CMOS Optical Preamplifier Design Using Graphical Circuit Analysis

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2.5.1 Mason’s Direct Rule 2.5 An Overview of Signal-Flow Graphs 38 The manipulation of signal-flow graphs is an effective and straightforward means of determining transfer functions for relatively small graphs. However, such manipula- tions quickly become unwieldy for larger graphs, and for such situations the transfer function can be computed directly. Comparing Equation (2.12) to the original signal-flow graph in Figure 2.20a, we notice that the transfer function can be expressed as (2.13) where = abc represents the forward transmission path from input to output, and = cd and L2 = bce represent the loop gains of the two feedback loops found in the graph. In general, the transfer function of a signal-flow graph can be derived using the following expression, commonly known as Mason’s Direct Rule [Mason,1960]: where and L 1 P 1 • P k = transmittance of the kth forward path from input x in, to output, x out • ∆ = 1 - (sum of all individual loop gains) + (sum of loop gain products of all possible sets of nontouching loops taken two at a time) - (sum of loop gain products of all possible sets of nontouching +... x out -------- x in x out x in loops taken three at a time) P 1 = ---------------------------------- 1 – ( L1 + L2) 1 -------- = -- ∑ Pk∆ k ∆ n k = 1 (2.14)
2.6 SUMMARY REFERENCES • ∆ k = the value of ∆ for that portion of the graph not touching the kth forward path. 2.6 Summary 39 In this chapter, we discussed the photodetector and optical preamplifier that make up the front-end of an optical receiver. The transimpedance amplifier is the most common preamplifier structure, and we described the three principal new requirements that we wish to address in this thesis: a wide dynamic range, ambient light rejection, and low-voltage operation. In preparation for our discussion of a graphical circuit analysis technique, we reviewed existing analysis techniques such as nodal analysis, and feedback analysis based on amplifier topology and return ratios. In addition, we reviewed the basic conventions of signal-flow graphs and out- lined Mason’s Direct Rule. S. B. Alexander, Optical Communication Receiver Design, SPIE Optical Engineering Press, London, UK, Chapter 6, pp. 173-201, 1997. J. R. Barry, Wireless Infrared Communications, Kluwer Academic Pub., Boston, Mass., Chapter 3, pp. 49-52, 1994. R. B. Blackman, “Effect of Feedback on Impedance,” Bell System Tech. Journal, vol. 22, pp. 269- 277, Oct. 1943. L. S. Bobrow, Elementary Linear Circuit Analysis, 2nd Ed., HRW Inc., New York, NY, 1987. H. W. Bode, Network Analysis and Feedback Amplifier Design, Van Nostrand, New York, 1945. E. Brass, U. Hilleringmann, and K. Schumacher, “System Integration of Optical Devices and Analog CMOS Amplifiers,” IEEE J. Solid-State Circuits, vol. 29, no. 8, pp. 1006-1010, August 1994. W. K. Chen, Active Network Analysis, World Scientific, Singapore, 1991. W. K. Chen, Graph Theory and Its Engineering Applications, World Scientific, Singapore, 1997. A. M. Davis, "Some Fundamental Topics in Introductory Circuit Analysis: A critique," IEEE Trans.on Education, vol. 43, no.3, pp. 330-335, August 2000. S. S. Haykin, Active Network Theory, Addison-Wesley, Reading, Massachusetts, Chapter 10, 1970.
Page 1 and 2: CMOS Optical Preamplifier Design Us
Page 3 and 4: To achieve low-voltage operation, w
Page 5 and 6: Table of Contents CHAPTER 1 INTRODU
Page 7 and 8: CHAPTER 1 1.1 OVERVIEW Introduction
Page 9 and 10: Information Source Modulator Drive
Page 11 and 12: 1.2 Thesis Outline 5 [Ohhata,1999].
Page 13 and 14: 1.2 Thesis Outline 7 technique call
Page 15 and 16: 1.2 Thesis Outline 9 Detector in St
Page 17 and 18: E e + - V bias 2.1 Photodetectors 1
Page 19 and 20: Diode Capacitance (pF) Diode capaci
Page 21 and 22: 2.2 Optical Preamplifier Structures
Page 23 and 24: 2.3 Transimpedance Amplifier Design
Page 27 and 28: I dc 2.3 Transimpedance Amplifier D
Page 31 and 32: Source Figure 2.11 General structur
Page 33 and 34: A = = For = 1V , the solution is v
Page 35 and 36: The gain of the forward amplifier c
Page 37 and 38: Feedback Analysis Using Return Rati
Page 39 and 40: 2.4 Circuit Analysis Techniques 33
Page 41 and 42: 2.5 An Overview of Signal-Flow Grap
Page 43: 1 x1 x2 2.5 An Overview of Signal-F
Page 47 and 48: Symp. Circuits Systems, vol. 3, pp.
Page 49 and 50: CHAPTER 3 New Transimpedance Amplif
Page 51 and 52: 3.1 A Differential Transimpedance A
Page 57 and 58: 3.2 A Feedback Topology for Ambient
Page 59 and 60: 3.2 A Feedback Topology for Ambient
Page 61 and 62: Transimpedance (dBΩ) 90 80 60 40
Page 63 and 64: 3.3 A Low-Voltage Transimpedance Am
Page 73 and 74: C 3 Φ1VB M 3 V B- =0.7V M 7 Figure
Page 77 and 78: 3.4 SUMMARY 3.4 Summary 71 In this
Page 79 and 80: 3.4 Summary 73 Y. Nakagome et al.,
Page 81 and 82: 4.1 Introduction 75 back topology o
Page 83 and 84: 4.2 Circuit Analysis Using Driving-
Page 91 and 92: 4.3 DPI/SFG: Combining DPI Analysis
Page 93 and 94: 4.4 Determining Port Impedances 87
Page 95 and 96:
v i R in v o R out 4.4 Determining
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id » ro and 1 ⁄ rid « Av ⁄ ro
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4.4 Determining Port Impedances 93
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4.4 Determining Port Impedances 95
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Z b r e g m 4.5 Analyzing Transisto
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4.5 Analyzing Transistor Circuits 9
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Figure 4.25 SFG for the source foll
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5.1 Analysis of the Low-Voltage Tra
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5.1 Analysis of the Low-Voltage Tra
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5.2 DEVELOPING AN ANALYTIC CIRCUIT
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Z in 5.2 Developing an Analytic Cir
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5.2 Developing an Analytic Circuit
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I n1 : i in I n2 -I n1 i scin ( sCi
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Page 129 and 130:
I nRf : 5.2 Developing an Analytic
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DC transimpedance gain: Pole locati
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Frequency (MHz) 500 450 400 350 300
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Pole frequencies(MHz) 500 450 400 3
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Optimizing Sensitivity 5.2 Developi
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Transimpedance Volts dB (lin) Gain
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CHAPTER 6 Implementation and Experi
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6.1 A 1V Optical Receiver Front-End
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6.1.2 Experimental Results 6.1 A 1V
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Gain(dB) 0 −1 −2 −3 −4 −5
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Clock signal of voltage doubler Eye
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6.2 Variable-Gain Transimpedance Am
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6.2.2 Experimental Results 6.2 Vari
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6.3 Summary and State-of-the-Art Co
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Reference Outputs Technology Supply
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CHAPTER 7 Conclusions 7.1 SUMMARY A
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7.2 Future Work 165 The significanc
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7.2 Future Work 167 supply and subs
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v s i ti that part of the SFG for Q
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Thus, P1 ′ = b = 500Ω ∆1 ′
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itive representation of circuit dyn
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Bipolar Transistor i scb Z b v b b
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CMOS Optical Preamplifier Design Using Graphical Circuit Analysis

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