Laplace Transform of Unit Step Function: The step function is shown in the Fig. 2.2. Such a function has zero value for all t < 0, while has a value A for t ≥ 0. Hence mathematically it is expressed as, where A is called magnitude of the step. In network analysis, the step function […]
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Laplace Transform Properties: The Laplace Transform Properties are namely, 1. Linearity: The transform of a finite sum of time functions is the sum of the Laplace transforms of the individual functions. So if F1(s), F2(s),……..Fn(s) are the Laplace transforms of the time functions f1(t), f2(t), ……….., fn(t) respectively then, Explain: Let us find the Laplace transform
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Definition of Laplace Transform: Here we are going to discuss one of such transform methods called Laplace Transform Method which transforms the time domain differential equations to the frequency domain. To understand the philosophy of transform method, let us see the analogy between transform method and the use of logarithms for arithmetic operations. Consider the
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Ladder Network Circuit Analysis: By using this Ladder Network Circuit Analysis, we can find the equivalent resistance by Continued Fractions Method. Consider a Ladder Network Circuit as shown in the Fig. 1.40. Let us calculate equivalent resistance by series parallel method first. So (t + u) is in parallel with s. The combination is in
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Nodal analysis: This Nodal analysis method is mainly based on Kirchhoff’s Current Law (KCL). This method uses the analysis of the different nodes of the network. We have already defined a node. Every junction point in a network, where two or more branches meet is called a node. One of the nodes is assumed as
Loop Analysis with Current Source or Mesh Analysis: This method of Loop Analysis is specially useful for the circuits that have many nodes and loops. The difference between application of Kirchhoff’s laws and loop analysis is, in loop analysis instead of branch currents, the loop currents are considered for writing the equations. The another difference
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Source Transformation Technique: Sometimes in the complex network, both the energy sources may be present. But in loop analysis, all the energy sources should be preferably voltage sources and in node analysis, all the energy sources should be preferably current sources. The source transformation technique is useful in converting voltage to current source transformation and current
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Cramer Rule: If the network is complex, the number of equations i.e. unknowns increases. In such case, the solution of simultaneous equations can be obtained by Cramer Rule for determinants. Let us say that set of simultaneous equations obtained is, as follows : Then Cramer’s Rule says that form a system determinant Δ or
Delta to Star Conversion and Star to Delta Conversion: In the complicated networks involving large number of elements, Delta to Star and Star to Delta Conversion considerably reduce the complexity of the network and network can be analysed very quickly. These transformations allow us to replace three star connected elements of network, by equivalent Delta
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AC Fundamentals: Let us discuss in brief, the AC Fundamentals necessary to analyse the networks consisting of various alternating current and voltage sources, resistances and inductive, capacitive reactances. An alternating current or voltage is the one which changes periodically both in Cycle magnitude and direction. Such Change in magnitude and direction is measured in terms
