Continuous Time Convolution Properties | Continuous Time Signal

Continuous Time Convolution For linear time-invariant (LTI) systems, the convolution is being utilized in order to achieve output response from the knowledge of input and impulse response. Given two continuous-time signals x(t) and h(t), the convolution is defined as $y\left( t \right)=\sum\limits_{\tau =-\infty }^{\infty }{x\left( \tau  \right)h\left( t-\tau  \right)d\tau }~~~~~~~~~~~~~~~~~~~~~~~~\left( …

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$A=\left[ \begin{matrix}   -1 & 0  \\   0 & -5  \\\end{matrix} \right]$ $~b=\left[ \begin{matrix}   1.25  \\   -1.25  \\\end{matrix} \right]$ $u=e$  

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Discrete Time Convolution Properties | Discrete Time Signal

Discrete-Time Convolution Convolution is such an effective tool that can be utilized to determine a linear time-invariant (LTI) system’s output from an input and the impulse response knowledge. Given two discrete time signals x[n] and h[n], the convolution is defined by $x\left[ n \right]*h\left[ n \right]=y\left[ n \right]=\sum\limits_{i=-\infty }^{\infty }{{}}x\left[ …

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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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