analyse and design a range of sinewave oscillators understand the design of multivibrators.


 Judith Black
 1 years ago
 Views:
Transcription
1 INTODUTION In this lesson, we investigate some forms of waveform generation using op amps. Of course, we could use basic transistor circuits, but it makes sense to simplify the analysis by considering the ideal op amp. We also see in this lesson how the op amp can be used in switching applications. YOU AIMS At the end of the lesson, you should be able to: analyse and design a range of sinewave oscillators use an op amp as a switch understand the design of multivibrators. STUDY SKILLS There is a fair amount of mathematical manipulation in this unit. Make sure you follow the steps. When you come to do the SelfAssessment Questions, remember that there are many ways of using electrical theory to analyse a circuit. Use that with which you are most comfortable. Teesside University 0
2 OSILLATOS Oscillators are waveform generators. Usually, it is their frequency of oscillation and wave shape that is important. Oscillators can be classified as: sinusoidal square wave others, e.g. triangular, staircase, trapezoidal, etc. We have found the general condition for oscillation in Lesson of this topic. emember the condition for oscillation is a gain of at least when the phase shift round a feedback loop is 0 at some frequency. We shall first investigate some oscillators giving sinusoidal output. SINE WAE OSILLATOS wien bridge oscillator Z Z 0 FIG. Teesside University 0
3 3 onsider the network of FIGUE. Z jω Series and / jω and Z ( jω ) Parallel and / jω /jω jω Hence, ( jω ) Z jω ( jω ) Z ( jω) Z ( jω) ( jω) ω / j jω / jω jω jω ( ω) 3 jω ()... Now, when does this expression have either 0 or 80 phase shift? When the above expression is purely real! The only way this can apply in this equation is if the real term in the denominator is 0; then the 'j' factors in the numerator and denominator cancel. Teesside University 0
4 4... ω 0 i.e. ( jω ) jω jω 0 3jω So the circuit will oscillate at a frequency given by Equation (): ω / or f ω / π / π Hz provided that is fed back to with a gain of 3 (to make the loop gain or more). Let us look at how we design an amplifier with a gain of 3. See FIGUE. 0 FIG. What should / be? Suggest suitable values, bearing in mind that resistor tolerances could bring the ratio below the critical value..... Teesside University 0
5 5 The gain of this amplifier is /, so / must be greater than. kω and 0 kω would be suitable, unless the resistor tolerance is very high. What determines the amplitude of the oscillation? Only the output range of the op amp limits it. Since the characteristic of the amplifier has a hard saturation, the circuit above would generate a distorted sine wave as illustrated in FIGUE 3. This is because there is a sudden gain reduction to almost 0. To minimize distortion, we should build in a soft saturation. FIGUE 4 shows a possible modification, and shows the complete oscillator. ve saturation 0 ve saturation FIG. 3 Teesside University 0
6 FIG. 4 We arrange for / > (say.) and ( )/ < (say.5). Then, 3 when the Zener diodes conduct, the gain falls below the crucial level required to maintain oscillation. This damps the oscillation, preventing it from building up. Suppose we want a ±0 peakpeak output. If 0, 0/3 (since the gain is nominally 3). Hence, there is about (00/3) 6.7 across and this is the value of the Zener diode we should choose (say 6.3). Another way of controlling the amplitude of oscillation is by using a voltage dependent resistor instead of. Teesside University 0
7 7 OLPITTS OSILLATO i x o L Z 0 FIG. 5 We want to find o / i in FIGUE 5. o x ( jω ) jω / jω jωl / jω ω L... 4 Also, Z (jω) is the complex impedance obtained from j ω L j ω j ω Z ( jω ) jωl / jω / jω jωl / jω / jω jω 3 ω L L jω... ( 5) Teesside University 0
8 8 We are now able to derive an expression for o / i. o i o x x i ω L Z Z ω L ω L j 3 jω... ( 6) Make sure you can derive this equation from the previous line. This is real when the imaginary terms of the denominator sum to 0. jω3l jω 0 ω L... ( 7) At this frequency, o i... 8 The negative sign in this equation indicates that there is a 80 phase shift. So, to oscillate at the frequency defined by Equation (7), we require an amplifier with a gain of / as shown in FIGUE 6. Note that the resistor plays no direct part in the circuit; it merely provides a convenient impedance between the amplifier and the frequency dependent elements. The above analysis is only one way of finding o / i ; you could use Thevenin or nodal analysis. It comes to the same thing. FIGUE 6 shows the complete oscillator. Teesside University 0
9 9 3 L 0 FIG. 6 SUMMAY OF SINEWAE OSILLATOS The analysis of all sinewave oscillators follows more or less the same pattern. The analysis can be fairly complex, and there are plenty of opportunities for making algebraic errors. The process steps are as follows.. Analyse a complex network.. Find at what ω the gain of the network is purely real. 3. Find the magnitude of the gain at this ω. 4. Design an amplifier to make the overall gain of. 5. Include a soft saturation characteristic. The ordinary 74 op amp is only useful over a low frequency range, say up to about 3 to 4 khz. Above these frequencies, slew rate limitations start to show up. So you need a higher frequency op amp, or you can use a simple transistor amplifier! Teesside University 0
10 0 THE OPEATIONAL AMPLIFIE AS A SWITH o o 0 o o o ve Saturation 0 ve Saturation FIG. 7 With a high gain op amp, any small difference between the inputs will send the output into saturation. If, in the circuit above, is positive then, if >, the output will go to negative saturation; on the other hand, a signal less than will cause the amplifier to go to positive saturation. emember that o A ( ). Hence, the circuit acts as a switch; o changes when. If we want to avoid the uncertain values of amplifier saturation, we can add the Zener diode network as shown above. The output is then clamped at voltages of Z D as shown above. The value of the resistor is not critical, but it has to supply the load current and the Zener diode current. o( sat) ( Z ) D > Load current Zener current Teesside University 0
11 LEEL DETETO WITH HYSTEESIS in ( Z D ) 3 0 FIG. 8 o ( Z D ) 0 in in in ( Z D ) h h FIG. 9 In this circuit, we have positive feedback from the output to the noninverting input. So the output can only be stable in the two saturation limits. There are therefore only two stable levels for. Switching of the output occurs when and so there are two different input voltages at which the output will switch. This is similar in concept to a thermostat which is used to switch on at a low temperature and off at a higher temperature to control an oven. Teesside University 0
12 Since there are two stable output levels, another name for this circuit is a bistable, or sometimes bistable multivibrator. It also performs the same function as a Schmitt trigger circuit. You will find all these names in textbooks. Switching occurs when. Z D But Note that can be either positive or negative, depending on the amplifier output. Also, Hence, in... 0 in So we can write down the equations for the two values of in at which the circuit output switches. in Z D h... 3 ( ) in Z D 3 h... ( ) where h is half the hysteresis voltage as shown in FIGUE ± o Z D Teesside University 0
13 3 NOTES. Note that is the midvoltage between the two input switching levels. (e.g. if we want to design a level detector that switches at 4 and 8, then ).. The voltage difference between the two input switching levels is the hysteresis h. 3. Many other forms of level detector are possible. They can all be analysed by considering the conditions when. 4. In practice, the slew rate of the common op amps limits the switching speed of the circuit. It is therefore better to use a comparator, an integrated circuit which much resembles the op amp, but is specifically designed for high slew rates. WOKED EXAMPLE Design a level detector which will switch at ± 5. Take ( Z D ) as 7. It is clear that, by adding equations () and (), we can eliminate h. in in So, if in 5 and in 5 then 0. Teesside University 0
14 4 Now substitute the figures into equation () /.8. 3 We should choose 3 8 kω and 0 kω. The value of is not critical; choose 0 kω. In designing level detectors, the significant errors will clearly be: accuracy and stability of the reference voltage stability and matching of the Zener diodes resistor tolerance errors due to op amp bias current and offset voltage. Teesside University 0
15 5 ASTABLE MULTIIBATO 3 ( Z D ) 0 FIG. 0 This circuit is a modification of the level detector and provides a continuous squarewave output. Typical waveforms are shown in FIGUE. A capacitor is charged and discharged via a resistor. Switching takes place when. Immediately after the output switches, the polarity of also changes, and the voltage across the capacitor charges towards this new level exponentially. Teesside University 0
16 6 ( Z D ) 0 t ( Z D ) T t 0 T FIG. Typical Waveforms As in the level detector, Z 3 D... ( 4) The equation for can be written by considering the initial and final voltages of an exponential with a time constant of. ( ) exp t /... 5 Z D You may find this a little hard to see. ompare this equation with that for the simple circuit shown below. We have to consider an initial condition; the exponential starts from and would continue until the asymptotic value [ Z D ], if switching did not intervene. Teesside University 0
17 7 B Final voltage ( B 0 ) t 0 t 0 Switch closes Initial capacitor voltage B As a check, put t 0 in equation (5) and remember e 0. Then put t infinity. Z D Z D Switching occurs when, and t T half the period of the cycle. Z 3 D Z D Z 3 D ( exp( T / ) ) Z 3 D Teesside University 0
18 8 Simplify by dividing by [ Z D ] and multiplying by ( 3 ): exp T / 3 3 exp( T / ) 3 3 exp( T / ) So exp( T / ) / 3 The full cycle period is T, since the circuit is symmetrical. It is interesting that the frequency does not depend on the Zener voltages. What errors would you expect between predicted and actual performance? The errors would be the same as for the level detector, plus the limitation of the amplifier slew rate, which means that the waveform will not be square, but a trapezoid. Teesside University 0
19 9 WOKED EXAMPLE What is the oscillation frequency of the astable multivibrator if 3 0 kω and 0 nf? Substitute the values into equation (6) to obtain the half period. T ln μs Frequency, f T 455 Hz. As with the level detector, there are many similar squarewave oscillator circuits. A very popular integrated circuit which can be used for oscillators or timers (as in the next section) is the type 555. MONOSTABLE MULTIIBATO This is the third circuit in this family of oscillators. The level detector had two stable states, while the astable had none; the monostable has one stable state. In other words, the monostable stays in a stable condition until it is triggered externally. It then produces a single pulse of defined length before recovering to its initial condition. Teesside University 0
20 0 T T Z D 3 0 FIG. ( Z D ) D 0 t ( Z D ) t 0 T m T r FIG. 3 Illustrative Waveforms The diode in FIGUE clamps the capacitor voltage at about 0.7, thus preventing the voltage rising to ; the circuit is in a stable condition. A negative trigger pulse, T, pulls down to the level of the capacitor voltage and initiates a negative output pulse of defined width. Immediately after the trigger pulse, the waveform is defined by the following equation, obtained by the same sort of considerations that generated the astable exponential equation. Teesside University 0
21 The capacitor starts to charge from D to ( Z D ). ( ) D Z D exp t / D... ( 7) Also ± Z D eset occurs when, and t T m the monostable period. Z 3 D ( exp( )) D D Z D Tm / earrange this equation in the same way as we did for the astable circuit. T m ( ) D Z / 3 ln... 9 ( Z D) Prove for yourself that this is true. NOTES. To ensure triggering, T must be greater than ( D ).. To reverse the output and trigger sense, change the polarity of the diode connection. 3. An expression for the recovery time can also be derived using a similar analysis. The recovery time is less than the monostable time, but can still be too long for convenience. If we demand another pulse before recovery Teesside University 0
22 is complete, the resultant period T m will be shorter. FIGUE 4 shows a modification to reduce the recovery time whilst leaving T m unaffected. 4. The monostable suffers from the same errors as the astable, and you will note that in this case T m depends on [ Z D ]. 4 << 4 ( Z D ) FIG. 4 WOKED EXAMPLE 3 Design a monostable with a T m of 0 seconds. As in all design problems there are choices to be made. The student finds it much easier to calculate T m if all the parameters of equation (9) are known. It is much harder to choose sensible values to give a desired answer! Let us choose Z 5.6, a readily available device, and assume that D 0.7. It also seems sensible to try making 3 (say 00 kω). Hence the 'ln' term yields the following value. Teesside University 0
23 3 ln ( ) ( ) D Z / 3 07 ln ( Z D). 56. ( ) 080. Hence, T m / It is best to use a high value of to keep the value of low and cheap. A reasonable solution would be to make 0 μf and. MΩ. Teesside University 0
24 4 SELFASSESSMENT QUESTIONS. Find the formulae for oscillation frequency and gain required for a Wien bridge oscillator where the two resistors are not equal as shown below. Z Z 0. Derive the formula for the frequency of oscillation of the Hartley oscillator based on the circuit below. What sort of amplifier is needed and what gain will be required if L mh and L 0.5 mh? Z L L 0 3. A phaseshift oscillator has the circuit shown opposite. Prove that j ω 6 ω 5jω j ω 3 3 Teesside University 0
25 5 emember that the into the amplifier loads the point. Hence find the ratio F / to cause oscillation. hoose components to give an oscillation frequency of khz. F x y Design a level detector to operate at input signal levels of 6 and. Assume [ Z D ] Design a squarewave generator to oscillate at a frequency of khz. 6. Show that the recovery time for the monostable circuit of FIGUE is given by the equation below. Tr ln D / Z { } 3 Teesside University 0
26 6 7. Find the input voltages at which the circuit below switches. in 0 kω 0 kω 0 z In the level detector circuit below, the two resistors no longer have the same value. BUT the is defined to be 5 or 5 (depending on the design requirement). Derive new formulae for the input switching levels and design a circuit to switch at 6 and. Assume ( Z D ) 0. in a b 3 Z D 0 Teesside University 0
27 7 NOTES Teesside University 0
28 8 ANSWES TO SELFASSESSMENT QUESTIONS. Put Z / jω jω jω and Z / jω / jω /jω jω Now Z Z Z jω jω jω jω Multiply above and below by jω (jω ). jω ( ) jω jω jω jω ( [ ] ) ω jω This is real when [ ω ( )] 0 i.e. ω At this frequency, jω jω( ). Teesside University 0
29 9 Therefore, to ensure oscillation, the gain of an accompanying amplifier must be greater than / /. Note: If we make, then ω / and the gain requirement is 3 as in the lesson.. We will follow the same steps as in the olpitts oscillator. jω L ω L / jω jωl ω L Z ( jω L ) ωl ω ωl ( / jω ωl ) ( j ) / j j j jωl jωl / jω ( jωl )( L ) ω ω L L ω ω L L Z Z ω L ω L ( j ω L )( ω L ) ω L L ( jωl ) ω L ω ( L L ). This simplifies to the expression below. jω 3 L L ω L L L jω ω L Teesside University 0
30 30 To make this real, the real part of the denominator must be zero. ω L L 0 ω L L i.e. At this frequency, jω 3 LL jωl ( ω L ) ω L ω L Now, using the frequency condition, substitute / L L for ω. L L To obtain an overall gain of, we need an amplifier gain of L /L. If L mh and L 0.5 mh, the required gain is. 3. Algebraically, this is probably one of the hardest problems which has been set. onsider the currents at the nodes x, y and. Note that, at, the current flows to the virtual earth via the righthand resistance. x jω x y j ω x /... A x y jω y j ω y /... B y j ω /... Multiply each equation by and put jω K. Teesside University 0
31 3... A K K x x y x K K... B x y y y ( ) K y... Arrange each of these three equations so that terms are gathered.... ( A) K K x Ky 0 Kx K y K 0... B Ky K 0... We must now eliminate x and y from these simultaneous equations. (A) (): ( )... ( D) K K K 0 x K (B) (K ) (): K K K K 0... D x ( ) This eliminates y. Now we need to remove x using equations (D) and (D). Teesside University 0
32 3 K (D) (K ) (D) gives equation (E) below. ( ) K3 K K K K K K 0 Gather all the terms in, multiplying out the brackets. An equation of the following form results. ( E) K3 F 0 where K 3 K K 3 K 4K 3 4K K 4K 4K F The coefficient F can be considerably simplified. K3 K3 6K ( 5K ) 0 The voltage gain may then be obtained by rearrangement. K 3 K3 6K 5K Now replace K with jω. j( ω) 6 ω 5jω j ω 3 3. Teesside University 0
33 33 This has been hard going; you need a clear head and a logical procedure to be successful. If you refer back to Lesson of this topic, you will find that the required gain is 9, and the frequency is defined as below. ω 6. f ω / π 0 3 From this, we can derive the required value of. π If we choose nf, then 3.5 kω. Select 33 kω as the nearest value in the E series. 4. Use equations () and () of the lesson text and substitute in the values given Add these equations to obtain the value of. 4 Teesside University 0
34 34 Substitute this value of into the first equation earrange to give a relationship bewtween and hoosing 0 kω and 3 7 kω would be close. hoose 0 kω (or any other convenient value). 5. f /T where T half the period of oscillation. So T / f Use equation (6) and substitute this value of T ln / 3 hoose 3 (this is almost always a sensible choice) / ln Some trial and error with standard component values gives 56 nf and 8. kω as a close fit. Teesside University 0
35 35 6. The exponential equation for the recovery time, T r, is as follows. Z D exp t / When t T r, D. Substitute in these values. D Z D exp Tr / Substitute for. D Z D Z 3 D exp Tr / Z 3 D earrange this equation to isolate the exponential term. Z D D 3 ( Z D) 3 r exp( T / ) exp ( T / ) r Z ( Z ) / D 3 Finally, Tr ln D / Z / 3 A few intermediate steps have been missed out here. Make sure you can fill them in. Teesside University 0
36 36 7. With 7.5 Zener diodes, the output voltages are ( ) / Z D / / 8.. Since 0, switching occurs when 0. Input current must flow via the 0 kω and kω resistors, giving the following relationship. in / Hence, the voltage at which the circuit switches is determined as follows in / / 373. This is an example of a different comparator, one that gives a positive output transition for a rising input voltage. 8. In this level detector, switching still takes place when, and is still defined in the same way; the only change is the relationship between the input voltage, and. in a in b a a b / / b in a b a b Teesside University 0
37 37 So we now have the two equations for the two input switching levels. in / Z D a b 3 /... A a b in ( ) / Z D a b 3 /... B a b Substitute the values in 6 and in and add equations (A) and (B). 6 / a b is either 5 or 5, but we must choose 5 in this case. b / a 30 / hoose b 56 kω and a 5 kω as appropriate E resistances to yield this ratio. Now substitute in equation (A), remembering that ( Z D ) 0. 6 ( 0) ( / 3. 75) ( ) 3 5 / / It is not possible to get very close to this ratio with just two resistors. 3 0 kω and kω is about the best. Teesside University 0
38 38 SUMMAY In this lesson, we have learnt how to design sinewave oscillators, by using the Barkhausen criterion of seeking the condition when the loop gain is when the phase shift round a feedback loop is 0. We have also investigated a family of circuits defined as follows: Bistable multivibrator or Level detector or Schmitt trigger or comparator Astable multivibrator or squarewave oscillator Monostable multivibrator or timer. All these circuits have been treated as op amp applications, but there are many other ways of obtaining the same result. Teesside University 0
CHAPTER 14 SIGNAL GENERATORS AND WAVEFORM SHAPING CIRCUITS
CHAPTER 4 SIGNA GENERATORS AND WAEFORM SHAPING CIRCUITS Chapter Outline 4. Basic Principles of Sinusoidal Oscillators 4. Op Amp RC Oscillators 4.3 C and Crystal Oscillators 4.4 Bistable Multivibrators
More informationassess the biasing requirements for transistor amplifiers
1 INTODUTION In this lesson we examine the properties of the bipolar junction transistor (JT) amd its typical practical characteristics. We then go on to devise circuits in which we can take best advantage
More informationNonlinear Opamp Circuits
deba21pratim@gmail.com Electronic Systems Group Department of Electrical Engineering IIT Bombay May 3, 2013 Overview of opamp operating regions Linear Region Occurs when the opamp output is stable i.e.
More informationBasic Principles of Sinusoidal Oscillators
Basic Principles of Sinusoidal Oscillators Linear oscillator Linear region of circuit: linear oscillation Nonlinear region of circuit: amplitudes stabilization Barkhausen criterion X S Amplifier A X O
More informationENGN3227 Analogue Electronics. Problem Sets V1.0. Dr. Salman Durrani
ENGN3227 Analogue Electronics Problem Sets V1.0 Dr. Salman Durrani November 2006 Copyright c 2006 by Salman Durrani. Problem Set List 1. Opamp Circuits 2. Differential Amplifiers 3. Comparator Circuits
More informationELECTRONIC 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 informationVer 3537 E1.1 Analysis of Circuits (2014) E1.1 Circuit Analysis. Problem Sheet 1 (Lectures 1 & 2)
Ver 3537 E. Analysis of Circuits () Key: [A]= easy... [E]=hard E. Circuit Analysis Problem Sheet (Lectures & ). [A] One of the following circuits is a series circuit and the other is a parallel circuit.
More information(d) describe the action of a 555 monostable timer and then use the equation T = 1.1 RC, where T is the pulse duration
Chapter 1  Timing Circuits GCSE Electronics Component 2: Application of Electronics Timing Circuits Learners should be able to: (a) describe how a RC network can produce a time delay (b) describe how
More informationSection 4. Nonlinear Circuits
Section 4 Nonlinear Circuits 1 ) Voltage Comparators V P < V N : V o = V ol V P > V N : V o = V oh One bit A/D converter, Practical gain : 10 3 10 6 V OH and V OL should be far apart enough Response Time:
More informationFrequency Dependent Aspects of Opamps
Frequency Dependent Aspects of Opamps Frequency dependent feedback circuits The arguments that lead to expressions describing the circuit gain of inverting and noninverting amplifier circuits with resistive
More informationDepartment of Electrical Engineering and Computer Sciences University of California, Berkeley. Final Exam Solutions
Electrical Engineering 42/00 Summer 202 Instructor: Tony Dear Department of Electrical Engineering and omputer Sciences University of alifornia, Berkeley Final Exam Solutions. Diodes Have apacitance?!?!
More informationTime 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 informationECE 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 informationHomework 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 informationEE101 IMPERIAL COLLEGE LONDON DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING EXAMINATIONS 2013 ANALYSIS OF CIRCUITS. Tuesday, 28 May 10:00 am
EE101 IMPERIAL COLLEGE LONDON DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING EXAMINATIONS 2013 ExamHeader: EEE/EIE PART I: MEng, Beng and ACGI ANALYSIS OF CIRCUITS Tuesday, 28 May 10:00 am Time allowed:
More informationOscillators. Figure 1: Functional diagram of an oscillator.
Oscillats Oscillats are electronic circuits, which are applied to generate periodic signals such sinusoidal, squarewave, triangular wave, pulse trains, clock signals etc. Oscillats are the essence of
More informationDesign 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 informationFigure 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 information55:041 Electronic Circuits The University of Iowa Fall Final Exam
Final Exam Name: Score Max: 135 Question 1 (1 point unless otherwise noted) a. What is the maximum theoretical efficiency for a classb amplifier? Answer: 78% b. The abbreviation/term ESR is often encountered
More informationECE3050 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 linearlog scales for the phase plots. On the magnitude
More informationFinal Exam. 55:041 Electronic Circuits. The University of Iowa. Fall 2013.
Final Exam Name: Max: 130 Points Question 1 In the circuit shown, the opamp is ideal, except for an input bias current I b = 1 na. Further, R F = 10K, R 1 = 100 Ω and C = 1 μf. The switch is opened at
More informationEE 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 informationElectronics for Analog Signal Processing  II Prof. K. Radhakrishna Rao Department of Electrical Engineering Indian Institute of Technology Madras
Electronics for Analog Signal Processing  II Prof. K. Radhakrishna Rao Department of Electrical Engineering Indian Institute of Technology Madras Lecture  14 Oscillators Let us consider sinusoidal oscillators.
More informationBiasing BJTs CHAPTER OBJECTIVES 4.1 INTRODUCTION
4 DC Biasing BJTs CHAPTER OBJECTIVES Be able to determine the dc levels for the variety of important BJT configurations. Understand how to measure the important voltage levels of a BJT transistor configuration
More informationHomework Assignment 09
Homework Assignment 09 Question 1 (Short Takes) Two points each unless otherwise indicated. 1. What is the 3dB bandwidth of the amplifier shown below if r π = 2.5K, r o = 100K, g m = 40 ms, and C L =
More informationElectronics 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 informationRLC Circuits and Resonant Circuits
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
More informationU1 is zero based because its noninverting terminal is connected to circuit common. Therefore, the circuit reference voltage is 0 V.
When you have completed this exercise, you will be able to operate a zenerclamped op amp comparator circuit using dc and ac voltages. You will verify your results with an oscilloscope. U1 is zero based
More informationE40M 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 informationOperational Amplifiers
Operational Amplifiers A Linear IC circuit Operational Amplifier (opamp) An opamp is a highgain amplifier that has high input impedance and low output impedance. An ideal opamp has infinite gain and
More informationCHAPTER 5 DC AND AC BRIDGE
5. Introduction HAPTE 5 D AND A BIDGE Bridge circuits, which are instruments for making comparison measurements, are widely used to measure resistance, inductance, capacitance, and impedance. Bridge circuits
More informationECE2210 Final given: Spring 08
ECE Final given: Spring 0. Note: feel free to show answers & work right on the schematic 1. (1 pts) The ammeter, A, reads 30 ma. a) The power dissipated by R is 0.7 W, what is the value of R. Assume that
More informationPHYS225 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 informationECE 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,
More informationWhere, τ is in seconds, R is in ohms and C in Farads. Objective of The Experiment
Introduction The famous multivibrator circuit was first introduced in a publication by Henri Abraham and Eugene Bloch in 1919. Multivibrators are electronic circuits designed for the purpose of applying
More informationThe Wien Bridge Oscillator Family
Downloaded from orbit.dtu.dk on: Dec 29, 207 The Wien Bridge Oscillator Family Lindberg, Erik Published in: Proceedings of the ICSES06 Publication date: 2006 Link back to DTU Orbit Citation APA): Lindberg,
More informationTwoPort Networks Admittance Parameters CHAPTER16 THE LEARNING GOALS FOR THIS CHAPTER ARE THAT STUDENTS SHOULD BE ABLE TO:
CHAPTER16 TwoPort Networks THE LEARNING GOALS FOR THIS CHAPTER ARE THAT STUDENTS SHOULD BE ABLE TO: Calculate the admittance, impedance, hybrid, and transmission parameter for twoport networks. Convert
More informationENGR4300 Spring 2009 Test 2. Name: SOLUTION. Section: 1(MR 8:00) 2(TF 2:00) 3(MR 6:00) (circle one) Question I (20 points): Question II (20 points):
ENGR43 Test 2 Spring 29 ENGR43 Spring 29 Test 2 Name: SOLUTION Section: 1(MR 8:) 2(TF 2:) 3(MR 6:) (circle one) Question I (2 points): Question II (2 points): Question III (17 points): Question IV (2 points):
More informationProblem 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 informationE40M. 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. 863866. Reader, Chapter 8 Noninverting Amp http://www.electronicstutorials.ws/opamp/opamp_3.html Inverting Amp http://www.electronicstutorials.ws/opamp/opamp_2.html
More informationDesigning Information Devices and Systems I Fall 2018 Lecture Notes Note Introduction: Opamps in Negative Feedback
EECS 16A Designing Information Devices and Systems I Fall 2018 Lecture Notes Note 18 18.1 Introduction: Opamps in Negative Feedback In the last note, we saw that can use an opamp as a comparator. However,
More informationCS 436 HCI Technology Basic Electricity/Electronics Review
CS 436 HCI Technology Basic Electricity/Electronics Review *Copyright 19972008, Perry R. Cook, Princeton University August 27, 2008 1 Basic Quantities and Units 1.1 Charge Number of electrons or units
More informationSolved Problems. Electric Circuits & Components. 11 Write the KVL equation for the circuit shown.
Solved Problems Electric Circuits & Components 11 Write the KVL equation for the circuit shown. 12 Write the KCL equation for the principal node shown. 12A In the DC circuit given in Fig. 1, find (i)
More informationNotes for course EE1.1 Circuit Analysis TOPIC 10 2PORT CIRCUITS
Objectives: Introduction Notes for course EE1.1 Circuit Analysis 45 Reexamination of 1port subcircuits Admittance parameters for port circuits TOPIC 1 PORT CIRCUITS Gain and port impedance from port
More informationStart with the transfer function for a secondorder highpass. s 2. ω o. Q P s + ω2 o. = G o V i
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
More informationLecture 4: RLC Circuits and Resonant Circuits
Lecture 4: RLC Circuits and Resonant Circuits RLC series circuit: What's V R? Simplest way to solve for V is to use voltage divider equation in complex notation: V X L X C V R = in R R + X C + X L L
More informationCARLETON UNIVERSITY. FINAL EXAMINATION December DURATION 3 HOURS No. of Students 130
ALETON UNIVESITY FINAL EXAMINATION December 005 DUATION 3 HOUS No. of Students 130 Department Name & ourse Number: Electronics ELE 3509 ourse Instructor(s): Prof. John W. M. ogers and alvin Plett AUTHOIZED
More informationThe Rayleigh Pulse Forming Network
The Rayleigh Pulse Forming Network The ideal power supply for many high current applications is one which supplies a square voltage wave over a short, but predetermined, time. Since these applications
More informationOPERATIONAL 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 Noninverting Configuration (Chapter 2.3) 2.4 Difference
More informationBASIC SQUARE WAVETRIANGULAR WAVE OSCILLATOR
BAS SQUAE WAVETANGULA WAVE OSLLATO. ircuit description NTEGATO SHMTT TGGE E E E B O by O +Vsat Vsat UT N N Vsup Vref LT The above oscillator is basically a switched integrator that outputs a triangular
More informationLecture 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 informationChapter 10 Instructor Notes
G. izzoni, Principles and Applications of lectrical ngineering Problem solutions, hapter 10 hapter 10 nstructor Notes hapter 10 introduces bipolar junction transistors. The material on transistors has
More informationExperiment 3: Resonance in LRC Circuits Driven by Alternating Current
Experiment 3: Resonance in LRC Circuits Driven by Alternating Current Introduction In last week s laboratory you examined the LRC circuit when constant voltage was applied to it. During this laboratory
More informationOperational Amplifier (OpAmp) Operational Amplifiers. OPAmp: Components. Internal Design of LM741
(OpAmp) 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 informationThe Approximating Impedance
Georgia Institute of Technology School of Electrical and Computer Engineering ECE 4435 Op Amp Design Laboratory Fall 005 DesignProject,Part A White Noise and Pink Noise Generator The following explains
More informationDelhi 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: Email: info@madeeasy.in Ph: 04546 CLASS TEST 089 ELECTCAL ENGNEENG Subject
More informationSchedule. ECEN 301 Discussion #20 Exam 2 Review 1. Lab Due date. Title Chapters HW Due date. Date Day Class No. 10 Nov Mon 20 Exam Review.
Schedule Date Day lass No. 0 Nov Mon 0 Exam Review Nov Tue Title hapters HW Due date Nov Wed Boolean Algebra 3. 3.3 ab Due date AB 7 Exam EXAM 3 Nov Thu 4 Nov Fri Recitation 5 Nov Sat 6 Nov Sun 7 Nov Mon
More informationAC 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.
More informationProblem 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 informationChapter 10 Sinusoidal Steady State Analysis Chapter Objectives:
Chapter 10 Sinusoidal Steady State Analysis Chapter Objectives: Apply previously learn circuit techniques to sinusoidal steadystate analysis. Learn how to apply nodal and mesh analysis in the frequency
More informationBasics of Network Theory (PartI)
Basics of Network Theory (PartI). A square waveform as shown in figure is applied across mh ideal inductor. The current through the inductor is a. wave of peak amplitude. V 0 0.5 t (m sec) [Gate 987: Marks]
More informationECE Circuit Theory. Final Examination. December 5, 2008
ECE 212 H1F Pg 1 of 12 ECE 212  Circuit Theory Final Examination December 5, 2008 1. Policy: closed book, calculators allowed. Show all work. 2. Work in the provided space. 3. The exam has 3 problems
More informationDC and AC Impedance of Reactive Elements
3/6/20 D and A Impedance of Reactive Elements /6 D and A Impedance of Reactive Elements Now, recall from EES 2 the complex impedances of our basic circuit elements: ZR = R Z = jω ZL = jωl For a D signal
More informationSelfDirected Course: Transitional Math Module 4: Algebra
Lesson #1: Solving for the Unknown with no Coefficients During this unit, we will be dealing with several terms: Variable a letter that is used to represent an unknown number Coefficient a number placed
More informationThe 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 informationNotes for course EE1.1 Circuit Analysis TOPIC 4 NODAL ANALYSIS
Notes for course EE1.1 Circuit Analysis 200405 TOPIC 4 NODAL ANALYSIS OBJECTIVES 1) To develop Nodal Analysis of Circuits without Voltage Sources 2) To develop Nodal Analysis of Circuits with Voltage
More informationSimultaneous equations for circuit analysis
Simultaneous equations for circuit analysis This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,
More informationSwitchedCapacitor Circuits David Johns and Ken Martin University of Toronto
SwitchedCapacitor 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 informationAC 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
More informationESE319 Introduction to Microelectronics. Output Stages
Output Stages Power amplifier classification Class A amplifier circuits Class A Power conversion efficiency Class B amplifier circuits Class B Power conversion efficiency Class AB amplifier circuits Class
More informationELEC 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.
More informationEE 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 informationLecture 37: Frequency response. Context
EECS 05 Spring 004, Lecture 37 Lecture 37: Frequency response Prof J. S. Smith EECS 05 Spring 004, Lecture 37 Context We will figure out more of the design parameters for the amplifier we looked at in
More informationEE 3CL4: Introduction to Control Systems Lab 4: Lead Compensation
EE 3CL4: Introduction to Control Systems Lab 4: Lead Compensation Tim Davidson Ext. 27352 davidson@mcmaster.ca Objective To use the root locus technique to design a lead compensator for a marginallystable
More informationrectangle, triangle, saw tooth, pulse, etc.
Nonsinusoidal Signal Geneatos ectangle, tiangle, saw tooth, pulse, etc. Multiibato cicuits: astable no stable states (two quasistable states; it emains in each state fo pedetemined times) monostable one
More informationProf. 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.
More informationExperiment 4. RC Circuits. Observe and qualitatively describe the charging and discharging (decay) of the voltage on a capacitor.
Experiment 4 RC Circuits 4.1 Objectives Observe and qualitatively describe the charging and discharging (decay) of the voltage on a capacitor. Graphically determine the time constant τ for the decay. 4.2
More informationResponse of SecondOrder Systems
Unit 3 Response of SecondOrder Systems In this unit, we consider the natural and step responses of simple series and parallel circuits containing inductors, capacitors and resistors. The equations which
More informationChapter 3: Capacitors, Inductors, and Complex Impedance
hapter 3: apacitors, Inductors, and omplex Impedance In this chapter we introduce the concept of complex resistance, or impedance, by studying two reactive circuit elements, the capacitor and the inductor.
More informationVI. 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 informationENGR4300 Fall 2005 Test 3A. Name. Section. Question 1 (25 points) Question 2 (25 points) Question 3 (25 points) Question 4 (25 points)
ENGR4 Test A Fall 5 ENGR4 Fall 5 Test A Name Section Question (5 points) Question (5 points) Question (5 points) Question 4 (5 points) Total ( points): Please do not write on the crib sheets. On all questions:
More informationClass #12: Experiment The Exponential Function in Circuits, Pt 1
Class #12: Experiment The Exponential Function in Circuits, Pt 1 Purpose: The objective of this experiment is to begin to become familiar with the properties and uses of the exponential function in circuits
More informationOperational amplifiers (Op amps)
Operational amplifiers (Op amps) Recall the basic twoport 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 informationLecture 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 informationCIRCUIT 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, secondorder and resonant circuits, damping and
More informationExperiment Guide for RC Circuits
GuideP1 Experiment Guide for RC Circuits I. Introduction 1. Capacitors A capacitor is a passive electronic component that stores energy in the form of an electrostatic field. The unit of capacitance is
More informationStudio 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. 232242 Twostage opamp Analysis Strategy Recognize
More informationQUIZ 1 SOLUTION. One way of labeling voltages and currents is shown below.
F 14 1250 QUIZ 1 SOLUTION EX: Find the numerical value of v 2 in the circuit below. Show all work. SOL'N: One method of solution is to use Kirchhoff's and Ohm's laws. The first step in this approach is
More informationCircuits Advanced Topics by Dr. Colton (Fall 2016)
ircuits Advanced Topics by Dr. olton (Fall 06). Time dependence of general and L problems General and L problems can always be cast into first order ODEs. You can solve these via the particular solution
More informationEECE 2510 Circuits and Signals, Biomedical Applications Final Exam Section 3. Name:
EECE 2510 Circuits and Signals, Biomedical Applications Final Exam Section 3 Instructions: Closed book, closed notes; Computers and cell phones are not allowed Scientific calculators are allowed Complete
More informationBandwidth of op amps. R 1 R 2 1 k! 250 k!
Bandwidth of op amps An experiment  connect a simple noninverting 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 informationEXPERIMENT 5A RC Circuits
EXPERIMENT 5A Circuits Objectives 1) Observe and qualitatively describe the charging and discharging (decay) of the voltage on a capacitor. 2) Graphically determine the time constant for the decay, τ =.
More informationSINUSOIDAL 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
More informationElectronic Circuits. Prof. Dr. Qiuting Huang Integrated Systems Laboratory
Electronic Circuits Prof. Dr. Qiuting Huang 6. Transimpedance Amplifiers, Voltage Regulators, Logarithmic Amplifiers, AntiLogarithmic Amplifiers Transimpedance Amplifiers Sensing an input current ii in
More informationENGR2300 Electronic Instrumentation Quiz 3 Fall 2013 Name Section. Question III (25 Points) Question IV (25 Points) Total (100 Points)
ENGR2300 Electronic Instrumentation Quiz 3 Fall 203 Name Section Question I (25 Points) Question II (25 Points) Question III (25 Points) Question I (25 Points) Total (00 Points) On all questions: SHOW
More informationDC Biasing. Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15Mar / 59
Contents Three States of Operation BJT DC Analysis FixedBias Circuit EmitterStabilized Bias Circuit Voltage Divider Bias Circuit DC Bias with Voltage Feedback Various Dierent Bias Circuits pnp Transistors
More informationHomework Assignment 11
Homework Assignment Question State and then explain in 2 3 sentences, the advantage of switched capacitor filters compared to continuoustime active filters. (3 points) Continuous time filters use resistors
More informationPhysics 364, Fall 2012, reading due your answers to by 11pm on Thursday
Physics 364, Fall 2012, reading due 20120920. 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 informationPhasors: Impedance and Circuit Anlysis. Phasors
Phasors: Impedance and Circuit Anlysis Lecture 6, 0/07/05 OUTLINE Phasor ReCap Capacitor/Inductor Example Arithmetic with Complex Numbers Complex Impedance Circuit Analysis with Complex Impedance Phasor
More informationIMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY AND MEDICINE UNIVERSITY OF LONDON DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING EXAMINATIONS 2010
Paper Number(s): E1.1 IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY AND MEDICINE UNIVERSITY OF LONDON DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING EXAMINATIONS 2010 EEE/ISE PART I: MEng, BEng and ACGI
More information