An operational amplifier (often op amp or opamp ) is a DC-coupled electronic voltage amplifier with a differential input , a (usually) single-ended output, and an extremely high gain . Its name comes from its original use of performing mathematical operations in analog computers .
122-515: By using negative feedback , an op amp circuit 's characteristics (e.g. its gain, input and output impedance , bandwidth , and functionality) can be determined by external components and have little dependence on temperature coefficients or engineering tolerance in the op amp itself. This flexibility has made the op amp a popular building block in analog circuits . Today, op amps are used widely in consumer, industrial, and scientific electronics. Many standard integrated circuit op amps cost only
244-419: A Darlington pair ). This current signal develops a voltage at the bases of output transistors Q14 and Q20 proportional to the h ie of the respective transistor. Output transistors Q14 and Q20 are each configured as an emitter follower, so no voltage gain occurs there; instead, this stage provides current gain, equal to the h fe of Q14 and Q20. The current gain lowers the output impedance and although
366-440: A physiologic negative feedback inhibition loop, such as the glucocorticoids secreted by the adrenal cortex . The hypothalamus secretes corticotropin-releasing hormone (CRH) , which directs the anterior pituitary gland to secrete adrenocorticotropic hormone (ACTH) . In turn, ACTH directs the adrenal cortex to secrete glucocorticoids, such as cortisol . Glucocorticoids not only perform their respective functions throughout
488-408: A Fourier synthesizer, a tide-predicting machine , which summed the individual harmonic components. Another category, not nearly as well known, used rotating shafts only for input and output, with precision racks and pinions. The racks were connected to linkages that performed the computation. At least one U.S. Naval sonar fire control computer of the later 1950s, made by Librascope, was of this type, as
610-428: A GBWP of hundreds of megahertz. For very high-frequency circuits, a current-feedback operational amplifier is often used. Modern integrated FET or MOSFET op amps approximate more closely the ideal op amp than bipolar ICs when it comes to input impedance and input bias currents. Bipolars are generally better when it comes to input voltage offset, and often have lower noise. Generally, at room temperature, with
732-459: A cascaded differential amplifier (outlined in dark blue) followed by a current-mirror active load . This constitutes a transconductance amplifier , turning a differential voltage signal at the bases of Q1, Q2 into a current signal into the base of Q15. It entails two cascaded transistor pairs, satisfying conflicting requirements. The first stage consists of the matched NPN emitter follower pair Q1, Q2 that provide high input impedance. The second
854-428: A comparatively intimate control and understanding of the problem, relative to digital simulations. Electronic analog computers are especially well-suited to representing situations described by differential equations. Historically, they were often used when a system of differential equations proved very difficult to solve by traditional means. As a simple example, the dynamics of a spring-mass system can be described by
976-403: A current i through R g equal to V in / R g : i = V in R g {\displaystyle i={\frac {V_{\text{in}}}{R_{\text{g}}}}} Since Kirchhoff's current law states that the same current must leave a node as enter it, and since the impedance into the (−) pin is near infinity per assumption 2, we can assume practically all of
1098-457: A decrease in a disturbance or the amplitude of an oscillation. The term " feedback " was well established by the 1920s, in reference to a means of boosting the gain of an electronic amplifier. Friis and Jensen described this action as "positive feedback" and made passing mention of a contrasting "negative feed-back action" in 1924. Harold Stephen Black came up with the idea of using negative feedback in electronic amplifiers in 1927, submitted
1220-492: A decrease in base drive for Q15. On the other hand, a small positive change in voltage at the non-inverting input (Q1 base) drives this transistor into conduction, reflected in an increase in current at the collector of Q3. This current drives Q7 further into conduction, which turns on current mirror Q5/Q6. Thus, the increase in Q3 emitter current is mirrored in an increase in Q6 collector current;
1342-416: A fairly large signal, and limited bandwidth, FET and MOSFET op amps now offer better performance. Sourced by many manufacturers, and in multiple similar products, an example of a bipolar transistor operational amplifier is the 741 integrated circuit designed in 1968 by David Fullagar at Fairchild Semiconductor after Bob Widlar 's LM301 integrated circuit design. In this discussion, we use the parameters of
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#17332021504381464-432: A few cents; however, some integrated or hybrid operational amplifiers with special performance specifications may cost over US$ 100. Op amps may be packaged as components or used as elements of more complex integrated circuits . The op amp is one type of differential amplifier . Other differential amplifier types include the fully differential amplifier (an op amp with a differential rather than single-ended output),
1586-609: A fully electronic analog computer at Peenemünde Army Research Center as an embedded control system ( mixing device ) to calculate V-2 rocket trajectories from the accelerations and orientations (measured by gyroscopes ) and to stabilize and guide the missile. Mechanical analog computers were very important in gun fire control in World War II, the Korean War and well past the Vietnam War; they were made in significant numbers. In
1708-482: A much larger voltage signal on output. The input stage with Q1 and Q3 is similar to an emitter-coupled pair (long-tailed pair), with Q2 and Q4 adding some degenerating impedance. The input impedance is relatively high because of the small current through Q1-Q4. A typical 741 op amp has a differential input impedance of about 2 MΩ. The common mode input impedance is even higher, as the input stage works at an essentially constant current. A differential voltage V in at
1830-444: A negative feedback loop. In this way, negative feedback loops in the environment have a stabilizing effect. Negative feedback as a control technique may be seen in the refinements of the water clock introduced by Ktesibios of Alexandria in the 3rd century BCE. Self-regulating mechanisms have existed since antiquity, and were used to maintain a constant level in the reservoirs of water clocks as early as 200 BCE. Negative feedback
1952-439: A patent application in 1928, and detailed its use in his paper of 1934, where he defined negative feedback as a type of coupling that reduced the gain of the amplifier, in the process greatly increasing its stability and bandwidth. Karl Küpfmüller published papers on a negative-feedback-based automatic gain control system and a feedback system stability criterion in 1928. Nyquist and Bode built on Black's work to develop
2074-400: A physical panel with connectors or, in more modern systems, as a software interface that allows virtual management of signal connections and routes. Output devices in analog machines can vary depending on the specific goals of the system. For example, they could be graphical indicators, oscilloscopes , graphic recording devices, TV connection module , voltmeter , etc. These devices allow for
2196-496: A positive temperature coefficient of reactivity . Whereas positive feedback tends to lead to instability via exponential growth , oscillation or chaotic behavior , negative feedback generally promotes stability. Negative feedback tends to promote a settling to equilibrium , and reduces the effects of perturbations. Negative feedback loops in which just the right amount of correction is applied with optimum timing, can be very stable, accurate, and responsive. Negative feedback
2318-406: A predictable transfer function. Since the open-loop gain of an op-amp is extremely large, a small differential input signal would drive the output of the amplifier to one rail or the other in the absence of negative feedback. A simple example of the use of feedback is the op-amp voltage amplifier shown in the figure. The idealized model of an operational amplifier assumes that the gain is infinite,
2440-507: A runaway condition. Even before the point where the phase shift becomes 180 degrees, stability of the negative feedback loop will become compromised, leading to increasing under- and overshoot following a disturbance. This problem is often dealt with by attenuating or changing the phase of the problematic frequencies in a design step called compensation. Unless the system naturally has sufficient damping, many negative feedback systems have low pass filters or dampers fitted. One use of feedback
2562-467: A simple example, if V in = 1 V and R f = R g , V out will be 2 V, exactly the amount required to keep V − at 1 V. Because of the feedback provided by the R f , R g network, this is a closed-loop circuit. Another way to analyze this circuit proceeds by making the following (usually valid) assumptions: The input signal V in appears at both (+) and (−) pins per assumption 1, resulting in
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#17332021504382684-473: A small-signal differential current in Q3 versus Q4 appears summed (doubled) at the base of Q15, the input of the voltage gain stage. The (class-A) voltage gain stage (outlined in magenta ) consists of the two NPN transistors Q15 and Q19 connected in a Darlington configuration and uses the output side of current mirror formed by Q12 and Q13 as its collector (dynamic) load to achieve its high voltage gain. The output sink transistor Q20 receives its base drive from
2806-407: A system. In a psychology context, on the other hand, negative refers to the valence of the feedback – attractive versus aversive, or praise versus criticism. In contrast, positive feedback is feedback in which the system responds so as to increase the magnitude of any particular perturbation, resulting in amplification of the original signal instead of stabilization. Any system in which there
2928-422: A theory of amplifier stability. Early researchers in the area of cybernetics subsequently generalized the idea of negative feedback to cover any goal-seeking or purposeful behavior. Analog computers An analog computer or analogue computer is a type of computation machine (computer) that uses physical phenomena such as electrical , mechanical , or hydraulic quantities behaving according to
3050-473: A unilateral feedback block has significant limitations. For methods of analysis that do not make these idealizations, see the article Negative feedback amplifier . The operational amplifier was originally developed as a building block for the construction of analog computers , but is now used almost universally in all kinds of applications including audio equipment and control systems . Operational amplifier circuits typically employ negative feedback to get
3172-444: A voltage on a particular wire). Therefore, each problem must be scaled so its parameters and dimensions can be represented using voltages that the circuit can supply —e.g., the expected magnitudes of the velocity and the position of a spring pendulum . Improperly scaled variables can have their values "clamped" by the limits of the supply voltage. Or if scaled too small, they can suffer from higher noise levels . Either problem can cause
3294-647: Is V BE / 50 kΩ, about 35 μA, as is the quiescent current in Q15, with its matching operating point. Thus, the quiescent currents are pairwise matched in Q1/Q2, Q3/Q4, Q5/Q6, and Q7/Q15. Quiescent currents in Q16 and Q19 are set by the current mirror Q12/Q13, which is running at ~1 mA. The collector current in Q19 tracks that standing current. In the circuit involving Q16 (variously named rubber diode or V BE multiplier),
3416-552: Is derived from a weighted sum of the error signal, integral of the error signal, and derivative of the error signal. The weights of the respective components depend on the application. Mathematically, the regulator signal is given by: where The negative feedback amplifier was invented by Harold Stephen Black at Bell Laboratories in 1927, and granted a patent in 1937 (US Patent 2,102,671) "a continuation of application Serial No. 298,155, filed August 8, 1928 ..."). There are many advantages to feedback in amplifiers. In design,
3538-487: Is independent of the open-loop gain A , the feedback is said to 'desensitize' the closed-loop gain to variations in A (for example, due to manufacturing variations between units, or temperature effects upon components), provided only that the gain A is sufficiently large. In this context, the factor (1+β A ) is often called the 'desensitivity factor', and in the broader context of feedback effects that include other matters like electrical impedance and bandwidth ,
3660-509: Is mirrored from Q8 into Q9, where it is summed with the collector current in Q10, the result being applied to the bases of Q3 and Q4. The quiescent currents through Q1 and Q3 (also Q2 and Q4) i 1 will thus be half of i 10 , of order ~10 μA. Input bias current for the base of Q1 (also Q2) will amount to i 1 / β; typically ~50 nA, implying a current gain h fe ≈ 200 for Q1 (also Q2). This feedback circuit tends to draw
3782-400: Is often referred to as homeostasis ; whereas in mechanics , the more common term is equilibrium . In engineering , mathematics and the physical, and biological sciences, common terms for the points around which the system gravitates include: attractors, stable states, eigenstates/eigenfunctions, equilibrium points, and setpoints . In control theory , negative refers to the sign of
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3904-522: Is one of the few fields where slide rules are still in widespread use, particularly for solving time–distance problems in light aircraft. In 1831–1835, mathematician and engineer Giovanni Plana devised a perpetual-calendar machine , which, through a system of pulleys and cylinders, could predict the perpetual calendar for every year from AD 0 (that is, 1 BC) to AD 4000, keeping track of leap years and varying day length. The tide-predicting machine invented by Sir William Thomson in 1872
4026-458: Is positive feedback together with a gain greater than one will result in a runaway situation. Both positive and negative feedback require a feedback loop to operate. However, negative feedback systems can still be subject to oscillations . This is caused by a phase shift around any loop. Due to these phase shifts the feedback signal of some frequencies can ultimately become in phase with the input signal and thus turn into positive feedback, creating
4148-513: Is striking in terms of mathematics. They can be modeled using equations of the same form. However, the difference between these systems is what makes analog computing useful. Complex systems often are not amenable to pen-and-paper analysis, and require some form of testing or simulation. Complex mechanical systems, such as suspensions for racing cars, are expensive to fabricate and hard to modify. And taking precise mechanical measurements during high-speed tests adds further difficulty. By contrast, it
4270-726: Is the PEAC (Practical Electronics analogue computer), published in Practical Electronics in the January 1968 edition. Another more modern hybrid computer design was published in Everyday Practical Electronics in 2002. An example described in the EPE hybrid computer was the flight of a VTOL aircraft such as the Harrier jump jet . The altitude and speed of the aircraft were calculated by
4392-491: Is the interaction between solar radiation , cloud cover , and planet temperature. In many physical and biological systems, qualitatively different influences can oppose each other. For example, in biochemistry, one set of chemicals drives the system in a given direction, whereas another set of chemicals drives it in an opposing direction. If one or both of these opposing influences are non-linear, equilibrium point(s) result. In biology , this process (in general, biochemical )
4514-404: Is the matched PNP common-base pair Q3, Q4 that eliminates the undesirable Miller effect ; it drives an active load Q7 plus matched pair Q5, Q6. That active load is implemented as a modified Wilson current mirror ; its role is to convert the (differential) input current signal to a single-ended signal without the attendant 50% losses (increasing the op amp's open-loop gain by 3 dB). Thus,
4636-497: Is to combine the two processes for the best efficiency. An example of such hybrid elementary device is the hybrid multiplier, where one input is an analog signal, the other input is a digital signal and the output is analog. It acts as an analog potentiometer, upgradable digitally. This kind of hybrid technique is mainly used for fast dedicated real time computation when computing time is very critical, as signal processing for radars and generally for controllers in embedded systems . In
4758-408: Is to make a system (say T ) self-regulating to minimize the effect of a disturbance (say D ). Using a negative feedback loop, a measurement of some variable (for example, a process variable , say E ) is subtracted from a required value (the 'set point' ) to estimate an operational error in system status, which is then used by a regulator (say R ) to reduce the gap between the measurement and
4880-405: Is very inexpensive to build an electrical equivalent of a complex mechanical system, to simulate its behavior. Engineers arrange a few operational amplifiers (op amps) and some passive linear components to form a circuit that follows the same equations as the mechanical system being simulated. All measurements can be taken directly with an oscilloscope . In the circuit, the (simulated) stiffness of
5002-427: Is widely used in mechanical and electronic engineering , and also within living organisms, and can be seen in many other fields from chemistry and economics to physical systems such as the climate. General negative feedback systems are studied in control systems engineering . Negative feedback loops also play an integral role in maintaining the atmospheric balance in various systems on Earth. One such feedback system
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5124-477: The Nyquist plot that identify stable feedback systems, including amplifiers and control systems. The figure shows a simplified block diagram of a negative feedback amplifier . The feedback sets the overall (closed-loop) amplifier gain at a value: where the approximate value assumes β A >> 1. This expression shows that a gain greater than one requires β < 1. Because the approximate gain 1/β
5246-399: The baroreflex in blood pressure regulation and erythropoiesis . Many biological processes (e.g., in the human anatomy ) use negative feedback. Examples of this are numerous, from the regulating of body temperature, to the regulating of blood glucose levels. The disruption of feedback loops can lead to undesirable results: in the case of blood glucose levels , if negative feedback fails,
5368-422: The chemical equilibrium to the opposite side of the reaction in order to reduce a stress. For example, in the reaction If a mixture of the reactants and products exists at equilibrium in a sealed container and nitrogen gas is added to this system, then the equilibrium will shift toward the product side in response. If the temperature is raised, then the equilibrium will shift toward the reactant side which, since
5490-458: The flight computer in aircraft , and for teaching control systems in universities. Perhaps the most relatable example of analog computers are mechanical watches where the continuous and periodic rotation of interlinked gears drives the second, minute and hour needles in the clock. More complex applications, such as aircraft flight simulators and synthetic-aperture radar , remained the domain of analog computing (and hybrid computing ) well into
5612-484: The hybrid-pi model to characterize the small-signal, grounded emitter characteristics of a transistor. In this model, the current gain of a transistor is denoted h fe , more commonly called the β. A small-scale integrated circuit , the 741 op amp shares with most op amps an internal structure consisting of three gain stages: Additionally, it contains current mirror (outlined red) bias circuitry and compensation capacitor (30 pF). The input stage consists of
5734-423: The instrumentation amplifier (usually built from three op amps), the isolation amplifier (with galvanic isolation between input and output), and negative-feedback amplifier (usually built from one or more op amps and a resistive feedback network). The amplifier's differential inputs consist of a non-inverting input (+) with voltage V + and an inverting input (−) with voltage V − ; ideally
5856-465: The spring constant and g {\displaystyle g} the gravity of Earth . For analog computing, the equation is programmed as y ¨ = − d m y ˙ − c m y − g {\displaystyle {\ddot {y}}=-{\tfrac {d}{m}}{\dot {y}}-{\tfrac {c}{m}}y-g} . The equivalent analog circuit consists of two integrators for
5978-482: The "Direct Analogy Electric Analog Computer" ("the largest and most impressive general-purpose analyzer facility for the solution of field problems") developed there by Gilbert D. McCann, Charles H. Wilts, and Bart Locanthi . Educational analog computers illustrated the principles of analog calculation. The Heathkit EC-1, a $ 199 educational analog computer, was made by the Heath Company, US c. 1960 . It
6100-419: The "feedback" generated by the thermostat "negates" the trend. The opposite tendency — called positive feedback — is when a trend is positively reinforced, creating amplification, such as the squealing "feedback" loop that can occur when a mic is brought too close to a speaker which is amplifying the very sounds the mic is picking up, or the runaway heating and ultimate meltdown of a nuclear reactor which has
6222-443: The 'improvement factor'. If the disturbance D is included, the amplifier output becomes: which shows that the feedback reduces the effect of the disturbance by the 'improvement factor' (1+β A ). The disturbance D might arise from fluctuations in the amplifier output due to noise and nonlinearity (distortion) within this amplifier, or from other noise sources such as power supplies. The difference signal I –β O at
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#17332021504386344-437: The 'set point' S , and subsequently used by the regulator (containing a 'controller' that commands gas control valves and an ignitor) ultimately to change the heat provided by a furnace (an 'effector') to counter the initial weather-related disturbance in heat input to the house. Error controlled regulation is typically carried out using a Proportional-Integral-Derivative Controller ( PID controller ). The regulator signal
6466-465: The 1950s to the 1970s, general-purpose analog computers were the only systems fast enough for real time simulation of dynamic systems, especially in the aircraft, military and aerospace field. In the 1960s, the major manufacturer was Electronic Associates of Princeton, New Jersey , with its 231R Analog Computer (vacuum tubes, 20 integrators) and subsequently its EAI 8800 Analog Computer (solid state operational amplifiers, 64 integrators). Its challenger
6588-410: The 1980s, since digital computers were insufficient for the task. This is a list of examples of early computation devices considered precursors of the modern computers. Some of them may even have been dubbed 'computers' by the press, though they may fail to fit modern definitions. The Antikythera mechanism , a type of device used to determine the positions of heavenly bodies known as an orrery ,
6710-508: The 4.5 kΩ resistor must be conducting about 100 μA, with Q16 V BE roughly 700 mV. Then V CB must be about 0.45 V and V CE at about 1.0 V. Because the Q16 collector is driven by a current source and the Q16 emitter drives into the Q19 collector current sink, the Q16 transistor establishes a voltage difference between the Q14 base and the Q20 base of ~1 V, regardless of
6832-515: The Antikythera mechanism would not reappear until a thousand years later. Many mechanical aids to calculation and measurement were constructed for astronomical and navigation use. The planisphere was first described by Ptolemy in the 2nd century AD. The astrolabe was invented in the Hellenistic world in either the 1st or 2nd centuries BC and is often attributed to Hipparchus . A combination of
6954-642: The Dumaresq were produced of increasing complexity as development proceeded. By 1912, Arthur Pollen had developed an electrically driven mechanical analog computer for fire-control systems , based on the differential analyser. It was used by the Imperial Russian Navy in World War I . Starting in 1929, AC network analyzers were constructed to solve calculation problems related to electrical power systems that were too large to solve with numerical methods at
7076-560: The Earth. As albedo increases, however, the amount of solar radiation decreases. This, in turn, affects the rest of the cycle. Cloud cover, and in turn planet albedo and temperature, is also influenced by the hydrological cycle . As planet temperature increases, more water vapor is produced, creating more clouds. The clouds then block incoming solar radiation, lowering the temperature of the planet. This interaction produces less water vapor and therefore less cloud cover. The cycle then repeats in
7198-416: The amplifier input is sometimes called the "error signal". According to the diagram, the error signal is: From this expression, it can be seen that a large 'improvement factor' (or a large loop gain β A ) tends to keep this error signal small. Although the diagram illustrates the principles of the negative feedback amplifier, modeling a real amplifier as a unilateral forward amplification block and
7320-404: The amplifier into clipping or saturation . The magnitude of A OL is not well controlled by the manufacturing process, and so it is impractical to use an open-loop amplifier as a stand-alone differential amplifier . Without negative feedback , and optionally positive feedback for regeneration , an open-loop op amp acts as a comparator , although comparator ICs are better suited. If
7442-568: The analog computer readout was limited chiefly by the precision of the readout equipment used, generally three or four significant figures. (Modern digital simulations are much better in this area. Digital arbitrary-precision arithmetic can provide any desired degree of precision.) However, in most cases the precision of an analog computer is absolutely sufficient given the uncertainty of the model characteristics and its technical parameters. Many small computers dedicated to specific computations are still part of industrial regulation equipment, but from
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#17332021504387564-676: The analog part of the computer and sent to a PC via a digital microprocessor and displayed on the PC screen. In industrial process control , analog loop controllers were used to automatically regulate temperature, flow, pressure, or other process conditions. The technology of these controllers ranged from purely mechanical integrators, through vacuum-tube and solid-state devices, to emulation of analog controllers by microprocessors. The similarity between linear mechanical components, such as springs and dashpots (viscous-fluid dampers), and electrical components, such as capacitors , inductors , and resistors
7686-518: The base of Q15 (the input of the voltage gain stage) is V in g m / 2. This portion of the op amp cleverly changes a differential signal at the op amp inputs to a single-ended signal at the base of Q15, and in a way that avoids wastefully discarding the signal in either leg. To see how, notice that a small negative change in voltage at the inverting input (Q2 base) drives it out of conduction, and this incremental decrease in current passes directly from Q4 collector to its emitter, resulting in
7808-403: The body but also negatively affect the release of further stimulating secretions of both the hypothalamus and the pituitary gland, effectively reducing the output of glucocorticoids once a sufficient amount has been released. Closed systems containing substances undergoing a reversible chemical reaction can also exhibit negative feedback in accordance with Le Chatelier's principle which shift
7930-472: The circuit in the diagram, assuming an ideal op amp, is the reciprocal of feedback voltage division ratio β: A real op-amp has a high but finite gain A at low frequencies, decreasing gradually at higher frequencies. In addition, it exhibits a finite input impedance and a non-zero output impedance. Although practical op-amps are not ideal, the model of an ideal op-amp often suffices to understand circuit operation at low enough frequencies. As discussed in
8052-407: The circuit to produce an incorrect simulation of the physical system. (Modern digital simulations are much more robust to widely varying values of their variables, but are still not entirely immune to these concerns: floating-point digital calculations support a huge dynamic range , but can suffer from imprecision if tiny differences of huge values lead to numerical instability .) The precision of
8174-407: The closed-loop gain A CL : A CL = V out V in = 1 + R f R g {\displaystyle A_{\text{CL}}={\frac {V_{\text{out}}}{V_{\text{in}}}}=1+{\frac {R_{\text{f}}}{R_{\text{g}}}}} An ideal op amp is usually considered to have the following characteristics: These ideals can be summarized by
8296-544: The common base node of Q3/Q4 to a voltage V com − 2 V BE , where V com is the input common-mode voltage. At the same time, the magnitude of the quiescent current is relatively insensitive to the characteristics of the components Q1–Q4, such as h fe , that would otherwise cause temperature dependence or part-to-part variations. Transistor Q7 drives Q5 and Q6 into conduction until their (equal) collector currents match that of Q1/Q3 and Q2/Q4. The quiescent current in Q7
8418-443: The common collectors of Q15 and Q19; the level-shifter Q16 provides base drive for the output source transistor Q14. The transistor Q22 prevents this stage from delivering excessive current to Q20 and thus limits the output sink current. The output stage (Q14, Q20, outlined in cyan) is a Class AB amplifier. It provides an output drive with impedance of ~50 Ω, in essence, current gain. Transistor Q16 (outlined in green) provides
8540-535: The common-mode voltage of Q14/Q20 bases. The standing current in Q14/Q20 will be a factor exp(100 mV mm/ V T ) ≈ 36 smaller than the 1 mA quiescent current in the class A portion of the op amp. This (small) standing current in the output transistors establishes the output stage in class AB operation and reduces the crossover distortion of this stage. A small differential input voltage signal gives rise, through multiple stages of current amplification, to
8662-515: The early 1970s, analog computer manufacturers tried to tie together their analog computers with a digital computers to get the advantages of the two techniques. In such systems, the digital computer controlled the analog computer, providing initial set-up, initiating multiple analog runs, and automatically feeding and collecting data. The digital computer may also participate to the calculation itself using analog-to-digital and digital-to-analog converters . The largest manufacturer of hybrid computers
8784-422: The emitter resistor of Q10, and 28 mV is V T , the thermal voltage at room temperature. In this case i 10 ≈ 20 μA. The biasing circuit of this stage is set by a feedback loop that forces the collector currents of Q10 and Q9 to (nearly) match. Any small difference in these currents provides drive for the common base of Q3 and Q4. The summed quiescent currents through Q1 and Q3 plus Q2 and Q4
8906-432: The equation m y ¨ + d y ˙ + c y = m g {\displaystyle m{\ddot {y}}+d{\dot {y}}+cy=mg} , with y {\displaystyle y} as the vertical position of a mass m {\displaystyle m} , d {\displaystyle d} the damping coefficient , c {\displaystyle c}
9028-445: The gain of the circuit. When negative feedback is used, the circuit's overall gain and response is determined primarily by the feedback network, rather than by the op-amp characteristics. If the feedback network is made of components with values small relative to the op amp's input impedance, the value of the op amp's open-loop response A OL does not seriously affect the circuit's performance. In this context, high input impedance at
9150-411: The glucose levels in the blood may begin to rise dramatically, thus resulting in diabetes . For hormone secretion regulated by the negative feedback loop: when gland X releases hormone X, this stimulates target cells to release hormone Y. When there is an excess of hormone Y, gland X "senses" this and inhibits its release of hormone X. As shown in the figure, most endocrine hormones are controlled by
9272-414: The increased collector currents shunts more from the collector node and results in a decrease in base drive current for Q15. Besides avoiding wasting 3 dB of gain here, this technique decreases common-mode gain and feedthrough of power supply noise. A current signal i at Q15's base gives rise to a current in Q19 of order i β (the product of the h fe of each of Q15 and Q19, which are connected in
9394-412: The input impedance is infinite, output resistance is zero, and input offset currents and voltages are zero. Such an ideal amplifier draws no current from the resistor divider. Ignoring dynamics (transient effects and propagation delay ), the infinite gain of the ideal op-amp means this feedback circuit drives the voltage difference between the two op-amp inputs to zero. Consequently, the voltage gain of
9516-486: The input terminals and low output impedance at the output terminal(s) are particularly useful features of an op amp. The response of the op-amp circuit with its input, output, and feedback circuits to an input is characterized mathematically by a transfer function ; designing an op-amp circuit to have a desired transfer function is in the realm of electrical engineering . The transfer functions are important in most applications of op amps, such as in analog computers . In
9638-407: The inverting input is held at ground (0 V), and the input voltage V in applied to the non-inverting input is positive, the output will be maximum positive; if V in is negative, the output will be maximum negative. If predictable operation is desired, negative feedback is used, by applying a portion of the output voltage to the inverting input. The closed-loop feedback greatly reduces
9760-531: The market pricing mechanism operates to match supply and demand , because mismatches between them feed back into the decision-making of suppliers and demanders of goods, altering prices and thereby reducing any discrepancy. However Norbert Wiener wrote in 1948: The notion of economic equilibrium being maintained in this fashion by market forces has also been questioned by numerous heterodox economists such as financier George Soros and leading ecological economist and steady-state theorist Herman Daly , who
9882-443: The mathematical principles in question ( analog signals ) to model the problem being solved. In contrast, digital computers represent varying quantities symbolically and by discrete values of both time and amplitude ( digital signals ). Analog computers can have a very wide range of complexity. Slide rules and nomograms are the simplest, while naval gunfire control computers and large hybrid digital/analog computers were among
10004-521: The mathematical understanding of the Gibbs phenomenon of overshoot in Fourier representation near discontinuities. In a differential analyzer, the output of one integrator drove the input of the next integrator, or a graphing output. The torque amplifier was the advance that allowed these machines to work. Starting in the 1920s, Vannevar Bush and others developed mechanical differential analyzers. The Dumaresq
10126-499: The most complicated. Complex mechanisms for process control and protective relays used analog computation to perform control and protective functions. Analog computers were widely used in scientific and industrial applications even after the advent of digital computers, because at the time they were typically much faster, but they started to become obsolete as early as the 1950s and 1960s, although they remained in use in some specific applications, such as aircraft flight simulators ,
10248-429: The multiplier in mathematical models for feedback. In delta notation, −Δoutput is added to or mixed into the input. In multivariate systems, vectors help to illustrate how several influences can both partially complement and partially oppose each other. Some authors, in particular with respect to modelling business systems , use negative to refer to the reduction in difference between the desired and actual behavior of
10370-403: The non-inverting amplifier on the right, the presence of negative feedback via the voltage divider R f , R g determines the closed-loop gain A CL = V out / V in . Equilibrium will be established when V out is just sufficient to pull the inverting input to the same voltage as V in . The voltage gain of the entire circuit is thus 1 + R f / R g . As
10492-574: The op amp amplifies only the difference in voltage between the two, which is called the differential input voltage . The output voltage of the op amp V out is given by the equation where A OL is the open-loop gain of the amplifier (the term "open-loop" refers to the absence of an external feedback loop from the output to the input). The magnitude of A OL is typically very large (100,000 or more for integrated circuit op amps, corresponding to +100 dB ). Thus, even small microvolts of difference between V + and V − may drive
10614-408: The op amp inputs (pins 3 and 2, respectively) gives rise to a small differential current in the bases of Q1 and Q2 i in ≈ V in / (2 h ie h fe ). This differential base current causes a change in the differential collector current in each leg by i in h fe . Introducing the transconductance of Q1, g m = h fe / h ie , the (small-signal) current at
10736-453: The op-amp model. The designer can then include these effects into the overall performance of the final circuit. Some parameters may turn out to have negligible effect on the final design while others represent actual limitations of the final performance. Real op amps differ from the ideal model in various aspects. Typical low-cost, general-purpose op amps exhibit a GBWP of a few megahertz. Specialty and high-speed op amps exist that can achieve
10858-583: The output impedance is not zero, as it would be in an ideal op amp, with negative feedback it approaches zero at low frequencies. The net open-loop small-signal voltage gain of the op amp is determined by the product of the current gain h fe of some 4 transistors. In practice, the voltage gain for a typical 741-style op amp is of order 200,000, and the current gain, the ratio of input impedance (~2−6 MΩ) to output impedance (~50 Ω) provides yet more (power) gain. The ideal op amp has infinite common-mode rejection ratio , or zero common-mode gain. In
10980-403: The output of a system, process, or mechanism is fed back in a manner that tends to reduce the fluctuations in the output, whether caused by changes in the input or by other disturbances. A classic example of negative feedback is a heating system thermostat — when the temperature gets high enough, the heater is turned OFF. When the temperature gets too cold, the heat is turned back ON. In each case
11102-561: The patch panel, various connections and routes can be set and switched to configure the machine and determine signal flows. This allows users to flexibly configure and reconfigure the analog computing system to perform specific tasks. Patch panels are used to control data flows , connect and disconnect connections between various blocks of the system, including signal sources, amplifiers, filters, and other components. They provide convenience and flexibility in configuring and experimenting with analog computations. Patch panels can be presented as
11224-654: The period 1930–1945 in the Netherlands, Johan van Veen developed an analogue computer to calculate and predict tidal currents when the geometry of the channels are changed. Around 1950, this idea was developed into the Deltar , a hydraulic analogy computer supporting the closure of estuaries in the southwest of the Netherlands (the Delta Works ). The FERMIAC was an analog computer invented by physicist Enrico Fermi in 1947 to aid in his studies of neutron transport. Project Cyclone
11346-419: The physical form of a signal may undergo multiple transformations. For example, a change in weather may cause a disturbance to the heat input to a house (as an example of the system T ) that is monitored by a thermometer as a change in temperature (as an example of an 'essential variable' E ). This quantity, then, is converted by the thermostat (a 'comparator') into an electrical error in status compared to
11468-465: The planisphere and dioptra , the astrolabe was effectively an analog computer capable of working out several different kinds of problems in spherical astronomy . The sector , a calculating instrument used for solving problems in proportion, trigonometry, multiplication and division, and for various functions, such as squares and cube roots, was developed in the late 16th century and found application in gunnery, surveying and navigation. The planimeter
11590-478: The possible construction of such calculators, but he had been stymied by the limited output torque of the ball-and-disk integrators . Several systems followed, notably those of Spanish engineer Leonardo Torres Quevedo , who built various analog machines for solving real and complex roots of polynomials ; and Michelson and Stratton, whose Harmonic Analyser performed Fourier analysis, but using an array of 80 springs rather than Kelvin integrators. This work led to
11712-405: The potentiometer was then equivalent to the formula of the equation being solved. Multiplication or division could be performed, depending on which dials were inputs and which was the output. Accuracy and resolution was limited and a simple slide rule was more accurate. However, the unit did demonstrate the basic principle. Analog computer designs were published in electronics magazines. One example
11834-519: The present circuit, if the input voltages change in the same direction, the negative feedback makes Q3/Q4 base voltage follow (with 2 V BE below) the input voltage variations. Now the output part (Q10) of Q10-Q11 current mirror keeps up the common current through Q9/Q8 constant in spite of varying voltage. Q3/Q4 collector currents, and accordingly the output current at the base of Q15, remain unchanged. Negative feedback Negative feedback (or balancing feedback ) occurs when some function of
11956-623: The previous section, the feedback circuit stabilizes the closed-loop gain and desensitizes the output to fluctuations generated inside the amplifier itself. An example of the use of negative feedback control is the ballcock control of water level (see diagram), or a pressure regulator . In modern engineering, negative feedback loops are found in engine governors , fuel injection systems and carburettors . Similar control mechanisms are used in heating and cooling systems, such as those involving air conditioners , refrigerators , or freezers . Some biological systems exhibit negative feedback such as
12078-500: The quiescent current for the output transistors and Q17 limits output source current. Biasing circuits provide appropriate quiescent current for each stage of the op amp. The resistor (39 kΩ) connecting the (diode-connected) Q11 and Q12, and the given supply voltage ( V S + − V S − ), determine the current in the current mirrors , (matched pairs) Q10/Q11 and Q12/Q13. The collector current of Q11, i 11 × 39 kΩ = V S + − V S − − 2 V BE . For
12200-399: The required value. The regulator modifies the input to the system T according to its interpretation of the error in the status of the system. This error may be introduced by a variety of possible disturbances or 'upsets', some slow and some rapid. The regulation in such systems can range from a simple 'on-off' control to a more complex processing of the error signal. In this framework,
12322-558: The reverse reaction is endothermic, will partially reduce the temperature. Self-organization is the capability of certain systems "of organizing their own behavior or structure". There are many possible factors contributing to this capacity, and most often positive feedback is identified as a possible contributor. However, negative feedback also can play a role. In economics, automatic stabilisers are government programs that are intended to work as negative feedback to dampen fluctuations in real GDP . Mainstream economics asserts that
12444-767: The same current i flows through R f , creating an output voltage V out = V in + i R f = V in + ( V in R g R f ) = V in + V in R f R g = V in ( 1 + R f R g ) {\displaystyle V_{\text{out}}=V_{\text{in}}+iR_{\text{f}}=V_{\text{in}}+\left({\frac {V_{\text{in}}}{R_{\text{g}}}}R_{\text{f}}\right)=V_{\text{in}}+{\frac {V_{\text{in}}R_{\text{f}}}{R_{\text{g}}}}=V_{\text{in}}\left(1+{\frac {R_{\text{f}}}{R_{\text{g}}}}\right)} By combining terms, we determine
12566-730: The speed of analog computers was their fully parallel computation, but this was also a limitation. The more equations required for a problem, the more analog components were needed, even when the problem wasn't time critical. "Programming" a problem meant interconnecting the analog operators; even with a removable wiring panel this was not very versatile. While a wide variety of mechanisms have been developed throughout history, some stand out because of their theoretical importance, or because they were manufactured in significant quantities. Most practical mechanical analog computers of any significant complexity used rotating shafts to carry variables from one mechanism to another. Cables and pulleys were used in
12688-445: The spring, for instance, can be changed by adjusting the parameters of an integrator. The electrical system is an analogy to the physical system, hence the name, but it is much less expensive than a mechanical prototype, much easier to modify, and generally safer. The electronic circuit can also be made to run faster or slower than the physical system being simulated. Experienced users of electronic analog computers said that they offered
12810-411: The state variables − y ˙ {\displaystyle -{\dot {y}}} (speed) and y {\displaystyle y} (position), one inverter, and three potentiometers. Electronic analog computers have drawbacks: the value of the circuit's supply voltage limits the range over which the variables may vary (since the value of a variable is represented by
12932-503: The time. These were essentially scale models of the electrical properties of the full-size system. Since network analyzers could handle problems too large for analytic methods or hand computation, they were also used to solve problems in nuclear physics and in the design of structures. More than 50 large network analyzers were built by the end of the 1950s. World War II era gun directors , gun data computers , and bomb sights used mechanical analog computers. In 1942 Helmut Hölzer built
13054-508: The two golden rules : The first rule only applies in the usual case where the op amp is used in a closed-loop design (negative feedback, where there is a signal path of some sort feeding back from the output to the inverting input). These rules are commonly used as a good first approximation for analyzing or designing op-amp circuits. None of these ideals can be perfectly realized. A real op amp may be modeled with non-infinite or non-zero parameters using equivalent resistors and capacitors in
13176-419: The type of feedback and amount of feedback are carefully selected to weigh and optimize these various benefits. Advantages of negative voltage feedback in amplifiers Though negative feedback has many advantages, amplifiers with feedback can oscillate . See the article on step response . They may even exhibit instability . Harry Nyquist of Bell Laboratories proposed the Nyquist stability criterion and
13298-569: The typical V S = ±20 V, the standing current in Q11 and Q12 (as well as in Q13) would be ~1 mA. A supply current for a typical 741 of about 2 mA agrees with the notion that these two bias currents dominate the quiescent supply current. Transistors Q11 and Q10 form a Widlar current mirror , with quiescent current in Q10 i 10 such that ln( i 11 / i 10 ) = i 10 × 5 kΩ / 28 mV, where 5 kΩ represents
13420-470: The visualization of analog signals and the representation of the results of measurements or mathematical operations. These are just general blocks that can be found in a typical analog computing machine. The actual configuration and components may vary depending on the specific implementation and the intended use of the machine. Analog computing devices are fast; digital computing devices are more versatile and accurate. The idea behind an analog-digital hybrid
13542-529: Was Electronic Associates . Their hybrid computer model 8900 was made of a digital computer and one or more analog consoles. These systems were mainly dedicated to large projects such as the Apollo program and Space Shuttle at NASA , or Ariane in Europe, especially during the integration step where at the beginning everything is simulated, and progressively real components replace their simulated parts. Only one company
13664-513: Was described as an early mechanical analog computer by British physicist, information scientist, and historian of science Derek J. de Solla Price . It was discovered in 1901, in the Antikythera wreck off the Greek island of Antikythera , between Kythera and Crete , and has been dated to c. 150~100 BC , during the Hellenistic period . Devices of a level of complexity comparable to that of
13786-653: Was Applied Dynamics of Ann Arbor, Michigan . Although the basic technology for analog computers is usually operational amplifiers (also called "continuous current amplifiers" because they have no low frequency limitation), in the 1960s an attempt was made in the French ANALAC computer to use an alternative technology: medium frequency carrier and non dissipative reversible circuits. In the 1970s, every large company and administration concerned with problems in dynamics had an analog computing center, such as: An analog computing machine consists of several main components: On
13908-567: Was a manual instrument to calculate the area of a closed figure by tracing over it with a mechanical linkage. The slide rule was invented around 1620–1630, shortly after the publication of the concept of the logarithm . It is a hand-operated analog computer for doing multiplication and division. As slide rule development progressed, added scales provided reciprocals, squares and square roots, cubes and cube roots, as well as transcendental functions such as logarithms and exponentials, circular and hyperbolic trigonometry and other functions . Aviation
14030-492: Was a mechanical calculating device invented around 1902 by Lieutenant John Dumaresq of the Royal Navy . It was an analog computer that related vital variables of the fire control problem to the movement of one's own ship and that of a target ship. It was often used with other devices, such as a Vickers range clock to generate range and deflection data so the gun sights of the ship could be continuously set. A number of versions of
14152-465: Was an analog computer developed by Reeves in 1950 for the analysis and design of dynamic systems. Project Typhoon was an analog computer developed by RCA in 1952. It consisted of over 4,000 electron tubes and used 100 dials and 6,000 plug-in connectors to program. The MONIAC Computer was a hydraulic analogy of a national economy first unveiled in 1949. Computer Engineering Associates was spun out of Caltech in 1950 to provide commercial services using
14274-454: Was implemented in the 17th century. Cornelius Drebbel had built thermostatically controlled incubators and ovens in the early 1600s, and centrifugal governors were used to regulate the distance and pressure between millstones in windmills . James Watt patented a form of governor in 1788 to control the speed of his steam engine , and James Clerk Maxwell in 1868 described "component motions" associated with these governors that lead to
14396-414: Was known as offering general commercial computing services on its hybrid computers, CISI of France, in the 1970s. The best reference in this field is the 100,000 simulation runs for each certification of the automatic landing systems of Airbus and Concorde aircraft. After 1980, purely digital computers progressed more and more rapidly and were fast enough to compete with analog computers. One key to
14518-409: Was of great utility to navigation in shallow waters. It used a system of pulleys and wires to automatically calculate predicted tide levels for a set period at a particular location. The differential analyser , a mechanical analog computer designed to solve differential equations by integration , used wheel-and-disc mechanisms to perform the integration. In 1876 James Thomson had already discussed
14640-441: Was programmed using patch cords that connected nine operational amplifiers and other components. General Electric also marketed an "educational" analog computer kit of a simple design in the early 1960s consisting of two transistor tone generators and three potentiometers wired such that the frequency of the oscillator was nulled when the potentiometer dials were positioned by hand to satisfy an equation. The relative resistance of
14762-536: Was the principal computer in the Mk. 56 Gun Fire Control System. Online, there is a remarkably clear illustrated reference (OP 1140) that describes the fire control computer mechanisms. For adding and subtracting, precision miter-gear differentials were in common use in some computers; the Ford Instrument Mark I Fire Control Computer contained about 160 of them. Integration with respect to another variable
14884-584: Was with the World Bank in 1988–1994. A basic and common example of a negative feedback system in the environment is the interaction among cloud cover , plant growth, solar radiation , and planet temperature. As incoming solar radiation increases, planet temperature increases. As the temperature increases, the amount of plant life that can grow increases. This plant life can then make products such as sulfur which produce more cloud cover. An increase in cloud cover leads to higher albedo , or surface reflectivity, of
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