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# Theory of Linear and nonlinear circuits - Engberg J.

Engberg J. Theory of Linear and nonlinear circuits - Wiley & sons , 1995. - 154 p.
ISBN 0-47-94825
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5.4.2 Graphic representation of the extended noise measure .... 95
5.5 References............................................................ 99
6 Noise of embedded networks 101
6.1 Lumped embedding ......................................................101
G.2 Reference plane transformation of noise parameters..................... 109
6.2.1 The equivalent noise two-port of a lossy transmission line . . 115
6.3 Noise parameters of interconnected two-ports..........................116
6.3.1 Two-ports in parallel...........................................117
6.3.2 Xwo-nnrt.s in c3.sca.dc................................... iiy
6.3.3 Albinssonâ€™s method of interconnected two-ports..................120
6.3.4 Matrix formulation.............................................. 12 i
6.4 Calculating noise parameters from deembedded data.....................121
6.4.1 Matrix formulation of the deembedding procedure.................124
6.4.2 Calculating noise parameters at a new frequency.................130
6.5 Transformer coupled feedback.......................................... 132
6.6 Mixed input...........................................................136
6.7 Transformation to common base and common collector.................... 137
Contents vii
6.8 Noise computations in computer aided design programs ....................138
6.9 References...............................................................138
II Non-linear systems 141
7 Noise in non-linear systems: Theory 143
7.1 Introduction.............................................................143
7.2 Preliminaries ........................................................... 144
7.2.1 System description................................................145
7.2.2 Representation of signals ........................................ 146
7.3 Noise sources............................................................150
7.3.1 Basic theory .....................................................151
7.3.2 Controlling variables.............................................156
7.3.3 Modulated noise source............................................162
7.3.4 Fundamental noise sources ........................................ L68
7.3.5 Some special cases................................................169
7.3.6 Algorithm.........................................................170
7.4 Responses................................................................ 171
7.4.1 Deterministic response............................................171
7.4.2 Noise response....................................................174
7.4.3 Total response ...................................................177
7.4.4 Some special cases................................................ L7S
7.5 References...............................................................179
8 Noise in non-linear systems: Examples and Conclusion 181
8.1 Example 1................................................................182
8.2 Example 2................................................................193
8.3 Example 3................................................................201
8.4 Conclusion ..............................................................214
9 Multi-port Volterra transfer functions 215
9.1 Introduction.............................................................215
9.2 Preliminaries ...........................................................216
9.2.1 Symmetry properties...............................................217
9.2.2 Determination of transfer functions...............................218
9.3 Theory...................................................................220
9.3.1 Relations for the linear system ..................................222
n " Non line.-.r rf^pon^e . ......................... 293
9.3.3 Transfer functions ...............................................226
9.3.4 Controlled variables .............................................22*
9.3.5 Controlling variables.............................................229
9.3.6 Algorithm ........................................................23 <
viii
Contents
9.4 Computer implementation...............................................'238
9.4.1 Some introductory considerations...............................'238
9.4.'2 Precalculated tables...........................................239
9.1.3 Program........................................................241
9.5 Some types of non-linear subsystems...................................'242
9.5.1 Type 1.........................................................242
9.5.2 Type 2.........................................................'242
9.5.3 Type 3.........................................................243
9.5.4 Type 4.........................................................243
9.5.5 Type 5.........................................................244
9.6 Examples..............................................................244
9.6.1 Example 1....................................................244
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