Basic System Properties

Definition of a System A common way of viewing a system is in terms of a “black box” with terminals, as illustrated in the following figure: In the figure, x1(t), x2(t)… xp(t) are the signals applied to the p input terminals of the system and y1 (t), y2 (t)… yq …

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Linear Difference Equations

Consider the single–input single –output discrete time system given by the input/output difference equation. $y\left( kT+nT \right)+\underset{i=0}{\overset{n-1}{\mathop \sum }}\,{{a}_{i}}y\left( kT+iT \right)=\underset{i=0}{\overset{m}{\mathop \sum }}\,{{b}_{i}}x\left( kT+iT \right)~~~~~~~~~~~~\left( 1 \right)$ In (1), T is a fixed real number, k is a variable that takes its values from the set of integers, and the …

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Source Transformation Example Problems with Solutions

A highly valuable byproduct of Thevenin’s and Norton’s theorem is the technique of source transformation. Source transformation is based on the observation that if a Thevenin’s network and Norton’s network are both equivalent to a particular source network, then they must also equivalent to each other. This observation allows you …

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Voltage divider Circuits and Current divider Circuits

In analyzing a series circuit, it becomes necessary to find voltage drop across one or more of the resistances. A simple voltage drop relationship may be obtained by referring to the following figure. The total current is given by, $I=\frac{E}{{{R}_{1}}+{{R}_{2}}+{{R}_{3}}}$ And the voltage drop are given by, ${{V}_{1}}=I{{R}_{1}}=E\frac{{{R}_{1}}}{{{R}_{1}}+{{R}_{2}}+{{R}_{3}}}~~~~\text{  }~~~\left( 1 …

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Power Factor Correction using Capacitor Bank

Power Factor Improvement

Power factor Ideally, all the supply voltage and current should be converted into true power in a load. When this is not a case, a certain kind of inefficiency occurs. The ratio of true power to apparent power is called the power factor of the load, \[\begin{matrix}   Power\text{ }Factor=\frac{true\text{ }Power}{Apparent\text{ …

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Apparent, Active and Reactive Power

This section covers basic concepts about apparent, active (real) and reactive power which is important ingredients in the analysis of a power system. Consider the general single-phase circuit with a sinusoidal voltage $v={{V}_{m}}sin\left( wt \right)$ applied. A current $i={{I}_{m}}sin(wt\pm \theta )$  results and is leading (θ is positive) for a capacitive …

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Maximum Power Transfer Theorem

Maximum Power Transfer Theorem Definition Maximum power transfer theorem states that maximum power output is obtained when the load resistance RL is equal to Thevenin resistance Rth as seen from load Terminals. Fig.1: Maximum Power Transfer Theorem Any circuit or network may be represented by a Thevenin equivalent circuit.  The Thevenin …

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Nodal Analysis or Node voltage Method

Nodal analysis or Node voltage method uses node voltages as circuit variables in order to analyze the circuit. The objective of this section is to obtain a set of simultaneous linear equations. However, unlike the mesh analysis method, the procedure developed in this section depends on the choice of certain …

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Comparison between Electrical and Magnetic Circuits

The most important differences between Electrical Circuit and Magnetic Circuit are discussed in this article on the basis of Exciting Force, Current & Flux Density, Lines of Force, Series & Parallel Circuit Behavior, Insulation, Energy, Temperature, and Circuits Representation. The following table keys out the main Differences between Electric and Magnetic …

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Hysteresis Loss | Eddy Current and Core Losses

Laminated Core

The area within the hysteresis loop is a product of B and H and this area represents the energy per unit volume that must be used per magnetization cycle to move the domains.  Hysteresis Loss With appropriate constants, the hysteresis loss can be given in watts per unit volume. An …

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Hysteresis Loop | Magnetization Curve

Hysteresis Loop

Hysteresis Loop Definition A curve, or loop, plotted on B-H coordinates showing how the magnetization of a ferromagnetic material varies when subjected to a periodically reversing magnetic field, is known as Hysteresis Loop. Hysteresis Definition Hysteresis is the lagging of the magnetization of a ferromagnetic material behind the magnetizing force …

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Mesh Current Analysis | Mesh Analysis

Two Loop Network

The mesh is a closed path which does not contain any other closed path within it. This section shows that a set of simultaneous linear equations can be written which describes the network. This set of equations depends on a choice of loop currents used in connection with Kirchhoff’s law. …

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Absolute and Relative Magnetic Permeability

Permeability is the measure of the ease, with which magnetic lines of force pass through a given material. The ability of a material to concentrate magnetic flux is called permeability and its symbol is the Greek lower case letter μ. Any material that is easily magnetized tends to concentrate magnetic …

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Magnetic Field Intensity | Definition Formula

Magnetomotive force, ℑ , per unit length, is called the magnetic field intensity H. Magnetic Field Intensity Unit Magnetic field intensity is also known as the magnetizing force which is measured is ampere-turns per meter (A-t/m). Of primary concern, however, is the magnetomotive force needed to establish a certain flux density, …

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