Preface |
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vii | |
Acknowledgments |
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xi | |
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1 | (10) |
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1.1 Synthesis of Passive Networks |
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1 | (3) |
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1.2 New Research Motivation: Inerter-Based Mechanical Control |
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4 | (5) |
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9 | (2) |
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2 Preliminaries of Passive Network Synthesis |
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11 | (26) |
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2.1 Positive-Real Function and Foster Preamble |
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11 | (4) |
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2.2 Synthesis of One-Port Lossless Networks |
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15 | (1) |
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16 | (3) |
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2.4 The Bott-Duffin Synthesis |
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19 | (6) |
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2.5 The Darlington Synthesis |
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25 | (2) |
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2.6 Graph Theory for Passive Networks |
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27 | (6) |
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33 | (4) |
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3 Biquadratic Synthesis of One-Port RLC Networks |
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37 | (90) |
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37 | (1) |
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3.2 Basic Notations and Results |
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38 | (3) |
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3.3 A Canonical Biquadratic Impedance |
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41 | (2) |
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3.4 Realizations of Biquadratic Impedances with No More than Four Elements |
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43 | (10) |
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3.4.1 Realizations with No More than Three Elements |
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43 | (1) |
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3.4.2 Realizations with Four Elements |
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44 | (9) |
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3.5 Realization of Biquadratic Impedances as Five-Element Bridge Networks |
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53 | (26) |
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54 | (4) |
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3.5.2 Five-Element Bridge Networks with Two Reactive Elements of the Same Type |
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58 | (9) |
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3.5.3 Five-Element Bridge Networks with One Inductor and One Capacitor |
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67 | (7) |
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74 | (5) |
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3.6 Generalized Synthesis without Real-Part Minimization for Biquadratic Impedances |
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79 | (10) |
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79 | (2) |
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3.6.2 Biquadratic Impedances with Real Zeros and Arbitrary Poles |
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81 | (4) |
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3.6.3 Further Generalization to General Biquadratic Impedances |
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85 | (4) |
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3.7 A Generalized Theorem of Reichert for Biquadratic Minimum Functions |
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89 | (17) |
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3.8 Seven-Element Series-Parallel Realizations of a Specific Class of Biquadratic Impedances |
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106 | (21) |
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108 | (2) |
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3.8.2 Realizations as Three-Reactive Seven-Element Series-Parallel Networks |
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110 | (2) |
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3.8.3 Realizations as Four-Reactive Seven-Element Series-Parallel Networks |
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112 | (9) |
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3.8.4 Realizations as Five-Reactive Seven-Element Series-Parallel Networks |
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121 | (5) |
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126 | (1) |
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4 Synthesis of n-Port Resistive Networks |
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127 | (40) |
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127 | (1) |
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4.2 A Review of n-Port Resistive Network Synthesis |
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128 | (13) |
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4.2.1 Realizations with n ≤ 3 |
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128 | (2) |
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4.2.2 General Properties of n-Port Resistive Networks |
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130 | (3) |
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4.2.3 Realizations of Admittance Matrices with n + 1 Terminals |
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133 | (5) |
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4.2.4 Realizations of Admittance Matrices with More than n 4-1 Terminals |
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138 | (3) |
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4.3 Synthesis of n-Port Resistive Networks Containing 2n Terminals |
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141 | (7) |
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4.3.1 A Necessary and Sufficient Condition for Realization |
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142 | (3) |
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4.3.2 Element Value Expressions |
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145 | (2) |
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147 | (1) |
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4.4 Minimal Realization of Three-Port Resistive Networks |
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148 | (19) |
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4.4.1 Minimal Realization with Four Terminals |
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150 | (1) |
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4.4.2 Realization with at Most Four Elements |
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151 | (6) |
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4.4.3 Realization with Five Elements |
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157 | (8) |
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165 | (2) |
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5 Mechanical Synthesis of Low-Complexity One-Port Networks |
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167 | (62) |
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167 | (5) |
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5.2 Realization of a Special Class of Admittances with One Damper, One Inerter, and Finite Springs |
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172 | (15) |
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5.2.1 Realizability Conditions when the Impedance of Spring Network Exists |
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173 | (9) |
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5.2.2 Final Realization Results |
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182 | (5) |
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5.3 Realizations of a Special Class of Admittances with Strictly Lower Complexity than Canonical Configurations |
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187 | (22) |
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5.3.1 Cases with Zero Coefficients |
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188 | (2) |
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190 | (2) |
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5.3.3 Realizations with No More than Four Elements |
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192 | (5) |
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5.3.4 Realizations of Five-Element Damper-Spring Networks |
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197 | (3) |
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5.3.5 Realizations of Five-Element Damper-Spring-Inerter Networks |
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200 | (8) |
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208 | (1) |
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5.4 Synthesis of a One-Damper One-Inerter Network Containing No More than Three Springs |
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209 | (20) |
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5.4.1 Realizability Conditions under a Particular Assumption |
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209 | (10) |
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5.4.2 Final Realization Results |
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219 | (4) |
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223 | (6) |
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229 | (2) |
Bibliography |
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231 | |