《电子工程师手册》学习资料（英文版）chapter 27 Operational amplifiers.pdf_大学文库

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, 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 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

with each input terminal. Normally, Zom is best represented by a parallel resistance and capacitance of 2RcM (which is >>RN)and CM/2. The dc bias currents at the input are represented by I and Ig current sources that would equal the input base currents if a differential bipolar transistor were used as the input stage of the op amp, or the input gate currents if FETs were used. The fact that the two transistors of the input stage of the op amp may not be perfectly balanced is represented by an equivalent input offset voltage source, Vos, in series with the e input. The smallest signal that can be amplified is always limited by the inherent random noise internal to the op amp itself. In Fig. 27. 3 the noise effects are represented by an equivalent input voltage source(ENv), which when multiplied by the gain of the op amp would equal the total output noise present if the inputs to the op amp were shorted. In a similar fashion, if the inputs to the op amp were open circuited, the total output noise ould equal the sum of the noise due to the equivalent input current sources(ENi* and ENI), each mult by their respective current gain to the output. Because noise is a random variable, this summation must be accomplished in a squared fashion, i. e, Eo(rms volt /Hz)=(ENV)'A+(ENI )2 AR+(ENT)A12 (27.6) Typically, the correlation(C) between the ENV and ENI sources is low, so the assumption of C=0 can be made. For the basic circuits of Fig. 27. 2(a)or(b), if the signal source v, is shorted then the output voltage due to he nonideal effects would be(using the model of Fig 27.3) 。=|Vos++A哪‖1+ +IBR (27.7) CMRR PSRR R provided that the loop gain(also called loop transmission in many texts)is related by the inequality R I R1+/A(s) 7.8 Inherent in Eq.(27. 8)is the usual condition that R, < ZIN and ZcM. If a resistor R, were in series with the noninverting input terminal, then a corresponding term must be added to the right hand side of Eq (27.7)of value -IB R2(R+ Re)/RI. On manufacturers' data sheets the individual values of Ib and I are not stated instead the average input bias current and offset current are specified as B+rB I offset=I*-IBl The output noise effects can be obtained using the model of Fig. 27.3 along with the circuits of Fig. 27. 2 as EOut (rms volts/Hz)=E +ef +(env+ e2X R1 27.10) (ENI"'RF+(ENI*)R2 where it is assumed that a resistor R2 is also in series with the noninverting input of either Fig. 27. 2(a)or(b). The thermal noise(often called Johnson or Nyquist noise)due to the resistors Ri, R2, and R is given by(in rms volt/Hz) e 2000 by CRC Press LLC

© 2000 by CRC Press LLC with each input terminal. Normally, ZCM is best represented by a parallel resistance and capacitance of 2RCM (which is >> RIN ) and CC M /2. The dc bias currents at the input are represented by IB + and IB – current sources that would equal the input base currents if a differential bipolar transistor were used as the input stage of the op amp, or the input gate currents if FETs were used. The fact that the two transistors of the input stage of the op amp may not be perfectly balanced is represented by an equivalent input offset voltage source, VOS , in series with the input. The smallest signal that can be amplified is always limited by the inherent random noise internal to the op amp itself. In Fig. 27.3 the noise effects are represented by an equivalent input voltage source (ENV), which when multiplied by the gain of the op amp would equal the total output noise present if the inputs to the op amp were shorted. In a similar fashion, if the inputs to the op amp were open circuited, the total output noise would equal the sum of the noise due to the equivalent input current sources (ENI+ and ENI–), each multiplied by their respective current gain to the output. Because noise is a random variable, this summation must be accomplished in a squared fashion, i.e., (27.6) Typically, the correlation (C) between the ENV and ENI sources is low, so the assumption of C ª 0 can be made. For the basic circuits of Fig. 27.2(a) or (b), if the signal source vI is shorted then the output voltage due to the nonideal effects would be (using the model of Fig. 27.3) (27.7) provided that the loop gain (also called loop transmission in many texts) is related by the inequality (27.8) Inherent in Eq. (27.8) is the usual condition that R1 > I I I I II B B B = B B + = - + - + - 2 ; offset * * E E R R E E R R R R R R F F F F F out rms volts /Hz ENV ENI ENI 2 2 1 2 1 2 2 2 2 2 1 2 22 2 2 2 1 2 1 1 ( ) () () () = Ê Ë Á ˆ ¯ ˜ ++ + ¥ + Ê Ë Á ˆ ¯ ˜ ++ + Ê Ë Á ˆ ¯ ˜ - +

E- 4kT R ES= 4kTR (27.11) E2 =4kTR where k is Boltzmanns constant and T is absolute temperature(Kelvin). To obtain the total output noise, one lust multiply the Eout expression of Eq (27. 10)by the noise bandwidth of the circuit, which typically is equal to /2 times the -3 dB signal bandwidth, for a single-pole response system [ Kennedy, 1988] SPICE Computer Models The use of op amps can be considerably simplified by computer-aided analysis using the program SPICE. SPICE originated with the University of California, Berkeley, in 1975 [Nagel, 1975], although more recent user-friendly commercial versions are now available such as HSPICE, HPSPICE, IS-SPICE, PSPICe, and ZSPiCe, to mention a few of those most widely used A simple macromodel for a near-ideal op amp could be simply stated with the SPICe subcircuit file(* indicates a comment that is not processed by the file) SUBCKT IDEALOA 123 "A near-ideal op amp: (1)is noninv,(2)is inv, and(3)is output. RIN 12 1E12 El(3,0)(1,2)1E8 ENDS IDEALOA (27.12) The circuit model for IDEALOA would appear as in Fig. 27. 4(a). A more complete model, but not including nonideal offset effects, could be constructed for the 741 op amp as the subcircuit file OA741, shown in Fig.274(b) SUBCKT OA741126 *A linear model for the 741 op amp: (1)is noninv,(2)is inv, and (6)is output. RiN= 2MEG, AOL =200,000, ROUT=75 ohm, Dominant open-loop pole at 5 Hz, gain-bandwidth product *is 1 mhz RIN 12 2MEG E(3,0)(1,2)2E5 Rl34100K C1 400.318UF: RI X CI= 5HZPOLE E2(5,0)(4,0)1.0 ROUT 75 ENDS OA741 (27.13) The most widely used op amp macromodel that includes dc offset effects is the Boyle model Boyle et al, 1974]. Most op amp manufacturers use this model, usually with additions to add more poles(and perha zeroes). The various resistor and capacitor values, as well as transistor, and current and voltage generator, values are intimately related to the specifications of the op amp, as shown earlier in the nonideal model of Fig. 27.3 The appropriate equations are too involved to list here; instead, the interested reader is referred to the article by Boyle in the listed references. The Boyle model does not accurately model noise effects, nor does it fully gA more circuits-oriented approach to modeling op amps can be obtained if the input transistors are removed nodel psrr and cmrr effects and a model formed by using passive components along with both fixed and dependent voltage and current sources. Such a model is shown in Fig. 27.5. This model not only includes all the basic nonideal effects of the op amp, allowing for multiple poles and zeroes, but can also accurately include ENV and ENI noise effects e 2000 by CRC Press LLC

© 2000 by CRC Press LLC (27.11) where k is Boltzmann’s constant and T is absolute temperature (°Kelvin). To obtain the total output noise, one must multiply the E2 out expression of Eq. (27.10) by the noise bandwidth of the circuit, which typically is equal to p/2 times the –3 dB signal bandwidth, for a single-pole response system [Kennedy, 1988]. SPICE Computer Models The use of op amps can be considerably simplified by computer-aided analysis using the program SPICE. SPICE originated with the University of California, Berkeley, in 1975 [Nagel, 1975], although more recent user-friendly commercial versions are now available such as HSPICE, HPSPICE, IS-SPICE, PSPICE, and ZSPICE, to mention a few of those most widely used. A simple macromodel for a near-ideal op amp could be simply stated with the SPICE subcircuit file (* indicates a comment that is not processed by the file) .SUBCKT IDEALOA 1 2 3 *A near-ideal op amp: (1) is noninv, (2) is inv, and (3) is output. RIN 1 2 1E12 E1 (3, 0) (1, 2) 1E8 .ENDS IDEALOA (27.12) The circuit model for IDEALOA would appear as in Fig. 27.4(a). A more complete model, but not including nonideal offset effects, could be constructed for the 741 op amp as the subcircuit file OA741, shown in Fig. 27.4(b). .SUBCKT OA741 1 2 6 *A linear model for the 741 op amp: (1) is noninv, (2) is inv, and *(6) is output. RIN = 2MEG, AOL = 200,000, ROUT = 75 ohm, *Dominant open - loop pole at 5 Hz, gain - bandwidth product *is 1 MHz. RIN 1 2 2MEG E1 (3, 0) (1, 2) 2E5 R1 3 4 100K C1 4 0 0.318UF ; R1 2 C1 = 5HZPOLE E2 (5, 0) (4, 0) 1.0 ROUT 5 6 75 .ENDS OA741 (27.13) The most widely used op amp macromodel that includes dc offset effects is the Boyle model [Boyle et al., 1974]. Most op amp manufacturers use this model, usually with additions to add more poles (and perhaps zeroes). The various resistor and capacitor values, as well as transistor, and current and voltage generator, values are intimately related to the specifications of the op amp, as shown earlier in the nonideal model of Fig. 27.3. The appropriate equations are too involved to list here; instead, the interested reader is referred to the article by Boyle in the listed references. The Boyle model does not accurately model noise effects, nor does it fully model PSRR and CMRR effects. A more circuits-oriented approach to modeling op amps can be obtained if the input transistors are removed and a model formed by using passive components along with both fixed and dependent voltage and current sources. Such a model is shown in Fig. 27.5. This model not only includes all the basic nonideal effects of the op amp, allowing for multiple poles and zeroes, but can also accurately include ENV and ENI noise effects. E kT R E kT R EF F kT R 1 2 1 2 2 2 2 4 4 4 = = =

© 2000 by CRC Press LLC A comparison of the SPICE macromodels with actual manufacturer’s data for the case of an LM318 op amp is demonstrated in Fig. 27.6, for the open-loop gain versus frequency specification. Defining Terms Boyle macromodel: A SPICE computer model for an op amp. Developed by G.R. Boyle in 1974. Equivalent noise current (ENI): A noise current source that is effectively in parallel with either the noninverting input terminal (ENI+) or the inverting input terminal (ENI–) and represents the total noise contributed by the op amp if either input terminal is open circuited. Equivalent noise voltage (ENV): A noise voltage source that is effectively in series with either the inverting or noninverting input terminal of the op amp and represents the total noise contributed by the op amp if the inputs were shorted. Ideal operational amplifier: An op amp having infinite gain from input to output, with infinite input resistance and zero output resistance and insensitive to the frequency of the signal. An ideal op amp is useful in first-order analysis of circuits. Operational amplifier (op amp): A dc amplifier having both an inverting and noninverting input and normally one output, with a very large gain from input to output. SPICE: A computer simulation program developed by the University of California, Berkeley, in 1975.Versions are available from several companies. The program is particularly advantageous for electronic circuit analysis, since dc, ac, transient, noise, and statistical analysis is possible. Related Topic 13.1 Analog Circuit Simulation FIGURE 27.5 A SPICE circuits-approach macromodel. D6 V2 D5 I sc+ I sc– R01 R02 G0 = I/R02 D3 D4 E2 VOUT L0 V1 (7) (13) (14) (17) (18) (3) (+) (–) (Input) (2) (1) (4) (7) (10) (3) (9) (11) (12) (5) (15) (23) (16) (19) (6) (20) (6) (21) (22) Ips Rps VCC Cp4 Rp4 Rp3 Rp2 VN VP DN2 DP2 DN1 ECMRR EPSRR CCMI RCMI CCM2 RCM2 DP1 RN1 CN2 RN2>>RN1 Rp1 Rslew E1=1xV(15) E2=1xV(6) Cp3 Cp2 Cp1 Rz1 G1 G2 G3 G4 D2 D1 VEE VOS I s– I s+ VCC CIN RIN -VEE (4) – + + – + – + – – + – + + + – – + – I slew+ I slew–