867 channel length modulation is neglected here since

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(8.67) (Channel-length modulation is neglected here.) Since , (8.68) If is near zero, then remains at , placing at the edge of conduction. As becomes more positive, falls to allow to carry a greater current. With its gate and drain at zero, operates in saturation. 8.4 Op Amp Nonidealities Our study in previous sections has dealt with a relatively idealized op amp model—except for the finite gain—so as to establish insight. In practice, however, op amps suffer from other imper- fections that may affect the performance significantly. In this section, we deal with such nonide- alities. 8.4.1 DC Offsets The op amp characteristics shown in Fig. 8.2 imply that if . In reality, a zero input difference may not give a zero output difference! Illustrated in Fig. 8.26(a), the characteristic is “offset” to the right or to the left; i.e., for , the input difference must be raised to a certain value, , called the input “offset voltage.” out V V in1 out V V os V os (c) (a) (b) V in1 Figure 8.26 (a) Offset in an op amp, (b) mismatch between input devices, (c) representation of offset. What causes offset? The internal circuit of the op amp experiences random asymmetries (“mismatches”) during fabrication and packaging. For example, as conceptually shown in Fig.
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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 394 (1) 394 Chap. 8 Operational Amplifier As A Black Box 8.26(b), the bipolar transistors sensing the two inputs may display slightly different base-emitter voltages. The same effect occurs for MOSFETs. We model the offset by a single voltage source placed in series with one of the inputs [Fig. 8.26(c)]. Since offsets are random and hence can be positive or negative, can appear at either input with arbitrary polarity. Why are DC offsets important? Let us reexamine some of the circuit topologies studied in Section 8.2 in the presence of op amp offsets. Depicted in Fig. 8.27, the noninverting amplifier now sees a total input of , thereby generating out V R 1 R 2 V os in V Figure 8.27 Offset in noninverting amplifier. (8.69) In other words, the circuit amplifies the offset as well as the signal, thus incurring accuracy limitations. Example 8.10 A truck weighing station employs an electronic pressure meter whose output is amplified by the circuit of Fig. 8.27. If the pressure meter generates 20 mV for every 100 kg of load and if the op amp offset is 2 mV, what is the accuracy of the weighing station? Solution An offset of 2 mV corresponds to a load of 10 kg. We therefore say the station has an error of kg in its measurements. Exercise What offset voltage is required for an accuracy of kg? DC offsets may also cause “saturation” in amplifiers. The following example illustrates this point. Example 8.11 An electrical engineering student constructs the circuit shown in Fig. 8.28 to amplify the signal produced by a microphone. The targeted gain is so that very low level sounds (i.e., microvolt signals) can be detected. Explain what happens if op amp exhibits an offset of 2 mV.
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