Physics
Second Order Op Amp Circuit
A second order op amp circuit is a type of electronic circuit that utilizes operational amplifiers to create a system with a second order transfer function. This means that the circuit's output response is influenced by both the input signal and its rate of change. Second order op amp circuits are commonly used in filter designs and control systems due to their ability to provide more complex frequency response characteristics.
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eBook - ePub- Nassir H. Sabah(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
18Signal Processing Using Operational Amplifiers
Overview
An operational amplifier, or op amp for short, is a high-gain voltage amplifier, designed to amplify signals in the frequency range from dc to a specified upper frequency. Operational amplifiers are so called because they were initially introduced to perform mathematical operations — such as addition, subtraction, differentiation, and integration — in analog computers that were commonly used to solve differential equations, before digital computers prevailed. Nowadays, op amps of high performance and low cost are widely available in integrated-circuit (IC) form, which makes them an important building block in a variety of signal-processing applications. A number of these applications are considered in this chapter.The most important feature of linear op amp circuits is the use of negative feedback to trade-off the high gain of the op amp for some desirable feature, thereby allowing such operations as precision amplification and integration. Op amps are at the heart of active filters of various types, whose performance is superior in many respects to that of passive filters, particularly in their allowing high Q
eBook - PDF- Muzaffer Ahmad Siddiqi(Author)
- 2020(Publication Date)
- Cambridge University Press(Publisher)
2.1 Introduction Circuit designers/users evaluate filters and the order of the filters needed is based on what are the given specifications. The filter order n can be small or large. There are techniques by which filters of order n ≥ 2 can be realized directly. Filters with order one or two can be used as such depending on the requirement; they can also be combined to provide filters of higher-order. Therefore, it is necessary to study the basic principles underlying the behavior of first- and second-order filter sections and the important terms used for their parameters before studying realization of higher order filters. A first-order section can easily be realized using RC components only; but such sections suffer from certain limitations as shall be shown in Section 2.2. Hence, it is advisable to use first-order active filters with inverting or non-inverting amplifiers. A comparative study of active first-order filters, along with a discussion on the non-ideal effect of operational amplifiers (OAs) on their frequency response is given in Section 2.3 and 2.4. Terminologies used for second-order active sections and characteristics associated with low pass (LP), high pass (HP), band pass (BP), band reject (BR), and all pass (AP) responses are included in Sections 2.5 to 2.11. Constraints of the finite bandwidth of the OA on second-order filters are briefly discussed in Section 2.12. Three application examples in Sections 2.3.2, 2.3.3, and 2.7.1 are included to show the utility of these simple filter structures. 2.2 First-order Filter Sections The transfer function of a physically realizable filter using a finite number of elements has to be a real rational function [2.1]. The rational function is a ratio of polynomials in the complex frequency s. It is repeated here from Chapter 1. First- and Second-order Filters apter 2
- Sudhanshu Maheshwari(Author)
- 2023(Publication Date)
- CRC Press(Publisher)
Chapter 5 Higher order analog filtersDOI: 10.1201/9781003403111-5The coverage on analog circuit design using current-mode techniques has now brought us to a level where more complex analog circuits can be understood. The simple interfacing analog blocks and single time constant circuits have been studied, which form the foundation for higher order circuit design. This chapter deals with the second order filters operating in the voltage and current modes. The mixed mode filter circuits are also covered. The current-mode building blocks used are CCII, CCCII and EXCCII. The electronic tuning aspects are discussed and the filter circuits with such features are also described. The design of higher order filter circuits can then be attempted using second order and first order sections. The realization of circuits using commercially available current-mode ICs is presented, with interesting extension of the study for laboratory exercises. The behaviour of circuits considering the non-ideal active building block is studied. Illustrative examples are given along with real design examples showing graphical results using SPICE.5.1 Second order analog filters
The order of a filter decides the rate at which the gain magnitude and phase response changes with the frequency of the signal. The first order filter circuits are limited by their simplicity to offer slow change in their characteristics, both magnitude and phase. Confining to the magnitude, the first order filters’ gain magnitude changes by 20 decibels per decade change in frequency. It is expressed as 20 dB/decade. For the low-pass function it is –20 dB/decade, while for the high-pass function it is +20 dB/decade. The all-pass function is designed to maintain a constant gain magnitude. For the second order analog filters, the changes in characteristics are relatively faster than first order filters. The gain magnitude changes for low-pass and high-pass are −40 dB/decade and +40 dB/decade, respectively. Most of the analog filter theory revolves around the second order filter design, because the higher order filters can be realized using such filters in conjunction with first order sections. This is especially true for active-RC filters designed using the cascade approach, although various other approaches are available in voluminous subject related texts. The types of second order filters based on the selection or rejection of frequency ranges/bands are of interest. The low-pass, high-pass, band-pass, band-reject and all-pass are five such filter types. As per their names, the frequency selection/rejection is easy to co-relate. The same is illustrated by Figures 5.1 , 5.2 and 5.3 , which show typical second order gain magnitude functions of five such filters. Figure 5.1 shows low-pass, high-pass and band-pass; Figure 5.2 shows band-reject; and Figure 5.3
eBook - PDF- BRUCE NEWBY(Author)
- 2014(Publication Date)
- Butterworth-Heinemann(Publisher)
2 A review of operational amplifiers 2.1 Introduction In subsequent chapters of this book the operational amplifier plays a promi-nent part in the many signal conditioning circuits considered. For this reason alone, it is important that the reader is given a fairly comprehensive review of the techniques involved when using these very common devices in a signal conditioning role. The term operational amplifier or op-amp was originally used by workers in the analogue computing industry to describe electronic devices which would undertake a variety of mathematical operations. In simple terms, the devices were very high gain d.c. voltage amplifiers each fitted with a different feedback circuit between its output and input to produce a specific mathematical function. The functions obtainable included simple amplification, differentia-tion, integration, addition, subtraction and the like. Many of the functions undertaken by the early analogue computers have now become the province of the ubiquitous digital computer, causing a large decline in the numbers of the former. But the operational amplifier has not suffered the same fate; it has been retained and further developed and now is extensively used in the analogue electronics field of instrumentation. While operational amplifiers can be built from discrete components, the present proliferation of these devices has been largely brought about by their ready availability commercially in modular and integrated form. Many manufacturers now market a very wide range of high performance operational amplifiers which by the addition of a few simple external components can be configured to undertake specific signal processing tasks. Not only can they be designed to undertake the usual mathematical operations, but they can also be arranged to simulate, for example, the performance of a proposed mechanical, hydraulic or electrical control system.
eBook - ePubIntroduction to Energy, Renewable Energy and Electrical Engineering
Essentials for Engineering Science (STEM) Professionals and Students
- Ewald F. Fuchs, Heidi A. Fuchs(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
8 Operational Amplifiers8.1 Introduction
The operational (OP) amplifier is a basic building block for the design of analog electronic systems such as feedback control circuits [1 ], where the angular velocity ω m (t), angular position θ m (t) = ∫ω m (t)dt, current i(t), and torque T(t) must be controlled. An OP amplifier with no external circuitry is a voltage amplifier with a very high open‐loop voltage gain that ideally approaches infinity A v → ∞, as shown in a symbolic manner in Figure 8.1 . Note that input/output voltages can be either time varying or time independent, and they can be either periodic or nonperiodic.OP amplifiers are integrated circuits (IC), which can be purchased off the shelf, and they contain transistors, diodes, resistors, and capacitors all fabricated on a single silicon chip. Inductors are bulky and are mostly avoided in OP amplifier designs. The analog electronic circuit of Figure 8.1 has two inputs: a negative (v − ) and a positive (v + ) input supplied by the voltages v in1 and v in2 , respectively, whose difference in voltage (v in2 − v in1 ) produces an output signal voltage v out that is a replica of the input voltage difference. The two‐input voltage approach is useful because stray signals/electric noise that appear on both inputs are cancelled, and only the voltage difference is amplified. An OP amplifier is also called a differential amplifier because the output voltage is a voltage that is A v times the voltage difference between the two inputs. During the past half century, OP amplifiers have been refined and improved to the extent that they have nearly ideal properties, and therefore we discuss in this textbook the performance of ideal OP amplifiers only. The understanding of nonideal properties of OP amplifiers requires detailed electronic knowledge [2
- J. David Irwin, David V. Kerns, Jr.(Authors)
- 2022(Publication Date)
- Wiley(Publisher)
CHAPTER 10 Operational Amplifiers and Applications LEARNING OBJECTIVES • To understand the characteristics of operational amplifiers and differential amplifiers • To understand the operation of the ideal op-amp model • To be able to recognize and analyze fundamental op-amp circuits • To understand the application of op-amps in the development of low-pass, high-pass, and bandpass filters • To be able to understand the use of op-amps to construct differentiator and integrator circuits • To understand multistage amplifier circuits • To be able to use op-amps in instrumentation and laboratory measurements and in industrial applications. INTRODUCTION The operational amplifier, or op amp as it is commonly known, is a fundamental component in analog electronic systems. Although it can be used in a variety of applications, it is widely used in instrumentation and measurement systems. An actual circuit diagram for a commercial op amp is the 741 Op Amp shown in Figure 10.1. Also shown in the figure are the pin connections for a dual in-line package, or DIP, which sup- ports its connection with other electronic components. Even a cursory examination of the circuit schematic for the op amp indicates that this is not a trivial network. It is typically constructed as an integrated circuit and may be purchased as a single device, in a DIP that contains several op amps or in a “surface mount” package. These elements are not only powerful devices in analog circuit design but are also inexpensive – less than a dollar for a chip in a package. Even after wading through the chapters in this book and developing a knowledge of transis- tors and their applications, the circuit diagram in Figure 10.1 may appear formidable. However, as sophisticated as it appears, it is really nothing more than a high-quality linear voltage ampli- fier. The details of how this circuit is designed are beyond the scope of this book, but follows basic principles described here.
- J Choma, W K Chen;;;(Authors)
- 2007(Publication Date)
- WSPC(Publisher)
MOS Technology Operational Amplifiers 633 + − − + + − V di Input Transconductor C c V x 1 V x 1 V o G mi 1 Output Buffer (a) A 2 V x 1 A 2 V x1 r i 2 r i 2 r o 2 r o 2 − + − + V x 2 V x 2 (b) (c) V x 1 G mi V di r oi V x 2 r ib r ob + − V o (1+A )C c 2 + − V x 2 − A 2 Phase Inverting Second Stage Figure 8.2. (a) The system schematic diagram of a two-stage operational amplifier. (b) Small signal, low frequency equivalent circuit of the phase inverting second stage ampli-fier. (c) Complete small signal, low frequency equivalent circuit of the entire two-stage op-amp. The output port is held open circuited. Fig. 8.2(b). In addition to providing enhanced open loop gain, the second stage exploits Miller capacitance multiplication to realize dominant pole compensation without the need for off chip capacitance. In particular, the Miller effect of the compensation capacitance, C c , results in a comparatively large effective capacitance, ( 1 + A 2 ) C c , across the input port of the second stage. Assuming that the output resistance, r oi , of the transconductor, the second stage input resistance, r i 2 , and the second stage gain magnitude, A 2 , are sufficiently large, a dominant open loop pole can be forged with a small, and therefore monolithically realizable, capacitance, C c . The output response of the second stage amplifier is applied to the voltage buffer, which is incorporated to facilitate the general purpose nature of the op-amp archi-tecture for a diversity of load terminations. The resultant open circuit, open 634 Feedback Networks: Theory and Circuit Applications loop, small signal model of the two-stage op-amp is the network depicted in Fig. 8.2(c), in which the feedback element, C c , is presumed to be the only significant capacitance in the basic architecture of Fig. 8.2(a). The simplified equivalent circuit in Fig. 8.2(c) confirms a dominant pole radial frequency, ω c , of ω c = 1 ( r oi r i 2 )( 1 + A 2 ) C c .
eBook - ePub- Karl Stephan(Author)
- 2015(Publication Date)
- Wiley(Publisher)
5 OP AMP CIRCUITS IN ANALOG ELECTRONICS 5.1 INTRODUCTION An operational amplifier (hereafter “op amp”) is a specially designed amplifier that can be used in a huge number of analog-circuit applications. It is fair to say that almost anything you can do in analog electronics without op amps is easier, smaller, and better performing if done with op amps. And some things are almost impossible to do without op amps or their functional equivalents. Why are op amps so important to analog electronics (and mixed-signal electronics as well)? Because they make the use of negative feedback easy and straightforward and confer its blessings on any circuit where they are used. To understand the importance of negative feedback for op amps, a little history is helpful. Although the concept of negative feedback was studied by nineteenth-century physicists such as James Clerk Maxwell, negative feedback as used in electronics was developed by a Bell Labs engineer named Harold S. Black, who in the 1920s was struggling with the problem of how to improve the repeater amplifiers the Bell System was trying to use to span the US continent with long-distance telephone lines. Nonlinearities were a significant problem, because in traveling through repeaters spaced every 25 miles or so along a cable, signals encountered distortion that was tolerable in one amplifier, but which accumulated to unacceptable levels as the signals passed through dozens of amplifiers in cascade. Black realized that if he built an amplifier with much more gain than necessary and then reduced the gain by “feeding back” a portion of its output signal to the input with the proper polarity, nonlinear distortion would decrease roughly in proportion to the amount of sacrificed gain. Gain, while not free, was relatively easy to obtain simply by cascading stages, and it turned out to be a good engineering trade-off to sacrifice inexpensive gain for the much-sought-after reduction in distortion
eBook - PDFAnalog Electronics
Analog Circuitry Explained
- Ian Hickman(Author)
- 2013(Publication Date)
- Newnes(Publisher)
Chapter 6 Active signal processing in the frequency domain In Chapter 2 we looked at passive circuits whose response was frequency selective, and in Chapter 3 we discussed operational amplifiers. In this chapter we bring these two items together and look at active filters and related topics. Active filters are preferred at audio frequencies since they enable all types of filters and phase equalizers to be realized with suitable combinations of resistors, capacitors and opamps. Thus the inductors that would be necessary for a passive filter can be dispensed with entirely; this is a real blessing since good quality high-value inductors, such as would be required for audio-frequency filtering purposes, are both bulky and expensive. First-order active circuits The least sophisticated filter, be it low pass or high pass, is the first-order or single-pole section. As noted in Chapter 2, this has a fixed shape providing a gradual transition from the pass band to a 6 dB/octave roll-off in the stop band. It was also noted that, to obtain exactly the calculated per-formance, a passive CR section should be driven from a zero source impedance and work into an infinite load impedance. Opamps can be used to provide the required source and load impedances. avoiding the otherwise necessary step of designing finite source and load impedances into the network itself-which in any case may not be practicable if they are not themselves resistive and, hence, frequency independent. Figure 6.1 shows two opamps used as buffer amplifiers, providing the CR section with a low source impedance and a high load impedance. The output amplifier is used in the non-inverting mode to provide a high input impedance and is shown connected to provide unity gain, though it could perfectly well provide a gain of greater than unity if required. The input amplifier is also shown as non-inverting, providing a very high input impedance and keeping the section as a whole non-inverting.
- Won Y. Yang, Jaekwon Kim, Kyung W. Park, Donghyun Baek, Sungjoon Lim, Jingon Joung, Suhyun Park, Han L. Lee, Woo June Choi, Taeho Im(Authors)
- 2019(Publication Date)
- Wiley(Publisher)
2 , respectively. Therefore, it has the transfer function as(5.5.2)This indicates that the OP Amp circuit in Figure 5.17 (b) works as a high‐pass filter (HPF) with the cutoff frequency of ωc= 1/R1 C and the DC gain of G(s)|s=0= 0.5.5.2 Second‐Order Active LPF/HPF
The transfer function of the Sallen‐Key circuit in Figure 5.18 (a) can be found by using the MATLAB function ‘SallenKey_xfer_ftn() ’ (introduced in Section 5.4.2 ) as>>syms s G1 G2 R3 R4 C1 C2 K >>Gs=SallenKey_xfer_ftn(G1,0,s*C1,G2,s*C2,(K-1)*R3,R3); pretty(simplify(Gs)) G1 G2 K - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 G1 G2 + C1 G2 s + C2 G1 s + C2 G2 s + C1 C2 s - C1 G2 K sSecond‐order active (Sallen‐Key) filters.Figure 5.18This means that the transfer function G(s) is(5.5.3)This transfer function having only a constant term in the numerator indicates that the circuit will function as a low‐pass filter (LPF).The transfer function of the Sallen‐Key circuit in Figure 5.18 (b) can also be found by using the MATLAB function ‘SallenKey_xfer_ftn()
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