Operational amplifiers (Op amps)

Size: px
Start display at page:

Download "Operational amplifiers (Op amps)"

Transcription

1 Operational amplifiers (Op amps) v R o R i v i Av i v View it as an ideal amp. Take the properties to the extreme: R i, R o 0, A.?!?!?!?! v v i Av i v A Consequences: No voltage dividers at input or output. (That s good.) No current flows into the input. (That s good.) The gain is infinite. (Is that good?) EE 230 op amps 1

2 How do we handle this infinite gain business? Av i In order to keep finite, then as A, v i 0. In other words, we must force the difference signal at the input to go to zero. How do we do that? With feedback, of course. Recall that the difference signal in a feedback arrangement must become very small if the gain is very big. 0, as A One input is connected to the source voltage in some fashion. The other input is connected to the feedback network. If the feedback is working properly, then v i v v _ 0. The condition of v v _ is called a virtual short at the input. This should be the case, if negative feedback is working in the circuit. EE 230 op amps 2

3 v s v v i 0 i 0 v s v v i 0 i 0 v v i Av i v A v negative feedback v i Av i v A negative feedback v s v v A v v i 0 i 0 negative feedback Don t really need the internal detail. Just use the rules. EE 230 op amps 3

4 Ideal op amp v v v non-inverting input v _ inverting input When using an op amp in a circuit: v v _ virtual short (assuming a proper negative feedback configuration.) i i _ 0 due to infinite input resistance Because R o 0, there are no voltage divider effects at output. This means that we can connect anything to the output without worrying about loading effects. (We will see later that there are potential output problems.) EE 230 op amps 4

5 Non-inverting amplifier v S Write a node equation at the inverting terminal. v v v s (virtual short due to feedback) i 0 (infinite input resistance) (Worth memorizing.) EE 230 op amps 5

6 Inverting amplifier v S Write a node equation at the inverting terminal. v v 0 (virtual ground!) i 0 (infinite input resistance) Note the negative sign! (Also worth memorizing.) EE 230 op amps 6

7 Non-inverting with gain of 10 ( 9 kω and 1kΩ) Inverting with gain of 10 ( 10 kω and 1kΩ) EE 230 op amps 7

8 Don t panic if the feedback loop gets crazier. 10 k! 10 k! v x R 4 v in i R1 1 k! i R2 R 3 1 k! i R3 i R4 ut Use the usual circuit analysis along with the op-amp rules. At the inverting terminal (note that v 0): i R1 i R2. v in v x at node x: i R2 i R3 i R4. v x v x R 3 v x R 4 ut Use the two equations to eliminate v x and solve for the gain: G ut v in R 4 R 4 R 3 Inserting the values: G 120. Big gain without big ratios. EE 230 op amps 8

9 Summing amp (weighted summer) v S3 v S2 v S1 R 3 R F At the inverting terminal: v v 0 (virtual ground). Write a node equation there. (Or use superposition.) Follow with second inverter if you don t like the negative sign. The virtually grounded inverting terminal becomes a summing node. EE 230 op amps 9

10 Difference amp We would like to amplify only the difference between va and vb. Anything this applied in common to both, will not be amplified. R2 At the inverting input: R1 vb va R3 R4 At the non-inverting input: if EE 230 v v then ( ) Difference only! (Check it.) op amps 10

11 With a difference amp, we really want to amplify only the differences between the two inputs. Any voltage that is in common should not come through (i.e. the gain for common-mode voltages should be zero.) v com v b v com v a v dif v com v dif v com R 3 R 4 If resistors are perfectly matched: G d v dif G d But if matching is imperfect: G d v dif G c v com The common-mode rejection ratio is a measure of how much of the common signal can leak through to the output. CMRR G d G c CMRR of 10,000 or better is not hard to achieve. EE 230 op amps 11

12 Unity gain buffer v s Non-inverting amp with 0 and. So G 1, meaning v s. What good is that? v 1 R o1 R i2 R o1 v 1 R i2 Connecting two circuits. If R o1 is not much smaller R i2, then much of the voltage is lost in the voltage divider, v i2 << v 1. High input resistance of op amp makes v v 1. Zero output resistance of op amp makes v i2. Since v, then v i2 v 1. The op amp served as a buffer between the two circuits, eliminated the voltage divider problem. EE 230 op amps 12

13 Simple application of unity-gain buffer You would like to use a potentiometer as a volume control or to provide a reference voltage. V S R P V S R P R P v adj R L v V S V R P adj S v adj R P R L V S R P v adj R L v RL v adj V S R P EE 230 op amps 13

14 Cascading amps The various types of circuits can serve as building blocks for more complicated circuits. R 4 v a v b R 3 1 inverting non-inverting 2 R 5 R 6 R 7 summing 3 EE 230 op amps 14

15 20 k! R5 10 k! R2 R1 vs 1 k! vo1 vo2 8 k! summing 2 k!. want vo2 / vs... Feedback loop around feedback loops!! EE 230 R3 R4 non-inverting. op amps 15

16 Integrating amplifier Use an inverting amp with a capacitor as the feedback element. vc C R vi(t) ir ic vo(t) () ( ) ( ) () () () ( ) ( ) () EE 230 () () () () ( ) ( ) The output signal, as a function of time, is proportional to the time integral of the input. op amps 16

17 v i (t) R C (t) ( ) ( ) ( ) If the input is a constant voltage, v i (t) V 1, then ( ) ( ) The output starts at whatever value it has t 0, and then ramps downward in time with slope V 1 /RC. If V 1 is negative, then the output ramps upward in time. If the input switches back and forth between two constant values (square wave), then the output ramps up and down correspondingly (sawtooth). V 1 v i (t) (t) t t V 2 t 0 EE 230 op amps 17 t 0

18 A practical concern with an integrating amp: If there is a small, but constant, DC voltage at the input (and we will see later that most op-amps have DC error voltages built in), then that will be integrated forever and the output will go to infinity. (In reality, it will saturate at the power supply limit.) to infinity C (t) and beyond! v R error 1 mv v DC o (t) v error RC t t This is a problem because at DC, the capacitor is an open circuit and the amplifier has essentially infinite DC gain. To make it better, put a resistor in parallel with the cap; >>. EE 230 op amps 18 v i (t) C (t)

19 Differentiating amplifier Can also differentiate. Switch resistor and capacitor. R v i (t) C i R i C (t) i C i R C dv C dt v R v C v 0 (t) RC dv i (t) dt However, not used much. If there is noise at the input, the differentiator tends to make it worse. The integrator, on the other hand, tends to average out the noise. EE 230 op amps 19

20 Instrumentation amplifier Recall the difference amp: R v 1 b v v a o R 3 R 4 If the ratios are matched: R 4 /R 3 /, then the circuit becomes a perfect difference amp with G d (v a v b ), where G d / and common-mode voltages are completely rejected (G c 0). But it could be better. First, the input resistances depend on the resistor values. Secondly it is difficult to adjust the gain, because the resistance ratios much remain matched. EE 230 op amps 20

21 An improvement Buffer amps can be added to increase the input resistance. Since the buffer amps have unity-gain, their outputs are equal to their input. The differencing amp on the right works exactly as before. v b v a v b v a v o (v a v b ) EE 230 op amps 21

22 Instrumentation amp A final modification turns this into a typical instrumentation amplifier. vy v vy ir3y vr4 vx vy ir4 vx R4 vy R3 v vx vx Use KVL: va va ir3x R1 R2 vo still true: R2 vo (va R1 vb ) ir3x ir3y ir4 vb ir4 (2R3 R4 ) vb R1 vb ir3xr3 ir4r4 ir3yr3 va since i 0 : EE 230 ir4 vb R3 R4 va R2 2R3 1 R4 vx vo R2 R1 2R3 1 R4 vx vy vy op amps 22

23 Adjustable instrumentation amp v y R 4 R R 3 1 R 3 v o v x 2R 3 R 4 1 v x v y EE 230 op amps 23

Operational amplifiers (Op amps)

Operational amplifiers (Op amps) Operational amplifiers (Op amps) Recall the basic two-port model for an amplifier. It has three components: input resistance, Ri, output resistance, Ro, and the voltage gain, A. v R o R i v d Av d v Also

More information

ECE2262 Electric Circuits. Chapter 4: Operational Amplifier (OP-AMP) Circuits

ECE2262 Electric Circuits. Chapter 4: Operational Amplifier (OP-AMP) Circuits ECE2262 Electric Circuits Chapter 4: Operational Amplifier (OP-AMP) Circuits 1 4.1 Operational Amplifiers 2 4. Voltages and currents in electrical circuits may represent signals and circuits can perform

More information

OPERATIONAL AMPLIFIER APPLICATIONS

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

More information

D is the voltage difference = (V + - V - ).

D is the voltage difference = (V + - V - ). 1 Operational amplifier is one of the most common electronic building blocks used by engineers. It has two input terminals: V + and V -, and one output terminal Y. It provides a gain A, which is usually

More information

E40M Review - Part 1

E40M Review - Part 1 E40M Review Part 1 Topics in Part 1 (Today): KCL, KVL, Power Devices: V and I sources, R Nodal Analysis. Superposition Devices: Diodes, C, L Time Domain Diode, C, L Circuits Topics in Part 2 (Wed): MOSFETs,

More information

EE 321 Analog Electronics, Fall 2013 Homework #3 solution

EE 321 Analog Electronics, Fall 2013 Homework #3 solution EE 32 Analog Electronics, Fall 203 Homework #3 solution 2.47. (a) Use superposition to show that the output of the circuit in Fig. P2.47 is given by + [ Rf v N + R f v N2 +... + R ] f v Nn R N R N2 R [

More information

EE-201 Review Exam I. 1. The voltage Vx in the circuit below is: (1) 3V (2) 2V (3) -2V (4) 1V (5) -1V (6) None of above

EE-201 Review Exam I. 1. The voltage Vx in the circuit below is: (1) 3V (2) 2V (3) -2V (4) 1V (5) -1V (6) None of above EE-201, Review Probs Test 1 page-1 Spring 98 EE-201 Review Exam I Multiple Choice (5 points each, no partial credit.) 1. The voltage Vx in the circuit below is: (1) 3V (2) 2V (3) -2V (4) 1V (5) -1V (6)

More information

EE100Su08 Lecture #9 (July 16 th 2008)

EE100Su08 Lecture #9 (July 16 th 2008) EE100Su08 Lecture #9 (July 16 th 2008) Outline HW #1s and Midterm #1 returned today Midterm #1 notes HW #1 and Midterm #1 regrade deadline: Wednesday, July 23 rd 2008, 5:00 pm PST. Procedure: HW #1: Bart

More information

Operational Amplifier (Op-Amp) Operational Amplifiers. OP-Amp: Components. Internal Design of LM741

Operational Amplifier (Op-Amp) Operational Amplifiers. OP-Amp: Components. Internal Design of LM741 (Op-Amp) s Prof. Dr. M. Zahurul Haq zahurul@me.buet.ac.bd http://teacher.buet.ac.bd/zahurul/ Department of Mechanical Engineering Bangladesh University of Engineering & Technology ME 475: Mechatronics

More information

Problem Set 4 Solutions

Problem Set 4 Solutions University of California, Berkeley Spring 212 EE 42/1 Prof. A. Niknejad Problem Set 4 Solutions Please note that these are merely suggested solutions. Many of these problems can be approached in different

More information

The equivalent model of a certain op amp is shown in the figure given below, where R 1 = 2.8 MΩ, R 2 = 39 Ω, and A =

The equivalent model of a certain op amp is shown in the figure given below, where R 1 = 2.8 MΩ, R 2 = 39 Ω, and A = The equivalent model of a certain op amp is shown in the figure given below, where R 1 = 2.8 MΩ, R 2 = 39 Ω, and A = 10 10 4. Section Break Difficulty: Easy Learning Objective: Understand how real operational

More information

PHYS225 Lecture 9. Electronic Circuits

PHYS225 Lecture 9. Electronic Circuits PHYS225 Lecture 9 Electronic Circuits Last lecture Field Effect Transistors Voltage controlled resistor Various FET circuits Switch Source follower Current source Similar to BJT Draws no input current

More information

Operational Amplifiers

Operational Amplifiers Operational Amplifiers A Linear IC circuit Operational Amplifier (op-amp) An op-amp is a high-gain amplifier that has high input impedance and low output impedance. An ideal op-amp has infinite gain and

More information

0 t < 0 1 t 1. u(t) =

0 t < 0 1 t 1. u(t) = A. M. Niknejad University of California, Berkeley EE 100 / 42 Lecture 13 p. 22/33 Step Response A unit step function is described by u(t) = ( 0 t < 0 1 t 1 While the waveform has an artificial jump (difficult

More information

Designing Information Devices and Systems I Spring 2018 Lecture Notes Note 20

Designing Information Devices and Systems I Spring 2018 Lecture Notes Note 20 EECS 16A Designing Information Devices and Systems I Spring 2018 Lecture Notes Note 20 Design Example Continued Continuing our analysis for countdown timer circuit. We know for a capacitor C: I = C dv

More information

DESIGN MICROELECTRONICS ELCT 703 (W17) LECTURE 3: OP-AMP CMOS CIRCUIT. Dr. Eman Azab Assistant Professor Office: C

DESIGN MICROELECTRONICS ELCT 703 (W17) LECTURE 3: OP-AMP CMOS CIRCUIT. Dr. Eman Azab Assistant Professor Office: C MICROELECTRONICS ELCT 703 (W17) LECTURE 3: OP-AMP CMOS CIRCUIT DESIGN Dr. Eman Azab Assistant Professor Office: C3.315 E-mail: eman.azab@guc.edu.eg 1 TWO STAGE CMOS OP-AMP It consists of two stages: First

More information

Frequency Dependent Aspects of Op-amps

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

More information

OPAMPs I: The Ideal Case

OPAMPs I: The Ideal Case I: The Ideal Case The basic composition of an operational amplifier (OPAMP) includes a high gain differential amplifier, followed by a second high gain amplifier, followed by a unity gain, low impedance,

More information

Chapter 2. Engr228 Circuit Analysis. Dr Curtis Nelson

Chapter 2. Engr228 Circuit Analysis. Dr Curtis Nelson Chapter 2 Engr228 Circuit Analysis Dr Curtis Nelson Chapter 2 Objectives Understand symbols and behavior of the following circuit elements: Independent voltage and current sources; Dependent voltage and

More information

Homework 3 Solution. Due Friday (5pm), Feb. 14, 2013

Homework 3 Solution. Due Friday (5pm), Feb. 14, 2013 University of California, Berkeley Spring 2013 EE 42/100 Prof. K. Pister Homework 3 Solution Due Friday (5pm), Feb. 14, 2013 Please turn the homework in to the drop box located next to 125 Cory Hall (labeled

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 : ND_EE_NW_Analog Electronics_05088 Delhi Noida Bhopal Hyderabad Jaipur Lucknow ndore Pune Bhubaneswar Kolkata Patna Web: E-mail: info@madeeasy.in Ph: 0-4546 CLASS TEST 08-9 ELECTCAL ENGNEENG Subject

More information

Electronics. Basics & Applications. group talk Daniel Biesinger

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

More information

Figure Circuit for Question 1. Figure Circuit for Question 2

Figure Circuit for Question 1. Figure Circuit for Question 2 Exercises 10.7 Exercises Multiple Choice 1. For the circuit of Figure 10.44 the time constant is A. 0.5 ms 71.43 µs 2, 000 s D. 0.2 ms 4 Ω 2 Ω 12 Ω 1 mh 12u 0 () t V Figure 10.44. Circuit for Question

More information

Analog Computing Technique

Analog Computing Technique Analog Computing Technique by obert Paz Chapter Programming Principles and Techniques. Analog Computers and Simulation An analog computer can be used to solve various types o problems. It solves them in

More information

Systematic methods for labeling circuits and finding a solvable set of equations, Operational Amplifiers. Kevin D. Donohue, University of Kentucky 1

Systematic methods for labeling circuits and finding a solvable set of equations, Operational Amplifiers. Kevin D. Donohue, University of Kentucky 1 Systematic methods for labeling circuits and finding a solvable set of equations, Operational Amplifiers Kevin D. Donohue, University of Kentucky Simple circuits with single loops or node-pairs can result

More information

Midterm Exam (closed book/notes) Tuesday, February 23, 2010

Midterm Exam (closed book/notes) Tuesday, February 23, 2010 University of California, Berkeley Spring 2010 EE 42/100 Prof. A. Niknejad Midterm Exam (closed book/notes) Tuesday, February 23, 2010 Guidelines: Closed book. You may use a calculator. Do not unstaple

More information

Solved Problems. Electric Circuits & Components. 1-1 Write the KVL equation for the circuit shown.

Solved Problems. Electric Circuits & Components. 1-1 Write the KVL equation for the circuit shown. Solved Problems Electric Circuits & Components 1-1 Write the KVL equation for the circuit shown. 1-2 Write the KCL equation for the principal node shown. 1-2A In the DC circuit given in Fig. 1, find (i)

More information

Chapter 5. Department of Mechanical Engineering

Chapter 5. Department of Mechanical Engineering Source Transformation By KVL: V s =ir s + v By KCL: i s =i + v/r p is=v s /R s R s =R p V s /R s =i + v/r s i s =i + v/r p Two circuits have the same terminal voltage and current Source Transformation

More information

INTRODUCTION TO ELECTRONICS

INTRODUCTION TO ELECTRONICS INTRODUCTION TO ELECTRONICS Basic Quantities Voltage (symbol V) is the measure of electrical potential difference. It is measured in units of Volts, abbreviated V. The example below shows several ways

More information

Start with the transfer function for a second-order high-pass. s 2. ω o. Q P s + ω2 o. = G o V i

Start with the transfer function for a second-order high-pass. s 2. ω o. Q P s + ω2 o. = G o V i 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

More information

E40M. Op Amps. M. Horowitz, J. Plummer, R. Howe 1

E40M. Op Amps. M. Horowitz, J. Plummer, R. Howe 1 E40M Op Amps M. Horowitz, J. Plummer, R. Howe 1 Reading A&L: Chapter 15, pp. 863-866. Reader, Chapter 8 Noninverting Amp http://www.electronics-tutorials.ws/opamp/opamp_3.html Inverting Amp http://www.electronics-tutorials.ws/opamp/opamp_2.html

More information

EIT Review. Electrical Circuits DC Circuits. Lecturer: Russ Tatro. Presented by Tau Beta Pi The Engineering Honor Society 10/3/2006 1

EIT Review. Electrical Circuits DC Circuits. Lecturer: Russ Tatro. Presented by Tau Beta Pi The Engineering Honor Society 10/3/2006 1 EIT Review Electrical Circuits DC Circuits Lecturer: Russ Tatro Presented by Tau Beta Pi The Engineering Honor Society 10/3/2006 1 Session Outline Basic Concepts Basic Laws Methods of Analysis Circuit

More information

Lecture 4: Feedback and Op-Amps

Lecture 4: Feedback and Op-Amps Lecture 4: Feedback and Op-Amps Last time, we discussed using transistors in small-signal amplifiers If we want a large signal, we d need to chain several of these small amplifiers together There s a problem,

More information

Unit 2: Modeling in the Frequency Domain. Unit 2, Part 4: Modeling Electrical Systems. First Example: Via DE. Resistors, Inductors, and Capacitors

Unit 2: Modeling in the Frequency Domain. Unit 2, Part 4: Modeling Electrical Systems. First Example: Via DE. Resistors, Inductors, and Capacitors Unit 2: Modeling in the Frequency Domain Part 4: Modeling Electrical Systems Engineering 582: Control Systems I Faculty of Engineering & Applied Science Memorial University of Newfoundland January 20,

More information

Lecture 6, ATIK. Switched-capacitor circuits 2 S/H, Some nonideal effects Continuous-time filters

Lecture 6, ATIK. Switched-capacitor circuits 2 S/H, Some nonideal effects Continuous-time filters Lecture 6, ATIK Switched-capacitor circuits 2 S/H, Some nonideal effects Continuous-time filters What did we do last time? Switched capacitor circuits The basics Charge-redistribution analysis Nonidealties

More information

20.2 Design Example: Countdown Timer

20.2 Design Example: Countdown Timer EECS 16A Designing Information Devices and Systems I Fall 018 Lecture Notes Note 0 0.1 Design Procedure Now that we ve analyzed many circuits, we are ready to focus on designing interesting circuits to

More information

Electronics Prof. D C Dube Department of Physics Indian Institute of Technology Delhi

Electronics Prof. D C Dube Department of Physics Indian Institute of Technology Delhi Electronics Prof. D C Dube Department of Physics Indian Institute of Technology Delhi Module No. 07 Differential and Operational Amplifiers Lecture No. 39 Summing, Scaling and Averaging Amplifiers (Refer

More information

First-order transient

First-order transient EIE209 Basic Electronics First-order transient Contents Inductor and capacitor Simple RC and RL circuits Transient solutions Constitutive relation An electrical element is defined by its relationship between

More information

A tricky node-voltage situation

A tricky node-voltage situation A tricky node-voltage situation The node-method will always work you can always generate enough equations to determine all of the node voltages. The method we have outlined well in almost all cases, but

More information

Series & Parallel Resistors 3/17/2015 1

Series & Parallel Resistors 3/17/2015 1 Series & Parallel Resistors 3/17/2015 1 Series Resistors & Voltage Division Consider the single-loop circuit as shown in figure. The two resistors are in series, since the same current i flows in both

More information

Problem Set 5 Solutions

Problem Set 5 Solutions University of California, Berkeley Spring 01 EE /0 Prof. A. Niknejad Problem Set 5 Solutions Please note that these are merely suggested solutions. Many of these problems can be approached in different

More information

Bandwidth of op amps. R 1 R 2 1 k! 250 k!

Bandwidth of op amps. R 1 R 2 1 k! 250 k! Bandwidth of op amps An experiment - connect a simple non-inverting op amp and measure the frequency response. From the ideal op amp model, we expect the amp to work at any frequency. Is that what happens?

More information

ECE2262 Electric Circuits. Chapter 5: Circuit Theorems

ECE2262 Electric Circuits. Chapter 5: Circuit Theorems ECE2262 Electric Circuits Chapter 5: Circuit Theorems 1 Equivalence Linearity Superposition Thevenin s and Norton s Theorems Maximum Power Transfer Analysis of Circuits Using Circuit Theorems 2 5. 1 Equivalence

More information

Homework 6 Solutions and Rubric

Homework 6 Solutions and Rubric Homework 6 Solutions and Rubric EE 140/40A 1. K-W Tube Amplifier b) Load Resistor e) Common-cathode a) Input Diff Pair f) Cathode-Follower h) Positive Feedback c) Tail Resistor g) Cc d) Av,cm = 1/ Figure

More information

Chapter 2 - DC Biasing - BJTs

Chapter 2 - DC Biasing - BJTs Objectives Chapter 2 - DC Biasing - BJTs To Understand: Concept of Operating point and stability Analyzing Various biasing circuits and their comparison with respect to stability BJT A Review Invented

More information

Quick Review. ESE319 Introduction to Microelectronics. and Q1 = Q2, what is the value of V O-dm. If R C1 = R C2. s.t. R C1. Let Q1 = Q2 and R C1

Quick Review. ESE319 Introduction to Microelectronics. and Q1 = Q2, what is the value of V O-dm. If R C1 = R C2. s.t. R C1. Let Q1 = Q2 and R C1 Quick Review If R C1 = R C2 and Q1 = Q2, what is the value of V O-dm? Let Q1 = Q2 and R C1 R C2 s.t. R C1 > R C2, express R C1 & R C2 in terms R C and ΔR C. If V O-dm is the differential output offset

More information

Design Engineering MEng EXAMINATIONS 2016

Design Engineering MEng EXAMINATIONS 2016 IMPERIAL COLLEGE LONDON Design Engineering MEng EXAMINATIONS 2016 For Internal Students of the Imperial College of Science, Technology and Medicine This paper is also taken for the relevant examination

More information

ELECTRONIC SYSTEMS. Basic operational amplifier circuits. Electronic Systems - C3 13/05/ DDC Storey 1

ELECTRONIC SYSTEMS. Basic operational amplifier circuits. Electronic Systems - C3 13/05/ DDC Storey 1 Electronic Systems C3 3/05/2009 Politecnico di Torino ICT school Lesson C3 ELECTONIC SYSTEMS C OPEATIONAL AMPLIFIES C.3 Op Amp circuits» Application examples» Analysis of amplifier circuits» Single and

More information

Chapter 2. - DC Biasing - BJTs

Chapter 2. - DC Biasing - BJTs Chapter 2. - DC Biasing - BJTs Objectives To Understand : Concept of Operating point and stability Analyzing Various biasing circuits and their comparison with respect to stability BJT A Review Invented

More information

DEPARTMENT OF COMPUTER ENGINEERING UNIVERSITY OF LAHORE

DEPARTMENT OF COMPUTER ENGINEERING UNIVERSITY OF LAHORE DEPARTMENT OF COMPUTER ENGINEERING UNIVERSITY OF LAHORE NAME. Section 1 2 3 UNIVERSITY OF LAHORE Department of Computer engineering Linear Circuit Analysis Laboratory Manual 2 Compiled by Engr. Ahmad Bilal

More information

Circuits Practice Websheet 18.1

Circuits Practice Websheet 18.1 Circuits Practice Websheet 18.1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. How much power is being dissipated by one of the 10-Ω resistors? a. 24

More information

Whereas the diode was a 1-junction device, the transistor contains two junctions. This leads to two possibilities:

Whereas the diode was a 1-junction device, the transistor contains two junctions. This leads to two possibilities: Part Recall: two types of charge carriers in semiconductors: electrons & holes two types of doped semiconductors: n-type (favor e-), p-type (favor holes) for conduction Whereas the diode was a -junction

More information

EIT Quick-Review Electrical Prof. Frank Merat

EIT Quick-Review Electrical Prof. Frank Merat CIRCUITS 4 The power supplied by the 0 volt source is (a) 2 watts (b) 0 watts (c) 2 watts (d) 6 watts (e) 6 watts 4Ω 2Ω 0V i i 2 2Ω 20V Call the clockwise loop currents i and i 2 as shown in the drawing

More information

ECE 220 Laboratory 4 Volt Meter, Comparators, and Timer

ECE 220 Laboratory 4 Volt Meter, Comparators, and Timer ECE 220 Laboratory 4 Volt Meter, Comparators, and Timer Michael W. Marcellin Please follow all rules, procedures and report requirements as described at the beginning of the document entitled ECE 220 Laboratory

More information

ECE2262 Electric Circuits. Chapter 6: Capacitance and Inductance

ECE2262 Electric Circuits. Chapter 6: Capacitance and Inductance ECE2262 Electric Circuits Chapter 6: Capacitance and Inductance Capacitors Inductors Capacitor and Inductor Combinations Op-Amp Integrator and Op-Amp Differentiator 1 CAPACITANCE AND INDUCTANCE Introduces

More information

ECE2262 Electric Circuits

ECE2262 Electric Circuits ECE2262 Electric Circuits Equivalence Chapter 5: Circuit Theorems Linearity Superposition Thevenin s and Norton s Theorems Maximum Power Transfer Analysis of Circuits Using Circuit Theorems 1 5. 1 Equivalence

More information

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

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

More information

Review of Circuit Analysis

Review of Circuit Analysis Review of Circuit Analysis Fundamental elements Wire Resistor Voltage Source Current Source Kirchhoff s Voltage and Current Laws Resistors in Series Voltage Division EE 42 Lecture 2 1 Voltage and Current

More information

Switched Capacitor Circuits II. Dr. Paul Hasler Georgia Institute of Technology

Switched Capacitor Circuits II. Dr. Paul Hasler Georgia Institute of Technology Switched Capacitor Circuits II Dr. Paul Hasler Georgia Institute of Technology Basic Switch-Cap Integrator = [n-1] - ( / ) H(jω) = - ( / ) 1 1 - e -jωt ~ - ( / ) / jωt (z) - z -1 1 (z) = H(z) = - ( / )

More information

At point G V = = = = = = RB B B. IN RB f

At point G V = = = = = = RB B B. IN RB f Common Emitter At point G CE RC 0. 4 12 0. 4 116. I C RC 116. R 1k C 116. ma I IC 116. ma β 100 F 116µ A I R ( 116µ A)( 20kΩ) 2. 3 R + 2. 3 + 0. 7 30. IN R f Gain in Constant Current Region I I I C F

More information

ECEN 325 Electronics

ECEN 325 Electronics ECEN 325 Electronics Operational Amplifiers Dr. Aydın İlker Karşılayan Texas A&M University Department of Electrical and Computer Engineering Opamp Terminals positive supply inverting input terminal non

More information

Electronic Circuits Summary

Electronic Circuits Summary Electronic Circuits Summary Andreas Biri, D-ITET 6.06.4 Constants (@300K) ε 0 = 8.854 0 F m m 0 = 9. 0 3 kg k =.38 0 3 J K = 8.67 0 5 ev/k kt q = 0.059 V, q kt = 38.6, kt = 5.9 mev V Small Signal Equivalent

More information

Module 2. DC Circuit. Version 2 EE IIT, Kharagpur

Module 2. DC Circuit. Version 2 EE IIT, Kharagpur Module 2 DC Circuit Lesson 5 Node-voltage analysis of resistive circuit in the context of dc voltages and currents Objectives To provide a powerful but simple circuit analysis tool based on Kirchhoff s

More information

ECE3050 Assignment 7

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

More information

Switched-Capacitor Circuits David Johns and Ken Martin University of Toronto

Switched-Capacitor Circuits David Johns and Ken Martin University of Toronto Switched-Capacitor Circuits David Johns and Ken Martin University of Toronto (johns@eecg.toronto.edu) (martin@eecg.toronto.edu) University of Toronto 1 of 60 Basic Building Blocks Opamps Ideal opamps usually

More information

Operational Amplifiers

Operational Amplifiers NDSU Operational Amplifiers ECE 06 JSG Operational Amplifiers An operational amplifier is a input device with V o k(v V ) where k is a large number. For short, the following symbol is used for an differential

More information

Time Varying Circuit Analysis

Time Varying Circuit Analysis MAS.836 Sensor Systems for Interactive Environments th Distributed: Tuesday February 16, 2010 Due: Tuesday February 23, 2010 Problem Set # 2 Time Varying Circuit Analysis The purpose of this problem set

More information

Homework Assignment 08

Homework Assignment 08 Homework Assignment 08 Question 1 (Short Takes) Two points each unless otherwise indicated. 1. Give one phrase/sentence that describes the primary advantage of an active load. Answer: Large effective resistance

More information

Biasing the CE Amplifier

Biasing the CE Amplifier Biasing the CE Amplifier Graphical approach: plot I C as a function of the DC base-emitter voltage (note: normally plot vs. base current, so we must return to Ebers-Moll): I C I S e V BE V th I S e V th

More information

Lecture 5: Using electronics to make measurements

Lecture 5: Using electronics to make measurements Lecture 5: Using electronics to make measurements As physicists, we re not really interested in electronics for its own sake We want to use it to measure something often, something too small to be directly

More information

VI. Transistor amplifiers: Biasing and Small Signal Model

VI. Transistor amplifiers: Biasing and Small Signal Model VI. Transistor amplifiers: iasing and Small Signal Model 6.1 Introduction Transistor amplifiers utilizing JT or FET are similar in design and analysis. Accordingly we will discuss JT amplifiers thoroughly.

More information

Designing Information Devices and Systems I Spring 2018 Lecture Notes Note 17

Designing Information Devices and Systems I Spring 2018 Lecture Notes Note 17 EECS 16A Designing Information Devices and Systems I Spring 2018 Lecture Notes Note 17 17.1 Capacitive Touchscreen Viewing the physical structure corresponding to one pixel on the capacitive screen, we

More information

Midterm Exam 2. Prof. Miloš Popović

Midterm Exam 2. Prof. Miloš Popović Midterm Exam 2 Prof. Miloš Popović 100 min timed, closed book test. Write your name at top of every page (or initials on later pages) Aids: single page (single side) of notes, handheld calculator Work

More information

Designing Information Devices and Systems I Fall 2018 Lecture Notes Note Introduction: Op-amps in Negative Feedback

Designing Information Devices and Systems I Fall 2018 Lecture Notes Note Introduction: Op-amps in Negative Feedback EECS 16A Designing Information Devices and Systems I Fall 2018 Lecture Notes Note 18 18.1 Introduction: Op-amps in Negative Feedback In the last note, we saw that can use an op-amp as a comparator. However,

More information

CIRCUITS AND ELECTRONICS. Dependent Sources and Amplifiers

CIRCUITS AND ELECTRONICS. Dependent Sources and Amplifiers 6.00 CIRCUITS AN ELECTRONICS ependent Sources and Amplifiers Review Nonlinear circuits can use the node method Small signal trick resulted in linear response Today ependent sources Amplifiers Reading:

More information

Physics 364, Fall 2012, reading due your answers to by 11pm on Thursday

Physics 364, Fall 2012, reading due your answers to by 11pm on Thursday Physics 364, Fall 2012, reading due 2012-09-20. Email your answers to ashmansk@hep.upenn.edu by 11pm on Thursday Course materials and schedule are at http://positron.hep.upenn.edu/p364 Assignment: This

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 7: Transistors and Amplifiers

Lecture 7: Transistors and Amplifiers Lecture 7: Transistors and Amplifiers Hybrid Transistor Model for small AC : The previous model for a transistor used one parameter (β, the current gain) to describe the transistor. doesn't explain many

More information

Input and Output Impedances with Feedback

Input and Output Impedances with Feedback EE 3 Lecture Basic Feedback Configurations Generalized Feedback Schemes Integrators Differentiators First-order active filters Second-order active filters Review from Last Time Input and Output Impedances

More information

EE 321 Analog Electronics, Fall 2013 Homework #8 solution

EE 321 Analog Electronics, Fall 2013 Homework #8 solution EE 321 Analog Electronics, Fall 2013 Homework #8 solution 5.110. The following table summarizes some of the basic attributes of a number of BJTs of different types, operating as amplifiers under various

More information

UNIT 4 DC EQUIVALENT CIRCUIT AND NETWORK THEOREMS

UNIT 4 DC EQUIVALENT CIRCUIT AND NETWORK THEOREMS UNIT 4 DC EQUIVALENT CIRCUIT AND NETWORK THEOREMS 1.0 Kirchoff s Law Kirchoff s Current Law (KCL) states at any junction in an electric circuit the total current flowing towards that junction is equal

More information

DC Biasing. Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Mar / 59

DC Biasing. Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Mar / 59 Contents Three States of Operation BJT DC Analysis Fixed-Bias Circuit Emitter-Stabilized Bias Circuit Voltage Divider Bias Circuit DC Bias with Voltage Feedback Various Dierent Bias Circuits pnp Transistors

More information

ECE1750, Spring Week 11 Power Electronics

ECE1750, Spring Week 11 Power Electronics ECE1750, Spring 2017 Week 11 Power Electronics Control 1 Power Electronic Circuits Control In most power electronic applications we need to control some variable, such as the put voltage of a dc-dc converter,

More information

Georgia Institute of Technology School of Electrical and Computer Engineering. Midterm-1 Exam (Solution)

Georgia Institute of Technology School of Electrical and Computer Engineering. Midterm-1 Exam (Solution) Georgia Institute of Technology School of Electrical and Computer Engineering Midterm-1 Exam (Solution) ECE-6414 Spring 2012 Friday, Feb. 17, 2012 Duration: 50min First name Solutions Last name Solutions

More information

Energy Storage Elements: Capacitors and Inductors

Energy Storage Elements: Capacitors and Inductors CHAPTER 6 Energy Storage Elements: Capacitors and Inductors To this point in our study of electronic circuits, time has not been important. The analysis and designs we have performed so far have been static,

More information

Thevenin equivalent circuits

Thevenin equivalent circuits Thevenin equivalent circuits We have seen the idea of equivalency used in several instances already. 1 2 1 2 same as 1 2 same as 1 2 R 3 same as = 0 V same as 0 A same as same as = EE 201 Thevenin 1 The

More information

Chapter 7. Chapter 7

Chapter 7. Chapter 7 Chapter 7 Combination circuits Most practical circuits have combinations of series and parallel components. You can frequently simplify analysis by combining series and parallel components. An important

More information

Homework Assignment 11

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

More information

EE40 Midterm Review Prof. Nathan Cheung

EE40 Midterm Review Prof. Nathan Cheung EE40 Midterm Review Prof. Nathan Cheung 10/29/2009 Slide 1 I feel I know the topics but I cannot solve the problems Now what? Slide 2 R L C Properties Slide 3 Ideal Voltage Source *Current depends d on

More information

Examination paper for TFY4185 Measurement Technique/ Måleteknikk

Examination paper for TFY4185 Measurement Technique/ Måleteknikk Page 1 of 14 Department of Physics Examination paper for TFY4185 Measurement Technique/ Måleteknikk Academic contact during examination: Patrick Espy Phone: +47 41 38 65 78 Examination date: 15 August

More information

Lecture 5: Using electronics to make measurements

Lecture 5: Using electronics to make measurements Lecture 5: Using electronics to make measurements As physicists, we re not really interested in electronics for its own sake We want to use it to measure something often, something too small to be directly

More information

Chapter 19 Lecture Notes

Chapter 19 Lecture Notes Chapter 19 Lecture Notes Physics 2424 - Strauss Formulas: R S = R 1 + R 2 +... C P = C 1 + C 2 +... 1/R P = 1/R 1 + 1/R 2 +... 1/C S = 1/C 1 + 1/C 2 +... q = q 0 [1-e -t/(rc) ] q = q 0 e -t/(rc τ = RC

More information

Module 2. DC Circuit. Version 2 EE IIT, Kharagpur

Module 2. DC Circuit. Version 2 EE IIT, Kharagpur Module DC Circuit Lesson 4 Loop Analysis of resistive circuit in the context of dc voltages and currents Objectives Meaning of circuit analysis; distinguish between the terms mesh and loop. To provide

More information

Analog Integrated Circuit Design Prof. Nagendra Krishnapura Department of Electrical Engineering Indian Institute of Technology, Madras

Analog Integrated Circuit Design Prof. Nagendra Krishnapura Department of Electrical Engineering Indian Institute of Technology, Madras Analog Integrated Circuit Design Prof. Nagendra Krishnapura Department of Electrical Engineering Indian Institute of Technology, Madras Lecture No - 42 Fully Differential Single Stage Opamp Hello and welcome

More information

Introduction to AC Circuits (Capacitors and Inductors)

Introduction to AC Circuits (Capacitors and Inductors) Introduction to AC Circuits (Capacitors and Inductors) Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/

More information

POLYTECHNIC UNIVERSITY Electrical Engineering Department. EE SOPHOMORE LABORATORY Experiment 2 DC circuits and network theorems

POLYTECHNIC UNIVERSITY Electrical Engineering Department. EE SOPHOMORE LABORATORY Experiment 2 DC circuits and network theorems POLYTECHNIC UNIVERSITY Electrical Engineering Department EE SOPHOMORE LABORATORY Experiment 2 DC circuits and network theorems Modified for Physics 18, Brooklyn College I. Overview of Experiment In this

More information

CS 436 HCI Technology Basic Electricity/Electronics Review

CS 436 HCI Technology Basic Electricity/Electronics Review CS 436 HCI Technology Basic Electricity/Electronics Review *Copyright 1997-2008, Perry R. Cook, Princeton University August 27, 2008 1 Basic Quantities and Units 1.1 Charge Number of electrons or units

More information

Biquad Filter. by Kenneth A. Kuhn March 8, 2013

Biquad Filter. by Kenneth A. Kuhn March 8, 2013 by Kenneth A. Kuhn March 8, 201 The biquad filter implements both a numerator and denominator quadratic function in s thus its name. All filter outputs have identical second order denominator in s and

More information

Studio 9 Review Operational Amplifier Stability Compensation Miller Effect Phase Margin Unity Gain Frequency Slew Rate Limiting Reading: Text sec 5.

Studio 9 Review Operational Amplifier Stability Compensation Miller Effect Phase Margin Unity Gain Frequency Slew Rate Limiting Reading: Text sec 5. Studio 9 Review Operational Amplifier Stability Compensation Miller Effect Phase Margin Unity Gain Frequency Slew Rate Limiting Reading: Text sec 5.2 pp. 232-242 Two-stage op-amp Analysis Strategy Recognize

More information

Electromechanical devices MM2EMD. Lecture 5 Using Operational Amplifiers (opamps) in the real world

Electromechanical devices MM2EMD. Lecture 5 Using Operational Amplifiers (opamps) in the real world University of Nottingham Electromechanical devices MM2EMD Lecture 5 Using Operational Amplifiers (opamps) in the real world Dr. roderick.mackenzie@nottingham.ac.uk Summer 2015 @rcimackenzie Released under

More information