1st Lecture W1, October In this lecture we are going get acquainted with the concept of lumped circuits, Kirchoff's current law and Kirchoff's voltage law, and constitutive relations of circuit elements. These equations form the mathematical model of a circuit. The number of equations and unknowns can be greatly reduced…
2nd Lecture W2, October Nodal analysis has one great disadvantage. It cannot handle elements for which branch currents cannot be explicitly expressed (e.g. independent voltage source). In this lecture we are going to introduce modified nodal analysis. If we cannot explicitly express a branch current with branch voltages we…
3rd Lecture W3, October Solving systems of linear equations is nothing new. Several approaches were developed in the past. For starters we take a look at Gaussian elimination. We examine its computational cost and show how it can fail. To improve the robustness of Gaussian elimination we introduce pivoting. Gaussian…
4th Lecture W1, November Sparse matrices are matrices where most entries are zero. Coefficient matrices corresponding to real-world circuits are sparse. This makes it possible to analyze large circuits without prohibitively large memory requirements. But there is a catch. Performing LU-decomposition of a sparse matrix must make sure that as…
5th Lecture W2, November When we introduce nonlinear elements we can no longer write equations in matrix form. Instead they are now written as a list of nonlinear equations. If the equations are twice continuously differentiable we can numerically solve them with the Newton-Raphson algorithm. The algorithm iteratively approaches the…