SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuits II. Solutions to Assignment 3 February 2005.

Size: px
Start display at page:

Download "SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuits II. Solutions to Assignment 3 February 2005."

Transcription

1 SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuit II Solution to Aignment 3 February Initial Condition Source 0 V battery witch flip at t 0 find i 3 (t) Component value: R 50kΩ R 2 50kΩ R 3 50kΩ C 00 µf L 0mH Initial value of cap voltage and inductor current: v C ( 0minu) 0voltR 3 5volt R + R 3 by voltage divider i L ( 0minu) 0volt 33.3 µamp R + R 3 Circuit for time greater than zero, including initial condition repreented a impule ource: Solve by uperpoition. Firt conider the current ource, with the voltage ource et to zero. By voltage divider, thi component of I 3 i I 3C 0voltR 3 C R + R 3 C + ( L + R 3 ) + R 2 ( L + R ) 3 0voltR 3 R + R 3 ( ) L 2 CR 2 R 3 + L + R 2 LC + R 2 + R 3 R 2 LC

2 2 and with number I 3C () ampec Note that the unit of tranformed current are amp-ec, becaue of the dt in the Laplace tranform integral. Next, conider the voltage ource, with the current ource et to zero. Uing the impedance een by the voltage ource, we have thi component of I 3 a I 3L L + R 3 0voltL R + R 3 + R 2 + C 0voltLCR 2 LC R 2 R + R 3 ( ) + CR 2 ( ) 2 CR 3 R 2 + L + R 2 LC + R 2 + R 3 R 2 LC and with number, I 3L () Adding the two component, we have the tranform of the total current a I 3 () I 3C () + I 3L () 0 R + R CR 3 R 2 + L + R 2 LC CR 2 R 3 + R 2 LC L R 2 + R 3 + R 2 LC or in number I 3 () Before inverion, check thi by IVT and FVT. We obtain i 3 ( 0plu) i ( ) 0

3 3 Thee value are right, ince i 3 equal the inductor current of 33.3 µa initially, and it die away to zero For the inverion, factor the denominator I 3 () ( ) a huge diparity in root The reidue at i ( ) e 0.267t 33.3 e 0.267t µamp The other reidue i ( ) exp.50 7 t negligible So i 3 ( t) 33.3 e 0.267t µamp for t > 0 2. Deign Circuit for Specific Tranfer Function Experimentation and looking at high and low frequency behaviour give They are not the only poible circuit that realize the given impedance and admittance. For example partial fraction expanion of the Z in for part (e) give thi alternative:

4 4 Z in () Alo note that the bilinear form in (d) and (e) have high frequency impedance lower than dc impedance, which ugget tructure with capacitor. If it had been the other way around, we probably would have ued inductor, intead. 3. Effect of Op Amp Frequency Repone (a) The op amp ha three break frequencie ω c : 2π50 ω c2 : 2π300 3 ω c3 : 2π It open loop tranfer function i then H a () A 0 ( + ω c ) ( + ω c2 ) + ω c3 ( ) We can determine A 0 from the unity gain bandwidthω t : 2π300 6 Set H a ( jω t ) which make A 0 : ( j ω t + ω c ) jω t + ω c2 ( ) ( + ) j ω t ω c3 A and ince ω t i much greater than all of the break frequencie, that gain i very cloe to ω t Thi i a very high value - but remember, it i ued for a model of frequency behaviour, and we are intereted in the repone when the frequencie are high enough to make the gain ag. The model i H a () : A 0 ( + ω c ) ( + ω c2 ) + ω c3 ( ) An alternative form i H a () + ω c A dc + + ω c2 ω c3

5 5 where the dc gain A dc i A 0 A dc : ω c ω c2 ω c3 A dc (b) Now we need the tranfer function of the inverting amplifier. For thi, we need the inverting amplifier gain G and the cloed-loop tranfer function. The inverting amp gain i G R f R i or G : 00 From the dicuion on pp and 3..9 of the lecture note, the cloed loop tranfer function i H() : H a () + H a () G + G + G From thi, we can find the bandwidth a the frequency for which the gain i 3 db. We can do thi in two way. The eaier way i numerical: find the ω for which H() i 3 db down from the deired G 00; that i H(jω) We could ue a numerical root finder or jut do trial and error. Either way, we get ω 3dB : rad/ f 3dB : ω 3dB 2π f 3dB Hz H( jω 3dB ) 70.7 which equal 00 / qrt(2). The other way i to ubtitute the form of H a () into H() and explore. We'll need thi, anyway, to determine if the bandwidth i enitive to the value of the dc gain or break frequencie. So make the ubtitution and rearrange into a form that make the feature reaonably clear. H () H a () + H a () G + G + G + ω c G + + ω c2 ω c3 ( + G) + A dc From thi form, we ee that departure from the deired value -G are determined by the complicated firt term of the denominator and how large it i compared with the econd term (i.e., ). To find the 3 db point (where the quared magnitude of the denominator equal 2) we could ubtitute jω and olve the reulting cubic. I won't bother, ince we got the reult 45. Mrad/ above. Of more interet i the enitivity to op amp parameter value, and the expreion above how u the following:

6 The firt term i inverely proportional to A dc, o the op amp dc gain directly affect the amplifier bandwidth ω 3dB. Since A dc i very large, the amplifier bandwidth mut be much greater than at leat the mallet o the break frequencie. In numerical fact, it i much greater than all of them, o that we can make the approximation 6 H () G 3 ( + G) + ω c ω c2 ω c3 A dc ω t G 3 ( + G) + for frequencie much greater than ω c3. From thi, we ee that all of the break frequencie, a well a the op amp dc gain, directly affect the amplifier bandwidth. We alo ee that the unity-gain frequency of the op amp i a ueful ummary of the other parameter. You could have come to the ame concluion numerically. You could have changed A dc or any of the break frequencie and recomputed the amplifier bandwidth. That would have demontrated enitivity to thoe parameter. Your computation might have looked like thi: ( ) H, A dc, ω c, ω c2, ω c3 : + ω c G + + ω c2 ω c3 ( + G) + A dc A dc : 20 0 change the dc gain a little ω : 20 7 a gue, a tarter value for root finding Find the new ω3db automatically, uing a canned root finder: root ( ) H jω, A dc, ω c, ω c2, ω c3, ω different from the previou value, o enitive to dc gain The point of thi invetigation i that the high frequency behaviour of an inverting amp i enitive t the op amp parameter. On the other hand, the gain of that inverting amp at lower frequencie (thoe for which the firt term i negligible) i quite inenitive to the op amp parameter - they could change b an order of magnitude and there would be little perceptible change. Alo (and thi wa not invetigated here), the frequency repone of active filter that have paband at leat an order of magnitude lower than the unity gain frequency are imilarly inenitive to the op amp parameter.

7 7 4. Tuning the Load (a) Firt, get the impedance of the load: Z l L R l L + R l Then the tranfer function relating load voltage to ource voltage i H v () Z l R + Z l R l R + R l R R l + R + R l ( ) L and the "tranfer admittance" relating load current to ource voltage i H i () R + Z l ( R + R l ) + R l + L R R l R + R l ( ) L (b) The pole-zero diagram and frequency repone are ketched below. (c) We want the parallel combination of load reitor and inductor and the capacitor to have a real impedance. Equivalently, we want real admittance, which i an eaier calculation, ince they are in parallel.

8 8 Y C C 0.0 j R l L 25 ω ω C at the upply frequency ω The upply frequency i ω : 2π400 ω rad/ To eliminate the imaginary component, et C : 25 2 ω C Farad Since the inductor and capacitor have cancelling admittance at the upply frequency, the circuit behave like a imple reitive voltage divider with R and R l at that frequency only. It i alo intereting that we have jut made LC ω -2. Thi i the ame condition that make the load reonant at the upply frequency. In the cae at hand, the parallel combination of R and R l i too mall for the parallel circuit to how reonance. (d) More work to get the tranfer function. The new load impedance i Z l and the voltage tranfer function i H v () Z l Z l + R ( ) ( + 229) We have two real pole, intead of complex pole, becaue the circuit ha too little reitance to how true reonance. However, the zero at 0 how that it i a bandpa circuit. The pole-zero diagram and frequency repone are ketched below.

9 9 5. Invere Filter The ditorting filter and the invere filter are hown in the ketch. The tranfer function of the invere filter i obtained from the impedance of the parallel RC circuit Z i R i C i R i + Z f R f C f R f + H c () Z f Z i C i C f + + R i C i R f C f (a) For H d () we want H c () The eaiet way to pick component to get thi tranfer function i. match dc gain (ignoring ign inverion): H c ( 0) 5 R f R i which make R f 50kΩ ince R i 0kΩ 2. match the zero: C i 20nF R i match high frequency gain (ignoring ign inverion): H c ( ) C i C f o C f 20nF

10 0 (b) If the zero of H d () are in the RHP (which they could be), then the invere filter ha correponding pole in the RHP, making it untable. So that won't work. (c) If the numerator of H d () i of lower degree than it denominator, then the numerator of the invere filter H c () ha higher degree than it denominator. At high frequencie, the gain can become huge. Th in't realitic, ince it could hugely amplify high frequency noie - and in fact it impule repone wou have infinite energy. An example i a differentiator, with H c (). It doen't exit over the whole frequency range out to infinity - other effect that we haven't modeled will caue the gain to drop at hig frequencie, allowing it to differentiate only over a limited frequency range. (d) If H d () i a bandtop filter (negligible repone in ome band), then the invere filter H d () /H d () mut have infinite gain in the ame band. Even with infiinite gain, it can't recover frequency component that were removed by H d (). (e) Now uppoe that H d () The invere filter H c () i "improper" - numerator degree higher than denom. + Sketch the pole-zero diagram and frequency repone of the two filter. The intereting part of H d () might run out to ω 0 to 3.6 rad/, where the repone i 20 to 30 db down. So let' aume we don't care about inverting it repone beyond thi point. Give the invere filter H c () another two pole, to make it tranfer function "proper" again. Where hould we put them? Firt, they hould be well away from the origin, o that they don't affect the invere filter repone at frequencie within the band. Perhap 30 rad/ away. Second, thi i like cacading our original invere filter with a two-pole lowpa. So let' make it a lowpa with only a little ditortion in the ignal band like a Butterworth or Beel filter. I'll go Butterworth, with pole -30 ± j30. The new invere filter i

11 H c' () ( + 2) ( + 3) ( ) ( + ) and it pole-zero diagram and frequency repone are

12 2 R R 2 R 3 50kΩ kΩ kΩ C 00 µf L 0mH 00 3

SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuits II. R 4 := 100 kohm

SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuits II. R 4 := 100 kohm SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuit II Solution to Aignment 3 February 2003. Cacaded Op Amp [DC&L, problem 4.29] An ideal op amp ha an output impedance of zero,

More information

Question 1 Equivalent Circuits

Question 1 Equivalent Circuits MAE 40 inear ircuit Fall 2007 Final Intruction ) Thi exam i open book You may ue whatever written material you chooe, including your cla note and textbook You may ue a hand calculator with no communication

More information

ECE Linear Circuit Analysis II

ECE Linear Circuit Analysis II ECE 202 - Linear Circuit Analyi II Final Exam Solution December 9, 2008 Solution Breaking F into partial fraction, F 2 9 9 + + 35 9 ft δt + [ + 35e 9t ]ut A 9 Hence 3 i the correct anwer. Solution 2 ft

More information

Lecture 10 Filtering: Applied Concepts

Lecture 10 Filtering: Applied Concepts Lecture Filtering: Applied Concept In the previou two lecture, you have learned about finite-impule-repone (FIR) and infinite-impule-repone (IIR) filter. In thee lecture, we introduced the concept of filtering

More information

Introduction to Laplace Transform Techniques in Circuit Analysis

Introduction to Laplace Transform Techniques in Circuit Analysis Unit 6 Introduction to Laplace Tranform Technique in Circuit Analyi In thi unit we conider the application of Laplace Tranform to circuit analyi. A relevant dicuion of the one-ided Laplace tranform i found

More information

MAE140 Linear Circuits Fall 2012 Final, December 13th

MAE140 Linear Circuits Fall 2012 Final, December 13th MAE40 Linear Circuit Fall 202 Final, December 3th Intruction. Thi exam i open book. You may ue whatever written material you chooe, including your cla note and textbook. You may ue a hand calculator with

More information

1. /25 2. /30 3. /25 4. /20 Total /100

1. /25 2. /30 3. /25 4. /20 Total /100 Circuit Exam 2 Spring 206. /25 2. /30 3. /25 4. /20 Total /00 Name Pleae write your name at the top of every page! Note: ) If you are tuck on one part of the problem, chooe reaonable value on the following

More information

5.5 Application of Frequency Response: Signal Filters

5.5 Application of Frequency Response: Signal Filters 44 Dynamic Sytem Second order lowpa filter having tranfer function H()=H ()H () u H () H () y Firt order lowpa filter Figure 5.5: Contruction of a econd order low-pa filter by combining two firt order

More information

ECE382/ME482 Spring 2004 Homework 4 Solution November 14,

ECE382/ME482 Spring 2004 Homework 4 Solution November 14, ECE382/ME482 Spring 2004 Homework 4 Solution November 14, 2005 1 Solution to HW4 AP4.3 Intead of a contant or tep reference input, we are given, in thi problem, a more complicated reference path, r(t)

More information

Lecture 6: Resonance II. Announcements

Lecture 6: Resonance II. Announcements EES 5 Spring 4, Lecture 6 Lecture 6: Reonance II EES 5 Spring 4, Lecture 6 Announcement The lab tart thi week You mut how up for lab to tay enrolled in the coure. The firt lab i available on the web ite,

More information

ECE-202 FINAL December 13, 2016 CIRCLE YOUR DIVISION

ECE-202 FINAL December 13, 2016 CIRCLE YOUR DIVISION ECE-202 Final, Fall 16 1 ECE-202 FINAL December 13, 2016 Name: (Pleae print clearly.) Student Email: CIRCLE YOUR DIVISION DeCarlo- 8:30-9:30 Talavage-9:30-10:30 2021 2022 INSTRUCTIONS There are 35 multiple

More information

Design of Digital Filters

Design of Digital Filters Deign of Digital Filter Paley-Wiener Theorem [ ] ( ) If h n i a caual energy ignal, then ln H e dω< B where B i a finite upper bound. One implication of the Paley-Wiener theorem i that a tranfer function

More information

Design By Emulation (Indirect Method)

Design By Emulation (Indirect Method) Deign By Emulation (Indirect Method he baic trategy here i, that Given a continuou tranfer function, it i required to find the bet dicrete equivalent uch that the ignal produced by paing an input ignal

More information

Linearteam tech paper. The analysis of fourth-order state variable filter and it s application to Linkwitz- Riley filters

Linearteam tech paper. The analysis of fourth-order state variable filter and it s application to Linkwitz- Riley filters Linearteam tech paper The analyi of fourth-order tate variable filter and it application to Linkwitz- iley filter Janne honen 5.. TBLE OF CONTENTS. NTOCTON.... FOTH-OE LNWTZ-LEY (L TNSFE FNCTON.... TNSFE

More information

( ) 2. 1) Bode plots/transfer functions. a. Draw magnitude and phase bode plots for the transfer function

( ) 2. 1) Bode plots/transfer functions. a. Draw magnitude and phase bode plots for the transfer function ECSE CP7 olution Spring 5 ) Bode plot/tranfer function a. Draw magnitude and phae bode plot for the tranfer function H( ). ( ) ( E4) In your magnitude plot, indicate correction at the pole and zero. Step

More information

Chapter 2 Sampling and Quantization. In order to investigate sampling and quantization, the difference between analog

Chapter 2 Sampling and Quantization. In order to investigate sampling and quantization, the difference between analog Chapter Sampling and Quantization.1 Analog and Digital Signal In order to invetigate ampling and quantization, the difference between analog and digital ignal mut be undertood. Analog ignal conit of continuou

More information

Chapter 13. Root Locus Introduction

Chapter 13. Root Locus Introduction Chapter 13 Root Locu 13.1 Introduction In the previou chapter we had a glimpe of controller deign iue through ome imple example. Obviouly when we have higher order ytem, uch imple deign technique will

More information

EE/ME/AE324: Dynamical Systems. Chapter 8: Transfer Function Analysis

EE/ME/AE324: Dynamical Systems. Chapter 8: Transfer Function Analysis EE/ME/AE34: Dynamical Sytem Chapter 8: Tranfer Function Analyi The Sytem Tranfer Function Conider the ytem decribed by the nth-order I/O eqn.: ( n) ( n 1) ( m) y + a y + + a y = b u + + bu n 1 0 m 0 Taking

More information

Digital Control System

Digital Control System Digital Control Sytem Summary # he -tranform play an important role in digital control and dicrete ignal proceing. he -tranform i defined a F () f(k) k () A. Example Conider the following equence: f(k)

More information

into a discrete time function. Recall that the table of Laplace/z-transforms is constructed by (i) selecting to get

into a discrete time function. Recall that the table of Laplace/z-transforms is constructed by (i) selecting to get Lecture 25 Introduction to Some Matlab c2d Code in Relation to Sampled Sytem here are many way to convert a continuou time function, { h( t) ; t [0, )} into a dicrete time function { h ( k) ; k {0,,, }}

More information

Given the following circuit with unknown initial capacitor voltage v(0): X(s) Immediately, we know that the transfer function H(s) is

Given the following circuit with unknown initial capacitor voltage v(0): X(s) Immediately, we know that the transfer function H(s) is EE 4G Note: Chapter 6 Intructor: Cheung More about ZSR and ZIR. Finding unknown initial condition: Given the following circuit with unknown initial capacitor voltage v0: F v0/ / Input xt 0Ω Output yt -

More information

March 18, 2014 Academic Year 2013/14

March 18, 2014 Academic Year 2013/14 POLITONG - SHANGHAI BASIC AUTOMATIC CONTROL Exam grade March 8, 4 Academic Year 3/4 NAME (Pinyin/Italian)... STUDENT ID Ue only thee page (including the back) for anwer. Do not ue additional heet. Ue of

More information

online learning Unit Workbook 4 RLC Transients

online learning Unit Workbook 4 RLC Transients online learning Pearon BTC Higher National in lectrical and lectronic ngineering (QCF) Unit 5: lectrical & lectronic Principle Unit Workbook 4 in a erie of 4 for thi unit Learning Outcome: RLC Tranient

More information

Department of Mechanical Engineering Massachusetts Institute of Technology Modeling, Dynamics and Control III Spring 2002

Department of Mechanical Engineering Massachusetts Institute of Technology Modeling, Dynamics and Control III Spring 2002 Department of Mechanical Engineering Maachuett Intitute of Technology 2.010 Modeling, Dynamic and Control III Spring 2002 SOLUTIONS: Problem Set # 10 Problem 1 Etimating tranfer function from Bode Plot.

More information

11.2 Stability. A gain element is an active device. One potential problem with every active circuit is its stability

11.2 Stability. A gain element is an active device. One potential problem with every active circuit is its stability 5/7/2007 11_2 tability 1/2 112 tability eading Aignment: pp 542-548 A gain element i an active device One potential problem with every active circuit i it tability HO: TABIITY Jim tile The Univ of Kana

More information

Digital Control System

Digital Control System Digital Control Sytem - A D D A Micro ADC DAC Proceor Correction Element Proce Clock Meaurement A: Analog D: Digital Continuou Controller and Digital Control Rt - c Plant yt Continuou Controller Digital

More information

CHAPTER 13 FILTERS AND TUNED AMPLIFIERS

CHAPTER 13 FILTERS AND TUNED AMPLIFIERS HAPTE FILTES AND TUNED AMPLIFIES hapter Outline. Filter Traniion, Type and Specification. The Filter Tranfer Function. Butterworth and hebyhev Filter. Firt Order and Second Order Filter Function.5 The

More information

Spring 2014 EE 445S Real-Time Digital Signal Processing Laboratory. Homework #0 Solutions on Review of Signals and Systems Material

Spring 2014 EE 445S Real-Time Digital Signal Processing Laboratory. Homework #0 Solutions on Review of Signals and Systems Material Spring 4 EE 445S Real-Time Digital Signal Proceing Laboratory Prof. Evan Homework # Solution on Review of Signal and Sytem Material Problem.. Continuou-Time Sinuoidal Generation. In practice, we cannot

More information

Reference:W:\Lib\MathCAD\Default\defaults.mcd

Reference:W:\Lib\MathCAD\Default\defaults.mcd 4/9/9 Page of 5 Reference:W:\Lib\MathCAD\Default\default.mcd. Objective a. Motivation. Finite circuit peed, e.g. amplifier - effect on ignal. E.g. how "fat" an amp do we need for audio? For video? For

More information

MODERN CONTROL SYSTEMS

MODERN CONTROL SYSTEMS MODERN CONTROL SYSTEMS Lecture 1 Root Locu Emam Fathy Department of Electrical and Control Engineering email: emfmz@aat.edu http://www.aat.edu/cv.php?dip_unit=346&er=68525 1 Introduction What i root locu?

More information

EE 508 Lecture 16. Filter Transformations. Lowpass to Bandpass Lowpass to Highpass Lowpass to Band-reject

EE 508 Lecture 16. Filter Transformations. Lowpass to Bandpass Lowpass to Highpass Lowpass to Band-reject EE 508 Lecture 6 Filter Tranformation Lowpa to Bandpa Lowpa to Highpa Lowpa to Band-reject Review from Lat Time Theorem: If the perimeter variation and contact reitance are neglected, the tandard deviation

More information

Laplace Transformation

Laplace Transformation Univerity of Technology Electromechanical Department Energy Branch Advance Mathematic Laplace Tranformation nd Cla Lecture 6 Page of 7 Laplace Tranformation Definition Suppoe that f(t) i a piecewie continuou

More information

EE Control Systems LECTURE 14

EE Control Systems LECTURE 14 Updated: Tueday, March 3, 999 EE 434 - Control Sytem LECTURE 4 Copyright FL Lewi 999 All right reerved ROOT LOCUS DESIGN TECHNIQUE Suppoe the cloed-loop tranfer function depend on a deign parameter k We

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. Erickon Department of Electrical, Computer, and Energy Engineering Univerity of Colorado, Boulder Cloed-loop buck converter example: Section 9.5.4 In ECEN 5797, we ued the CCM mall ignal model to

More information

EE C128 / ME C134 Problem Set 1 Solution (Fall 2010) Wenjie Chen and Jansen Sheng, UC Berkeley

EE C128 / ME C134 Problem Set 1 Solution (Fall 2010) Wenjie Chen and Jansen Sheng, UC Berkeley EE C28 / ME C34 Problem Set Solution (Fall 200) Wenjie Chen and Janen Sheng, UC Berkeley. (0 pt) BIBO tability The ytem h(t) = co(t)u(t) i not BIBO table. What i the region of convergence for H()? A bounded

More information

Digital Signal Processing

Digital Signal Processing Digital Signal Proceing IIR Filter Deign Manar Mohaien Office: F8 Email: manar.ubhi@kut.ac.kr School of IT Engineering Review of the Precedent Lecture Propertie of FIR Filter Application of FIR Filter

More information

Main Topics: The Past, H(s): Poles, zeros, s-plane, and stability; Decomposition of the complete response.

Main Topics: The Past, H(s): Poles, zeros, s-plane, and stability; Decomposition of the complete response. EE202 HOMEWORK PROBLEMS SPRING 18 TO THE STUDENT: ALWAYS CHECK THE ERRATA on the web. Quote for your Parent' Partie: 1. Only with nodal analyi i the ret of the emeter a poibility. Ray DeCarlo 2. (The need

More information

Chapter 17 Amplifier Frequency Response

Chapter 17 Amplifier Frequency Response hapter 7 Amplifier Frequency epone Microelectronic ircuit Deign ichard. Jaeger Travi N. Blalock 8/0/0 hap 7- hapter Goal eview tranfer function analyi and dominant-pole approximation of amplifier tranfer

More information

A Simple Approach to Synthesizing Naïve Quantized Control for Reference Tracking

A Simple Approach to Synthesizing Naïve Quantized Control for Reference Tracking A Simple Approach to Syntheizing Naïve Quantized Control for Reference Tracking SHIANG-HUA YU Department of Electrical Engineering National Sun Yat-Sen Univerity 70 Lien-Hai Road, Kaohiung 804 TAIAN Abtract:

More information

Tuning of High-Power Antenna Resonances by Appropriately Reactive Sources

Tuning of High-Power Antenna Resonances by Appropriately Reactive Sources Senor and Simulation Note Note 50 Augut 005 Tuning of High-Power Antenna Reonance by Appropriately Reactive Source Carl E. Baum Univerity of New Mexico Department of Electrical and Computer Engineering

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. Erickon Department of Electrical, Computer, and Energy Engineering Univerity of Colorado, Boulder ZOH: Sampled Data Sytem Example v T Sampler v* H Zero-order hold H v o e = 1 T 1 v *( ) = v( jkω

More information

Solving Differential Equations by the Laplace Transform and by Numerical Methods

Solving Differential Equations by the Laplace Transform and by Numerical Methods 36CH_PHCalter_TechMath_95099 3//007 :8 PM Page Solving Differential Equation by the Laplace Tranform and by Numerical Method OBJECTIVES When you have completed thi chapter, you hould be able to: Find the

More information

EE Control Systems LECTURE 6

EE Control Systems LECTURE 6 Copyright FL Lewi 999 All right reerved EE - Control Sytem LECTURE 6 Updated: Sunday, February, 999 BLOCK DIAGRAM AND MASON'S FORMULA A linear time-invariant (LTI) ytem can be repreented in many way, including:

More information

HOMEWORK ASSIGNMENT #2

HOMEWORK ASSIGNMENT #2 Texa A&M Univerity Electrical Engineering Department ELEN Integrated Active Filter Deign Methodologie Alberto Valde-Garcia TAMU ID# 000 17 September 0, 001 HOMEWORK ASSIGNMENT # PROBLEM 1 Obtain at leat

More information

ME 375 FINAL EXAM SOLUTIONS Friday December 17, 2004

ME 375 FINAL EXAM SOLUTIONS Friday December 17, 2004 ME 375 FINAL EXAM SOLUTIONS Friday December 7, 004 Diviion Adam 0:30 / Yao :30 (circle one) Name Intruction () Thi i a cloed book eamination, but you are allowed three 8.5 crib heet. () You have two hour

More information

Lecture 8. PID control. Industrial process control ( today) PID control. Insights about PID actions

Lecture 8. PID control. Industrial process control ( today) PID control. Insights about PID actions Lecture 8. PID control. The role of P, I, and D action 2. PID tuning Indutrial proce control (92... today) Feedback control i ued to improve the proce performance: tatic performance: for contant reference,

More information

Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web: Ph:

Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web:     Ph: Serial : LS_B_EC_Network Theory_0098 CLASS TEST (GATE) Delhi Noida Bhopal Hyderabad Jaipur Lucknow ndore Pune Bhubanewar Kolkata Patna Web: E-mail: info@madeeay.in Ph: 0-4546 CLASS TEST 08-9 ELECTRONCS

More information

The Laplace Transform , Haynes Miller and Jeremy Orloff

The Laplace Transform , Haynes Miller and Jeremy Orloff The Laplace Tranform 8.3, Hayne Miller and Jeremy Orloff Laplace tranform baic: introduction An operator take a function a input and output another function. A tranform doe the ame thing with the added

More information

EE40 Lec 13. Prof. Nathan Cheung 10/13/2009. Reading: Hambley Chapter Chapter 14.10,14.5

EE40 Lec 13. Prof. Nathan Cheung 10/13/2009. Reading: Hambley Chapter Chapter 14.10,14.5 EE4 Lec 13 Filter and eonance Pro. Nathan Cheung 1/13/9 eading: Hambley Chapter 6.6-6.8 Chapter 14.1,14.5 Slide 1 Common Filter Traner Function v. Freq H ( ) H( ) Low Pa High Pa Frequency H ( ) H ( ) Frequency

More information

Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web: Ph:

Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web:     Ph: Serial : LS_N_A_Network Theory_098 Delhi Noida Bhopal Hyderabad Jaipur Lucknow ndore Pune Bhubanewar Kolkata Patna Web: E-mail: info@madeeay.in Ph: 0-4546 CLASS TEST 08-9 NSTRUMENTATON ENGNEERNG Subject

More information

Lecture #9 Continuous time filter

Lecture #9 Continuous time filter Lecture #9 Continuou time filter Oliver Faut December 5, 2006 Content Review. Motivation......................................... 2 2 Filter pecification 2 2. Low pa..........................................

More information

Example: Amplifier Distortion

Example: Amplifier Distortion 4/6/2011 Example Amplifier Ditortion 1/9 Example: Amplifier Ditortion Recall thi circuit from a previou handout: 15.0 R C =5 K v ( t) = v ( t) o R B =5 K β = 100 _ vi( t ) 58. R E =5 K CUS We found that

More information

The Operational Amplifier

The Operational Amplifier The Operational Amplifier The operational amplifier i a building block of modern electronic intrumentation. Therefore, matery of operational amplifier fundamental i paramount to any practical application

More information

Lecture 17: Analytic Functions and Integrals (See Chapter 14 in Boas)

Lecture 17: Analytic Functions and Integrals (See Chapter 14 in Boas) Lecture 7: Analytic Function and Integral (See Chapter 4 in Boa) Thi i a good point to take a brief detour and expand on our previou dicuion of complex variable and complex function of complex variable.

More information

Follow The Leader Architecture

Follow The Leader Architecture ECE 6(ESS) Follow The Leader Architecture 6 th Order Elliptic andpa Filter A numerical example Objective To deign a 6th order bandpa elliptic filter uing the Follow-the-Leader (FLF) architecture. The pecification

More information

The Measurement of DC Voltage Signal Using the UTI

The Measurement of DC Voltage Signal Using the UTI he Meaurement of DC Voltage Signal Uing the. INRODUCION can er an interface for many paive ening element, uch a, capacitor, reitor, reitive bridge and reitive potentiometer. By uing ome eternal component,

More information

Correction for Simple System Example and Notes on Laplace Transforms / Deviation Variables ECHE 550 Fall 2002

Correction for Simple System Example and Notes on Laplace Transforms / Deviation Variables ECHE 550 Fall 2002 Correction for Simple Sytem Example and Note on Laplace Tranform / Deviation Variable ECHE 55 Fall 22 Conider a tank draining from an initial height of h o at time t =. With no flow into the tank (F in

More information

HIGHER-ORDER FILTERS. Cascade of Biquad Filters. Follow the Leader Feedback Filters (FLF) ELEN 622 (ESS)

HIGHER-ORDER FILTERS. Cascade of Biquad Filters. Follow the Leader Feedback Filters (FLF) ELEN 622 (ESS) HIGHER-ORDER FILTERS Cacade of Biquad Filter Follow the Leader Feedbac Filter (FLF) ELEN 6 (ESS) Than for ome of the material to David Hernandez Garduño CASCADE FILTER DESIGN N H ( ) Π H ( ) H ( ) H (

More information

Automatic Control Systems. Part III: Root Locus Technique

Automatic Control Systems. Part III: Root Locus Technique www.pdhcenter.com PDH Coure E40 www.pdhonline.org Automatic Control Sytem Part III: Root Locu Technique By Shih-Min Hu, Ph.D., P.E. Page of 30 www.pdhcenter.com PDH Coure E40 www.pdhonline.org VI. Root

More information

NOTE: The items d) and e) of Question 4 gave you bonus marks.

NOTE: The items d) and e) of Question 4 gave you bonus marks. MAE 40 Linear ircuit Summer 2007 Final Solution NOTE: The item d) and e) of Quetion 4 gave you bonu mark. Quetion [Equivalent irciut] [4 mark] Find the equivalent impedance between terminal A and B in

More information

ECE-202 Exam 1 January 31, Name: (Please print clearly.) CIRCLE YOUR DIVISION DeCarlo DeCarlo 7:30 MWF 1:30 TTH

ECE-202 Exam 1 January 31, Name: (Please print clearly.) CIRCLE YOUR DIVISION DeCarlo DeCarlo 7:30 MWF 1:30 TTH ECE-0 Exam January 3, 08 Name: (Pleae print clearly.) CIRCLE YOUR DIVISION 0 0 DeCarlo DeCarlo 7:30 MWF :30 TTH INSTRUCTIONS There are multiple choice worth 5 point each and workout problem worth 40 point.

More information

FUNDAMENTALS OF POWER SYSTEMS

FUNDAMENTALS OF POWER SYSTEMS 1 FUNDAMENTALS OF POWER SYSTEMS 1 Chapter FUNDAMENTALS OF POWER SYSTEMS INTRODUCTION The three baic element of electrical engineering are reitor, inductor and capacitor. The reitor conume ohmic or diipative

More information

Designing Circuits Synthesis - Lego

Designing Circuits Synthesis - Lego Deigning Circuit Synthei Lego Port a pair of terminal to a cct Oneport cct; meaure I and at ame port I Drivingpoint impedance input impedance equiv impedance Twoport Tranfer function; meaure input at one

More information

ECEN620: Network Theory Broadband Circuit Design Fall 2018

ECEN620: Network Theory Broadband Circuit Design Fall 2018 ECEN60: Network Theory Broadband Circuit Deign Fall 08 Lecture 6: Loop Filter Circuit Sam Palermo Analog & Mixed-Signal Center Texa A&M Univerity Announcement HW i due Oct Require tranitor-level deign

More information

DIFFERENTIAL EQUATIONS

DIFFERENTIAL EQUATIONS DIFFERENTIAL EQUATIONS Laplace Tranform Paul Dawkin Table of Content Preface... Laplace Tranform... Introduction... The Definition... 5 Laplace Tranform... 9 Invere Laplace Tranform... Step Function...4

More information

( ) ( ) ω = X x t e dt

( ) ( ) ω = X x t e dt The Laplace Tranform The Laplace Tranform generalize the Fourier Traform for the entire complex plane For an ignal x(t) the pectrum, or it Fourier tranform i (if it exit): t X x t e dt ω = For the ame

More information

Lecture 4. Chapter 11 Nise. Controller Design via Frequency Response. G. Hovland 2004

Lecture 4. Chapter 11 Nise. Controller Design via Frequency Response. G. Hovland 2004 METR4200 Advanced Control Lecture 4 Chapter Nie Controller Deign via Frequency Repone G. Hovland 2004 Deign Goal Tranient repone via imple gain adjutment Cacade compenator to improve teady-tate error Cacade

More information

EE 508 Lecture 16. Filter Transformations. Lowpass to Bandpass Lowpass to Highpass Lowpass to Band-reject

EE 508 Lecture 16. Filter Transformations. Lowpass to Bandpass Lowpass to Highpass Lowpass to Band-reject EE 508 Lecture 6 Filter Tranformation Lowpa to Bandpa Lowpa to Highpa Lowpa to Band-reject Review from Lat Time Theorem: If the perimeter variation and contact reitance are neglected, the tandard deviation

More information

Control Systems Analysis and Design by the Root-Locus Method

Control Systems Analysis and Design by the Root-Locus Method 6 Control Sytem Analyi and Deign by the Root-Locu Method 6 1 INTRODUCTION The baic characteritic of the tranient repone of a cloed-loop ytem i cloely related to the location of the cloed-loop pole. If

More information

Homework Assignment No. 3 - Solutions

Homework Assignment No. 3 - Solutions ECE 6440 Summer 2003 Page 1 Homework Aignment o. 3 Problem 1 (10 point) Aume an LPLL ha F() 1 and the PLL parameter are 0.8V/radian, K o 100 MHz/V, and the ocillation frequency, f oc 500MHz. Sketch the

More information

ECE 3510 Root Locus Design Examples. PI To eliminate steady-state error (for constant inputs) & perfect rejection of constant disturbances

ECE 3510 Root Locus Design Examples. PI To eliminate steady-state error (for constant inputs) & perfect rejection of constant disturbances ECE 350 Root Locu Deign Example Recall the imple crude ervo from lab G( ) 0 6.64 53.78 σ = = 3 23.473 PI To eliminate teady-tate error (for contant input) & perfect reection of contant diturbance Note:

More information

7.2 INVERSE TRANSFORMS AND TRANSFORMS OF DERIVATIVES 281

7.2 INVERSE TRANSFORMS AND TRANSFORMS OF DERIVATIVES 281 72 INVERSE TRANSFORMS AND TRANSFORMS OF DERIVATIVES 28 and i 2 Show how Euler formula (page 33) can then be ued to deduce the reult a ( a) 2 b 2 {e at co bt} {e at in bt} b ( a) 2 b 2 5 Under what condition

More information

G(s) = 1 s by hand for! = 1, 2, 5, 10, 20, 50, and 100 rad/sec.

G(s) = 1 s by hand for! = 1, 2, 5, 10, 20, 50, and 100 rad/sec. 6003 where A = jg(j!)j ; = tan Im [G(j!)] Re [G(j!)] = \G(j!) 2. (a) Calculate the magnitude and phae of G() = + 0 by hand for! =, 2, 5, 0, 20, 50, and 00 rad/ec. (b) ketch the aymptote for G() according

More information

Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web: Ph:

Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web:     Ph: Serial :. PT_EE_A+C_Control Sytem_798 Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubanewar olkata Patna Web: E-mail: info@madeeay.in Ph: -4546 CLASS TEST 8-9 ELECTRICAL ENGINEERING Subject

More information

Advanced D-Partitioning Analysis and its Comparison with the Kharitonov s Theorem Assessment

Advanced D-Partitioning Analysis and its Comparison with the Kharitonov s Theorem Assessment Journal of Multidiciplinary Engineering Science and Technology (JMEST) ISSN: 59- Vol. Iue, January - 5 Advanced D-Partitioning Analyi and it Comparion with the haritonov Theorem Aement amen M. Yanev Profeor,

More information

Solutions. Digital Control Systems ( ) 120 minutes examination time + 15 minutes reading time at the beginning of the exam

Solutions. Digital Control Systems ( ) 120 minutes examination time + 15 minutes reading time at the beginning of the exam BSc - Sample Examination Digital Control Sytem (5-588-) Prof. L. Guzzella Solution Exam Duration: Number of Quetion: Rating: Permitted aid: minute examination time + 5 minute reading time at the beginning

More information

Chapter 9: Controller design. Controller design. Controller design

Chapter 9: Controller design. Controller design. Controller design Chapter 9. Controller Deign 9.. Introduction 9.2. Eect o negative eedback on the network traner unction 9.2.. Feedback reduce the traner unction rom diturbance to the output 9.2.2. Feedback caue the traner

More information

Part A: Signal Processing. Professor E. Ambikairajah UNSW, Australia

Part A: Signal Processing. Professor E. Ambikairajah UNSW, Australia Part A: Signal Proceing Chapter 5: Digital Filter Deign 5. Chooing between FIR and IIR filter 5. Deign Technique 5.3 IIR filter Deign 5.3. Impule Invariant Method 5.3. Bilinear Tranformation 5.3.3 Digital

More information

Bogoliubov Transformation in Classical Mechanics

Bogoliubov Transformation in Classical Mechanics Bogoliubov Tranformation in Claical Mechanic Canonical Tranformation Suppoe we have a et of complex canonical variable, {a j }, and would like to conider another et of variable, {b }, b b ({a j }). How

More information

376 CHAPTER 6. THE FREQUENCY-RESPONSE DESIGN METHOD. D(s) = we get the compensated system with :

376 CHAPTER 6. THE FREQUENCY-RESPONSE DESIGN METHOD. D(s) = we get the compensated system with : 376 CHAPTER 6. THE FREQUENCY-RESPONSE DESIGN METHOD Therefore by applying the lead compenator with ome gain adjutment : D() =.12 4.5 +1 9 +1 we get the compenated ytem with : PM =65, ω c = 22 rad/ec, o

More information

Thermal Resistance Measurements and Thermal Transient Analysis of Power Chip Slug-Up and Slug-Down Mounted on HDI Substrate

Thermal Resistance Measurements and Thermal Transient Analysis of Power Chip Slug-Up and Slug-Down Mounted on HDI Substrate Intl Journal of Microcircuit and Electronic Packaging Thermal Reitance Meaurement and Thermal Tranient Analyi of Power Chip Slug-Up and Slug-Down Mounted on HDI Subtrate Claudio Sartori Magneti Marelli

More information

RaneNote BESSEL FILTER CROSSOVER

RaneNote BESSEL FILTER CROSSOVER RaneNote BESSEL FILTER CROSSOVER A Beel Filter Croover, and It Relation to Other Croover Beel Function Phae Shift Group Delay Beel, 3dB Down Introduction One of the way that a croover may be contructed

More information

R L R L L sl C L 1 sc

R L R L L sl C L 1 sc 2260 N. Cotter PRACTICE FINAL EXAM SOLUTION: Prob 3 3. (50 point) u(t) V i(t) L - R v(t) C - The initial energy tored in the circuit i zero. 500 Ω L 200 mh a. Chooe value of R and C to accomplih the following:

More information

( 1) EE 313 Linear Signals & Systems (Fall 2018) Solution Set for Homework #10 on Laplace Transforms

( 1) EE 313 Linear Signals & Systems (Fall 2018) Solution Set for Homework #10 on Laplace Transforms EE 33 Linear Signal & Sytem (Fall 08) Solution Set for Homework #0 on Laplace Tranform By: Mr. Houhang Salimian & Prof. Brian L. Evan Problem. a) xt () = ut () ut ( ) From lecture Lut { ()} = and { } t

More information

DIFFERENTIAL EQUATIONS Laplace Transforms. Paul Dawkins

DIFFERENTIAL EQUATIONS Laplace Transforms. Paul Dawkins DIFFERENTIAL EQUATIONS Laplace Tranform Paul Dawkin Table of Content Preface... Laplace Tranform... Introduction... The Definition... 5 Laplace Tranform... 9 Invere Laplace Tranform... Step Function...

More information

1 Routh Array: 15 points

1 Routh Array: 15 points EE C28 / ME34 Problem Set 3 Solution Fall 2 Routh Array: 5 point Conider the ytem below, with D() k(+), w(t), G() +2, and H y() 2 ++2 2(+). Find the cloed loop tranfer function Y () R(), and range of k

More information

BASIC INDUCTION MOTOR CONCEPTS

BASIC INDUCTION MOTOR CONCEPTS INDUCTION MOTOS An induction motor ha the ame phyical tator a a ynchronou machine, with a different rotor contruction. There are two different type of induction motor rotor which can be placed inide the

More information

Control Systems Engineering ( Chapter 7. Steady-State Errors ) Prof. Kwang-Chun Ho Tel: Fax:

Control Systems Engineering ( Chapter 7. Steady-State Errors ) Prof. Kwang-Chun Ho Tel: Fax: Control Sytem Engineering ( Chapter 7. Steady-State Error Prof. Kwang-Chun Ho kwangho@hanung.ac.kr Tel: 0-760-453 Fax:0-760-4435 Introduction In thi leon, you will learn the following : How to find the

More information

EE105 - Fall 2005 Microelectronic Devices and Circuits

EE105 - Fall 2005 Microelectronic Devices and Circuits EE5 - Fall 5 Microelectronic Device and ircuit Lecture 9 Second-Order ircuit Amplifier Frequency Repone Announcement Homework 8 due tomorrow noon Lab 7 next week Reading: hapter.,.3. Lecture Material Lat

More information

Root Locus Contents. Root locus, sketching algorithm. Root locus, examples. Root locus, proofs. Root locus, control examples

Root Locus Contents. Root locus, sketching algorithm. Root locus, examples. Root locus, proofs. Root locus, control examples Root Locu Content Root locu, ketching algorithm Root locu, example Root locu, proof Root locu, control example Root locu, influence of zero and pole Root locu, lead lag controller deign 9 Spring ME45 -

More information

Feedback Control Systems (FCS)

Feedback Control Systems (FCS) Feedback Control Sytem (FCS) Lecture19-20 Routh-Herwitz Stability Criterion Dr. Imtiaz Huain email: imtiaz.huain@faculty.muet.edu.pk URL :http://imtiazhuainkalwar.weebly.com/ Stability of Higher Order

More information

CONTROL SYSTEMS. Chapter 2 : Block Diagram & Signal Flow Graphs GATE Objective & Numerical Type Questions

CONTROL SYSTEMS. Chapter 2 : Block Diagram & Signal Flow Graphs GATE Objective & Numerical Type Questions ONTOL SYSTEMS hapter : Bloc Diagram & Signal Flow Graph GATE Objective & Numerical Type Quetion Quetion 6 [Practice Boo] [GATE E 994 IIT-Kharagpur : 5 Mar] educe the ignal flow graph hown in figure below,

More information

Lecture 15 - Current. A Puzzle... Advanced Section: Image Charge for Spheres. Image Charge for a Grounded Spherical Shell

Lecture 15 - Current. A Puzzle... Advanced Section: Image Charge for Spheres. Image Charge for a Grounded Spherical Shell Lecture 15 - Current Puzzle... Suppoe an infinite grounded conducting plane lie at z = 0. charge q i located at a height h above the conducting plane. Show in three different way that the potential below

More information

EECS2200 Electric Circuits. RLC Circuit Natural and Step Responses

EECS2200 Electric Circuits. RLC Circuit Natural and Step Responses 5--4 EECS Electric Circuit Chapter 6 R Circuit Natural and Step Repone Objective Determine the repone form of the circuit Natural repone parallel R circuit Natural repone erie R circuit Step repone of

More information

S_LOOP: SINGLE-LOOP FEEDBACK CONTROL SYSTEM ANALYSIS

S_LOOP: SINGLE-LOOP FEEDBACK CONTROL SYSTEM ANALYSIS S_LOOP: SINGLE-LOOP FEEDBACK CONTROL SYSTEM ANALYSIS by Michelle Gretzinger, Daniel Zyngier and Thoma Marlin INTRODUCTION One of the challenge to the engineer learning proce control i relating theoretical

More information

SAMPLING. Sampling is the acquisition of a continuous signal at discrete time intervals and is a fundamental concept in real-time signal processing.

SAMPLING. Sampling is the acquisition of a continuous signal at discrete time intervals and is a fundamental concept in real-time signal processing. SAMPLING Sampling i the acquiition of a continuou ignal at dicrete time interval and i a fundamental concept in real-time ignal proceing. he actual ampling operation can alo be defined by the figure belo

More information

ME2142/ME2142E Feedback Control Systems

ME2142/ME2142E Feedback Control Systems Root Locu Analyi Root Locu Analyi Conider the cloed-loop ytem R + E - G C B H The tranient repone, and tability, of the cloed-loop ytem i determined by the value of the root of the characteritic equation

More information

EE C245 ME C218 Introduction to MEMS Design

EE C245 ME C218 Introduction to MEMS Design EE C45 ME C8 Introduction to MEMS Deign Fall 007 Prof. Clark T.-C. Nguyen Dept. of Electrical Engineering & Computer Science Univerity of California at Berkeley Berkeley, CA 9470 Lecture 5: Output t Sening

More information

Homework 12 Solution - AME30315, Spring 2013

Homework 12 Solution - AME30315, Spring 2013 Homework 2 Solution - AME335, Spring 23 Problem :[2 pt] The Aerotech AGS 5 i a linear motor driven XY poitioning ytem (ee attached product heet). A friend of mine, through careful experimentation, identified

More information

Chapter 4. The Laplace Transform Method

Chapter 4. The Laplace Transform Method Chapter 4. The Laplace Tranform Method The Laplace Tranform i a tranformation, meaning that it change a function into a new function. Actually, it i a linear tranformation, becaue it convert a linear combination

More information