit

To find the step response of an RC circuit To find the step response of an RC circuit v( t) v( ) [ v( t) v( )] e tt The time constant = RC The final capacitor voltage v() The initial capacitor voltage v(t ) To find the step response of an RL circuit

More information

IC6501 CONTROL SYSTEMS

IC6501 CONTROL SYSTEMS DHANALAKSHMI COLLEGE OF ENGINEERING CHENNAI DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING YEAR/SEMESTER: II/IV IC6501 CONTROL SYSTEMS UNIT I SYSTEMS AND THEIR REPRESENTATION 1. What is the mathematical

More information

Chapter 8: Converter Transfer Functions

Chapter 8: Converter Transfer Functions Chapter 8. Converter Transer Functions 8.1. Review o Bode plots 8.1.1. Single pole response 8.1.2. Single zero response 8.1.3. Right hal-plane zero 8.1.4. Frequency inversion 8.1.5. Combinations 8.1.6.

More information

'XNH8QLYHUVLW\ (GPXQG73UDWW-U6FKRRORI(QJLQHHULQJ. EGR 224 Spring Test II. Michael R. Gustafson II

'XNH8QLYHUVLW\ (GPXQG73UDWW-U6FKRRORI(QJLQHHULQJ. EGR 224 Spring Test II. Michael R. Gustafson II 'XNH8QLYHUVLW\ (GPXQG73UDWW-U6FKRRORI(QJLQHHULQJ EGR 224 Spring 2017 Test II Michael R. Gustafson II Name (please print) In keeping with the Community Standard, I have neither provided nor received any

More information

Lecture 4: R-L-C Circuits and Resonant Circuits

Lecture 4: R-L-C Circuits and Resonant Circuits Lecture 4: R-L-C Circuits and Resonant Circuits RLC series circuit: What's V R? Simplest way to solve for V is to use voltage divider equation in complex notation: V X L X C V R = in R R + X C + X L L

More information

UNIVERSITY 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. 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 information

R-L-C Circuits and Resonant Circuits

R-L-C Circuits and Resonant Circuits P517/617 Lec4, P1 R-L-C Circuits and Resonant Circuits Consider the following RLC series circuit What's R? Simplest way to solve for is to use voltage divider equation in complex notation. X L X C in 0

More information

PROBLEMS OF CHAPTER 4: INTRODUCTION TO PASSIVE FILTERS.

PROBLEMS OF CHAPTER 4: INTRODUCTION TO PASSIVE FILTERS. PROBEMS OF CHAPTER 4: INTRODUCTION TO PASSIVE FITERS. April 4, 27 Problem 4. For the circuit shown in (a) we want to design a filter with the zero-pole diagram shown in (b). C X j jω e g (t) v(t) - σ (a)

More information

Sophomore Physics Laboratory (PH005/105)

Sophomore 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 information

Designing Information Devices and Systems II Spring 2016 Anant Sahai and Michel Maharbiz Midterm 2

Designing Information Devices and Systems II Spring 2016 Anant Sahai and Michel Maharbiz Midterm 2 EECS 16B Designing Information Devices and Systems II Spring 2016 Anant Sahai and Michel Maharbiz Midterm 2 Exam location: 145 Dwinelle (SIDs ending in 1 and 5) PRINT your student ID: PRINT AND SIGN your

More information

Sinusoidal Response of RLC Circuits

Sinusoidal Response of RLC Circuits Sinusoidal Response of RLC Circuits Series RL circuit Series RC circuit Series RLC circuit Parallel RL circuit Parallel RC circuit R-L Series Circuit R-L Series Circuit R-L Series Circuit Instantaneous

More information

ECE3050 Assignment 7

ECE3050 Assignment 7 ECE3050 Assignment 7. Sketch and label the Bode magnitude and phase plots for the transfer functions given. Use loglog scales for the magnitude plots and linear-log scales for the phase plots. On the magnitude

More information

Andrea Zanchettin Automatic Control AUTOMATIC CONTROL. Andrea M. Zanchettin, PhD Spring Semester, Linear systems (frequency domain)

Andrea Zanchettin Automatic Control AUTOMATIC CONTROL. Andrea M. Zanchettin, PhD Spring Semester, Linear systems (frequency domain) 1 AUTOMATIC CONTROL Andrea M. Zanchettin, PhD Spring Semester, 2018 Linear systems (frequency domain) 2 Motivations Consider an LTI system Thanks to the Lagrange s formula we can compute the motion of

More information

Analysis and Design of Analog Integrated Circuits Lecture 12. Feedback

Analysis and Design of Analog Integrated Circuits Lecture 12. Feedback Analysis and Design of Analog Integrated Circuits Lecture 12 Feedback Michael H. Perrott March 11, 2012 Copyright 2012 by Michael H. Perrott All rights reserved. Open Loop Versus Closed Loop Amplifier

More information

Single-Time-Constant (STC) Circuits This lecture is given as a background that will be needed to determine the frequency response of the amplifiers.

Single-Time-Constant (STC) Circuits This lecture is given as a background that will be needed to determine the frequency response of the amplifiers. Single-Time-Constant (STC) Circuits This lecture is given as a background that will be needed to determine the frequency response of the amplifiers. Objectives To analyze and understand STC circuits with

More information

(b) A unity feedback system is characterized by the transfer function. Design a suitable compensator to meet the following specifications:

(b) A unity feedback system is characterized by the transfer function. Design a suitable compensator to meet the following specifications: 1. (a) The open loop transfer function of a unity feedback control system is given by G(S) = K/S(1+0.1S)(1+S) (i) Determine the value of K so that the resonance peak M r of the system is equal to 1.4.

More information

EC CONTROL SYSTEM UNIT I- CONTROL SYSTEM MODELING

EC CONTROL SYSTEM UNIT I- CONTROL SYSTEM MODELING EC 2255 - CONTROL SYSTEM UNIT I- CONTROL SYSTEM MODELING 1. What is meant by a system? It is an arrangement of physical components related in such a manner as to form an entire unit. 2. List the two types

More information

CDS 101/110 Homework #7 Solution

CDS 101/110 Homework #7 Solution Amplitude Amplitude CDS / Homework #7 Solution Problem (CDS, CDS ): (5 points) From (.), k i = a = a( a)2 P (a) Note that the above equation is unbounded, so it does not make sense to talk about maximum

More information

Frequency methods for the analysis of feedback systems. Lecture 6. Loop analysis of feedback systems. Nyquist approach to study stability

Frequency methods for the analysis of feedback systems. Lecture 6. Loop analysis of feedback systems. Nyquist approach to study stability Lecture 6. Loop analysis of feedback systems 1. Motivation 2. Graphical representation of frequency response: Bode and Nyquist curves 3. Nyquist stability theorem 4. Stability margins Frequency methods

More information

First and Second Order Circuits. Claudio Talarico, Gonzaga University Spring 2015

First and Second Order Circuits. Claudio Talarico, Gonzaga University Spring 2015 First and Second Order Circuits Claudio Talarico, Gonzaga University Spring 2015 Capacitors and Inductors intuition: bucket of charge q = Cv i = C dv dt Resist change of voltage DC open circuit Store voltage

More information

Control Systems I. Lecture 9: The Nyquist condition

Control Systems I. Lecture 9: The Nyquist condition Control Systems I Lecture 9: The Nyquist condition adings: Guzzella, Chapter 9.4 6 Åstrom and Murray, Chapter 9.1 4 www.cds.caltech.edu/~murray/amwiki/index.php/first_edition Emilio Frazzoli Institute

More information

Lecture 6 Classical Control Overview IV. Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore

Lecture 6 Classical Control Overview IV. Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore Lecture 6 Classical Control Overview IV Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore Lead Lag Compensator Design Dr. Radhakant Padhi Asst.

More information

BIOEN 302, Section 3: AC electronics

BIOEN 302, Section 3: AC electronics BIOEN 3, Section 3: AC electronics For this section, you will need to have very present the basics of complex number calculus (see Section for a brief overview) and EE5 s section on phasors.. Representation

More information

Lecture 15 Nyquist Criterion and Diagram

Lecture 15 Nyquist Criterion and Diagram Lecture Notes of Control Systems I - ME 41/Analysis and Synthesis of Linear Control System - ME86 Lecture 15 Nyquist Criterion and Diagram Department of Mechanical Engineering, University Of Saskatchewan,

More information

H(s) = 2(s+10)(s+100) (s+1)(s+1000)

H(s) = 2(s+10)(s+100) (s+1)(s+1000) Problem 1 Consider the following transfer function H(s) = 2(s10)(s100) (s1)(s1000) (a) Draw the asymptotic magnitude Bode plot for H(s). Solution: The transfer function is not in standard form to sketch

More information

Poles and Zeros in z-plane

Poles and Zeros in z-plane M58 Mixed Signal Processors page of 6 Poles and Zeros in z-plane z-plane Response of discrete-time system (i.e. digital filter at a particular frequency ω is determined by the distance between its poles

More information

'XNH8QLYHUVLW\ (GPXQG73UDWW-U6FKRRORI(QJLQHHULQJ. ECE 110 Fall Test II. Michael R. Gustafson II

'XNH8QLYHUVLW\ (GPXQG73UDWW-U6FKRRORI(QJLQHHULQJ. ECE 110 Fall Test II. Michael R. Gustafson II 'XNH8QLYHUVLW\ (GPXQG73UDWW-U6FKRRORI(QJLQHHULQJ ECE 110 Fall 2016 Test II Michael R. Gustafson II Name (please print) In keeping with the Community Standard, I have neither provided nor received any assistance

More information

Electronics II. Final Examination

Electronics II. Final Examination The University of Toledo f6fs_elct7.fm - Electronics II Final Examination Problems Points. 5. 0 3. 5 Total 40 Was the exam fair? yes no The University of Toledo f6fs_elct7.fm - Problem 5 points Given is

More information

Automatic Control (MSc in Mechanical Engineering) Lecturer: Andrea Zanchettin Date: Student ID number... Signature...

Automatic Control (MSc in Mechanical Engineering) Lecturer: Andrea Zanchettin Date: Student ID number... Signature... Automatic Control (MSc in Mechanical Engineering) Lecturer: Andrea Zanchettin Date: 29..23 Given and family names......................solutions...................... Student ID number..........................

More information

Controls Problems for Qualifying Exam - Spring 2014

Controls Problems for Qualifying Exam - Spring 2014 Controls Problems for Qualifying Exam - Spring 2014 Problem 1 Consider the system block diagram given in Figure 1. Find the overall transfer function T(s) = C(s)/R(s). Note that this transfer function

More information

I. Frequency Response of Voltage Amplifiers

I. Frequency Response of Voltage Amplifiers I. Frequency Response of Voltage Amplifiers A. Common-Emitter Amplifier: V i SUP i OUT R S V BIAS R L v OUT V Operating Point analysis: 0, R s 0, r o --->, r oc --->, R L ---> Find V BIAS such that I C

More information

EE348L Lecture 1. EE348L Lecture 1. Complex Numbers, KCL, KVL, Impedance,Steady State Sinusoidal Analysis. Motivation

EE348L Lecture 1. EE348L Lecture 1. Complex Numbers, KCL, KVL, Impedance,Steady State Sinusoidal Analysis. Motivation EE348L Lecture 1 Complex Numbers, KCL, KVL, Impedance,Steady State Sinusoidal Analysis 1 EE348L Lecture 1 Motivation Example CMOS 10Gb/s amplifier Differential in,differential out, 5 stage dccoupled,broadband

More information

OPERATIONAL AMPLIFIER APPLICATIONS

OPERATIONAL AMPLIFIER APPLICATIONS OPERATIONAL AMPLIFIER APPLICATIONS 2.1 The Ideal Op Amp (Chapter 2.1) Amplifier Applications 2.2 The Inverting Configuration (Chapter 2.2) 2.3 The Non-inverting Configuration (Chapter 2.3) 2.4 Difference

More information

Chapter 9: Controller design

Chapter 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 information

ROOT LOCUS. Consider the system. Root locus presents the poles of the closed-loop system when the gain K changes from 0 to. H(s) H ( s) = ( s)

ROOT LOCUS. Consider the system. Root locus presents the poles of the closed-loop system when the gain K changes from 0 to. H(s) H ( s) = ( s) C1 ROOT LOCUS Consider the system R(s) E(s) C(s) + K G(s) - H(s) C(s) R(s) = K G(s) 1 + K G(s) H(s) Root locus presents the poles of the closed-loop system when the gain K changes from 0 to 1+ K G ( s)

More information

Control Systems. University Questions

Control Systems. University Questions University Questions UNIT-1 1. Distinguish between open loop and closed loop control system. Describe two examples for each. (10 Marks), Jan 2009, June 12, Dec 11,July 08, July 2009, Dec 2010 2. Write

More information

EE221 - Practice for the Midterm Exam

EE221 - Practice for the Midterm Exam EE1 - Practice for the Midterm Exam 1. Consider this circuit and corresponding plot of the inductor current: Determine the values of L, R 1 and R : L = H, R 1 = Ω and R = Ω. Hint: Use the plot to determine

More information

Chapter 2. Classical Control System Design. Dutch Institute of Systems and Control

Chapter 2. Classical Control System Design. Dutch Institute of Systems and Control Chapter 2 Classical Control System Design Overview Ch. 2. 2. Classical control system design Introduction Introduction Steady-state Steady-state errors errors Type Type k k systems systems Integral Integral

More information

Op-Amp Circuits: Part 3

Op-Amp Circuits: Part 3 Op-Amp Circuits: Part 3 M. B. Patil mbpatil@ee.iitb.ac.in www.ee.iitb.ac.in/~sequel Department of Electrical Engineering Indian Institute of Technology Bombay Introduction to filters Consider v(t) = v

More information

Use of a Notch Filter in a Tuned Mode for LISA.

Use of a Notch Filter in a Tuned Mode for LISA. Use of a Notch Filter in a Tuned Mode for LISA. Giorgio Fontana September 00 Abstract. During interferometric measurements the proof mass must be free from any controlling force within a given observation

More information

EE1-01 IMPERIAL COLLEGE LONDON DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING EXAMINATIONS 2013 ANALYSIS OF CIRCUITS. Tuesday, 28 May 10:00 am

EE1-01 IMPERIAL COLLEGE LONDON DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING EXAMINATIONS 2013 ANALYSIS OF CIRCUITS. Tuesday, 28 May 10:00 am EE1-01 IMPERIAL COLLEGE LONDON DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING EXAMINATIONS 2013 ExamHeader: EEE/EIE PART I: MEng, Beng and ACGI ANALYSIS OF CIRCUITS Tuesday, 28 May 10:00 am Time allowed:

More information

Problem Weight Score Total 100

Problem Weight Score Total 100 EE 350 EXAM IV 15 December 2010 Last Name (Print): First Name (Print): ID number (Last 4 digits): Section: DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO Problem Weight Score 1 25 2 25 3 25 4 25 Total

More information

FREQUENCY-RESPONSE DESIGN

FREQUENCY-RESPONSE DESIGN ECE45/55: Feedback Control Systems. 9 FREQUENCY-RESPONSE DESIGN 9.: PD and lead compensation networks The frequency-response methods we have seen so far largely tell us about stability and stability margins

More information

EKT 119 ELECTRIC CIRCUIT II. Chapter 3: Frequency Response of AC Circuit Sem2 2015/2016 Dr. Mohd Rashidi Che Beson

EKT 119 ELECTRIC CIRCUIT II. Chapter 3: Frequency Response of AC Circuit Sem2 2015/2016 Dr. Mohd Rashidi Che Beson EKT 9 ELECTRIC CIRCUIT II Chapter 3: Frequency Response of AC Circuit Sem 05/06 Dr. Mohd Rashidi Che Beson TRANSFER FUNCTION (TF Frequency response can be obtained by using transfer function. DEFINITION:

More information

FATIMA MICHAEL COLLEGE OF ENGINEERING & TECHNOLOGY

FATIMA MICHAEL COLLEGE OF ENGINEERING & TECHNOLOGY FATIMA MICHAEL COLLEGE OF ENGINEERING & TECHNOLOGY Senkottai Village, Madurai Sivagangai Main Road, Madurai - 625 020. An ISO 9001:2008 Certified Institution DEPARTMENT OF ELECTRONICS AND COMMUNICATION

More information

Part IB Paper 6: Information Engineering LINEAR SYSTEMS AND CONTROL. Glenn Vinnicombe HANDOUT 4. The Frequency ResponseG(jω)

Part IB Paper 6: Information Engineering LINEAR SYSTEMS AND CONTROL. Glenn Vinnicombe HANDOUT 4. The Frequency ResponseG(jω) Part IB Paper 6: Information Engineering LINEAR SYSEMS AND CONROL Glenn Vinnicombe HANDOU 4 he Frequency ResponseG(jω) x(t) 2π ω y(t) G(jω) argg(jω) ω t t Asymptotically stable LI systemg(s) x(t)=cos(ωt)

More information

Fourier series. XE31EO2 - Pavel Máša. Electrical Circuits 2 Lecture1. XE31EO2 - Pavel Máša - Fourier Series

Fourier series. XE31EO2 - Pavel Máša. Electrical Circuits 2 Lecture1. XE31EO2 - Pavel Máša - Fourier Series Fourier series Electrical Circuits Lecture - Fourier Series Filtr RLC defibrillator MOTIVATION WHAT WE CAN'T EXPLAIN YET Source voltage rectangular waveform Resistor voltage sinusoidal waveform - Fourier

More information

Second-order filters. EE 230 second-order filters 1

Second-order filters. EE 230 second-order filters 1 Second-order filters Second order filters: Have second order polynomials in the denominator of the transfer function, and can have zeroth-, first-, or second-order polynomials in the numerator. Use two

More information

Plan of the Lecture. Goal: wrap up lead and lag control; start looking at frequency response as an alternative methodology for control systems design.

Plan of the Lecture. Goal: wrap up lead and lag control; start looking at frequency response as an alternative methodology for control systems design. Plan of the Lecture Review: design using Root Locus; dynamic compensation; PD and lead control Today s topic: PI and lag control; introduction to frequency-response design method Goal: wrap up lead and

More information

Today. 1/25/11 Physics 262 Lecture 2 Filters. Active Components and Filters. Homework. Lab 2 this week

Today. 1/25/11 Physics 262 Lecture 2 Filters. Active Components and Filters. Homework. Lab 2 this week /5/ Physics 6 Lecture Filters Today Basics: Analog versus Digital; Passive versus Active Basic concepts and types of filters Passband, Stopband, Cut-off, Slope, Knee, Decibels, and Bode plots Active Components

More information

Lectures 16 & 17 Sinusoidal Signals, Complex Numbers, Phasors, Impedance & AC Circuits. Nov. 7 & 9, 2011

Lectures 16 & 17 Sinusoidal Signals, Complex Numbers, Phasors, Impedance & AC Circuits. Nov. 7 & 9, 2011 Lectures 16 & 17 Sinusoidal Signals, Complex Numbers, Phasors, Impedance & AC Circuits Nov. 7 & 9, 2011 Material from Textbook by Alexander & Sadiku and Electrical Engineering: Principles & Applications,

More information

Radar Dish. Armature controlled dc motor. Inside. θ r input. Outside. θ D output. θ m. Gearbox. Control Transmitter. Control. θ D.

Radar Dish. Armature controlled dc motor. Inside. θ r input. Outside. θ D output. θ m. Gearbox. Control Transmitter. Control. θ D. Radar Dish ME 304 CONTROL SYSTEMS Mechanical Engineering Department, Middle East Technical University Armature controlled dc motor Outside θ D output Inside θ r input r θ m Gearbox Control Transmitter

More information

Compensator Design to Improve Transient Performance Using Root Locus

Compensator Design to Improve Transient Performance Using Root Locus 1 Compensator Design to Improve Transient Performance Using Root Locus Prof. Guy Beale Electrical and Computer Engineering Department George Mason University Fairfax, Virginia Correspondence concerning

More information

Homework Assignment 11

Homework Assignment 11 Homework Assignment Question State and then explain in 2 3 sentences, the advantage of switched capacitor filters compared to continuous-time active filters. (3 points) Continuous time filters use resistors

More information

1 (20 pts) Nyquist Exercise

1 (20 pts) Nyquist Exercise EE C128 / ME134 Problem Set 6 Solution Fall 2011 1 (20 pts) Nyquist Exercise Consider a close loop system with unity feedback. For each G(s), hand sketch the Nyquist diagram, determine Z = P N, algebraically

More information

Electronic Circuits EE359A

Electronic Circuits EE359A Electronic Circuits EE359A Bruce McNair B26 bmcnair@stevens.edu 21-216-5549 Lecture 22 569 Second order section Ts () = s as + as+ a 2 2 1 ω + s+ ω Q 2 2 ω 1 p, p = ± 1 Q 4 Q 1 2 2 57 Second order section

More information

Microwave Oscillators Design

Microwave Oscillators Design Microwave Oscillators Design Oscillators Classification Feedback Oscillators β Α Oscillation Condition: Gloop = A β(jω 0 ) = 1 Gloop(jω 0 ) = 1, Gloop(jω 0 )=2nπ Negative resistance oscillators Most used

More information

The general form for the transform function of a second order filter is that of a biquadratic (or biquad to the cool kids).

The general form for the transform function of a second order filter is that of a biquadratic (or biquad to the cool kids). nd-order filters The general form for the transform function of a second order filter is that of a biquadratic (or biquad to the cool kids). T (s) A p s a s a 0 s b s b 0 As before, the poles of the transfer

More information

Lecture 16 FREQUENCY RESPONSE OF SIMPLE CIRCUITS

Lecture 16 FREQUENCY RESPONSE OF SIMPLE CIRCUITS Lecture 6 FREQUENCY RESPONSE OF SIMPLE CIRCUITS Ray DeCarlo School of ECE Purdue University West Lafayette, IN 47907-285 decarlo@ecn.purdue.edu EE-202, Frequency Response p 2 R. A. DeCarlo I. WHAT IS FREQUENCY

More information

Test II Michael R. Gustafson II

Test II Michael R. Gustafson II 'XNH8QLYHUVLW\ (GPXQG73UDWW-U6FKRRORI(QJLQHHULQJ EGR 224 Spring 2016 Test II Michael R. Gustafson II Name (please print) In keeping with the Community Standard, I have neither provided nor received any

More information

(amperes) = (coulombs) (3.1) (seconds) Time varying current. (volts) =

(amperes) = (coulombs) (3.1) (seconds) Time varying current. (volts) = 3 Electrical Circuits 3. Basic Concepts Electric charge coulomb of negative change contains 624 0 8 electrons. Current ampere is a steady flow of coulomb of change pass a given point in a conductor in

More information

SAMPLE SOLUTION TO EXAM in MAS501 Control Systems 2 Autumn 2015

SAMPLE SOLUTION TO EXAM in MAS501 Control Systems 2 Autumn 2015 FACULTY OF ENGINEERING AND SCIENCE SAMPLE SOLUTION TO EXAM in MAS501 Control Systems 2 Autumn 2015 Lecturer: Michael Ruderman Problem 1: Frequency-domain analysis and control design (15 pt) Given is a

More information

ECE 486 Control Systems

ECE 486 Control Systems ECE 486 Control Systems Spring 208 Midterm #2 Information Issued: April 5, 208 Updated: April 8, 208 ˆ This document is an info sheet about the second exam of ECE 486, Spring 208. ˆ Please read the following

More information

Active Filter Design by Carsten Kristiansen Napier University. November 2004

Active Filter Design by Carsten Kristiansen Napier University. November 2004 by Carsten Kristiansen November 2004 Title page Author: Carsten Kristiansen. Napier No: 0400772. Assignment partner: Benjamin Grydehoej. Assignment title:. Education: Electronic and Computer Engineering.

More information

ESE319 Introduction to Microelectronics. Feedback Basics

ESE319 Introduction to Microelectronics. Feedback Basics Feedback Basics Stability Feedback concept Feedback in emitter follower One-pole feedback and root locus Frequency dependent feedback and root locus Gain and phase margins Conditions for closed loop stability

More information

Frequency Response Techniques

Frequency Response Techniques 4th Edition T E N Frequency Response Techniques SOLUTION TO CASE STUDY CHALLENGE Antenna Control: Stability Design and Transient Performance First find the forward transfer function, G(s). Pot: K 1 = 10

More information

2.161 Signal Processing: Continuous and Discrete

2.161 Signal Processing: Continuous and Discrete MIT OpenCourseWare http://ocw.mit.edu.6 Signal Processing: Continuous and Discrete Fall 008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. M MASSACHUSETTS

More information

2. The following diagram illustrates that voltage represents what physical dimension?

2. The following diagram illustrates that voltage represents what physical dimension? BioE 1310 - Exam 1 2/20/2018 Answer Sheet - Correct answer is A for all questions 1. A particular voltage divider with 10 V across it consists of two resistors in series. One resistor is 7 KΩ and the other

More information

CORRESPONDENCE BETWEEN PHASOR TRANSFORMS AND FREQUENCY RESPONSE FUNCTION IN RLC CIRCUITS

CORRESPONDENCE BETWEEN PHASOR TRANSFORMS AND FREQUENCY RESPONSE FUNCTION IN RLC CIRCUITS CORRESPONDENCE BETWEEN PHASOR TRANSFORMS AND FREQUENCY RESPONSE FUNCTION IN RLC CIRCUITS Hassan Mohamed Abdelalim Abdalla Polytechnic Department of Engineering and Architecture, University of Studies of

More information

Boise State University Department of Electrical Engineering ECE461 Control Systems. Control System Design in the Frequency Domain

Boise State University Department of Electrical Engineering ECE461 Control Systems. Control System Design in the Frequency Domain Boise State University Department of Electrical Engineering ECE6 Control Systems Control System Design in the Frequency Domain Situation: Consider the following block diagram of a type- servomechanism:

More information

Some of the different forms of a signal, obtained by transformations, are shown in the figure. jwt e z. jwt z e

Some of the different forms of a signal, obtained by transformations, are shown in the figure. jwt e z. jwt z e Transform methods Some of the different forms of a signal, obtained by transformations, are shown in the figure. X(s) X(t) L - L F - F jw s s jw X(jw) X*(t) F - F X*(jw) jwt e z jwt z e X(nT) Z - Z X(z)

More information

Laplace Transform Analysis of Signals and Systems

Laplace Transform Analysis of Signals and Systems Laplace Transform Analysis of Signals and Systems Transfer Functions Transfer functions of CT systems can be found from analysis of Differential Equations Block Diagrams Circuit Diagrams 5/10/04 M. J.

More information

EE-202 Exam III April 13, 2015

EE-202 Exam III April 13, 2015 EE-202 Exam III April 3, 205 Name: (Please print clearly.) Student ID: CIRCLE YOUR DIVISION DeCarlo-7:30-8:30 Furgason 3:30-4:30 DeCarlo-:30-2:30 202 2022 2023 INSTRUCTIONS There are 2 multiple choice

More information

Review of Linear Time-Invariant Network Analysis

Review of Linear Time-Invariant Network Analysis D1 APPENDIX D Review of Linear Time-Invariant Network Analysis Consider a network with input x(t) and output y(t) as shown in Figure D-1. If an input x 1 (t) produces an output y 1 (t), and an input x

More information