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

Read More »## 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[ …

Read More »## 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 …

Read More »## 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 …

Read More »## 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 …

Read More »## 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 …

Read More »## Impedance, Inductive Reactance and Capacitive Reactance

Impedance is the combined resistance in the flow of current because of resistive and reactive elements in the circuit. It is measured is ohm and calculated as follows; $Z=R+jX$ Inductive Reactance Consider a sinusoidal current to be flowing in the pure inductance as shown in the following Fig. that is …

Read More »## Power Factor Correction using Capacitor Bank

The ratio of true power to apparent power in an AC Circuit is called the power factor and can be expressed as follows: \[PF=\frac{True\text{ Power P}}{Apparent\text{ Power S}}\] It is also defined as the ratio of resistance to the impedance (series circuit): \[PF=\frac{\operatorname{Resistance}\text{ R}}{\operatorname{Impedance}\text{ Z}}\] Since R/Z is the …

Read More »## 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 …

Read More »## 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 …

Read More »## 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 …

Read More »## 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 …

Read More »## Hysteresis Loss | Eddy Current and Core Losses

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 …

Read More »## Hysteresis Loop | Magnetization Curve

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 …

Read More »## Mesh Current Analysis | Mesh Analysis

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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