Mathematical Models in Electrical Circuits: Theory and Applications

Inhaltsverzeichnis

• I. Dissipative operators and differential equations on Banach spaces.
• 1.0. Introduction.
• 1.1. Duality type functionals.
• 1.2. Dissipative operators.
• 1.3. Semigroups of linear operators.
• 1.4. Linear differential equations on Banach spaces.
• 1.5. Nonlinear differential equations on Banach spaces.
• II. Lumped parameter approach of nonlinear networks with transistors.
• 2.0. Introduction.
• 2.1. Mathematical model.
• 2.2. Dissipativity.
• 2.3. DC equations.
• 2.4. Dynamic behaviour.
• 2.5. An example.
• III. lp-solutions of countable infinite systems of equations and applications to electrical circuits.
• 3.0. Introduction.
• 3.1. Statement of the problem and preliminary results.
• 3.2. Properties of continuous lp-solutions.
• 3.3. Existence of continuous lp-solutions for the quasiautonomous case.
• 3.4. Truncation errors in linear case.
• 3.5. Applications to infinite circuits.
• IV. Mixed-type circuits with distributed and lumped parameters as correct models for integrated structures.
• 4.0. Why mixed-type circuits?.
• 4.1. Examples.
• 4.2. Statement of the problem.
• 4.3. Existence and uniqueness for dynamic system.
• 4.4. The steady state problem.
• 4.5. Other qualitative results.
• 4.6. Bibliographical comments.
• V. Asymptotic behaviour of mixed-type circuits. Delay time predicting.
• 5.0. Introduction.
• 5.1. Remarks on delay time evaluation.
• 5.2. Asymptotic stability. Upper bound of delay time.
• 5.3. A nonlinear mixed-type circuit.
• 5.4. Comments.
• VI. Numerical approximation of mixed models for digital integrated circuits.
• 6.0. Introduction.
• 6.1. The mathematical model.
• 6.2. Construction of the system of FEM-equations.
• 6.2.1. Space discretization of reg-lines.
• 6.2.2. FEM-equations of lines.
• 6.3. FEM-equations of the model.
• 6.4. Residual evaluations.
• 6.5. Steady state.
• 6.6. The delay time and its a-priori upper bound.
• 6.7. Examples.
• 6.8. Concluding remarks.
• Appendix I.
• List of symbols.
• References.