CMOS Optical Preamplifier Design Using Graphical Circuit Analysis

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2.4 Circuit Analysis Techniques 28 Direct nodal analysis is mathematically exact and straightforward to solve with the aid of calculators or computers capable of matrix operations. However, notice that the solution required the substitution of numbers into the parameters; had we kept the parameters and performed a symbolic analysis of the circuit, the resulting expressions would have been very complex and far too cumbersome to provide much insight into the circuit’s operation. Topology-Based Feedback Analysis v s ′ R out Greater insight into the effect of feedback on this amplifier can be obtained using topology-based analysis. Although other interpretations are possible, the feedback amplifier in Figure 2.13 can be seen as series-shunt configuration in which the output voltage is sampled and then mixed back to the input as a voltage signal. Fol- lowing the process outlined in [Sedra,1998], we can partition the circuit into a forward amplifier and feedback network as shown in Figure 2.14. a) R s v be1 + - g m v be1 r e R || E R f v c1 R 1 r π v o = -------- = 9.43Ω i test g m v c1 v o ′ R || 2 ( R f + RE) Figure 2.14 Topology-based feedback analysis: small-signal circuits for a) forward amplifier and b) feedback network. b) v f ′ R E R f v o ′
The gain of the forward amplifier can be expressed as where vo ′ ------ = – gm × R || 2 ( R f + RE) v c1 vc1 ------ = – αie( R || 1 rπ) = vs ′ 2.4 Circuit Analysis Techniques 29 The feedback network, comprised of a simple resistor divider can be expressed as Thus the resulting loop gain is Aβ = 671.6 × 0.053 = 35.62 . To determine the closed-loop gain, we apply the standard closed-loop feedback expression The input resistance of the forward amplifier can be seen to be Although not immediately apparent, the source resistance R s must be included when determining since the derivation of the feedback equation assumes that R s is absorbed into the input resistance of the forward amplifier. The output resistance of the forward amplifier is vo ′ vo ′ A = ------ = ------ × ------ ≈ 671.6 vs ′ vs ′ v c1 With the application of feedback, the input resistance is increased while the output resistance is decreased, both by a factor of ( 1 + Aβ) = 36.62 . As such, the port v c1 ( β + 1) ( re + R || E R f ) α( R || 1 rπ) --------------------------------------------------------------------- × – ------------------------------- Rs + ( β + 1) ( re + R || E R f ) re + R || E R f β RE RE + R f = --------------------- = 0.053 v o A 671.6 Gain = A f = ---- = ----------------- = ----------------------- = 18.34 1 + Aβ 1 + 35.62 v i RinA = Rs + ( β + 1) ( re + R || E R f ) = 1000 + 101 × ( 9.9 + 28 || 500) Ω = 4.678kΩ R inA RoutA = R || 2 ( R f + RE) = 1000 || ( 500 + 28) Ω = 345.5Ω
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: A = = For = 1V , the solution is v
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 and 44: 1 x1 x2 2.5 An Overview of Signal-F
Page 45 and 46: 2.6 SUMMARY REFERENCES • ∆ k =
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 85 and 86:
4.2 Circuit Analysis Using Driving-
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Page 89 and 90:
Page 91 and 92:
4.3 DPI/SFG: Combining DPI Analysis
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4.4 Determining Port Impedances 87
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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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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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