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Resistor Circuits
Published in Richard C. Dorf, Ronald J. Tallarida, Pocket Book of Electrical Engineering Formulas, 2018
Richard C. Dorf, Ronald J. Tallarida
A source transformation is a procedure for transforming one source into another while retaining the terminal characteristics of the original source. The transformation of a voltage source in series with a resistance Rs into a current source in parallel with a resistance Rp is summarized in Figure 14.2(a).
Circuit Equivalence
Published in Nassir H. Sabah, Circuit Analysis with PSpice, 2017
The following should be noted concerning source transformation:Because of circuit equivalence, source transformation must preserve polarities of voltages and directions of currents at the terminals of the two sources. To ascertain this in a given circuit, the two sources are temporarily disconnected from the rest of the circuit, so that iL = 0 in Figure 3.30, for example. The assigned positive direction of the ideal voltage source element in Figure 3.30a makes terminal ‘a’ positive with respect to terminal ‘b’. Similarly, in Figure 3.30b, the assigned positive direction of the ideal current source element is such that iSRC flowing in Rsrc makes terminal ‘a’ positive with respect to terminal ‘b’.The equivalence between the two sources applies at the specified terminals only. It does not apply inside the sources. For example, the power delivered by the ideal source elements is quite different in the two cases, as illustrated in Example 3.5.An ideal voltage source cannot be transformed to an ideal current source, and conversely. Thus, Rsrc = 0 for an ideal voltage source, which makes iSRC = vSRC/Rsrc → ∞. Similarly, Rsrc → ∞ for an ideal current source, which makes vSRC = RsrciSRC → ∞. Infinite values of vSRC and iSRC imply that the corresponding sources are not valid. This is in accordance with ideal voltage and current sources being basic circuit elements, where a basic circuit element cannot be represented in terms of other basic circuit elements, as mentioned in Section 1.8. Nonideal sources are not basic circuit elements. They can therefore be represented in terms of basic circuit elements, and linear-output voltage sources can be transformed to linear-output current sources, and conversely.
Efficient computation of derivatives for solving optimization problems in R and Python using SWIG-generated interfaces to ADOL-C†
Published in Optimization Methods and Software, 2018
K. Kulshreshtha, S.H.K. Narayanan, J. Bessac, K. MacIntyre
Algorithmic differentiation (AD) [15] is a technique to compute derivatives of functions represented as evaluation procedures efficiently and accurately with round-off error within machine precision [16]. Various programming tools have been developed in the past to compute derivatives of programs written in high-level languages such as Fortran, C and C++. Such tools fall into two main categories. Some are built on a programming-language parser and compiler in order to output augmented program code that will, when executed, compute the desired derivatives along with the original output of the program. This technique is known as source transformation. Examples include Tapenade [17], ADIC2 [24], OpenAD [34] and TAF [13]. Others rely on the capability of object-oriented programming languages to overload operators and functions in order to perform additional tasks besides those that they would for built-in data types. Naturally, these tools are called operator overloading tools. Prominent examples are ADOL-C [40], CppAD [7], dco/c++ [23], Adept [18] and CoDiPack [27]. The community website http://www.autodiff.org provides further information about tools and references on AD.