Circuit Theory (analysis and synthesis) by A.Chakrabarti: A Must-Read Book for Electrical Engineers
that is, an assembly circuit is not fully determined until we specify the connections between the functional units. the reason is that the circuit topology completely determines the distribution of signals and power within the chip. the connections between the circuits are the non-idealities of the layout. if we have the freedom of arranging the circuit topology, we should take this freedom into account in the analysis of the chip layout.
circuit theory by a.chakrabarti pdf free download
.. the algebra of circuits is conveniently represented as a face lattice of the edge lattice of the dual graph associated to the circuit. another useful concept is a spanning forest of a graph. the set of all the forests of g is denoted by forests. the full set of forests of a graph g is called the wdcf of g. for some g, the full set of spanning forests of g is called the wdcf. the wdcf of a graph is an important invariant of the graph.
this paper is concerned with the analysis of chips in 3-d. thus a chip layout is treated as a surface and, accordingly, as a 1-complex. the problem of chip layout is converted into the problem of 1-complexes in a 3-dimensional space. the analysis of 1-complexes is equivalent to the analysis of complexes without holes. we begin with a careful generalization of'split-up' to an operation on 1-complexes which turns out to be a key for the analysis of 3-d chips.
vectors in a vector space can be visualized as linear combinations of basis elements. a basis of a vector space is a collection of vectors that forms a linear independent subset of the vector space. a vector in a vector space is called a zero vector if it is the zero of the vector space. a subspace of a vector space is called a vector subspace of the vector space if every vector of the subspace can be written as a linear combination of vectors of the subspace. a subspace of a vector space is called a proper subspace of the vector space if it is a vector subspace of the vector space but it is not equal to the vector space itself. a vector subspace of a vector space is called an ideal in the vector space if it is a vector subspace of the vector space and it is a proper subspace of itself.