## Steady State Error | Feedback Systems

Steady State Error High loop gains were shown advantageous to reduce the sensitivity to modeling accuracy, parameter variations, and disturbance inputs. They will now prove equally desirable from the point of view of the reduction of steady-state errors in feedback systems. Consider the unity feedback system in Figure 1. The …

## Laplace Transform Properties in Signal and Systems

The Laplace transform fulfills a number of properties that are quite valuable in various applications. In particular, by using these properties, it is possible to derive many new transform pairs from a basic set of pairs. In this tutorial, we state most fundamental properties of the Laplace transform. Linearity If …

## Laplace Transform:Introduction and Example

Laplace Transform Definition The Laplace transform X(s) is a complex-valued function of the complex variable s. In other words, given a complex number s, the value X(s) of the transform at the point s is, in general, a complex number. Given a function x (t) of the continuous-time variable t, …

## Z Transform Introduction | Z Transform Properties

INTRODUCTION TO Z-TRANSFORM  For the sake of analyzing continuous-time linear time-invariant (LTI) system, Laplace transformation is utilized. And z-transform is applied for the analysis of discrete-time LTI system.  Z-transform is fundamentally a numerical tool applied for a transition of a time domain into frequency domain and is a mathematical function …

## Continuous Time Graphical Convolution Example

This is the continuation of the PREVIOUS TUTORIAL. Steps for Graphical Convolution First of all re-write the signals as functions of τ: x(τ) and h(τ) Flip one of the signals around t = 0 to get either x(-τ) or h(-τ) Best practice is to flip the signal with shorter interval …

## 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 …

## 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 …

## 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 …

## 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 …