# EE221 Circuits II. Chapter 14 Frequency Response

Size: px
Start display at page:

## Transcription

1 EE22 Circuits II Chapter 4 Frequency Response

2 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 filters 2

3 4. Introduction What is Frequency Response of a Circuit? It is the variation in a circuit s behavior with change in signal frequency and may also be considered as the variation of the gain and phase with frequency. 3

4 4.2 Transfer Function The transfer function H(ω) of a circuit is the frequencydependent ratio of a phasor output Y(ω) (voltage or current ) to a phasor input X(ω) (voltage or current). H( ω) Y( ω) = = H( ω) X( ω) φ 4

5 4.2 Transfer Function Four possible transfer functions: H( ω ) = Voltage gain = V o( ω) V ( ω) i H( ω ) = Transfer Impedance = V o( ω) I ( ω) i H( ω) Y( ω) = = H( ω) φ X( ω) H( ω ) = Current gain = Io( ω) I ( ω) i H( ω ) = Transfer Admittance = Io( ω) V ( ω) i 5

6 4.2 Transfer Function Example For the RC circuit shown below, obtain the transfer function Vo/Vs and its frequency response. Let v s = V m cosωt. 6

7 4.2 Transfer Function Solution: The transfer function is H( ω) = V V o s jωc = = R + / jω C + jω RC The magnitude is H( ω) = 2, + ( ω / ω o ) The phase is ω φ = tan ω o ω o =/RC 7 Low Pass Filter

8 4.2 Transfer Function Example 2 Obtain the transfer function Vo/Vs of the RL circuit shown below, assuming v s = V m cosωt. Sketch its frequency response. 8

9 4.2 Transfer Function Solution: The transfer function is H( ω) = V V o s jω L = = R + jω L R + jω L, H( ω ) = The magnitude is ω 2 + ( o ) ω High Pass Filter The phase is φ = 90 tan ω o = R/L ω ω o 9

10 4.4 Bode Plots Bode Plots are semilog plots of the magnitude (in db) and phase (in deg.) of the transfer function versus frequency. H = He jφ H db = 20 log 0 H 0

11 Bode Plot of Gain K

12 Bode Plot of a zero (jω) 2

13 Bode plot of a zero 3

14 Bode Plot of a quadratic pole 4

15 Summary 5

16 Summary

17 Example 7

18 Example 2 8

19 Example 3

20 4.4 Series Resonance Resonance is a condition in an RLC circuit in which the capacitive and inductive reactance are equal in magnitude, thereby resulting in purely resistive impedance. Resonance frequency: Z = R + j ( ω L ω C ) ωo = rad/s or LC fo = Hz 2π LC 20

21 4.4 Series Resonance The features of series resonance: Z= R+ j( ωl ) ωc The impedance is purely resistive, Z = R; The supply voltage Vs and the current I are in phase, so cos θ = ; The magnitude of the transfer function H(ω) = Z(ω) is minimum; The inductor voltage and capacitor voltage can be much more than the source voltage. 2

22 4.4 Series Resonance The frequency response of the resonance circuit current is I = I = R 2 V m + ( ω L / ω C) 2 Z = R + j ( ω L ) ω C The average power absorbed by the RLC circuit is P( ω) = The highest power dissipated occurs at resonance: P( 2 I ω o 2 ) R = 2 V R 2 m 22

23 4 4 Series Resonance Half-power frequencies ω and ω 2 are frequencies at which the dissipated power is half the maximum value: P( ω ) = P( ω ) = 2 (V / 2) R 2 m 2 = 2 Vm 4R The half-power frequencies are obtained by setting Z equal to 2 R. R 2 + ω = + 2L R ( ) 2L LC ω R 2 2 = + ω o = ω ω2 + 2L R ( ) 2L LC Bandwidth B B = ω ω 2 23

24 4.4 Series Resonance Quality factor, Q = ω o L R = ω CR o The relationship between the B, Q and ωo: The quality factor is the ratio Rof B ω= o the resonant frequency to its 2 o ω QL bandwidth. If the bandwidth is narrow, the quality factor of the resonant circuit is high. If the band of frequencies is wide, the quality factor is low. 24

25 Example: 25

26 4.5 Parallel Resonance It occurs when imaginary part of Y is zero Y = R + j ( ω C ) ω L Resonance frequency: ω o = rad/s or fo = LC 2π LC Hz 26

27 4.5 Series Parallel Resonance Summary of series and parallel resonance circuits: characteristic Series circuit Parallel circuit ω o LC LC Q B ωol R or ω o Q ω RC o R ω L o or ω RC ω o Q o ω, ω 2 Q 0, ω, ω 2 ω o + ( ) ± 2Q B ω o ± 2 ω 2Q 2 o 2 ωo ω o + ( ) ± 2Q 2Q B ω o ± 2 27

28 4.5 Resonance Example 4 Calculate the resonant frequency of the circuit in the figure shown below. Answer: ω = 9 = rad/s 28

29 4.6 Passive Filters A filter is a circuit that is designed to pass signals with desired frequencies and reject or attenuate others. Passive filter consists of only passive element R, L and C. There are four types of filters. Low Pass High Pass Band Pass Band Stop 29

30 Low-pass and high-pass filters

31 Band-pass and band-reject filters

32 Magnitude and Frequency Scaling Example: 4 th order low-pass filter Corner Frequency: rad/sec Resistance: Ω Corner Frequency: 00π krad/sec Resistance: 0 kω 32

33 Low Pass Filter (Active) 33

34 High Pass Filter (Active) 34

35 Band Pass Filter (Active) 35

36 Band Reject Filter (Active) 36

### 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

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.

### 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

### MODULE-4 RESONANCE CIRCUITS

Introduction: MODULE-4 RESONANCE CIRCUITS Resonance is a condition in an RLC circuit in which the capacitive and inductive Reactance s are equal in magnitude, there by resulting in purely resistive impedance.

### 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

### Single Phase Parallel AC Circuits

Single Phase Parallel AC Circuits 1 Single Phase Parallel A.C. Circuits (Much of this material has come from Electrical & Electronic Principles & Technology by John Bird) n parallel a.c. circuits similar

### Chapter 33. Alternating Current Circuits

Chapter 33 Alternating Current Circuits 1 Capacitor Resistor + Q = C V = I R R I + + Inductance d I Vab = L dt AC power source The AC power source provides an alternative voltage, Notation - Lower case

### 1 Phasors and Alternating Currents

Physics 4 Chapter : Alternating Current 0/5 Phasors and Alternating Currents alternating current: current that varies sinusoidally with time ac source: any device that supplies a sinusoidally varying potential

### 6.1 Introduction

6. Introduction A.C Circuits made up of resistors, inductors and capacitors are said to be resonant circuits when the current drawn from the supply is in phase with the impressed sinusoidal voltage. Then.

### 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

### REACTANCE. By: Enzo Paterno Date: 03/2013

REACTANCE REACTANCE By: Enzo Paterno Date: 03/2013 5/2007 Enzo Paterno 1 RESISTANCE - R i R (t R A resistor for all practical purposes is unaffected by the frequency of the applied sinusoidal voltage or

### Handout 11: AC circuit. AC generator

Handout : AC circuit AC generator Figure compares the voltage across the directcurrent (DC) generator and that across the alternatingcurrent (AC) generator For DC generator, the voltage is constant For

Sinusoidal Steady-State Analysis Mauro Forti October 27, 2018 Constitutive Relations in the Frequency Domain Consider a network with independent voltage and current sources at the same angular frequency

### 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

### 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

### AC Circuits Homework Set

Problem 1. In an oscillating LC circuit in which C=4.0 μf, the maximum potential difference across the capacitor during the oscillations is 1.50 V and the maximum current through the inductor is 50.0 ma.

### AC Circuit Analysis and Measurement Lab Assignment 8

Electric Circuit Lab Assignments elcirc_lab87.fm - 1 AC Circuit Analysis and Measurement Lab Assignment 8 Introduction When analyzing an electric circuit that contains reactive components, inductors and

### Electrical Circuits Lab Series RC Circuit Phasor Diagram

Electrical Circuits Lab. 0903219 Series RC Circuit Phasor Diagram - Simple steps to draw phasor diagram of a series RC circuit without memorizing: * Start with the quantity (voltage or current) that is

### 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

### 2 Signal Frequency and Impedances First Order Filter Circuits Resonant and Second Order Filter Circuits... 13

Lecture Notes: 3454 Physics and Electronics Lecture ( nd Half), Year: 7 Physics Department, Faculty of Science, Chulalongkorn University //7 Contents Power in Ac Circuits Signal Frequency and Impedances

### Announcements: Today: more AC circuits

Announcements: Today: more AC circuits I 0 I rms Current through a light bulb I 0 I rms I t = I 0 cos ωt I 0 Current through a LED I t = I 0 cos ωt Θ(cos ωt ) Theta function (is zero for a negative argument)

### Consider a simple RC circuit. We might like to know how much power is being supplied by the source. We probably need to find the current.

AC power Consider a simple RC circuit We might like to know how much power is being supplied by the source We probably need to find the current R 10! R 10! is VS Vmcosωt Vm 10 V f 60 Hz V m 10 V C 150

### 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

### Frequency Response part 2 (I&N Chap 12)

Frequency Response part 2 (I&N Chap 12) Introduction & TFs Decibel Scale & Bode Plots Resonance Scaling Filter Networks Applications/Design Frequency response; based on slides by J. Yan Slide 3.1 Example

### 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

### Poles, Zeros, and Frequency Response

Complex Poles Poles, Zeros, and Frequency esponse With only resistors and capacitors, you're stuck with real poles. If you want complex poles, you need either an op-amp or an inductor as well. Complex

### SCHOOL OF MATHEMATICS MATHEMATICS FOR PART I ENGINEERING. Self-paced Course

SCHOOL OF MATHEMATICS MATHEMATICS FOR PART I ENGINEERING Self-paced Course MODULE 26 APPLICATIONS TO ELECTRICAL CIRCUITS Module Topics 1. Complex numbers and alternating currents 2. Complex impedance 3.

### 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

### RLC Series Circuit. We can define effective resistances for capacitors and inductors: 1 = Capacitive reactance:

RLC Series Circuit In this exercise you will investigate the effects of changing inductance, capacitance, resistance, and frequency on an RLC series AC circuit. We can define effective resistances for

### Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur

Module 4 Single-phase circuits ersion EE T, Kharagpur esson 6 Solution of urrent in Parallel and Seriesparallel ircuits ersion EE T, Kharagpur n the last lesson, the following points were described:. How

### 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

### 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

### ECE 2100 Circuit Analysis

ECE 00 Circuit Analysis Lessn 6 Chapter 4 Sec 4., 4.5, 4.7 Series LC Circuit C Lw Pass Filter Daniel M. Litynski, Ph.D. http://hmepages.wmich.edu/~dlitynsk/ ECE 00 Circuit Analysis Lessn 5 Chapter 9 &

### Alternating Current Circuits

Alternating Current Circuits AC Circuit An AC circuit consists of a combination of circuit elements and an AC generator or source. The output of an AC generator is sinusoidal and varies with time according

### EE 40: Introduction to Microelectronic Circuits Spring 2008: Midterm 2

EE 4: Introduction to Microelectronic Circuits Spring 8: Midterm Venkat Anantharam 3/9/8 Total Time Allotted : min Total Points:. This is a closed book exam. However, you are allowed to bring two pages

### ELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT

Chapter 31: ELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT 1 A charged capacitor and an inductor are connected in series At time t = 0 the current is zero, but the capacitor is charged If T is the

### Oscillations and Electromagnetic Waves. March 30, 2014 Chapter 31 1

Oscillations and Electromagnetic Waves March 30, 2014 Chapter 31 1 Three Polarizers! Consider the case of unpolarized light with intensity I 0 incident on three polarizers! The first polarizer has a polarizing

### mywbut.com Lesson 16 Solution of Current in AC Parallel and Seriesparallel

esson 6 Solution of urrent in Parallel and Seriesparallel ircuits n the last lesson, the following points were described:. How to compute the total impedance/admittance in series/parallel circuits?. How

### 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

### Alternating Current Circuits. Home Work Solutions

Chapter 21 Alternating Current Circuits. Home Work s 21.1 Problem 21.11 What is the time constant of the circuit in Figure (21.19). 10 Ω 10 Ω 5.0 Ω 2.0µF 2.0µF 2.0µF 3.0µF Figure 21.19: Given: The circuit

### Electric Circuit Theory

Electric Circuit Theory Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 Chapter 11 Sinusoidal Steady-State Analysis Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 Contents and Objectives 3 Chapter Contents 11.1

### Lecture 9 Time Domain vs. Frequency Domain

. Topics covered Lecture 9 Time Domain vs. Frequency Domain (a) AC power in the time domain (b) AC power in the frequency domain (c) Reactive power (d) Maximum power transfer in AC circuits (e) Frequency

### Inductive & Capacitive Circuits. Subhasish Chandra Assistant Professor Department of Physics Institute of Forensic Science, Nagpur

Inductive & Capacitive Circuits Subhasish Chandra Assistant Professor Department of Physics Institute of Forensic Science, Nagpur LR Circuit LR Circuit (Charging) Let us consider a circuit having an inductance

### ELEC 2501 AB. Come to the PASS workshop with your mock exam complete. During the workshop you can work with other students to review your work.

It is most beneficial to you to write this mock midterm UNDER EXAM CONDITIONS. This means: Complete the midterm in 3 hour(s). Work on your own. Keep your notes and textbook closed. Attempt every question.

### CIRCUIT ANALYSIS II. (AC Circuits)

Will Moore MT & MT CIRCUIT ANALYSIS II (AC Circuits) Syllabus Complex impedance, power factor, frequency response of AC networks including Bode diagrams, second-order and resonant circuits, damping and

### Sinusoids and Phasors

CHAPTER 9 Sinusoids and Phasors We now begins the analysis of circuits in which the voltage or current sources are time-varying. In this chapter, we are particularly interested in sinusoidally time-varying

### Electric Circuits I Final Examination

The University of Toledo s8fs_elci7.fm - EECS:300 Electric Circuits I Electric Circuits I Final Examination Problems Points.. 3. Total 34 Was the exam fair? yes no The University of Toledo s8fs_elci7.fm

### EE292: Fundamentals of ECE

EE292: Fundamentals of ECE Fall 2012 TTh 10:00-11:15 SEB 1242 Lecture 18 121025 http://www.ee.unlv.edu/~b1morris/ee292/ 2 Outline Review RMS Values Complex Numbers Phasors Complex Impedance Circuit Analysis

### Driven RLC Circuits Challenge Problem Solutions

Driven LC Circuits Challenge Problem Solutions Problem : Using the same circuit as in problem 6, only this time leaving the function generator on and driving below resonance, which in the following pairs

Sinusoidal Steady State Analysis 9 Assessment Problems AP 9. [a] V = 70/ 40 V [b] 0 sin(000t +20 ) = 0 cos(000t 70 ).. I = 0/ 70 A [c] I =5/36.87 + 0/ 53.3 =4+j3+6 j8 =0 j5 =.8/ 26.57 A [d] sin(20,000πt

### Learnabout Electronics - AC Theory

Learnabout Electronics - AC Theory Facts & Formulae for AC Theory www.learnabout-electronics.org Contents AC Wave Values... 2 Capacitance... 2 Charge on a Capacitor... 2 Total Capacitance... 2 Inductance...

### Total No. of Questions :09] [Total No. of Pages : 03

EE 4 (RR) Total No. of Questions :09] [Total No. of Pages : 03 II/IV B.Tech. DEGREE EXAMINATIONS, APRIL/MAY- 016 Second Semester ELECTRICAL & ELECTRONICS NETWORK ANALYSIS Time: Three Hours Answer Question

### Sinusoidal Steady State Analysis (AC Analysis) Part I

Sinusoidal Steady State Analysis (AC Analysis) Part I Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/

### 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

### Impedance/Reactance Problems

Impedance/Reactance Problems. Consider the circuit below. An AC sinusoidal voltage of amplitude V and frequency ω is applied to the three capacitors, each of the same capacitance C. What is the total reactance

### Impedance and Loudspeaker Parameter Measurement

ECEN 2260 Circuits/Electronics 2 Spring 2007 2-26-07 P. Mathys Impedance and Loudspeaker Parameter Measurement 1 Impedance Measurement Many elements from which electrical circuits are built are two-terminal

### AC analysis - many examples

AC analysis - many examples The basic method for AC analysis:. epresent the AC sources as complex numbers: ( ). Convert resistors, capacitors, and inductors into their respective impedances: resistor Z

### 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,

### Note 11: Alternating Current (AC) Circuits

Note 11: Alternating Current (AC) Circuits V R No phase difference between the voltage difference and the current and max For alternating voltage Vmax sin t, the resistor current is ir sin t. the instantaneous

### 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

### Physics 115. AC circuits Reactances Phase relationships Evaluation. General Physics II. Session 35. R. J. Wilkes

Session 35 Physics 115 General Physics II AC circuits Reactances Phase relationships Evaluation R. J. Wilkes Email: phy115a@u.washington.edu 06/05/14 1 Lecture Schedule Today 2 Announcements Please pick

### ECE 201 Fall 2009 Final Exam

ECE 01 Fall 009 Final Exam December 16, 009 Division 0101: Tan (11:30am) Division 001: Clark (7:30 am) Division 0301: Elliott (1:30 pm) Instructions 1. DO NOT START UNTIL TOLD TO DO SO.. Write your Name,

Sinusoidal Steady-State Analysis Almost all electrical systems, whether signal or power, operate with alternating currents and voltages. We have seen that when any circuit is disturbed (switched on or

### Physics 115. AC: RL vs RC circuits Phase relationships RLC circuits. General Physics II. Session 33

Session 33 Physics 115 General Physics II AC: RL vs RC circuits Phase relationships RLC circuits R. J. Wilkes Email: phy115a@u.washington.edu Home page: http://courses.washington.edu/phy115a/ 6/2/14 1

### CHAPTER 45 COMPLEX NUMBERS

CHAPTER 45 COMPLEX NUMBERS EXERCISE 87 Page 50. Solve the quadratic equation: x + 5 0 Since x + 5 0 then x 5 x 5 ( )(5) 5 j 5 from which, x ± j5. Solve the quadratic equation: x x + 0 Since x x + 0 then

### Plumber s LCR Analogy

Plumber s LCR Analogy Valve V 1 V 2 P 1 P 2 The plumber s analogy of an LC circuit is a rubber diaphragm that has been stretched by pressure on the top (P 1 ) side. When the valve starts the flow, the

### Prof. Anyes Taffard. Physics 120/220. Voltage Divider Capacitor RC circuits

Prof. Anyes Taffard Physics 120/220 Voltage Divider Capacitor RC circuits Voltage Divider The figure is called a voltage divider. It s one of the most useful and important circuit elements we will encounter.

### EE313 Fall 2013 Exam #1 (100 pts) Thursday, September 26, 2013 Name. 1) [6 pts] Convert the following time-domain circuit to the RMS Phasor Domain.

Name If you have any questions ask them. Remember to include all units on your answers (V, A, etc). Clearly indicate your answers. All angles must be in the range 0 to +180 or 0 to 180 degrees. 1) [6 pts]

### 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

### EE 3120 Electric Energy Systems Study Guide for Prerequisite Test Wednesday, Jan 18, pm, Room TBA

EE 3120 Electric Energy Systems Study Guide for Prerequisite Test Wednesday, Jan 18, 2006 6-7 pm, Room TBA First retrieve your EE2110 final and other course papers and notes! The test will be closed book

### SINUSOIDAL STEADY STATE CIRCUIT ANALYSIS

SINUSOIDAL STEADY STATE CIRCUIT ANALYSIS 1. Introduction A sinusoidal current has the following form: where I m is the amplitude value; ω=2 πf is the angular frequency; φ is the phase shift. i (t )=I m.sin

### 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

### Lecture 11 - AC Power

- AC Power 11/17/2015 Reading: Chapter 11 1 Outline Instantaneous power Complex power Average (real) power Reactive power Apparent power Maximum power transfer Power factor correction 2 Power in AC Circuits

### 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

### I. Impedance of an R-L circuit.

I. Impedance of an R-L circuit. [For inductor in an AC Circuit, see Chapter 31, pg. 1024] Consider the R-L circuit shown in Figure: 1. A current i(t) = I cos(ωt) is driven across the circuit using an AC

### 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

### 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

### Basic RL and RC Circuits R-L TRANSIENTS: STORAGE CYCLE. Engineering Collage Electrical Engineering Dep. Dr. Ibrahim Aljubouri

st Class Basic RL and RC Circuits The RL circuit with D.C (steady state) The inductor is short time at Calculate the inductor current for circuits shown below. I L E R A I L E R R 3 R R 3 I L I L R 3 R

### 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,

### Chapter 10: Sinusoidal Steady-State Analysis

Chapter 10: Sinusoidal Steady-State Analysis 1 Objectives : sinusoidal functions Impedance use phasors to determine the forced response of a circuit subjected to sinusoidal excitation Apply techniques

### 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

### ECE 202 Fall 2013 Final Exam

ECE 202 Fall 2013 Final Exam December 12, 2013 Circle your division: Division 0101: Furgason (8:30 am) Division 0201: Bermel (9:30 am) Name (Last, First) Purdue ID # There are 18 multiple choice problems

### RLC Circuit (3) We can then write the differential equation for charge on the capacitor. The solution of this differential equation is

RLC Circuit (3) We can then write the differential equation for charge on the capacitor The solution of this differential equation is (damped harmonic oscillation!), where 25 RLC Circuit (4) If we charge

### Network Analysis (Subject Code: 06ES34) Resonance

Network Analysis (Subject Code: 06ES34) Resonance Introduction Resonance Classification of Resonance Circuits Series Resonance Circuit Parallel Resonance Circuit Frequency Response of Series and Parallel

### Chapter 9 Objectives

Chapter 9 Engr8 Circuit Analysis Dr Curtis Nelson Chapter 9 Objectives Understand the concept of a phasor; Be able to transform a circuit with a sinusoidal source into the frequency domain using phasor

### Part 4: Electromagnetism. 4.1: Induction. A. Faraday's Law. The magnetic flux through a loop of wire is

1 Part 4: Electromagnetism 4.1: Induction A. Faraday's Law The magnetic flux through a loop of wire is Φ = BA cos θ B A B = magnetic field penetrating loop [T] A = area of loop [m 2 ] = angle between field

### Electronics. Basics & Applications. group talk Daniel Biesinger

Electronics Basics & Applications group talk 23.7.2010 by Daniel Biesinger 1 2 Contents Contents Basics Simple applications Equivalent circuit Impedance & Reactance More advanced applications - RC circuits

### Physics 4B Chapter 31: Electromagnetic Oscillations and Alternating Current

Physics 4B Chapter 31: Electromagnetic Oscillations and Alternating Current People of mediocre ability sometimes achieve outstanding success because they don't know when to quit. Most men succeed because

### 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

### Module 25: Outline Resonance & Resonance Driven & LRC Circuits Circuits 2

Module 25: Driven RLC Circuits 1 Module 25: Outline Resonance & Driven LRC Circuits 2 Driven Oscillations: Resonance 3 Mass on a Spring: Simple Harmonic Motion A Second Look 4 Mass on a Spring (1) (2)

### 20. Alternating Currents

University of hode sland DigitalCommons@U PHY 204: Elementary Physics Physics Course Materials 2015 20. lternating Currents Gerhard Müller University of hode sland, gmuller@uri.edu Creative Commons License

### Frequency Response DR. GYURCSEK ISTVÁN

DR. GYURCSEK ISTVÁN Frequency Response Sources and additional materials (recommended) Dr. Gyurcsek Dr. Elmer: Theories in Electric Circuits, GlobeEdit, 2016, ISBN:978-3-330-71341-3 Ch. Alexander, M. Sadiku:

### Electric Circuits I FINAL EXAMINATION

EECS:300, Electric Circuits I s6fs_elci7.fm - Electric Circuits I FINAL EXAMINATION Problems Points.. 3. 0 Total 34 Was the exam fair? yes no 5//6 EECS:300, Electric Circuits I s6fs_elci7.fm - Problem

### LCR Series Circuits. AC Theory. Introduction to LCR Series Circuits. Module. What you'll learn in Module 9. Module 9 Introduction

Module 9 AC Theory LCR Series Circuits Introduction to LCR Series Circuits What you'll learn in Module 9. Module 9 Introduction Introduction to LCR Series Circuits. Section 9.1 LCR Series Circuits. Amazing

### 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

### Supplemental Notes on Complex Numbers, Complex Impedance, RLC Circuits, and Resonance

Supplemental Notes on Complex Numbers, Complex Impedance, RLC Circuits, and Resonance Complex numbers Complex numbers are expressions of the form z = a + ib, where both a and b are real numbers, and i

### Expressions for f r (T ) and Q i (T ) from Mattis-Bardeen theory

8 Appendix A Expressions for f r (T ) and Q i (T ) from Mattis-Bardeen theory The Mattis-Bardeen theory of the anomalous skin effect in superconductors [0] may be used to derive the behavior of the resonance

### ( s) N( s) ( ) The transfer function will take the form. = s = 2. giving ωo = sqrt(1/lc) = 1E7 [rad/s] ω 01 := R 1. α 1 2 L 1.

Problem ) RLC Parallel Circuit R L C E-4 E-0 V a. What is the resonant frequency of the circuit? The transfer function will take the form N ( ) ( s) N( s) H s R s + α s + ω s + s + o L LC giving ωo sqrt(/lc)