# Solution as depicted in fig 128a we short the output

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Solution As depicted in Fig. 1.28(a), we short the output port and seek the value of . Since the voltage g m π v π v π r R L in v i 1 Short Circuit i Nor g m v R L in (a) (b) Figure 1.28 across is now forced to zero, this resistor carries no current. A KCL at the output node thus yields (1.29)

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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 19 (1) Sec. 1.4 Chapter Summary 19 (1.30) Also, from Example 1.8, ( . The Norton equivalent therefore emerges as shown in Fig. 1.28(b). To check the validity of this model, we observe that the flow of through produces a voltage of , the same as the output voltage of the original circuit. Exercise Repeat the above example if a resistor of value is added between the top terminal of and the output node. Example 1.12 Determine the Norton equivalent of the circuit shown in Fig. 1.22 if the output port is interest. Solution Shorting the output port as illustrated in Fig. 1.29(a), we note that carries no current. Thus, i Nor g m v in (a) (b) g m π v π v π r R L i 1 in v π r 1 + ( ) π r R L g m π r ) R L π r + (1+ Figure 1.29 (1.31) Also, (why?), yielding (1.32) With the aid of found in Example 1.10, we construct the Norton equivalent depicted in Fig. 1.29(b). Exercise What happens if ? 1.4 Chapter Summary Electronic functions appear in many devices, including cellphones, digital cameras, laptop computers, etc.
BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 20 (1) 20 Chap. 1 Introduction to Microelectronics Amplification is an essential operation in many analog and digital systems. Analog circuits process signals that can assume various values at any time. By contrast, digital circuits deal with signals having only two levels and switching between these values at known points in time. Despite the “digital revolution,” analog circuits find wide application in most of today’s electronic systems. The voltage gain of an amplifier is defined as and sometimes expressed in decibels (dB) as . Kirchoff’s current law (KCL) states that the sum of all currents flowing into any node is zero. Kirchoff’s voltage law (KVL) states that the sum of all voltages around any loop is zero. Norton’s theorem allows simplifying a one-port circuit to a current source in parallel with an impedance. Similarly, Thevenin’s theorem reduces a one-port circuit to a voltage source in series with an impedance.

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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 21 (1) 2 Basic Physics of Semiconductors Microelectronic circuits are based on complex semiconductor structures that have been under active research for the past six decades. While this book deals with the analysis and design of circuits , we should emphasize at the outset that a good understanding of devices is essential to our work. The situation is similar to many other engineering problems, e.g., one cannot design a high-performance automobile without a detailed knowledge of the engine and its limitations.
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