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 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 (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