# Example 16 figure 121 shows another amplifier

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Example 1.6 Figure 1.21 shows another amplifier topology. Compute the gain. g m π v π v π r R L out v in v i 1 Figure 1.21 What is the dimension of ?

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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 14 (1) 14 Chap. 1 Introduction to Microelectronics Solution Noting that in fact appears in parallel with , we write a KVL across these two components: (1.10) The KCL at the output node is similar to (1.8). Thus, (1.11) Interestingly, this type of amplifier does not invert the signal. Exercise Repeat the above example if . Example 1.7 A third amplifier topology is shown in Fig. 1.22. Determine the voltage gain. g m π v π v π r R out v i 1 in v E Figure 1.22 Solution We first write a KVL around the loop consisting of , , and : (1.12) That is, . Next, noting that the currents and flow into the output node, and the current flows out of it, we write a KCL: (1.13) Substituting for gives (1.14) and hence (1.15)
BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 15 (1) Sec. 1.3 Basic Concepts 15 (1.16) Note that the voltage gain always remains below unity. Would such an amplifier prove useful at all? In fact, this topology exhibits some important properties that make it a versatile building block. Exercise Repeat the above example if . The above three examples relate to three amplifier topologies that are studied extensively in Chapter 5. Thevenin and Norton Equivalents While Kirchoff’s laws can always be utilized to solve any circuit, the Thevenin and Norton theorems can both simplify the algebra and, more impor- tantly, provide additional insight into the operation of a circuit. Thevenin’s theorem states that a (linear) one-port network can be replaced with an equivalent circuit consisting of one voltage source in series with one impedance. Illustrated in Fig. 1.23(a), the term “port” refers to any two nodes whose voltage difference is of interest. The equivalent V j Port j Thev Thev Z v X v X i Thev Z (a) (b) Figure 1.23 (a) Thevenin equivalent circuit, (b) computation of equivalent impedance. voltage, , is obtained by leaving the port open and computing the voltage created by the actual circuit at this port. The equivalent impedance, , is determined by setting all indepen- dent voltage and current sources in the circuit to zero and calculating the impedance between the two nodes. We also call the impedance “seen” when “looking” into the output port [Fig. 1.23(b)]. The impedance is computed by applying a voltage source across the port and obtaining the resulting current. A few examples illustrate these principles. Example 1.8 Suppose the input voltage source and the amplifier shown in Fig. 1.20 are placed in a box and only the output port is of interest [Fig. 1.24(a)]. Determine the Thevenin equivalent of the circuit. Solution We must compute the open-circuit output voltage and the impedance seen when looking into the

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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 16 (1) 16 Chap. 1 Introduction to Microelectronics g m π v π v π r R L in v i 1 g m π v π v π r i 1 in v = 0 X v X i R L out v (c) (a) (b) R L g m R L
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