What is an Operational Amplifier - Term Paper Example

Case study report on Operational Amplifier (Op-Amp) CT1033N: Introduction to Electronics ID: Report Structure Report Structure 2 1Introduction4 1.1Origins and Development of the Operational Amplifier 4 1.2Block Diagram 6 1.3Advantages/Disadvantages 6 2Circuit and Operation 7 2.1Non-Inverting Operation 7 2.2Inverting Operation 8 2.3Standard op-amps 9 2.3.1 LM741 9 2.3.2 TL072 10 3Applications 11 3.1Differentiator 11 3.2Integrator 12 3.3Comparator 12 4Design and Simulations 13 4.1The Adder 13 4.2Simulation and Comparison of Results 14 5References 17 6Appendix 17 List of Figures Figure 1 - Circuit Diagram Element 4 Figure 2 - Op-Amp Internal Stages 6 Figure 3 - Non-Inverting Amplifier Circuit 7 Figure 4 - Inverting Amplifier Circuit 8 Figure 5 - Table of Op-Amp Properties 9 Figure 6 - LM741 Pinout 9 Figure 7 - LM741 Frequency Response 10 Figure 8 - TL072 Pinout 10 Figure 9 - TL072 Frequency Response 11 Figure 10 - Differentiator Circuit Diagram 11 Figure 11 - Integrator Circuit Diagram 12 Figure 12 - Comparator Circuit Diagram 12 Figure 13 - Adder Circuit Diagram 13 Figure 14 - Simulation Parameters 15 Figure 15 - Simulation Results 15 Figure 16 - Saturation Characteristic 16 Figure 17 - List of Manufacturers 17 Figure 18 - Cost Comparison of UK Suppliers 18 Figure 19 - Comparison of Common Op-Amps 18 1 Introduction An operational amplifier, or op-amp for short, is a DC-coupled, high gain, voltage amplifier. They form the basis of a wide array of electronic circuits, including amplifiers, buffers, comparators, and analogue-digital/digital-analogue converters. An op-amp is represented in schematic notation by the following symbol: Figure 1 - Circuit Diagram Element Where V+ and V- are the differential inputs, VS+ and VS-, are the positive and negative supply voltages, and Vout is the output of the amplifier. While they are represented as a single element, op-amps are in fact composed of many circuit elements, and are conventionally sold as monolithically integrated silicon chips. 1.1 Origins and Development of the Operational Amplifier The operational amplifier can trace its origins back to fledgling telecommunications industry in the United States at the turn of the 19th century. With the invention of the telephone, there was demand to carry electronic voice communications over longer and longer distances. The challenge was to build signal repeating equipment that minimized problems like distortion and crosstalk, so that multi-channel communications could be carried from one side of the country to the other. Advances in electronic equipment and amplifier design eventually led to the development of the first operational amplifiers at Bell Labs in the 1940s. Vacuum tube devices were essential to the development of amplifier technology, because they made possible for the first time the non-linear manipulation of voltage and current. “The Fleming Diode”, patented in 1904 by J.A. Fleming [1], was the first major breakthrough in this respect because it allowed for the rectification of current. Then in 1906, Lee De Forest [2] built upon this work with “The Audion”, a three-element triode vacuum tube that was the first device capable of signal amplification. Amplifiers built in the following years suffered from stability problems, as they used a positive feedback principle, and distortion due to the generation of harmonics by vacuum tubes. Harold Black [3], in 1927 while searching for a means of improving linearity and stability of currently-used positive feedback amplifiers, came up with the negative feedback amplifier principle. The idea of deliberately sacrificing gain in to improve stability ran counter to conventional ideas at the time, and it took 9 years for the original patent application to be accepted. Once implemented, however, the advantages of this approach quickly became clear. Within a few years the theory for stable amplifier design was formalized by Nyquist and Bode, two names now synonymous with fundamental electrical engineering principles, during their work at Bell Labs. At this point it is important to distinguish an “operational” amplifier from other types, in particular because the term itself was coined some years after the invention of the devices themselves. Jung [4] outlines a loose definition of what constitutes an “operational amplifier” as follows: General purpose, meaning that the amplifier uses bipolar power supplies with output signal ranges centred around 0V DC-coupled, meaning that the signals handled include DC potentials as well as AC signals High gain, meaning a DC gain in excess of 100x or 60 dB Inverting mode operation, meaning that the signal return is understood to be ground Feedback amplification that could be used with a variety of feedback elements for a variety of applications The first amplifier to fit this rather broad definition was invented by Karl Swartzel of Bell Labs, in a patent filed in 1941. It played an important role in improving the accuracy of an artillery detector developed at Bell Labs for World War II. The term “operational amplifier” was finally coined in 1947 by Prof. John Ragazzini [5]: "As an amplifier so connected can perform the mathematical operations of arithmetic and calculus on the voltages applied to its input, it is hereafter termed an ‘operational amplifier’." This recognition of the ability of amplifier circuits to produce well-defined mathematical results heralded the start of their regular use in a major application, namely analogue computing. Additional features were added to the design, starting with the inclusion of an explicit non-inverting input in 1947. This addition of a differential input, although it did not immediately catch onto popularity, opened up a wide range of new applications. The invention of the transistor, the integrated circuit (or IC), and the planar IC process heralded an entirely new era of solid state op-amps that would eventually push out the old vacuum tube-based devices. These were developed through the 1950’s and sold as printed circuit boards (PCBs) with discrete transistors and hand-selected resistors. In 1962, the first op-amps to be sold as “black boxes” inside potted packages were released. This was followed shortly afterwards by the reduction of the op-amp circuit to a single monolithic IC, as is done today, in 1963. Since the late 1960’s the development of op-amps has proceeded apace with improvements in semiconductor processing technology. 1.2 Block Diagram An op-amp can be further broken down into a series of three simpler amplifiers, the individual properties of which vary from op-amp to op-amp depending on the application requirements. Figure 2 - Op-Amp Internal Stages Differential amplifier: provides low noise amplification, high input impedance, and sometimes carries out differential to single-ended conversion. Voltage amplifier: provides high voltage gain, negative feedback stability through dominant pole compensation, and single-ended output in cases where this is not done in the differential stage. Output amplifier: provides higher output current, low output impedance, current limiting, and short circuit protection. 1.3 Advantages/Disadvantages Many of the advantages of modern op-amps stem from their reduction to a standardized and mass-produced component. While they are sold and can be treated theoretically as a black box with a well-defined set of properties, they are in reality rather complicated integrated circuits in their own right. Quality controls in the manufacturing process ensure that performance is reliable and to specification. Op-amps are used in very wide range of circuits, with their function largely determined by externally connected feedback elements. This makes them extremely flexible. The well-engineered internal circuitry of op-amps can also make them something of a liability to the amateur electronics designer. One cannot be lulled into a false sense of security. While their function within a set operating range is near-ideal, the designer must always be mindful of those limits. Some of the limits are obvious, such as finite limits on gain, output current, bandwidth, saturation voltage, and slew rate. Others are more subtle, but can still be critical depending on the application. Such factors include finite input and output impedances, temperature effects, noise, drift, and power supply ripple rejection. 2 Circuit and Operation The simple op-amp model relates the input voltages to the output voltages: Where AV is the open-loop DC gain. Additionally, an ideal op-amp is considered to have the following properties, and they are considered to hold for all input voltages: -Infinite open-loop gain (AV = ∞) -Infinite voltage range available at the output -Infinite input impedance, meaning that no current flows between the differential inputs -Zero input current, meaning there are neither bias nor leakage currents -Zero input offset voltage, meaning that V+ = V- -Zero output impedance, meaning that the output voltage does not change with output current The above characteristics will be used with the simple op-amp model to describe the two most basic configurations for an op-amp circuit. The result of the analysis in each case will be the relation between input and output voltage. 2.1 Non-Inverting Operation Figure 3 - Non-Inverting Amplifier Circuit From the simple op-amp model: Substitute the appropriate nodal voltages at the inverting and non-inverting terminals to put the equation entirely in terms of input and output voltages: Re-arrange to separate Vout and Vin: Here we note that for an ideal op-amp the open-loop gain is infinite, and thus the first term can be disregarded: This is easily reduced to the final input-output relation: The fact that Vin and Vout have the same sign demonstrates the non-inverting characteristic. 2.2 Inverting Operation Figure 4 - Inverting Amplifier Circuit The non-inverting input is tied to ground, and by the infinite input impedance property the inverting terminal is then a virtual ground. Since there is no input current, the same current that flows between Vin and the inverting terminal also flows from the output to the inverting terminal: Re-arranging this yields the input-output relation: 2.3 Standard op-amps This section details the properties of two of the most commonly-used op-amps on the market: the LM741[6] and the TL072 [7]. Some of their basic properties are summarized below: Amplifier GBP Open Loop Gain Input Impedance Common mode rejection ratio Slew Rate LM741 1 MHz 106 dB 2.0 MΩ 90 dB 0.5 V/μs TL072 3 MHz 88 dB 1.0 TΩ 70 dB 8V/ μs Figure 5 - Table of Op-Amp Properties 2.3.1 LM741 Since its introduction in 1968, the 741 architecture has been the canonical op-amp design, because it incorporated a compensation capacitor, rather than requiring the addition of one externally. Figure 6 - LM741 Pinout Figure 7 - LM741 Frequency Response 2.3.2 TL072 The TL072 features JFET inputs that increase input impedance. They are intended for high-fidelity or audio pre-amplification applications. Unlike the LM741, the TL072 contains two op-amps in one package. Figure 8 - TL072 Pinout Figure 9 - TL072 Frequency Response 3 Applications This section describes three of the most basic and ubiquitous circuits that can be built using op-amps. They often serve as building blocks for larger circuits that serve more complicated functions. 3.1 Differentiator As the name implies, the function of a differentiator circuit is to produce an output proportional to the derivative of the input. It is also known as a high-pass filter, which attenuates low frequency signals and amplifies high frequency signals. Figure 10 - Differentiator Circuit Diagram The capacitor C acts as a DC block, while the resistor R provides inverting feedback. The non-inverting input is grounded, and so the op-amp tries to drive the inverting input to ground as well. This means that any changes in the input voltage Vin will cause current to flow from the output to the inverting input. 3.2 Integrator An integrator circuit serves the opposite function of a differentiator. It provides an output proportional to the integral of the input, and acts as a low-pass filter. Figure 11 - Integrator Circuit Diagram Important to the proper function of this circuit is that the input voltage not have a DC component, otherwise the output voltage will rise to a level that is outside the operational range of the op-amp. 3.3 Comparator A comparator circuit is interesting in that it exploits the non-ideal properties of the op-amp to provide a logical comparison between two input signals. The ‘circuit’ is in fact nothing more than the op-amp itself: Figure 12 - Comparator Circuit Diagram Op-amps typically have a very high (>10 000) open-loop gain factor. Recalling the simple op-amp model: For supply voltages normally used in logic circuits (+/- 5- 10 V), a difference of even a millivolt will cause the output to quickly swing towards saturation. This means that if V+ is greater than V- the output will be equal to the positive saturation voltage, and if V+ is lesser than V- the output will be equal to the negative saturation voltage. One of the most common uses of comparators is in analog-to-digital conversion, where they perform the necessary quantization for each bit. 4 Design and Simulations 4.1 The Adder The following circuit is an example of an inverting summing amplifier, or an ‘adder’. It is an expanded version of the previously described inverting amplifier configuration, where the currents produced by multiple voltage sources are channelled through the feedback resistor. The voltage at the output of the op-amp will be the sum of the various inputs, scaled by the ratio of the feedback resistance to the respective input resistances. Figure 13 - Adder Circuit Diagram List of Variables: R1 – Input resistor for V1 R2 – Input resistor for V2 R3 – Input resistor for V3 R4 – Feedback resistor V4 – Negative supply voltage V5 – Positive supply voltage V1, V2, V3 – Variable voltage sources Since the non-inverting input of the op-amp is tied to ground, the negative input becomes a virtual ground. Modelling the op-amp as ideal, no current flows into the device and all of the current from the variable voltage sources must be countered by an equivalent current flowing from the output of the op-amp through the feedback resistor: This can be re-written in terms of the voltages and resistances: And thus it is clear in the case of R1 = R2 = R3 = R4 that the output is simply the negative of the input voltages: Circuits that perform such mathematical operations, albeit more complicated than simple addition, were the basis of analogue computing in the middle of the 20th century. The stability and accuracy of the amplifiers in those computers was critical to getting correct results in applications with little tolerance for error: weapons guidance systems. 4.2 Simulation and Comparison of Results The first thing to verify is the basic functioning of the circuit. The following table is a set of hand calculations based on the analysis presented in the previous section. All resistors in this case are set to a value of 1 kΩ, with supply voltages of +/- 10 V. Simulation # V1 V2 V3 Vout 1 1 1 1 -3 2 -1 1 1 -1 3 3 2 1 -6 4 4 3 3 -10 Figure 14 - Simulation Parameters The following graph shows the results of a DC simulation performed in SIMetrix. A DC sweep analysis was performed on the value of V1 for a short interval around the voltage from the table above in order to produce a single data point on the graph for each simulation. Figure 15 - Simulation Results The results of the simulation match the hand-calculated predictions, with the exception of simulation 4, where the simulated value is considerably less than the predicted value of -10. To investigate this further, a DC sweep was performed on V1 from -10V to 10V with the other two sources held at 1V. Figure 16 - Saturation Characteristic What is displayed here is the saturation characteristic of the TL072. SIMetrix uses a realistic model of the op-amp that can take into consideration this kind of non-linearity. Checking the data sheet of the TL072 shows that it is indeed intended for operation only within 1.5V of the supply, corresponding in this case to 8.5 V. The other feature confirmed by this graph is that the circuit can deliver both positive and negative voltages. 5 References 1) John A. Fleming, "Instrument for Converting Alternating Electric Currents into Continuous Currents," US Patent 803,684, filed April 19, 1905, issued Nov. 7, 1905. See also UK Patent 24,850, filed Nov. 16, 1904. 2) Lee De Forest, "Device for Amplifying Feeble Electrical Currents," US Patent 841,387, filed October 25, 1906, issued January 15, 1907. 3) Harold S. Black, "Inventing the Negative Feedback Amplifier," IEEE Spectrum, December, 1977. 4) Walt Jung. “Op Amp Applications Handbook”. 2005 Burlington, MA, USA: Elsevier. 5) John R. Ragazzini, Robert H. Randall and Frederick A. Russell, "Analysis of Problems in Dynamics by Electronic Circuits," Proceedings of the IRE, vol. 35, May 1947, pp. 444-452. 6) National Semiconductor. (2000). LM741 datasheet. Retrieved Jan. 13, 2011 from http://www.national.com/ds/LM/LM741.pdf 7) Texas Instruments. (1978). TL072 datasheet. Retrieved Jan. 13, 2001 from http://focus.ti.com/lit/ds/symlink/tl072.pdf 8) Operational amplifier. (2011, January 3). In Wikipedia, The Free Encyclopedia. Retrieved 03:32, January 13, 2011, from http://en.wikipedia.org/wiki/Op_amp 6 Appendix Advanced Linear Devices Micrel Semiconductor Renesas Technology Corp Advances Monolithic Systems Micro Networks Integrated Products ROHM Analog Devices Micropac Industries STMicroelectronics Fairchild Semiconductor Mimix Broadband Texas Instruments Frequency Devices M.S. Kennedy corporation TOREX Semiconductor Ltd Intersil National Transys Electronics Linear Technology NEC Triquint Semiconductor Maxim Integrated products NJR Zarlink Semiconductor Microchip ON Semiconductor Figure 17 - List of Manufacturers UK Supplier LM741 Price (£) TL072 Price (£) RS components 0.56 0.27 Farnell 0.44 0.31 Maplin electronics 0.95 N/A Bowood electronics 0.30 0.50 Rapid 0.36 0.33 RSH electronics 0.30 0.50 Figure 18 - Cost Comparison of UK Suppliers Type: Supply V min +/- V Supply V max +/- V Input Range +/- 15V supply +/- V Output range +/- V Max Output current mA Input Resisistance MΩ Slew rate V/s Open loop gain dB Internal frequency compensation Short circuit protection 709 9 18 10 14 10 0.25 0.5 93 N N 741 2 18 15 14 25 2 0.5 106 Y Y 1458 2 18 15 14 25 1 0.5 104 Y Y 4136 2 18 15 14 25 5 1 110 Y Y CA3140 2 18 -15/+23 13 10 1.5x10^6 9 100 Y Y LF356 3 18 15 13 15 10^6 12 106 Y Y LF357 3 18 15 13 15 10^6 50 106 Y Y TL074 5 18 15 13 20 10^6 13 106 Y Y TL084 5 18 15 13 20 10^6 13 106 Y Y OP15 3 18 16 13 6.5 10^6 5 106 Y Y OP16 3 18 16 13 6.5 10^6 9 106 Y Y OP17 3 18 16 13 6.5 10^6 25 106 Y Y OP27 4 22 15 13 17 2000 2.8 115 Y Y OP227 4 22 15 13 17 2000 2.8 115 Y Y OP77 3 22 15 14 12 2x10^5 0.3 138 Y Y Figure 19 - Comparison of Common Op-Amps Read More