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for the 6061 is 0005 pA (5 10 15 A)! This extremely low value is due to the MOS construction of the ampli er (see 9 for a discussion of MOS stage input impedance)
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Input Resistance The speci cations related to input offset current are mirrored by the input resistance
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speci cations The 741 has a respectable typical input resistance of 6 M ; the 6061 has an input resistance greater than 10 T (1 teraohm = 1012 ) Once again, this is the result of MOS construction Large-Signal Voltage Gain The 741 lists a typical value of 50 V/mV (or 5 104 ) for its open-loop voltage gain; the 6061 lists values greater than or equal to 2,000 V/mV (or 2 106 ) CMRR The typical common-mode rejection ratio is 95 db for the 741 and 85 dB for the 6061 Slew rate 07 V/ s for the 741 and 35 V/ms for the 6061 Bandwidth The bandwidth for the 741 is listed as 15 MHz (this would be the unity gain bandwidth), while the 6061 lists a 100-kHz gain-bandwidth product Output short circuit current 25 mA for both devices Note that, while the LMC6061 is certainly superior to the LM741 op-amp in a number of categories, there are certain features (eg, bandwidth and slew rate) that might cause a designer to prefer the 741 for a speci c application
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1217 In Example 1212, we implicitly assumed that the gain of each ampli er was constant for frequencies up to the cutoff frequency This is, in practice, not true, since the individual op-amp closed-loop gain starts dropping below the DC gain value according to the equation
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Thus, the calculations carried out in the example are only approximate Find an expression for the closed-loop gain of the cascade ampli er [Hint: The combined gain is equal to the product of the individual closed-loop gains] What is the actual gain in dB at the cutoff frequency, 0 , for the cascade ampli er
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1218 What is the 3-dB bandwidth of the cascade ampli er of Example 1212 [Hint: The gain of the cascade ampli er is the product of the individual op-amp frequency responses Compute the magnitude of this product and set the magnitude of the product of the individual frequency responses equal to (1/ 2) 10,000, and then solve for ]
Manufacturers generally supply values for the parameters discussed in this section in their device data speci cations Typical data sheets for common op-amps may be found in the accompanying CD-ROM
CONCLUSION
This chapter has described the fundamental properties and limitations of the operational ampli er
Ideal ampli ers represent fundamental building blocks of electronic instrumentation With the concept of the ideal ampli ers in mind, one can design practical ampli ers, lters, integrators, and other useful signal-processing circuits The operational ampli er closely approximates the characteristics of an ideal ampli er The analysis of op-amp circuits may be carried out very easily, if it is assumed that the op-amp s input resistance and open-loop gain are very large The inverting, noninverting, and differential ampli er con gurations permit the design of useful electronic ampli ers simply by selecting a few external resistors If energy-storage elements are used in the construction of op-amp circuits, it is possible to accomplish the functions of ltering, integration, and differentiation
12
Operational Ampli ers
The properties of summing ampli ers and integrators make it possible to build analog computers, which serve as an aid in the solution of differential equations, and in the simulation of dynamic systems When op-amps are employed in more advanced applications, it is important to know that there are limitations on their performance that are not predicted by the simple op-amp model introduced at the beginning of the chapter These include voltage supply limits, frequency response limits, offset voltages and currents, slew rate limits, and nite common-mode rejection ratio In general, it is not dif cult to compensate for these limitations in the design of op-amp circuits
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