By Farid N. Najm
A Definitive textual content on constructing circuit simulators
Circuit Simulation provides a transparent description of the numerical strategies and algorithms which are a part of sleek circuit simulators, with a spotlight at the most ordinarily used simulation modes: DC research and brief research. confirmed in a graduate path on circuit simulation on the college of Toronto, this distinct textual content offers the reader with enough aspect and mathematical rigor to put in writing his/her personal easy circuit simulator. there's specific insurance all through of the mathematical and numerical options which are the foundation for a number of the simulation issues, which enables an entire realizing of functional simulation thoughts. moreover, Circuit Simulation:
Explores a couple of glossy concepts from numerical research that aren't synthesized wherever else
Covers community equation formula intimately, with an emphasis on converted nodal research
supplies a complete remedy of the main appropriate features of linear and nonlinear method resolution options
States all theorems with out evidence so that it will keep the focal point at the end-goal of supplying assurance of useful simulation equipment
offers plentiful references for additional research
permits novices to circuit simulation to appreciate the cloth in a concrete and holistic demeanour
With challenge units and desktop tasks on the finish of each bankruptcy, Circuit Simulation is ideal for a graduate direction in this subject. it's also a realistic reference for layout engineers and computer-aided layout practitioners, in addition to researchers and builders in either and academia.Content:
Chapter 1 creation (pages 1–12):
Chapter 2 community Equations (pages 13–47):
Chapter three answer of Linear Algebraic Circuit Equations (pages 49–126):
Chapter four answer of Nonlinear Algebraic Circuit Equations (pages 127–200):
Chapter five resolution of Differential Circuit Equations (pages 201–303):
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Extra resources for Circuit Simulation
For a connected, linear, resistive circuit, with no controlled sources, that meets the consistency requirements, it can be shown that G is an M-matrix. In this case, G−1 ≥ 0 exists and the network is uniquely solvable. 4 Modified Nodal Analysis We are now ready to present modified nodal analysis, originally described in Ho et al. (1975). To handle voltage sources, the key idea is to not insist on eliminating their currents, but to retain those currents as additional variables. For of these new variables, we add a new equation, namely the branch equation for that (voltage source) element.
14) Because one row of M can always be written in terms of all the rest, then one equation of Mi = 0 is redundant. 15) It can be shown that, for a connected, loopless, directed graph Gd , the set of rows of the reduced incidence matrix A are linearly independent. 16) el ∈Ein j This observation will be useful later on. Example For the network in Fig. 12, and using the edge labels adopted in Fig. 20) 0 0 I −AT v This gives (m + n − 1) independent equations in (2m + n − 1) unknowns. The element equations provide another m independent equations in the same unknowns.
When in group 2, the capacitor element stamp is as shown in Fig. 30. For an inductor, with element equation v + − v − = LdiL /dt, and a reference direction for current from n+ to n− , as shown in Fig. 31, the element stamp is as shown in Fig. 32. Element stamps for other (resistive) element types are constructed as we saw previously. Frequency Domain The above techniques for equation formulation can be applied in the frequency domain, for circuits with linear capacitors and inductors. 28: A capacitor.