MatLAB Transfer Functions, Bode Plots, and Complex Numbers.

Slides:



Advertisements
Similar presentations
Since Therefore Since.
Advertisements

Complex Numbers in Engineering (Chapter 5 of Rattan/Klingbeil text)
Lecture 1 Matlab Exercise
A synthetic noise generator M. Hueller LTPDA meeting, AEI Hannover 27/04/2007.
Complex Numbers.
Fundamentals of Electric Circuits Chapter 14 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Describing the graph of a Parabola
Flow Charts, Loop Structures
Frequency Response Methods and Stability
Systems: Definition Filter
1 ECE 3336 Introduction to Circuits & Electronics Note Set #12 Frequency Response More About Filters Spring 2015, TUE&TH 5:30-7:00 pm Dr. Wanda Wosik.
Out response, Poles, and Zeros
Active Filters. This is not in the lab manual While the circuit that will be used is very similar to the one described in the lab manual, the steps in.
Circuits II EE221 Unit 3 Instructor: Kevin D. Donohue Instantaneous, Average, RMS, and Apparent Power, and, Maximum Power Transfer, and Power Factors.
RC Filters B. Furman 02SEP2014. Mechatronics Concept Map System to Control Sensor Signal Conditioning Controller (Hardware & Software) Power Interface.
Chapter 14 Frequency Response
Motivation Music as a combination of sounds at different frequencies
Introduction to Engineering MATLAB – 1 Introduction to MATLAB Agenda Introduction Arithmetic Operations MATLAB Windows Command Window Defining Variables.
9.9 The Fundamental Theorem of Algebra
Matlab Basics Tutorial. Vectors Let's start off by creating something simple, like a vector. Enter each element of the vector (separated by a space) between.
Circuits II EE221 Unit 4 Instructor: Kevin D. Donohue
Study Guide Final. Closed book/Closed notes Bring a calculator or use a mathematical program on your computer The length of the exam is the standard 2.
5.4 Complex Numbers. Let’s see… Can you find the square root of a number? A. E.D. C.B.
Recap Sum and Product Functions Matrix Size Function Variance and Standard Deviation Random Numbers Complex Numbers.
EE 1270 Introduction to Electric Circuits Suketu Naik 0 EE 1270: Introduction to Electric Circuits Lecture 17: 1) Sinusoidal Source 2) Complex Numbers.
Unit 8 Phasors.
Eigenvalues The eigenvalue problem is to determine the nontrivial solutions of the equation Ax= x where A is an n-by-n matrix, x is a length n column.
BY: MARIAH & JON 13.4 INVERSE OF SINE AND TANGENT.
© The McGraw-Hill Companies, Inc McGraw-Hill 1 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I C.
All materials are taken from “Fundamentals of electric circuits”
FILTERS. Filter The purpose of a filter is to pass signals of certain frequencies,
Lecture 7: First Order Filter and Bode Plot
Frequency Response Analysis and Stability
 5-9 Complex Numbers Objective: Students will be able to add, subtract, multiply, and divide complex numbers.
Phasors and Kirchhoff’s Current Law
5-7: COMPLEX NUMBERS Goal: Understand and use complex numbers.
ChE 182 Chemical Process Dynamics and Control
Root Locus Method. Root Locus Method Root Locus Method.
Simulated Inductance Experiment 25.
11.4 Roots of Complex Numbers
G(s) Input (sinusoid) Time Output Ti me InputOutput A linear, time-invariant single input and single output (SISO) system. The input to this system is.
How do I use the imaginary unit i to write complex numbers?
Aim: What is the complex number? Do Now: Solve for x: 1. x 2 – 1 = 0 2. x = 0 3. (x + 1) 2 = – 4 Homework: p.208 # 6,8,12,14,16,44,46,50.
ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Fourth Edition, by Allan R. Hambley, ©2008 Pearson Education, Inc. Lecture 18 Bode Plot, High Pass.
Variable-Frequency Response Analysis Network performance as function of frequency. Transfer function Sinusoidal Frequency Analysis Bode plots to display.
6.6 – Complex Numbers Complex Number System: This system of numbers consists of the set of real numbers and the set of imaginary numbers. Imaginary Unit:
UTN synthetic noise generator M. Hueller LTPDA meeting, Barcelona 26/06/2007.
Lesson 20: Process Characteristics- 2nd Order Lag Process
Lesson 15: Bode Plots of Transfer Functions
Speech Signal Processing
ECE 1304 Introduction to Electrical and Computer Engineering
Network Analysis and Synthesis
Chapter 3: Frequency Response of AC Circuit Sem2 2015/2016
Chapter 4 MATLAB Programming
Filters: Intuitive Understanding
Simulink A Simple Intro.
Methods of Determining Stability
Imaginary Numbers.
Sinusoids: continuous time
RC Filters B. Furman 09FEB2016.
Fundamentals of Electric Circuits Chapter 14
Objectives Student will learn how to define and use imaginary and complex numbers.
Introduction to MATLAB
The instantaneous power
Example Combination of Systems Transfer Function:
Matlab Basics Tutorial
Complex Numbers in Engineering (Chapter 5 of Rattan/Klingbeil text)
7.7 Complex Numbers.
Methods of Determining Stability
Presentation transcript:

MatLAB Transfer Functions, Bode Plots, and Complex Numbers

Defining a Vector Three elements t=[0,.1,3] or t=[0.1 3] t = Four Elements t=[0:3] t = Elements that include 0, then 0.1, and then increments of 1 until it reaches the largest number ≤ 3 t=[0,.1:3] t = Thirty one elements between 0 and 3 in increments of 0.1 t=[0:.1:3] t =

MatLAB Suppose you have determined that the transfer function for your filter is: You can put this transfer function into MatLAB – Define two vectors A = [A n, A n-1, ….., A 1, A 0 ] where n, m ≥ 0 and B = [B m, B m-1, ….., B 1, B 0 ] n does not have to equal m – H = tf(A,B)

Example High pass filter with a single-pole/single-zero Let RC = 10 4 s/rad – A = [0, 10e3] – B = [1 10e3] – H = tf(A,B) 10000s H = is returned when you run the program 10000s + 1

MatLAB: Bode Plots Once you have entered the transfer function into MatLAB, you can use a predefined function ‘bode’ to automatically generate plots of the magnitude and phase vs. frequency. Enter: bode(H)

Bode Plot Parameters

Complex Numbers The default symbol for √-1 is i. However, MatLAB does recognize that j is equivalent to i. – The coefficient of the imaginary number must be placed before the ‘i’ or ‘j’. If you typed c = 2-3j, MatLAB interprets it as c = i – To find components of complex number real(c) returns 2 imag(c) returns -3

Magnitude and Phase Magnitude of a complex number – Is the square root of the square of the real component plus the square of the imaginary component Phase of a complex number – Is the arc tangent of the imaginary component divided by the real component Must change to degrees if the output of the arc tangent is given in radians