DOCSLIB.ORG

Op Amp Differentiator and Integrator

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Op Amp Differentiator and Integrator EE 420 L ELECTRONICS II LABORATORY 4: OP AMP DIFFERENTIATOR & INTEGRATOR DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING UNIVERSITY OF NEVADA, LAS VEGAS 1 OBJECTIVE Investigate the operation and characteristics of an Op-Amp as a differentiator, and an integrator. 2 COMPONENTS & EQUIPMENT Power Supply Breadboard, Jump wires Function Generator Resistors Multimeter Capacitors Oscilloscope Op Amp (LM 741 or similar) 3 BACKGROUND REVIEW 1) Which of the follows can used to convert the digital signal to analog signal? (a) A comparator (d) An integrator (b) An averaging amplifier (e) A differentiator (c) A scaling adder 2) The output voltage of an integrator is proportional to the (a) frequency of the input (d) a and c (b) period of the input (e) b and c (c) RC time constant DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 1 EE 420L ELECTRONICS II 3) The output voltage of a differentiator is proportional to the (a) frequency of the input (d) a and c (b) period of the input (e) b and c (c) RC time constant 4) In an integrator, the feedback element is a (a) resistor (d) zener diode (b) capacitor (e) none of the above (c) inductor 5) In a differentiator, the feedback element is a (a) resistor (d) Zener diode (b) capacitor (e) none of the above (c) inductor 6) When a triangular waveform is applied to the input of a differentiator, the output is (a) a square wave (d) a saw tooth wave (b) a triangular wave (e) a sine wave (c) either a or b 7) When a square wave is applied to the input of an integrator, the output is (a) a square wave (d) a saw tooth wave (b) a triangular wave (e) a sine wave (c) either a or b 8) When a sine wave is applied to the input of an integrator, the output is (a) a sine wave (d) a triangular wave (b) a cosine wave (e) either a or b (c) a square wave DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 2 EE 420L ELECTRONICS II 4 LAB DELIVERIES: 4.1 PRELAB: 1. Review the knowledge of the frequency response of Op Amp circuits, part of which are listed in the previous section. Answer the problems in the previous section. 2. Read the datasheet of LM741 Op Amp http://www.ti.com/lit/ds/symlink/lm741.pdf 3. Use hand calculations and computer simulations (LTspice) for both inputs and outputs of the following two circuits, respectively. 1) Apply input frequency of 400Hz, 1kHz, and 30kHz for Circuit 1, one at a time. 2) Apply input frequency of 100Hz, 4kHz, and 10kHz for Circuit 2, one at a time. Figure 1 Op Amp Circuit 1 Figure 2 Op Amp Circuit 2 DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 3 EE 420L ELECTRONICS II Circuit 1 Circuit 2 400 HZ 1 kHZ 30 kHZ 10 kHZ 4 kHZ 100 HZ Hand Calculation Output Voltage LTspice Simulation Output Voltage Measured Output Voltage 4.2 LAB EXPERIMENTS: 1. Implement Op Amp Circuit 1; record (photos) and measure the output voltage. Fill in the table above with the measured value, and compare the difference with your hand calculation and LTspice simulation results. 2. Implement Op Amp Circuit 2. Fill in the table above with the measured value, and compare the difference with your hand calculation and LTspice simulation results. 4.3 POSTLAB REPORT: Include the following elements in the report document: Section Element Theory of operation 1 Include a brief description of every element and phenomenon that appear during the experiments. Prelab report 1) Complete the required calculations 2 2) Simulate the circuits, and fill in the tables 3) What functions do Circuit 1 & 2 implement, respectively? Results of the experiments 3 Experiments Experiment Results 1~2 1) Record all results, and take photos if necessary Answer the questions Questions Question What component/replacement did you use if the one in manual was not 4 1 available? What are the major difference between them? What can you conclude after comparing the results among hand 2 calculations, LTspice simulations and real circuit measurements? 5 Conclusions DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 4 EE 420L ELECTRONICS II Write down your conclusions, things learned, problems encountered during the lab and how they were solved, etc. Images Paste images (e.g. scratches, drafts, screenshots, photos, etc.) in Postlab report document (only .docx, .doc or .pdf format is accepted). If the sizes of images are too large, convert them to jpg/jpeg format first, and then paste them in the document. 6 Attachments (If needed) Zip your projects. Send through WebCampus as attachments, or provide link to the zip file on Google Drive / Dropbox, etc. 5 REFERENCES & ACKNOWLEDGEMENTS I appreciate the help and advices from faculty/staff members and TAs during the composing of this instruction manual. I would also thank students for any valuable feedback so that we can offer better higher education to the students. DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 5 .
Load more

Recommended publications
  • Integer-And Fractional-Order Integral and Derivative Two-Port Summations: Practical Design Considerations
    applied sciences Article Integer-and Fractional-Order Integral and Derivative Two-Port Summations: Practical Design Considerations Roman Sotner 1,* , Ondrej Domansky 1, Jan Jerabek 1 , Norbert Herencsar 1 , Jiri Petrzela 1 and Darius Andriukaitis 2 1 SIX Research Center, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 3082/12, 616 00 Brno, Czech Republic; [email protected] (O.D.); [email protected] (J.J.); [email protected] (N.H.); [email protected] (J.P.) 2 Department of Electronics Engineering, Faculty of Electrical and Electronics Engineering, Kaunas University of Technology, Studentu st. 48-209, LT-51367 Kaunas, Lithuania; [email protected] * Correspondence: [email protected]; Tel.: +420-541-146-560 Received: 14 November 2019; Accepted: 12 December 2019; Published: 19 December 2019 Abstract: This paper targets on the design and analysis of specific types of transfer functions obtained by the summing operation of integer-order and fractional-order two-port responses. Various operations provided by fractional-order, two-terminal devices have been studied recently. However, this topic needs to be further studied, and the topologies need to be analyzed in order to extend the state of the art. The studied topology utilizes the passive solution of a constant-phase element (with order equal to 0.5) implemented by parallel resistor–capacitor circuit (RC) sections operating as a fractional-order two-port. The integer-order part is implemented by operational amplifier-based lossless integrators and differentiators in branches with electronically adjustable gain, useful for time constant tuning. Four possible cases of the fractional-order and integer-order two-port interconnections are analyzed analytically, by PSpice simulations and also experimentally in the frequency range between 10 Hz and 1 MHz.
    [Show full text]
  • Operational Amplifier Circuits
    Operational Amplifier Circuits Review: Ideal Op-amp in an open loop configuration Ip Vp + + + Ro Vo Vi Ri _ AVi Vn _ In An ideal op-amp is characterized with infinite open–loop gain A →∞ The other relevant conditions for an ideal op-amp are: 1. Ip =In =0 2. Ri =∞ 3. Ro = 0 Ideal op-amp in a negative feedback configuration When an op-amp is arranged with a negative feedback the ideal rules are: 1. Ip =In =0 : input current constraint 2. Vn = Vp : input voltage constraint These rules are related to the requirement/assumption for large open-loop gain A →∞, and they form the basis for op-amp circuit analysis. The voltage Vn tracks the voltage Vp and the “control” of Vn is accomplished via the feedback network. Chaniotakis and Cory. 6.071 Spring 2006 Page 1 Operational Amplifier Circuits as Computational Devices So far we have explored the use of op amps to multiply a signal by a constant. For the R2 inverting amplifier the multiplication constant is the gain − R1 and for the non inverting R2 amplifier the multiplication constant is the gain 1+ R1 . Op amps may also perform other mathematical operations ranging from addition and subtraction to integration, differentiation and exponentiation.1 We will next explore these fundamental “operational” circuits. Summing Amplifier A basic summing amplifier circuit with three input signals is shown on Figure 1. I I R1 1 F RF Vin1 I R2 2 N V 1 in2 Vout R3 I3 Vin3 Figure 1. Summing amplifier Current conservation at node N1 gives I12+ II+=3IF (1.1) By relating the currents I1, I2 and I3 to their corresponding voltage and resistance by Ohm’s law and noting that the voltage at node N1 is zero (ideal op-amp rule) Equation (1.1) becomes VVV V in12++in in3=−out (1.2) R12RR3RF 1 The term operational amplifier was first used by John Ragazzini et.
    [Show full text]
  • Chapter 13: Basic Op-Amp Circuits
    Chapter 13: Basic Op-Amp Circuits In the last chapter, you learned about the principles, operation, and characteristics of the operational amplifier. Op-amps are used in such a wide variety of circuits and applications that it is impossible to cover all of them in one chapter, or even in one book. Therefore, in this chapter, four fundamentally important circuits are covered to give you a foundation in op-amp circuits. The basic circuits for op-amp’s are 1- Comparators 2- Summing Amplifiers 3- Integrators and Differentiators 13.1: Comparators A comparator is a specialized nonlinear op-amp circuit that compares between two input voltages and produces an output state that indicates which one is greater. Comparators are designed to be fast and frequently have other capabilities to optimize the comparison function. In this application, the op-amp is used in the open-loop configuration, with the input voltage on one input and a reference voltage on the other. 13.1: Comparators One application of an op-amp used as a comparator is to determine when an input voltage exceeds a certain level Sin wave Zero-Level Detection The figure shown is the zero- level detector circuit; the inverting (-) input is grounded to produce a zero level (reference to compare with), and the input signal voltage is applied to the noninverting (+) input Since Vin is at noninverting input As shown in figure; Any Vin above the zero will produce a +ve saturated output (+Vout(max)) any Vin below the zero will produce a –ve saturated output (-Vout(min)) Saturation of the output is due to the open-loop op-amp that have a very high voltage gain very small difference voltage between the two inputs drives the amplifier into saturation (non linear operation) 13.1: Comparators Nonzero-Level Detection The reference voltage can be set to non zero voltage (+ve ot -ve) by adding a dc voltage or voltage divider or zener or ….
    [Show full text]
  • A Single Resistor Tunable Grounded Capacitor Dual-Input Differentiator
    Circuits and Systems, 2015, 6, 49-54 Published Online March 2015 in SciRes. http://www.scirp.org/journal/cs http://dx.doi.org/10.4236/cs.2015.63005 A Single Resistor Tunable Grounded Capacitor Dual-Input Differentiator Koushick Mathur1, Palaniandavar Venkateswaran2, Rabindranath Nandi2* 1Department of Electronics & Communication Engineering, UIT, University of Burdwan, Bardhaman, India 2Department of Electronics & Telecommunication Engineering, Jadavpur University, Kolkata, India Email: [email protected], [email protected], *[email protected] Received 18 February 2015; accepted 9 March 2015; published 11 March 2015 Copyright © 2015 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract A new current feedback amplifier (CFA) based dual-input differentiator (DID) design with grounded capacitor is presented; its time constant (τo) is independently tunable by a single resistor. The proposed circuit yields a true DID function with ideal CFA devices. Analysis with nonideal devices having parasitic capacitance (Cp) shows extremely low but finite phase error (θe); suitable design θe could be minimized significantly. The design is practically active-insensitive relative to port mismatch errors (ε) of the active element. An allpass phase shifter circuit implementation is de- rived with slight modification of the differentiator. Satisfactory experimental results had been ve- rified on typical wave processing and phase-selective filter design applications. Keywords CFA, Tunable Differentiator, Dual-Input Differentiator, Wave Shaper 1. Introduction Differentiator and integrator functional blocks find a variety of applications in signal conditioning, wave pro- cessing and shaping, as process controller, phase compensator, and as pre-emphasis unit in radio engineering [1].
    [Show full text]
  • Experiment No.11 §Differentiator Op-Amp §
    Power Electronics lap. Dep.of Electrical Techniques Fatima raad abed Second stage Experiment no.11 § Differentiator Op-amp § 11.1 Objective: To design and study the differentiator operational amplifier. 11.2 Theory: The basic operational amplifier differentiator circuit produces an output signal, which is the first derivative of the input signal. Figure (1) Here, the position of the capacitor and resistor have been reversed and now the reactance, XC is connected to the input terminal of the inverting amplifier while the resistor, Rƒ forms the negative feedback element across the operational amplifier as normal. 1 Power Electronics lap. Dep.of Electrical Techniques Fatima raad abed Second stage This operational amplifier circuit performs the mathematical operation of Differentiation, which is it “produces a voltage output which is directly proportional to the input voltage’s rate-of-change with respect to time“. In other words the faster or larger the change to the input voltage signal, the greater the input current, the greater will be the output voltage change in response, becoming more of a “spike” in shape. As with the integrator circuit, we have a resistor and capacitor forming an RC Network across the operational amplifier and the reactance (XC) of the capacitor plays a major role in the performance of an Op-amp Differentiator. An ideal voltage output for the op-amp differentiator is given as: Differentiator OP-amp Waveforms:- If we apply a constantly changing signal such as a Square-wave, Triangular or Sine-wave type signal to the input of a Differentiator amplifier circuit the resultant output signal will be changed and whose final shape is dependent upon the RC time constant of the Resistor/Capacitor combination.
    [Show full text]
  • Differentiator and Integrator Circuits
    Differentiator and integrator circuits By introducing electrical reactance into the feedback loops of op-amp amplifier circuits, we can cause the output to respond to changes in the input voltage over time. Drawing their names from their respective calculus functions, the integrator produces a voltage output proportional to the product (multiplication) of the input voltage and time; and the differentiator (not to be confused with differential) produces a voltage output proportional to the input voltage's rate of change. Capacitance can be defined as the measure of a capacitor's opposition to changes in voltage. The greater the capacitance, the more the opposition. Capacitors oppose voltage change by creating current in the circuit: that is, they either charge or discharge in response to a change in applied voltage. So, the more capacitance a capacitor has, the greater its charge or discharge current will be for any given rate of voltage change across it. The equation for this is quite simple: The dv/dt fraction is a calculus expression representing the rate of voltage change over time. If the DC supply in the above circuit were steadily increased from a voltage of 15 volts to a voltage of 16 volts over a time span of 1 hour, the current through the capacitor would most likely be very small, because of the very low rate of voltage change (dv/dt = 1 volt / 3600 seconds). However, if we steadily increased the DC supply from 15 volts to 16 volts over a shorter time span of 1 second, the rate of voltage change would be much higher, and thus the charging current would be much higher (3600 times higher, to be exact).
    [Show full text]
  • Chapter 15 Time Response of Reactive Circuits
    Chapter 15 Time Response of Reactive Circuits Objectives • Explain the operation of an RC integrator • Analyze an RC integrator with a single input pulse • Analyze an RC integrator with repetitive input pulses • Analyze an RC differentiator with a single input pulse 1 Objectives • Analyze an RC differentiator with repetitive input pulses • Analyze the operation of an RL integrator • Analyze the operation of an RL differentiator The RC Integrator • When a pulse generator is connected to the input of an RC integrator, the capacitor will charge and discharge in response to the pulses 2 The RC Integrator • The rate of charging and discharging depends on the RC time constant τ = RC • For an ideal pulse, both edges are considered to be instantaneous – The capacitor appears as a short to an instantaneous change in current and as an open to dc – The voltage across the capacitor cannot change instantaneously - it can change only exponentially Capacitor Voltage • In an RC integrator, the output is the capacitor voltage • The capacitor charges during the time that the pulse is high • If the pulse is at its high level long enough, the capacitor will fully charge to the voltage amplitude of the pulse • The capacitor discharges during the time that the pulse is low 3 Response of RC Integrators to Single-Pulse Inputs • A capacitor will fully charge if the pulse width is equal to or greater than 5 time constants (5τ) • At the end of the pulse, the capacitor fully discharges back through the source When the Pulse Width is Equal to or Greater than 5 Time
    [Show full text]
  • Passive Integrator and Differentiator Circuits
    Passive integrator and differentiator circuits 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/, or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA. The terms and conditions of this license allow for free copying, distribution, and/or modification of all licensed works by the general public. Resources and methods for learning about these subjects (list a few here, in preparation for your research): 1 Questions Question 1 f(x) dx Calculus alert! R Calculus is a branch of mathematics that originated with scientific questions concerning rates of change. The easiest rates of change for most people to understand are those dealing with time. For example, a student watching their savings account dwindle over time as they pay for tuition and other expenses is very concerned with rates of change (dollars per year being spent). In calculus, we have a special word to describe rates of change: derivative. One of the notations used to express a derivative (rate of change) appears as a fraction. For example, if the variable S represents the amount of money in the student’s savings account and t represents time, the rate of change of dollars over time would be written like this: dS dt The following set of figures puts actual numbers to this hypothetical scenario: • Date: November 20 • Saving account balance (S) = $12,527.33 dS • Rate of spending dt = -5,749.01 per year List some of the equations you have seen in your study of electronics containing derivatives, and explain how rate of change relates to the real-life phenomena described by those equations.
    [Show full text]
  • Operational Amplifier Applications
    Operational Amplifier Applications Student Workbook 91572-00 Ê>{Y4èRÆ3oË Edition 4 3091572000503 FOURTH EDITION Second Printing, March 2005 Copyright March, 2003 Lab-Volt Systems, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form by any means, electronic, mechanical, photocopied, recorded, or otherwise, without prior written permission from Lab-Volt Systems, Inc. Information in this document is subject to change without notice and does not represent a commitment on the part of Lab-Volt Systems, Inc. The Lab-Volt F.A.C.E.T.® software and other materials described in this document are furnished under a license agreement or a nondisclosure agreement. The software may be used or copied only in accordance with the terms of the agreement. ISBN 0-86657-234-1 Lab-Volt and F.A.C.E.T.® logos are trademarks of Lab-Volt Systems, Inc. All other trademarks are the property of their respective owners. Other trademarks and trade names may be used in this document to refer to either the entity claiming the marks and names or their products. Lab-Volt System, Inc. disclaims any proprietary interest in trademarks and trade names other than its own. Lab-Volt License Agreement By using the software in this package, you are agreeing to 6. Registration. Lab-Volt may from time to time update the become bound by the terms of this License Agreement, CD-ROM. Updates can be made available to you only if a Limited Warranty, and Disclaimer. properly signed registration card is filed with Lab-Volt or an authorized registration card recipient.
    [Show full text]
  • Electronic Circuits Ii Unit 4 Wave Shaping Circuits
    ELECTRONIC CIRCUITS II UNIT 4 WAVE SHAPING CIRCUITS Topics to be covered • RC & RL Integrator and Differentiator circuits • Storage, Delay and Calculation of Transistor Switching Times • Speed-up Capacitor • Diode clippers • Diode comparator • Clampers • Collector coupled and Emitter coupled Astable multivibrator • Monostable multivibrator • Bistable multivibrators • Triggering methods for Bistable multivibrators • Schmitt trigger circuit. RC Integrator • The RC integrator is a series connected Resistor-Capacitor network that produces an output signal which corresponds to the mathematical process of integration. • For a passive RC integrator circuit, the input is connected to a resistance while the output voltage is taken from across a capacitor being the exact opposite to the RC Differentiator Circuit. The capacitor charges up when the input is high and discharges when the input is low. • A passive RC network is nothing more than a resistor in series with a capacitor, that is a fixed resistance in series with a capacitor that has a frequency dependant reactance which decreases as the frequency across its plates increases. • Thus at low frequencies the reactance, Xc of the capacitor is high while at high frequencies its reactance is low due to the standard capacitive reactance formula of Xc = 1/(2πƒC). • Then if the input signal is a sine wave, an rc integrator will simply act as a simple low pass filter (LPF) with a cut-off or corner frequency that corresponds to the RC time constant (tau, τ) of the series network and whose output is reduced above this cut-off frequency point. Thus when fed with a pure sine wave an RC integrator acts as a passive low pass filter.
    [Show full text]
  • UNIT -1 LINEAR WAVE SHAPPING Contents: • High Pass, Low Pass
    UNIT -1 LINEAR WAVE SHAPPING Contents: High pass, Low pass circuits High pass and Low pass circuits response for: 1. Sine wave 2. Step 3. Pulse 4. Square 5. Ramp 6. Exponential High pass RC as differentiator Low pass RC as integrator Attenuators and its applications RL circuits RLC circuits Solved problems 1 GVPCEW INTRODUCTION Linear systems are those that satisfy both homogeneity and additivity. (i) Homogeneity: Let x be the input to a linear system and y the corresponding output, as shown in Fig. 1.1. If the input is doubled (2x), then the output is also doubled (2y). In general, a system is said to exhibit homogeneity if, for the input nx to the system, the corresponding output is ny (where n is an integer). Thus, a linear system enables us to predict the output. FIGURE 1.1 A linear system (ii) Additivity: For two input signals x1 and x2 applied to a linear system, let y1 and y2 be the corresponding output signals. Further, if (x1 + x2) is the input to the linear system and (y1 + y2) the corresponding output, it means that the measured response will just be the sum of its responses to each of the inputs presented separately. This property is called additivity. Homogeneity and additivity, taken together, comprise the principle of superposition. (iii) Shift invariance: Let an input x be applied to a linear system at time t1. If the same input is applied at a different time instant t2, the two outputs should be the same except for the corresponding shift in time.
    [Show full text]
  • Semistate Implementation: Differentiator Example*
    CIR(UIrS SYSTEMS SIGNAL PRO(ESS VOL. 5' NO. I, 1986 SEMISTATE IMPLEMENTATION: DIFFERENTIATOR EXAMPLE* Mona EIwakkad Zaghloul I and Robert W. Newcomb 2 Abstract. It is shown that the semistate equations can be transformed via a linear transformation into a form which is useful for physical realizations. The result is applied to the example of a semistate described differentiator which is then realized through an op-amp circuit composed of integrators. 1. Introduction Recently there has been a large interest in the semistate theory of circuits [1]-[7]. This is because the semistate description is a natural one for circuits which is also very general and contains the state variable one as a special case when the latter exists. The semistate equations for nonlinear time-varying circuits were described in [1] in the canonical form of (idx/dt + (B(x,t) = fi)u (la) y = ~3x (lb) where u = input, y = output, x = semistate, and (t, 33, ~ are constant matrices. 63 (.,.) is a nonlinear time-varying operator. In the linear case many authors have considered the solution of the semistate equations, where the equivalent standard canonical form is used in the analysis [3]-[5]. In a somewhat different approach the Drazin inverse has been used in the analysis of such systems to obtain the solutions in "one fell swoop" [5], [6]. However, except in [2], semistate theory has not been used in the design of circuits. This is in contrast to one of the distinct advantages resulting because of the * Received April 17, 1985; revised June 18, 1985. This research was supported in part by NSF Grant ENG ECS 83-17877.
    [Show full text]