EE301 Electronics I , Fall
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1 EE301 Electronics I , Fall
2 1. Introduction to Microelectronics (1 Week/3 Hrs.) Introduction, Historical Background, Basic Consepts 2. Rewiev of Semiconductors (1 Week/3 Hrs.) Semiconductor materials and their properties, Covalent Bond Model, Drift currents and Mobility, Impurities in Semiconductors, Electron and Hole Concentrations In Doped Semiconductor, Mobility and Resistivity in Doped Semiconductors, Diffusion Currents, Energy Band Model 3. Diodes & Applications of Diodes (2 Weeks/6 Hrs.) The Ideal Diode, pn junction as a Diode, Large-Signal and Small-Signal Operation, the i v Characteristics of the Diode, Applications of Diodes: Half-wave And Full- Wave Rectifier Circuits, Voltage Regulation, Limiting Circuits, Voltage Doublers, Diodes as Level Shifters.. 4. Bipolar Junction Transistors (BJTs) & BJT Amplifiers (3 Weeks/9 Hrs.) Physical Structure of The BJTs, Operation of BJTs in Active Mode, BJT Models and Characteristics, Large-Signal Model, the i v Characteristics, Concept of Transconductance, Small-Signal Model, Early Effect, Operation of BJTs in Saturation Mode, NPN and PNP Transistors. General Considerations for BJT Amplifiers, Biasing. 5. MOS Transistors & CMOS Amplifiers (3 Weeks/9 Hrs.) Structure of MOSFET, Operation of MOSFET, Qualitative Analysis, Derivation of I-V Characteristics, Channel-Length Modulation, Large-Signal Model, Small-Signal Model 6. Operational Amplifiers (Op-Amps) (2 Weeks/6 Hrs.) General Considerations, Op-Amp-Based Circuits, Noninverting Amplifier, Inverting Amplifier, Integrator and Differentiator, Voltage Adder, Nonlinear Functions, Precision Rectifier. 7. Cascaded Stages & Current Mirrors (2 Weeks/6 Hrs.) Cascaded Stages, Cascade as a Current Source, Cascade as an Amplifier, Current Mirrors, Initial Thoughts, Bipolar Current Mirror, MOS Current Mirror.
3 The term operational amplifier (op amp) was coined in the 1940s, well before the invention of the transistor and the integrated circuit. Op-amps realized by vacuum tubes served as the core of electronic integrators, differentiators, etc., thus forming systems whose behavior followed a given differential equation. Called analog computers, such circuits were used to study the stability of differential equations that arose in fields such as control or power systems. Since each op amp implemented a mathematical operation (e.g., integration), the term operational amplifier was born. Op-amps find wide application in today s discrete and integrated electronics. In the cellphones integrated op amps serve as building blocks in (active) filters. Similarly, the analog-to-digital converter(s) used in digital cameras often employ op-amps. The outline of this chapter is shown below:
4 The operational amplifier can be abstracted as a black box having two inputs and one output. Shown in Fig. 8.1(a), the op amp symbol distinguishes between the two inputs by the plus and minus sign; V in1 and V in2 are called the noninverting and inverting inputs, respectively. We view the op-amp as a circuit that amplifies the difference between the two inputs, arriving at the equivalent circuit depicted infig. 8.1(b). The voltage gain is denoted by A 0 :
5 It is instructive to plot V out as a function of one input while the other remains at zero.
6 How does the ideal op amp behave? Such an op amp would provide an infinite voltage gain, an infinite input impedance, a zero output impedance, and infinite speed. In fact, the first-order analysis of an op-amp-based circuit typically begins with this idealization, quickly revealing the basic function of the circuit. We can then consider the effect of the op-amp nonidealities on the performance. The very high gain of the op-amp leads to an important observation. Since realistic circuits produce finite output swings, e.g., 2V, the difference between V in1 and V in2 in Fig. 8.1(a) isalways small: In other words, the op-amp, along with the circuitry around it, brings V in1 and V in2 close to each other. Following the above idealization, we may say V in1 = V in2 if A 0 =.
7
8
9 Non-inverting Amplifier
10
11 Non-inverting Amplifier
12 Inverting Amplifier
13 Inverting Amplifier
14 Inverting Amplifier
15 Integrator & Differentiator Our study of the inverting topology in previous sections has assumed a resistive network around the op-amp. In general, it is possible to employ complex impedances instead (Fig. 8.9). We can write; where the gain of the op-amp is assumed large. If Z 1 or Z 2 is a capacitor, two interesting functions result.
16
17
18 Integrator
19
20
21
22 Differentiator
23 Summing Amplifier (Voltage Adder) The need for adding voltages arises in many applications. For example, in audio recording, for example, a number of microphones may convert the sounds of various musical instruments to voltages, and these voltages must then be added to create the overall musical piece. This operation is called mixing in the audio industry. For example, in noise cancelling headphones, the environmental noise is applied to an inverting amplifier and subsequently added to the signal so as to cancel itself.
24 It is possible to implement useful nonlinear functions through the use of op-amps and nonlinear devices such as transistors. The virtual ground property plays an essential role here as well.
25 Precision Rectifier The rectifier circuits suffer from a dead zone due to the finite voltage required to turn on the diodes. That is, if the input signal amplitude is less than approximately 0.7 V, the diodes remain off and the output voltage remains at zero. This drawback prohibits the use of the circuit in high-precision applications, e.g., if a small signal received by a cellphone must be rectified to determine its amplitude. It is possible to place a diode around an op amp to form a precision rectifier, i.e., a circuit that rectifies even very small signals. Let us begin with a unity-gain buffer tied to a resistive load [Fig. 8.22(a)].
26 Precision Rectifier We note that the high gain of the op amp ensures that node X tracks V in (for both positive and negative cycles). Now suppose we wish to hold X at zero during negative cycles, i.e., break the connection between the output of the op amp and its inverting input. This can be accomplished as depicted in Fig. 8.22(b), where D 1 is inserted in the feedback loop. Note that V out is sensed at X rather than at the output ofthe op-amp.
27 Logarithmic Amplifier Consider the circuit of Fig. 8.24, where a bipolar transistor is placed around the opamp. With an ideal op amp, R 1 carries a current equal to V in /R 1 and so does Q 1. Logarithmic amplifiers ( logamps ) prove useful in applications where the input signal level may vary by a large factor. It may be desirable in such cases to amplify weak signals and attenuate ( compress ) strong signals hence a logarithmic dependence. Note that Q 1 operates in the active region because both the base and the collector remain at zero. What happens if V in becomes negative?
28 Square-root Amplifier Recognizing that the logarithmic amplifier of Fig in fact implements the inverse function of the exponential characteristic, we surmise that replacing the bipolar transistor with a MOSFET leads to a square-root amplifier. Illustrated in Fig. 8.25, such a circuit requires that M 1 carry a current equal to V in /R 1 : If V in is near zero, then V out remains at V TH, placing M 1 at the edge of conduction. As V in becomes more positive, V out falls to allow M 1 to carry a greater current. With its gate and drain at zero, M 1 operates in saturation.
29 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 imperfections that may affect the performance significantly. In this section, we deal with such nonidealities.
30 DC Offsets The op-amp characteristics imply that V out = 0 if V in1 = V in2. 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 V out = 0, the input difference must be raised to a certain value, V os, called the input offset voltage. What causes offset? The internal circuit of the op-amp experiences random asymmetries ( mismatches ) during fabrication and packaging. For example, as shown conceptually in Fig. 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, V os can appear at either input with arbitrary polarity.
31 DC Offsets Why are DC offsets important? Let us reexamine some of the circuit topologies studied in Section 8.2 in the presence of opamp offsets. Depicted in Fig. 8.27, the noninverting amplifier now sees a total input of V in + V os, thereby generating In other words, the circuit amplifies the offset as well as the signal, thus incurring accuracy limitations.
32 DC Offsets
33
34 Input Bias Current Op-amps implemented in bipolar technology draw a base current from each input. While relatively small ( μa), the input bias currents may create inaccuracies insome circuits. As shown in Fig. 8.30, each bias current is modeled by a current source tied between the corresponding input and ground. Nominally, I B1 = I B2.
35 Input Bias Current Let us study the effect of the input currents on the noninverting amplifier. As depicted infig. 8.31(a), I B1 has no effect on the circuit because it flows through a voltage source. The current I B2, on the other hand, flows through R 1 and R 2, introducing an error. Using superposition and setting V in to zero, we arrive at the circuit in Fig. 8.31(b),
36 Input Bias Current Fig. 8.31(b), which can be transformed to that in Fig. 8.31(c) if I B2 and R 2 are replaced with their Thevenin equivalent. Interestingly, the circuit now resembles the inverting amplifier, thereby yielding; (if the op amp gain is infinite.)
37 Input Bias Current The error due to the input bias current appears similar to the DC offset effects illustrated in Fig. 8.27, corrupting the output. However, unlike DC offsets, this phenomenon is not random; for a given bias current in the bipolar transistors used in the op-amp, the base currents drawn from the inverting and noninverting inputs remain approximately equal. We may therefore seek a method of canceling this error. For example, we can insert a corrective voltage in series with the noninverting input so as to drive V out to zero (Fig. 8.32). Since V corr sees a noninverting amplifier, we have
38 Input Bias Current
39 Input Bias Current V corr depends on I B2 and hence the current gain of transistors. Since β varies with process and temperature, V corr cannot remain at a fixed value and must track β. V corr can be also obtained by passing a base current through a resistor equal to R 1 R 2, leading to the topology shown in Fig Here, if I B1 = I B2, then V out = 0 for V in = 0. (take the finite gain of the op amp into account and prove that V out is still near zero.) Observe that the input bias currents have an identical effect on the inverting amplifier. Thus, the correction technique shown in Fig applies to this circuit as well. In reality, asymmetries in the op-amp s internal circuitry introduce a slight (random) mismatch between I B1 and I B2. Problem 8.53 (in the book) studies the effect of this mismatch on the output in Fig
40 Finite Input and Output Impedances Actual op-amps do not provide an infinite input impedance or a zero output impedance the latter often creating limitations in the design. We analyze the effect of this nonideality ononecircuit here. Consider the inverting amplifier shown in Fig. 8.42(a), assuming the op amp suffers from an output resistance, R out. How should the circuit be analyzed? We return to the model in Fig. 8.1 and place R out in series with the output voltage source [Fig. 8.42(b)]. We must solve the circuit in the presence of R out.
41 Finite Input and Output Impedances Recognizing that the current flowing through R out is equal to ( A 0 v X v out )/R out, we write a KVL from v in to v out through R 2 and R 1 :
42 Speed Limitations Finite Bandwidth: Our study of op-amps has thus far assumed no speed limitations. In reality, the internal capacitances of the op-amp degrade the performance at high frequencies. Another critical issue in the use of op amps is stability; if placed in the topologies seen above, some op-amps may oscillate. Arising from the internal circuitry of the op-amp, this phenomenon often requires internal or external stabilization, also called frequency compensation. Slew Rate: In addition to bandwidth and stability problems, another interesting effect is observed in op amps that relates to their response to large signals. The slewing is a nonlinear phenomenon
43 END OF CHAPTER 6 Dr. Yılmaz KALKAN
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