Kennedy, E.J., Wait,J V"Operational Amplifiers The Electrical Engineering Handbook Ed. Richard C. Dorf Boca raton crc Press llc. 2000
Kennedy, E.J., Wait, J.V. “Operational Amplifiers” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
27 Operational amplifiers E J. Kennedy University of Tennessee 27.1 Ideal and Practical Models Op Amp. Practical Op Amps. SPICE Computer Models John V Wait University of Arizona(Retired) Noninverting Circuits 27.1 Ideal and Practical models E Kennedy The concept of the operational amplifier(usually referred to as an op amp)originated at the beginning of the Second World War with the use of vacuum tubes in dc amplifier designs developed by the George A Philbrick Co [some of the early history of operational amplifiers is found in williams, 1991]. The op amp was the basic building block for early electronic servomechanisms, for synthesizers, and in particular for analog computers used to solve differential equations. with the advent of the first monolithic integrated-circuit (IC)op amp in 1965(the HA709, designed by the late Bob widlar, then with Fairchild Semiconductor), the availability of op amps was no longer a factor, while within a few years the cost of these devices(which had been as high as $200 each) rapidly plummeted to close to that of individual discrete transistors Although the digital computer has now largely supplanted the analog computer in mathematically intensive applications, the use of inexpensive operational amplifiers in instrumentation applications, in pulse shaping, in filtering, and in signal processing applications in general has continued to grow. There are currently many commercial manufacturers whose main products are high-quality op amps. This competitiveness has ensured a marketplace featuring a wide range of relatively inexpensive devices suitable for use by electronic engineer physicists, chemists, biologists, and almost any discipline that requires obtaining quantitative analog data from instrumented experiments. Most operational amplifier circuits can be analyzed, at least for first-order calculations, by considering the op amp to be an"ideal"device. For more quantitative information, however, and particularly when frequency response and dc offsets are important, one must refer to a more "practical"model that includes the internal limitations of the device. If the op amp is characterized by a really complete model, the resulting circuit ma be quite complex, leading to rather laborious calculations. Fortunately, however, computer analysis using the program SPICE significantly reduces the problem to one of a simple input specification to the computer. Today, nearly all the op amp manufacturers provide SPICe models for their line of devices, with excellent correlation obtained between the computer simulation and the actual measured results. The Ideal Op amp An ideal operational amplifier is a dc-coupled amplifier having two inputs and normally one output(although in a few infrequent cases there may be a differential output). The inputs are designated as noninverting (designated or NI)and inverting(designated -or Inv ) The amplified signal is the differential signal, between the two inputs, so that the output voltage as indicated in Fig. 27.1 is c 2000 by CRC Press LLC
© 2000 by CRC Press LLC 27 Operational Amplifiers 27.1 Ideal and Practical Models The Ideal Op Amp • Practical Op Amps • SPICE Computer Models 27.2 Applications Noninverting Circuits 27.1 Ideal and Practical Models E.J. Kennedy The concept of the operational amplifier (usually referred to as an op amp) originated at the beginning of the Second World War with the use of vacuum tubes in dc amplifier designs developed by the George A. Philbrick Co. [some of the early history of operational amplifiers is found in Williams, 1991]. The op amp was the basic building block for early electronic servomechanisms, for synthesizers, and in particular for analog computers used to solve differential equations. With the advent of the first monolithic integrated-circuit (IC) op amp in 1965 (the mA709, designed by the late Bob Widlar, then with Fairchild Semiconductor), the availability of op amps was no longer a factor, while within a few years the cost of these devices (which had been as high as $200 each) rapidly plummeted to close to that of individual discrete transistors. Although the digital computer has now largely supplanted the analog computer in mathematically intensive applications, the use of inexpensive operational amplifiers in instrumentation applications, in pulse shaping, in filtering, and in signal processing applications in general has continued to grow. There are currently many commercial manufacturers whose main products are high-quality op amps. This competitiveness has ensured a marketplace featuring a wide range of relatively inexpensive devices suitable for use by electronic engineers, physicists, chemists, biologists, and almost any discipline that requires obtaining quantitative analog data from instrumented experiments. Most operational amplifier circuits can be analyzed, at least for first-order calculations, by considering the op amp to be an “ideal” device. For more quantitative information, however, and particularly when frequency response and dc offsets are important, one must refer to a more “practical” model that includes the internal limitations of the device. If the op amp is characterized by a really complete model, the resulting circuit may be quite complex, leading to rather laborious calculations. Fortunately, however, computer analysis using the program SPICE significantly reduces the problem to one of a simple input specification to the computer. Today, nearly all the op amp manufacturers provide SPICE models for their line of devices, with excellent correlation obtained between the computer simulation and the actual measured results. The Ideal Op Amp An ideal operational amplifieris a dc-coupled amplifier having two inputs and normally one output (although in a few infrequent cases there may be a differential output). The inputs are designated as noninverting (designated + or NI) and inverting (designated – or Inv.). The amplified signal is the differential signal, ve, between the two inputs, so that the output voltage as indicated in Fig. 27.1 is E.J. Kennedy University of Tennessee John V. Wait University of Arizona (Retired)
AoL(VB-VA ve →∞ FIGURE 27.1 Configuration for an ideal op amp vout aorvb-vo) (27.1) The general characteristics of an ideal op amp can be summarized as follows: The open-loop gain Aot is infinite. Or, since the output signal Wout is finite, then the differential input ignal ve must approach zero 2. The input resistance RoN is infinite, while the output resistance Ro is zero 3. The amplifier has zero current at the input (ia and iB in Fig. 27.1 are zero), but the op amp can either ink or source an infinite curr the 4. The op amp is not sensitive to a common signal on both inputs (i.e, vA=vB); thus, the output voltage hange due to a common input signal will be zero. This common signal is referred to as a common- mode signal, and manufacturers specify this effect by an op amp's common-mode rejection ratio( CMrr), which relates the ratio of the open-loop gain(Aou) of the op amp to the common-mode gain(acm) Hence, for an ideal op amp Cmrr =oo. 5. A somewhat analogous specification to the Cmrr is the power-supply rejection ratio(PSRR), which elates the ratio of a power supply voltage change to an equivalent input voltage change produced by the change in the power supply. Because an ideal op amp can operate with any power supply, without restriction then for the ideal device psrr oo 6. The gain of the op amp is not a function of frequency. This implies an infinite bandwidth. Although the foregoing requirements for an ideal op amp appear to be impossible to achieve practically, modern devices can quite closely approximate many of these conditions. An op amp with a field-effect transistor (FET) on the input would certainly not have zero input current and infinite input resistance, but a current of <10 PA and an rn=102Q2 is obtainable and is a reasonable approximation to the ideal conditions. Further, although a CMRR and PsrR of infinity are not possible, there are several commercial op amps available with ralues of 140 dB (i. e, a ratio of 107). Open-loop gains of several precision op amps now have reached values of >10, although certainly not infinity. The two most difficult ideal conditions to approach are the ability handle large output currents and the requirement of a gain independence with frequency Using the ideal model conditions it is quite simple to evaluate the two basic op amp circuit configurations, d(2)the noninvertin designat Fig.27.2 For the ideal inverting amplifier, since the open-loop gain is infinite and since the output voltage v, is finite then the input differential voltage(often referred to as the error signal) ve must approach zero, or the input 0 R The feedback current iF must equal it, and the output voltage must then be due to the voltage drop across re,or RE RI e 2000 by CRC Press LLC
© 2000 by CRC Press LLC (27.1) The general characteristics of an ideal op amp can be summarized as follows: 1. The open-loop gain AOL is infinite. Or, since the output signal vout is finite, then the differential input signal ve must approach zero. 2. The input resistance RIN is infinite, while the output resistance RO is zero. 3. The amplifier has zero current at the input (iA and iB in Fig. 27.1 are zero), but the op amp can either sink or source an infinite current at the output. 4. The op amp is not sensitive to a common signal on both inputs (i.e., vA = vB); thus, the output voltage change due to a common input signal will be zero. This common signal is referred to as a commonmode signal, and manufacturers specify this effect by an op amp’s common-mode rejection ratio (CMRR), which relates the ratio of the open-loop gain (AOL) of the op amp to the common-mode gain (ACM). Hence, for an ideal op amp CMRR = •. 5. A somewhat analogous specification to the CMRR is the power-supply rejection ratio (PSRR), which relates the ratio of a power supply voltage change to an equivalent input voltage change produced by the change in the power supply. Because an ideal op amp can operate with any power supply, without restriction, then for the ideal device PSRR = •. 6. The gain of the op amp is not a function of frequency. This implies an infinite bandwidth. Although the foregoing requirements for an ideal op amp appear to be impossible to achieve practically, modern devices can quite closely approximate many of these conditions.An op amp with a field-effect transistor (FET) on the input would certainly not have zero input current and infinite input resistance, but a current of <10 pA and an RIN = 1012 W is obtainable and is a reasonable approximation to the ideal conditions. Further, although a CMRR and PSRR of infinity are not possible, there are several commercial op amps available with values of 140 dB (i.e., a ratio of 107 ). Open-loop gains of several precision op amps now have reached values of >107 , although certainly not infinity. The two most difficult ideal conditions to approach are the ability to handle large output currents and the requirement of a gain independence with frequency. Using the ideal model conditions it is quite simple to evaluate the two basic op amp circuit configurations, (1) the inverting amplifier and (2) the noninverting amplifier, as designated in Fig. 27.2. For the ideal inverting amplifier, since the open-loop gain is infinite and since the output voltage vo is finite, then the input differential voltage (often referred to as the error signal) ve must approach zero, or the input current is (27.2) The feedback current iF must equal iI , and the output voltage must then be due to the voltage drop across RF , or (27.3) FIGURE 27.1 Configuration for an ideal op amp. v A v v out = OL B - A ( ) i v v R v R I I I = - = e - 1 1 0 v i R v i R R R v o F F I F F = - + = - = - I Ê Ë Á ˆ ¯ e ˜ 1
v 0 R1 FIGURE 27.2 Illustration of (a)the inverting amplifier and(b) the noninverting amplifier. Source: E J. Kennedy, Opera tional Amplifier Circuits, Theory and Applications, New York: Holt, Rinehart and winston, 1988, Pp. 4, 6. With permission The inverting connection thus has a voltage gain v /v, of -R/R, an input resistance seen by v, of R, ohms [from Eq.(27. 2)], and an output resistance of 0 Q2. By a similar analysis for the noninverting circuit of Fig. 27. 2(b), since ve is zero, then signal v, must appear across resistor Ru, producing a current of v/R, which must flow through resistor RF. Hence the output voltage is the sum of the voltage drops across re and r + As opposed to the inverting connection, the input resistance seen by the source v, is now equal to an infinite resistance, since Ro for the ideal Practical Op Amps A nonideal op amp is characterized not only by finite open-loop gain, input and output resistance, finite currents,and cy bandwidths, but also by various nonidealities due to the construction of the op amp ircuit or external connections. A complete model for a practical op amp is illustrated in Fig. 27. 3. The nonideal e 2000 by CRC Press LLC
© 2000 by CRC Press LLC The inverting connection thus has a voltage gain vo /vI of – RF /R1, an input resistance seen by vI of R1 ohms [from Eq. (27.2)], and an output resistance of 0 W. By a similar analysis for the noninverting circuit of Fig. 27.2(b), since ve is zero, then signal vI must appear across resistor R1, producing a current of vI /R1, which must flow through resistor RF . Hence the output voltage is the sum of the voltage drops across RF and R1, or (27.4) As opposed to the inverting connection, the input resistance seen by the source vI is now equal to an infinite resistance, since RIN for the ideal op amp is infinite. Practical Op Amps A nonideal op amp is characterized not only by finite open-loop gain, input and output resistance, finite currents, and frequency bandwidths, but also by various nonidealities due to the construction of the op amp circuit or external connections. A complete model for a practical op amp is illustrated in Fig. 27.3. The nonideal FIGURE 27.2 Illustration of (a) the inverting amplifier and (b) the noninverting amplifier. (Source: E.J. Kennedy, Operational Amplifier Circuits, Theory and Applications, New York: Holt, Rinehart and Winston, 1988, pp. 4, 6. With permission.) v R v R v R R v o F I I F = I Ê Ë Á ˆ ¯ ˜ + = + Ê Ë Á ˆ ¯ ˜ 1 1 1
ENI (Inv) ①b 22CM IGURE 27.3 A model for a practical op amp illustrating nonideal effects. Source: E J. Kennedy, Operational Amplifier Circuits, Theory and Applications, New York: Holt, Rinehart and Winston, 1988, Pp 53, 126. With permission. effects of the PSRR and CMRr are represented by the input series voltage sources of A upply /PSRR and M/CMRR, where AVsupply would be any total change of the two power supply voltages, Vde and vde, from their nominal values, while VM is the voltage common to both inputs of the op amp. The open-loop gain of the op amp is no longer infinite but is modeled by a network of the output impedance Zout(which may be merely a resistor but could also be a series R-L network) in series with a source A(s), which includes all the open-loop poles and zeroes of the op amp as (1+…) A(s) (27.5) 1+ where Aot is the finite dc open-loop gain, while poles are at frequencies Opl,(p2,... and zeroes are at Ozi etc. The differential input resistance is ZIN, which is typically a resistance RIN in parallel with a capacitor C Similarly, the common-mode input impedance Zom is established by placing an impedance 2Zcm in parallel e 2000 by CRC Press LLC
© 2000 by CRC Press LLC effects of the PSRR and CMRR are represented by the input series voltage sources of DVsupply /PSRR and VC M /CMRR, where DVsupply would be any total change of the two power supply voltages, V+ dc and V– dc , from their nominal values, while VCM is the voltage common to both inputs of the op amp. The open-loop gain of the op amp is no longer infinite but is modeled by a network of the output impedance Zout (which may be merely a resistor but could also be a series R-L network) in series with a source A(s), which includes all the open-loop poles and zeroes of the op amp as (27.5) where AOL is the finite dc open-loop gain, while poles are at frequencies wp1, wp2 , . . . and zeroes are at wZ 1, etc. The differential input resistance is ZIN , which is typically a resistance RIN in parallel with a capacitor CIN. Similarly, the common-mode input impedance ZCM is established by placing an impedance 2ZCM in parallel FIGURE 27.3 A model for a practical op amp illustrating nonideal effects. (Source: E.J. Kennedy, Operational Amplifier Circuits, Theory and Applications, New York: Holt, Rinehart and Winston, 1988, pp. 53, 126. With permission.) A s A s s s OL Z p p ( ) ( ) ( ) = + Ê Ë Á ˆ ¯ ˜ + ××× + Ê Ë Á ˆ ¯ ˜ + Ê Ë Á ˆ ¯ ˜ + ××× 1 1 111 1 1 2 w w w