RLC Circuits and Resonant Circuits


 Valerie Webb
 2 years ago
 Views:
Transcription
1 P517/617 Lec4, P1 RLC 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 cosw t L C R R in R R + X C + X L in R R + 1 jwc + jwl Using complex notation for the apply voltage in 0 coswt Re al( 0 e jwt ), R 0 e jwt R R + j wl  1 ˆ Ë wc We are interested in the both the magnitude of R and its phase with respect to in. First the magnitude: 0 e jwt R R R + j wl  1 ˆ 0 R R + wl  1 ˆ The following plots show R and in for an RLC circuit with: R 100 W, L 0.1 H, and C 0.1 mf at a frequency of 100 Hz. Note: R << in at this frequency. R and in are not in phase at this frequency. The little wiggles on R are real! This behavior is due to the transient solution (homogeneous solution) to the differential eq. describing the circuit. After a few cycles this contribution to R has died out.
2 P517/617 Lec4, P The following Bode plot shows the magnitude of R / in vs. frequency. 1e1 1e7 cos wt in out
3 P517/617 Lec4, P3 The phase of R with respect to in can be found by writing R in purely polar notation. For the denominator we have: Ï R + j wl  1 ˆ Ë wc R + wl  1 È 1 wl  Ô Ô ˆ 1 expì j tan Í wc Í R Ô Ó Î Ô We can define the phase angle f using tan f Imaginary X/Real X for complex X. We can now write for R in complex form: R o R e jwt e jf R + wl  1 ˆ j(w t f ) R e This phase angle is defined as: wl  1 tan f wc R Note: depending on L, C, and w, the phase angle can be positive or negative! In this example, if wl > 1/wC, then R (t) lags in (t). ( f) 1e1 1e out in cosw t
4 P517/617 Lec4, P4 Finally, we can write down the solution for by taking the real part of the above equation: j( wtf ) R Re al 0 R e R + wl  1 ˆ 0 Rcos(wt  f ) R + wl  1 ˆ Some things to note: In general C (t), R (t), and L (t) are all out of phase with the applied voltage. I(t) and R (t) are in phase in a series RLC circuit. The amplitude of C, R, and L depend on w. The table below summarizes the 3 cases with the following definitions: [ ] 1/ Z R + (wl 1 / wc) tan f (wl 1 / wc) / R oltage Magnitude Phase R R/Z f L wl/z p/  f C 1/wCZ p/  f RLC circuits are resonant circuits, as the energy in the system "resonates" between the inductor and capacitor. "Ideal" capacitors and inductors do not dissipate energy. However, resistors dissipate energy or alternately, resistors do not store energy. Resonant Frequency: At the resonant frequency the imaginary part of the impedance vanishes. For the series RLC circuit the impedance (Z) is: Z R + X L + X C R + j(wl 1 / wc) [ ] 1/ Z R +(wl  1/ wc) At resonance (series, parallel etc), we have wl 1 / wc and: 1 w R LC At the resonant frequency the following are true for a series RLC circuit: a) R is maximum (ideally in ) b) f 0 c) C L L in in R C ( or can be >!) C L in The circuit acts like a narrow band pass filter.
5 P517/617 Lec4, P5 There is an exact analogy between an RLC circuit and a harmonic oscillator (mass attached to spring): m d x dt + B dx + kx 0 damped harmonic oscillator dt L d q dt + R dq dt + q 0 undriven RLC circuit C x q (electric charge), L m, k 1/C B (coefficient of damping) R Q (quality factor) of a circuit: determines how well the RLC circuit stores energy Q p (max energy stored)/(energy lost) per cycle Q is related to sharpness of the resonance peak: P517/617 Lec4, P6
6 The maximum energy stored in the inductor is LI / with I I MAX. There is no energy stored in the capacitor at this instant because I and C are 90 0 out of phase. The energy lost in one cycle is (Power)x(time for cycle) I RMS R p 1 w I maxr p R w R ˆ pá LI Max Ë Q p Á RI Max ˆ w R Ë w R L R There is another popular, equivalent expression for Q w R Q w U  w L where w U (w L ) is the upper (lower) 3 db frequency of the resonance curve. Q is related to sharpness of the resonance peak. I'll skip the derivation here as it involves a bit of algebra. However the two crucial points of the derivation include noting that: R 1 in 1 + Q w  w Á R ˆ Ë w R w and at the upper and lower 3 db points: QÁ w  w R ˆ ±1 Ë w R w Note: Q can be measured from the shape of the resonance curve, one does not need to know R, L, or C to find Q!
7 Example: Audio filter (band pass filter) Audio filter is matched to the frequency range of the ear (00,000 Hz). P517/617 Lec4, P7 Let's design an audio filter using low and high pass RC circuits. Ideally, the frequency response is flat over 00,000 Hz, and rolls off sharply at frequencies below 0 Hz and above 0,000 Hz. Set 3 db points as follows: lower 3 db point : 0 Hz 1/pR 1 C 1 upper 3 db point: x10 4 Hz 1/pR C If we put these two filters together we don't want the nd stage to affect the 1 st stage. We can accomplish this by making the impedance of the nd (Z ) stage much larger than R 1. Remember R 1 is in parallel with Z. Z 1 R 1 +1 / jwc 1 Z R +1 / jwc In order to insure that the second stage does not "load" down the first stage we need: R >> R 1 since at high frequencies Z fi R We can now pick and calculate values for the R's and C's in the problem. Let C 1 1 mf, then R 1 1/(0Hz pc 1 ) 8 kw Let R > 100R 1 fi R 1 MW, and C 1/(x104 Hz pr ) 8 pf Thus we find the following R's and C's: R 1 8 kw, C 1 1 mf R 1 MW, C 8 pf
8 P517/617 Lec4, P8 Exact derivation for above filter: In the above circuit we treated the two RC filters as independent. Why did this work? We want to calculate the gain ( out / in ) of the following circuit: Working from right to left, we have: out a X / (X + R ) a in Z 1 / Z T Z T is the total impedance of the circuit as seen from the input while Z 1 is the parallel impedance of R 1 and R, in series with C. ( ) Z 1 R 1 R + X and Z R 1 + R + X T X 1 + Z 1 We can now solve for a : a in R 1 ( R + X ) X 1 ( R 1 + R + X ) + R 1 ( R + X ) Finally we can solve for the gain G out / in : out R 1 X in X 1 ( R 1 + R + X ) + R 1 ( R + X ) We can relate this to our previous result by rewriting the above as: out in X R 1 R + X ˆ R R + X 1 R X 1 1 Á Ë If we now remember the approximation (R 1 << R + X ) made on the previous page to insure that the second stage did not load down the first then we get the following: out R 1 X in R 1 + X 1 R + X The gain of the circuit looks like the product of two filters, one high pass and one low pass! If we calculate the gain of this circuit in db, then the over all gain is the sum of the gain of each piece: Gain in db 0 logá outˆ Ë in R 0 logá 1 ˆ + 0 logá X ˆ Ë R 1 + X 1 Ë R + X The gain of successive filters measured in db's add.
9 P517/617 Lec4, P9 Another Example: Calculate I and the phase angle between in and I for the following circuit: a) First calculate I. The total current out of the input source (I) is related to in and the total impedance (Z T ) of the circuit by Ohm s law: I in / Z T The total impedance of the circuit is given by the parallel impedance of the two branches: 1 / Z T 1 / Z 1 +1 / Z Z 1 R 1 + X 1 Z R + X Putting in numerical values for the R's and X's we have: Z j37.7 W Z 10  j53.1 W Z T j11.8 W We can now find the magnitude of the current (an RMS value since in is given as RMS). I in / Z T 30 / 68.4 W 3.36 A b) Calculate the phase angle between in and I: Its easiest to solve this by writing and Z in polar form: in (30)e jwt Z T (68.4)e jf tanf Im Z T / Re Z T 11.8/ 67.4 f Finally we can write for the current: j(w t f ) I (30 / 68.4)e Taking the real part of I we get: I 3.36cos(wt ) A Thus the current lags the voltage by
P517/617 Lec3, P1 RLC AC Circuits
P517/617 Lec3, P1 RLC AC Circuits What does AC stand for? AC stands for "Alternating Current". Most of the time however, we are interested in the voltage at a point in the circuit, so we'll concentrate
More informationECE215 Lecture 16 Date:
Lecture 16 Date: 20.10.2016 Bode Plot (contd.) Series and Parallel Resonance Example 1 Find the transfer function H(ω) with this Bode magnitude plot Example 2 Find the transfer function H(ω) with this
More informationPhasors. Phasors. by Prof. Dr. Osman SEVAİOĞLU Electrical and Electronics Engineering Department. ^ V cos (wt + θ) ^ V sin (wt + θ)
V cos (wt θ) V sin (wt θ) by Prof. Dr. Osman SEVAİOĞLU Electrical and Electronics Engineering Department EE 209 Fundamentals of Electrical and Electronics Engineering, Prof. Dr. O. SEVAİOĞLU, Page 1 Vector
More informationChapter 13. RLC Circuits and Resonance
Chapter 13 RLC Circuits and Resonance Impedance of Series RLC Circuits A series RLC circuit contains both inductance and capacitance Since X L and X C have opposite effects on the circuit phase angle,
More informationCapacitors and Inductors
P517/617 ec2, P1 Capacitors and Inductors 1) Capacitance: Capacitance (C) is defined as the ratio of charge (Q) to voltage () on an object. Define capacitance by: C = Q/ = Coulombs/olt = Farad. Capacitance
More informationR f. V i. ET 438a Automatic Control Systems Technology Laboratory 4 Practical Differentiator Response
ET 438a Automatic Control Systems Technology Laboratory 4 Practical Differentiator Response Objective: Design a practical differentiator circuit using common OP AMP circuits. Test the frequency response
More informationChapter 13. RLC Circuits and Resonance. Objectives
Chapter 13 RLC Circuits and Resonance Objectives Determine the impedance of a series RLC circuit Analyze series RLC circuits Analyze a circuit for series resonance Analyze series resonant filters Analyze
More informationChapter 12. RL Circuits. Objectives
Chapter 12 RL Circuits Objectives Describe the relationship between current and voltage in an RL circuit Determine impedance and phase angle in a series RL circuit Analyze a series RL circuit Determine
More informationEXPERIMENT 5: SERIES AND PARALLEL RLC RESONATOR CIRCUITS
EXPERIMENT 5: SERIES AND PARALLEL RLC RESONATOR CIRCUITS Equipment List S 1 BK Precision 4011 or 4011A 5 MHz Function Generator OS BK 2120B Dual Channel Oscilloscope V 1 BK 388B Multimeter L 1 Leeds &
More informationLab 2: AC Measurements Capacitors and Inductors
Lab 2: AC Measurements Capacitors and Inductors Introduction The second most common component after resistors in electronic circuits is the capacitor. It is a twoterminal device that stores an electric
More informationLesson 27. (1) Root Mean Square. The emf from an AC generator has the time dependence given by
Lesson 27 () Root Mean Square he emf from an AC generator has the time dependence given by ℇ = ℇ "#$% where ℇ is the peak emf, is the angular frequency. he period is he mean square value of the emf is
More informationEðlisfræði 2, vor 2007
[ Assignment View ] [ Pri Eðlisfræði 2, vor 2007 31. Alternating Current Circuits Assignment is due at 2:00am on Wednesday, March 21, 2007 Credit for problems submitted late will decrease to 0% after the
More informationRLC Resonant Circuits
C esonant Circuits Andrew McHutchon April 20, 203 Capacitors and Inductors There is a lot of inconsistency when it comes to dealing with reactances of complex components. The format followed in this document
More informationReactance and Impedance
Reactance and Impedance Capacitance in AC Circuits Professor Andrew H. Andersen 1 Objectives Describe capacitive ac circuits Analyze inductive ac circuits Describe the relationship between current and
More informationExperiment 08: RLC Circuits and Resonance Dr. Pezzaglia
Mar9 RLC Circuit Page Experiment 8: RLC Circuits and Resonance Dr. Pezzaglia Theory When a system at a stable equilibrium is displaced, it will tend to oscillate. An Inductor combined with Capacitor will
More informationFrequency response: Resonance, Bandwidth, Q factor
Frequency response: esonance, Bandwidth, Q factor esonance. Let s continue the exploration of the frequency response of circuits by investigating the series circuit shown on Figure. C + V  Figure The
More informationFilters and Waveform Shaping
Physics 333 Experiment #3 Fall 211 Filters and Waveform Shaping Purpose The aim of this experiment is to study the frequency filtering properties of passive (R, C, and L) circuits for sine waves, and the
More informationSimple Harmonic Motion: AC circuits: alternating current electricity
Simple Harmonic Motion: AC circuits: alternating current electricity Alternating current (AC) circuits explained using time and phasor animations. Impedance, phase relations, resonance and RMS quantities.
More informationRLC Circuits. OBJECTIVES To observe free and driven oscillations of an RLC circuit.
ircuits It doesn t matter how beautiful your theory is, it doesn t matter how smart you are. If it doesn t agree with experiment, it s wrong. ichard Feynman (19181988) OBJETIVES To observe free and driven
More informationChapter 22: Alternating current. What will we learn in this chapter?
Chapter 22: Alternating current What will we learn in this chapter? Contents: Phasors and alternating currents Resistance and reactance Series R L C circuit Power in accircuits Series resonance Parallel
More informationChapt ha e pt r e r 12 RL Circuits
Chapter 12 RL Circuits Sinusoidal Response of RL Circuits The inductor voltage leads the source voltage Inductance causes a phase shift between voltage and current that depends on the relative values of
More informationKirchhoff s Laws in Dynamic Circuits
Kirchhoff s Laws in Dynamic Circuits Dynamic circuits are circuits that contain capacitors and inductors. Later we will learn to analyze some dynamic circuits by writing and soling differential equations.
More informationLecture 21. AC Circuits, Reactance.
Lecture 1. AC Circuits, Reactance. Outline: Power in AC circuits, Amplitude and RMS values. Phasors / Complex numbers. Resistors, Capacitors, and Inductors in the AC circuits. Reactance and Impedance.
More informationExperiment 16 ANALOG FOURIER ANALYSIS. Experiment setup 4. Prelab problems 6. Experiment procedure 7. Appendix A: an effective highq filter A1
16i Experiment 16 ANALOG FOURIER ANALYI Introduction 1 Theory 1 Experiment setup 4 Prelab problems 6 Experiment procedure 7 Appendix A: an effective highq filter A1 16ii 161 1/31/14 INTRODUCTION In
More informationFilters & Wave Shaping
Module 8 AC Theory Filters & Wave Shaping Passive Filters & Wave Shaping What you'll learn in Module 8. Module 8 Introduction Recognise passive filters with reference to their response curves. High pass,
More informationε: Voltage output of Signal Generator (also called the Source voltage or Applied
Experiment #10: LR & RC Circuits Frequency Response EQUIPMENT NEEDED Science Workshop Interface Power Amplifier (2) Voltage Sensor graph paper (optional) (3) Patch Cords Decade resistor, capacitor, and
More informationChapter 21 BandPass Filters and Resonance
Chapter 21 BandPass Filters and Resonance In Chapter 20, we discussed lowpass and highpass filters. The simplest such filters use RC components resistors and capacitors. It is also possible to use resistors
More informationCircuits with inductors and alternating currents. Chapter 20 #45, 46, 47, 49
Circuits with inductors and alternating currents Chapter 20 #45, 46, 47, 49 RL circuits Ch. 20 (last section) Symbol for inductor looks like a spring. An inductor is a circuit element that has a large
More informationStep response of an RLC series circuit
School of Engineering Department of Electrical and Computer Engineering 332:224 Principles of Electrical Engineering II Laboratory Experiment 5 Step response of an RLC series circuit 1 Introduction Objectives
More informationLCR Parallel Circuits
Module 10 AC Theory Introduction to What you'll learn in Module 10. The LCR Parallel Circuit. Module 10.1 Ideal Parallel Circuits. Recognise ideal LCR parallel circuits and describe the effects of internal
More informationDirect versus Alternating Current Things We Can Measure
Phil Sherrod W4PHS Direct versus Alternating Current Things We Can Measure Direct Current (DC) Alternating Current (AC) Voltage Voltage (peak, RMS) Current Current (peak, effective) Power True power, Apparent
More informationApril 8. Physics 272. Spring Prof. Philip von Doetinchem
Physics 272 April 8 Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html Prof. Philip von Doetinchem philipvd@hawaii.edu Phys272  Spring 14  von Doetinchem  218 LC in parallel
More informationPractice Problems  Chapter 33 Alternating Current Circuits
Multiple Choice Practice Problems  Chapter 33 Alternating Current Circuits 4. A highvoltage powerline operates at 500 000 Vrms and carries an rms current of 500 A. If the resistance of the cable is
More informationFILTER CIRCUITS. A filter is a circuit whose transfer function, that is the ratio of its output to its input, depends upon frequency.
FILTER CIRCUITS Introduction Circuits with a response that depends upon the frequency of the input voltage are known as filters. Filter circuits can be used to perform a number of important functions in
More informationFREQUENCY RESPONSE AND PASSIVE FILTERS LABORATORY. We start with examples of a few filter circuits to illustrate the concept.
FREQUENCY RESPONSE AND PASSIVE FILTERS LABORATORY In this experiment we will analytically determine and measure the frequency response of networks containing resistors, AC source/sources, and energy storage
More information12.4 UNDRIVEN, PARALLEL RLC CIRCUIT*
+ v C C R L  v i L FIGURE 12.24 The parallel secondorder RLC circuit shown in Figure 2.14a. 12.4 UNDRIVEN, PARALLEL RLC CIRCUIT* We will now analyze the undriven parallel RLC circuit shown in Figure
More informationLC Resonant Circuits Dr. Roger King June Introduction
LC Resonant Circuits Dr. Roger King June 01 Introduction Secondorder systems are important in a wide range of applications including transformerless impedancematching networks, frequencyselective networks,
More informationYour Comments. This was a very confusing prelecture. Do you think you could go over thoroughly how the LC circuits work qualitatively?
Your omments I am not feeling great about this mierm...some of this stuff is really confusing still and I don't know if I can shove everything into my brain in time, especially after spring break. an you
More informationLRC Circuits. Purpose. Principles PHYS 2211L LAB 7
Purpose This experiment is an introduction to alternating current (AC) circuits. Using the oscilloscope, we will examine the voltage response of inductors, resistors and capacitors in series circuits driven
More informationA complex number W consists of real and imaginary parts a and b respectively, and the imaginary constant j which is the square root of negative one.
eactance and Impedance A Voltage and urrent In a D circuit, we learned that the relationship between voltage and current was V=I, also known as Ohm's law. We need to find a similar law for A circuits,
More informationLecture 4: Sensor interface circuits
Lecture : Sensor interface circuits g eview of circuit theory n oltage, current and resistance n apacitance and inductance n omplex number representations g Measurement of resistance n oltage dividers
More informationElectrical Resonance RLC circuits
Purpose: To investigate resonance phenomena that result from forced motion near a system's natural frequency. In this case the system will be a variety of RLC circuits. Theory: You are already familiar
More informationPhysics 9 Fall 2009 Homework 9  Solutions
. Chapter 36  Exercise 5. Physics 9 Fall 2009 Homework 9  s What are V R and V C if the emf frequency in the figure is 0 khz? The voltage are V R = IR, and V C = IX C, where the capitative reactance
More informationResonance. Objectives
Resonance Objectives Determine the impedance of a series RLC circuit Analyze series RLC circuits Analyze a circuit for series resonance Analyze series resonant filters Analyze parallel RLC circuits Analyze
More informationChapter 12 Driven RLC Circuits
hapter Driven ircuits. A Sources... . A ircuits with a Source and One ircuit Element... 3.. Purely esistive oad... 3.. Purely Inductive oad... 6..3 Purely apacitive oad... 8.3 The Series ircuit...
More informationLab #4 Capacitors and Inductors. Capacitor and Inductor Transient Response
Capacitor and Inductor Transient Response Capacitor Theory Like resistors, capacitors are also basic circuit elements. Capacitors come in a seemingly endless variety of shapes and sizes, and they can all
More informationAlternatingCurrent Circuits
hapter 1 Alternatingurrent ircuits 1.1 A Sources... 11. Simple A circuits... 13 1..1 Purely esistive load... 13 1.. Purely Inductive oad... 15 1..3 Purely apacitive oad... 17 1.3 The Series ircuit...
More informationProf. Anchordoqui Problems set # 11 Physics 169 May 5, 2015
rof. Anchordoqui roblems set # hysics 69 May 5, 5. A semicircular conductor of radius.5 m is rotated about the axis A at a constant rate of rev/min (Fig. ). A uniform magnetic field in all of the lower
More informationRC Circuits. 1 Introduction. 2 Capacitors
1 RC Circuits Equipment DataStudio with 750 interface, RLC circuit board, 2 voltage sensors (no alligator clips), 2x35 in. leads, 12 in. lead Reading Review operation of DataStudio oscilloscope. Review
More informationPhysics 102: Lecture 13 RLC circuits & Resonance
Physics 102: Lecture 13 L circuits & esonance L Physics 102: Lecture 13, Slide 1 I = I max sin(2pft) V = I max sin(2pft) V in phase with I eview: A ircuit L V = I max X sin(2pft p/2) V lags I IE I V t
More informationRESONANCE AND FILTERS
14221 RESONANCE AND FILTERS Experiment 1, Resonant Frequency and Circuit Impedance For more courses visit www.ciewc.edu OBJECTIVES 1. To verify experimentally our theoretical predictions concerning the
More informationBasic Electrical Theory
Basic Electrical Theory Impedance PJM State & Member Training Dept. PJM 2014 10/24/2013 Objectives Identify the components of Impedance in AC Circuits Calculate the total Impedance in AC Circuits Identify
More informationChapter 30 Inductance, Electromagnetic Oscillations, and AC Circuits. Copyright 2009 Pearson Education, Inc.
Chapter 30 Inductance, Electromagnetic Oscillations, and AC Circuits 301 Mutual Inductance Mutual inductance: a changing current in one coil will induce a current in a second coil: Coil 1 produces a flux
More informationLow Pass Filter Rise Time vs Bandwidth
AN121 Dataforth Corporation Page 1 of 7 DID YOU KNOW? The number googol is ten raised to the hundredth power or 1 followed by 100 zeros. Edward Kasner (18781955) a noted mathematician is best remembered
More informationUsing the Impedance Method
Using the Impedance Method The impedance method allows us to completely eliminate the differential equation approach for the determination of the response of circuits. In fact the impedance method even
More informationFirst Order Circuits. EENG223 Circuit Theory I
First Order Circuits EENG223 Circuit Theory I First Order Circuits A firstorder circuit can only contain one energy storage element (a capacitor or an inductor). The circuit will also contain resistance.
More informationMAKE SURE TA & TI STAMPS EVERY PAGE BEFORE YOU START
Laboratory Section: Last Revised on December 15, 2014 Partners Names Grade EXPERIMENT 10 Electronic Circuits 0. PreLaboratory Work [2 pts] 1. How are you going to determine the capacitance of the unknown
More informationFrequency Response of BJT & JFET
Alexandria High Institute for Engineering & Technology Frequency Response of BJT & JFET Course ECE241 Chapter (2) Sameh Selim )1) Logarithms To clarify the relationship between the variables of a logarithmic
More informationFourier Series Analysis
School of Engineering Department of Electrical and Computer Engineering 332:224 Principles of Electrical Engineering II aboratory Experiment 6 Fourier Series Analysis 1 Introduction Objectives The aim
More informationLCR Series Circuits. AC Theory. Introduction to LCR Series Circuits. Module 9. 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
More informationUNIVERSITY OF NORTH CAROLINA AT CHARLOTTE. Department of Electrical and Computer Engineering
UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE Department of Electrical and Computer Engineering Experiment No. 9  Resonance in Series and parallel RLC Networks Overview: An important consideration in the
More informationLAB #1: TIME AND FREQUENCY RESPONSES OF SERIES RLC CIRCUITS Updated July 19, 2003
SFSU  ENGR 3 ELECTRONICS LAB LAB #: TIME AND FREQUENCY RESPONSES OF SERIES RLC CIRCUITS Updated July 9, 3 Objective: To investigate the step, impulse, and frequency responses of series RLC circuits. To
More informationChapter 10. RC Circuits. Objectives
Chapter 10 RC Circuits Objectives Describe the relationship between current and voltage in an RC circuit Determine impedance and phase angle in a series RC circuit Analyze a series RC circuit Determine
More informationChapter 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 halfplane zero 8.1.4. Frequency inversion 8.1.5. Combinations 8.1.6.
More informationFrequency response of a general purpose singlesided OpAmp amplifier
Frequency response of a general purpose singlesided OpAmp amplifier One configuration for a general purpose amplifier using an operational amplifier is the following. The circuit is characterized by:
More informationPeriodic Motion or Oscillations. Physics 232 Lecture 01 1
Periodic Motion or Oscillations Physics 3 Lecture 01 1 Periodic Motion Periodic Motion is motion that repeats about a point of stable equilibrium Stable Equilibrium Unstable Equilibrium A necessary requirement
More informationElectrical Circuits I Lecture 1
Electrical Circuits I Lecture Course Contents Basic dc circuit elements, series and parallel Networks Ohm's law and Kirchoff's laws Nodal Analysis Mesh Analysis Source Transformation
More informationFUNDAMENTALS OF ENGINEERING (FE) EXAMINATION
January 8, 008 1:55 Appc Sheet number 1 Page number 77 magenta black A P P E N D I X C FUNDAMENTALS OF ENGINEERING (FE) EXAMINATION C.1 INTRODUCTION The Fundamentals of Engineering (FE) examination 1 is
More informationBharathwaj Muthuswamy EE100 Active Filters
Bharathwaj Muthuswamy EE100 mbharat@cory.eecs.berkeley.edu 1. Introduction Active Filters In this chapter, we will deal with active filter circuits. Why even bother with active filters? Answer: Audio.
More informationBasic AC Reactive Components IMPEDANCE
Basic AC Reactive Components Whenever inductive and capacitive components are used in an AC circuit, the calculation of their effects on the flow of current is important. EO 1.9 EO 1.10 EO 1.11 EO 1.12
More informationRESISTANCE, REACTANCE AND IMPEDANCE A Primer. Douglas Brooks, PhD UltraCAD Design, Inc. PART 2, REACTANCE
RESISTANCE, REACTANCE AND IMPEDANCE A Primer Douglas Brooks, PhD UltraCAD Design, Inc. PART 2, REACTANCE This is part 2 of a 3part series on resistance, reactance and impedance. Most of us are familiar
More informationTransistor Tuned Amplifiers
5 Transistor Tuned Amplifiers 389 Transistor Tuned Amplifiers 5. Tuned Amplifiers 5. Distinction between Tuned Amplifiers and other Amplifiers 5.3 Analysis of Parallel Tuned Circuit 5.4 Characteristics
More informationApplication Note AN 1095
Application Note AN 1095 Design of the Inverter Output Filter for Motor Drives with IRAMS Power Modules Cesare Bocchiola Table of Contents Page Section 1: Introduction...2 Section 2 : Output Filter Design
More informationSlide 1 / 26. Inductance. 2011 by Bryan Pflueger
Slide 1 / 26 Inductance 2011 by Bryan Pflueger Slide 2 / 26 Mutual Inductance If two coils of wire are placed near each other and have a current passing through them, they will each induce an emf on one
More informationEE 221 AC Circuit Power Analysis. Instantaneous and average power RMS value Apparent power and power factor Complex power
EE 1 AC Circuit Power Analysis Instantaneous and average power RMS value Apparent power and power factor Complex power Instantaneous Power Product of timedomain voltage and timedomain current p(t) =
More informationNZQA registered unit standard 20431 version 2 Page 1 of 7. Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians
NZQA registered unit standard 0431 version Page 1 of 7 Title Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians Level 3 Credits 7 Purpose This unit standard covers
More informationImpedance Matching and Matching Networks. Valentin Todorow, December, 2009
Impedance Matching and Matching Networks Valentin Todorow, December, 2009 RF for Plasma Processing  Definition of RF What is RF? The IEEE Standard Dictionary of Electrical and Electronics Terms defines
More informationBode Diagrams of Transfer Functions and Impedances ECEN 2260 Supplementary Notes R. W. Erickson
Bode Diagrams of Transfer Functions and Impedances ECEN 2260 Supplementary Notes. W. Erickson In the design of a signal processing network, control system, or other analog system, it is usually necessary
More informationExperiment V: The AC Circuit, Impedance, and Applications to High and Low Pass Filters
Experiment : The AC Circuit, Impedance, and Applications to High and Low Pass Filters I. eferences Halliday, esnick and Krane, Physics, ol. 2, 4th Ed., Chapters 33 Purcell, Electricity and Magnetism, Chapter
More informationChapter 15 10/14/2014
Chapter 15 Analyze series and parallel ac circuits to find Voltage Current Power Total impedance, admittance Apply known circuit theories Kirchhoff s current, voltage laws Voltage or current divider rule
More information7.1 POWER IN AC CIRCUITS
C H A P T E R 7 AC POWER he aim of this chapter is to introduce the student to simple AC power calculations and to the generation and distribution of electric power. The chapter builds on the material
More informationPHYS 189 Final Exam: Practice March, 2014
PHYS 189 Final Exam: Practice March, 2014 Name: Answer the questions in the spaces provided on the question sheets. If you run out of room for an answer, continue on the back of the page. Multiple choice
More informationAC Impedance and HighPass Filters
Lab 7 AC Impedance and HighPass Filters In this lab you will become familiar with the concept of AC impedance and apply it to the frequency response of a highpass filter. 7.1 AC Impedance Just as Ohm
More informationPHY2049 Exam #2 Solutions Fall 2012
PHY2049 Exam #2 Solutions Fall 2012 1. The diagrams show three circuits consisting of concentric circular arcs (either half or quarter circles of radii r, 2r, and 3r) and radial segments. The circuits
More informationAC RL and RC Circuits
AC RL and RC Circuits When a sinusoidal AC voltage is applied to an RL or RC circuit, the relationship between voltage and current is altered. The voltage and current still have the same frequency and
More informationDesigning Stable Compensation Networks for Single Phase Voltage Mode Buck Regulators
Designing Stable Compensation Networks for Single Phase Voltage Mode Buck Regulators Technical Brief December 3 TB47. Author: Doug Mattingly Assumptions This Technical Brief makes the following assumptions:.
More informationSIMULATIONS OF PARALLEL RESONANT CIRCUIT POWER ELECTRONICS COLORADO STATE UNIVERSITY
SIMULATIONS OF PARALLEL RESONANT CIRCUIT POWER ELECTRONICS COLORADO STATE UNIVERSITY Page 1 of 25 PURPOSE: The purpose of this lab is to simulate the LCC circuit using MATLAB and ORCAD Capture CIS to better
More informationQuestions. Question 1
Question 1 Questions Explain why transformers are used extensively in longdistance power distribution systems. What advantage do they lend to a power system? file 02213 Question 2 Are the transformers
More informationAn Introduction to the Mofied Nodal Analysis
An Introduction to the Mofied Nodal Analysis Michael Hanke May 30, 2006 1 Introduction Gilbert Strang provides an introduction to the analysis of electrical circuits in his book Introduction to Applied
More informationAuthor: Ramon Cerda, Senior Applications Engineer, Raltron Electronics Corp NW 19 St Miami, FL
Quartz rystal PrimerPart Author: Ramon erda, Senior Applications Engineer, Raltron Electronics orp. 065 NW 9 St Miami, FL 3372 email: rcerda@raltron.com Introduction For crystal oscillator design and
More informationES250: Electrical Science. HW7: Energy Storage Elements
ES250: Electrical Science HW7: Energy Storage Elements Introduction This chapter introduces two more circuit elements, the capacitor and the inductor whose elements laws involve integration or differentiation;
More informationINTRODUCTION SELF INDUCTANCE. Introduction. Self inductance. Mutual inductance. Transformer. RLC circuits. AC circuits
Chapter 13 INDUCTANCE Introduction Self inductance Mutual inductance Transformer RLC circuits AC circuits Magnetic energy Summary INTRODUCTION Faraday s important contribution was his discovery that achangingmagneticflux
More informationIntroduction to Complex Numbers in Physics/Engineering
Introduction to Complex Numbers in Physics/Engineering ference: Mary L. Boas, Mathematical Methods in the Physical Sciences Chapter 2 & 14 George Arfken, Mathematical Methods for Physicists Chapter 6 The
More informationAlternating Current. Asist. Prof. Dr. Aytaç Gören Asist. Prof. Dr. Levent Çetin
Asist. Prof. Dr. Aytaç Gören Asist. Prof. Dr. Levent Çetin 30.10.2012 Contents Alternating Voltage Phase Phasor Representation of AC Behaviors of Basic Circuit Components under AC Resistance, Reactance
More informationExperiment #11: LRC Circuit (Power Amplifier, Voltage Sensor)
Experiment #11: LRC Circuit (Power Amplifier, Voltage Sensor) Concept: circuits Time: 30 m SW Interface: 750 Windows file: RLC.SWS EQUIPMENT NEEDED Science Workshop Interface Power Amplifier (2) Voltage
More informationCharacterizing Resonant Series RLC Circuits : Two Challenging Experiments Using Either LabView. Software of National Instruments or VEE of Hewlett
Characterizing Resonant Series RLC Circuits : Two Challenging Experiments Using Either LabView Software of National Instruments or VEE of Hewlett Packard Software for Data Acquisition Via the GPIB Bus
More informationVectors and Phasors. A supplement for students taking BTEC National, Unit 5, Electrical and Electronic Principles. Owen Bishop
Vectors and phasors Vectors and Phasors A supplement for students taking BTEC National, Unit 5, Electrical and Electronic Principles Owen Bishop Copyrught 2007, Owen Bishop 1 page 1 Electronics Circuits
More informationA Resonant Circuit. I. Equipment
Physics 14 ab Manual A Resonant Circuit Page 1 A Resonant Circuit I. Equipment Oscilloscope Capacitor substitution box Resistor substitution box Inductor Signal generator Wires and alligator clips II.
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4  ALTERNATING CURRENT
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4  ALTERNATING CURRENT 4 Understand singlephase alternating current (ac) theory Single phase AC
More informationApplications of SecondOrder Differential Equations
Applications of SecondOrder Differential Equations Secondorder linear differential equations have a variety of applications in science and engineering. In this section we explore two of them: the vibration
More information