CHAPTER-I MICROWAVE TRANSMISSION LINES the Electromagnetic Spectrum Is the Range of All Possible Frequencies of Electromagnetic
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Ec6503 - Transmission Lines and Waveguides Transmission Lines and Waveguides Unit I - Transmission Line Theory 1
EC6503 - TRANSMISSION LINES AND WAVEGUIDES TRANSMISSION LINES AND WAVEGUIDES UNIT I - TRANSMISSION LINE THEORY 1. Define – Characteristic Impedance [M/J–2006, N/D–2006] Characteristic impedance is defined as the impedance of a transmission line measured at the sending end. It is given by 푍 푍0 = √ ⁄푌 where Z = R + jωL is the series impedance Y = G + jωC is the shunt admittance 2. State the line parameters of a transmission line. The line parameters of a transmission line are resistance, inductance, capacitance and conductance. Resistance (R) is defined as the loop resistance per unit length of the transmission line. Its unit is ohms/km. Inductance (L) is defined as the loop inductance per unit length of the transmission line. Its unit is Henries/km. Capacitance (C) is defined as the shunt capacitance per unit length between the two transmission lines. Its unit is Farad/km. Conductance (G) is defined as the shunt conductance per unit length between the two transmission lines. Its unit is mhos/km. 3. What are the secondary constants of a line? The secondary constants of a line are 푍 i. Characteristic impedance, 푍0 = √ ⁄푌 ii. Propagation constant, γ = α + jβ 4. Why the line parameters are called distributed elements? The line parameters R, L, C and G are distributed over the entire length of the transmission line. Hence they are called distributed parameters. They are also called primary constants. The infinite line, wavelength, velocity, propagation & Distortion line, the telephone cable 5. What is an infinite line? [M/J–2012, A/M–2004] An infinite line is a line where length is infinite. -
Frequency Response
EE105 – Fall 2015 Microelectronic Devices and Circuits Frequency Response Prof. Ming C. Wu [email protected] 511 Sutardja Dai Hall (SDH) Amplifier Frequency Response: Lower and Upper Cutoff Frequency • Midband gain Amid and upper and lower cutoff frequencies ωH and ω L that define bandwidth of an amplifier are often of more interest than the complete transferfunction • Coupling and bypass capacitors(~ F) determineω L • Transistor (and stray) capacitances(~ pF) determineω H Lower Cutoff Frequency (ωL) Approximation: Short-Circuit Time Constant (SCTC) Method 1. Identify all coupling and bypass capacitors 2. Pick one capacitor ( ) at a time, replace all others with short circuits 3. Replace independent voltage source withshort , and independent current source withopen 4. Calculate the resistance ( ) in parallel with 5. Calculate the time constant, 6. Repeat this for each of n the capacitor 7. The low cut-off frequency can be approximated by n 1 ωL ≅ ∑ i=1 RiSCi Note: this is an approximation. The real low cut-off is slightly lower Lower Cutoff Frequency (ωL) Using SCTC Method for CS Amplifier SCTC Method: 1 n 1 fL ≅ ∑ 2π i=1 RiSCi For the Common-Source Amplifier: 1 # 1 1 1 & fL ≅ % + + ( 2π $ R1SC1 R2SC2 R3SC3 ' Lower Cutoff Frequency (ωL) Using SCTC Method for CS Amplifier Using the SCTC method: For C2 : = + = + 1 " 1 1 1 % R3S R3 (RD RiD ) R3 (RD ro ) fL ≅ $ + + ' 2π # R1SC1 R2SC2 R3SC3 & For C1: R1S = RI +(RG RiG ) = RI + RG For C3 : 1 R2S = RS RiS = RS gm Design: How Do We Choose the Coupling and Bypass Capacitor Values? • Since the impedance of a capacitor increases with decreasing frequency, coupling/bypass capacitors reduce amplifier gain at low frequencies. -
Feedback Amplifiers
UNIT II FEEDBACK AMPLIFIERS & OSCILLATORS FEEDBACK AMPLIFIERS: Feedback concept, types of feedback, Amplifier models: Voltage amplifier, current amplifier, trans-conductance amplifier and trans-resistance amplifier, feedback amplifier topologies, characteristics of negative feedback amplifiers, Analysis of feedback amplifiers, Performance comparison of feedback amplifiers. OSCILLATORS: Principle of operation, Barkhausen Criterion, types of oscillators, Analysis of RC-phase shift and Wien bridge oscillators using BJT, Generalized analysis of LC Oscillators, Hartley and Colpitts’s oscillators with BJT, Crystal oscillators, Frequency and amplitude stability of oscillators. 1.1 Introduction: Feedback Concept: Feedback: A portion of the output signal is taken from the output of the amplifier and is combined with the input signal is called feedback. Need for Feedback: • Distortion should be avoided as far as possible. • Gain must be independent of external factors. Concept of Feedback: Block diagram of feedback amplifier consist of a basic amplifier, a mixer (or) comparator, a sampler, and a feedback network. Figure 1.1 Block diagram of an amplifier with feedback A – Gain of amplifier without feedback. A = X0 / Xi Af – Gain of amplifier with feedback.Af = X0 / Xs β – Feedback ratio. β = Xf / X0 X is either voltage or current. 1.2 Types of Feedback: 1. Positive feedback 2. Negative feedback 1.2.1 Positive Feedback: If the feedback signal is in phase with the input signal, then the net effect of feedback will increase the input signal given to the amplifier. This type of feedback is said to be positive or regenerative feedback. Xi=Xs+Xf Af = = = Af= Here Loop Gain: The product of open loop gain and the feedback factor is called loop gain. -
Unit I Microwave Transmission Lines
UNIT I MICROWAVE TRANSMISSION LINES INTRODUCTION Microwaves are electromagnetic waves with wavelengths ranging from 1 mm to 1 m, or frequencies between 300 MHz and 300 GHz. Apparatus and techniques may be described qualitatively as "microwave" when the wavelengths of signals are roughly the same as the dimensions of the equipment, so that lumped-element circuit theory is inaccurate. As a consequence, practical microwave technique tends to move away from the discrete resistors, capacitors, and inductors used with lower frequency radio waves. Instead, distributed circuit elements and transmission-line theory are more useful methods for design, analysis. Open-wire and coaxial transmission lines give way to waveguides, and lumped-element tuned circuits are replaced by cavity resonators or resonant lines. Effects of reflection, polarization, scattering, diffraction, and atmospheric absorption usually associated with visible light are of practical significance in the study of microwave propagation. The same equations of electromagnetic theory apply at all frequencies. While the name may suggest a micrometer wavelength, it is better understood as indicating wavelengths very much smaller than those used in radio broadcasting. The boundaries between far infrared light, terahertz radiation, microwaves, and ultra-high-frequency radio waves are fairly arbitrary and are used variously between different fields of study. The term microwave generally refers to "alternating current signals with frequencies between 300 MHz (3×108 Hz) and 300 GHz (3×1011 Hz)."[1] Both IEC standard 60050 and IEEE standard 100 define "microwave" frequencies starting at 1 GHz (30 cm wavelength). Electromagnetic waves longer (lower frequency) than microwaves are called "radio waves". Electromagnetic radiation with shorter wavelengths may be called "millimeter waves", terahertz radiation or even T-rays. -
Wave Guides & Resonators
UNIT I WAVEGUIDES & RESONATORS INTRODUCTION Microwaves are electromagnetic waves with wavelengths ranging from 1 mm to 1 m, or frequencies between 300 MHz and 300 GHz. Apparatus and techniques may be described qualitatively as "microwave" when the wavelengths of signals are roughly the same as the dimensions of the equipment, so that lumped-element circuit theory is inaccurate. As a consequence, practical microwave technique tends to move away from the discrete resistors, capacitors, and inductors used with lower frequency radio waves. Instead, distributed circuit elements and transmission-line theory are more useful methods for design, analysis. Open-wire and coaxial transmission lines give way to waveguides, and lumped-element tuned circuits are replaced by cavity resonators or resonant lines. Effects of reflection, polarization, scattering, diffraction, and atmospheric absorption usually associated with visible light are of practical significance in the study of microwave propagation. The same equations of electromagnetic theory apply at all frequencies. While the name may suggest a micrometer wavelength, it is better understood as indicating wavelengths very much smaller than those used in radio broadcasting. The boundaries between far infrared light, terahertz radiation, microwaves, and ultra-high-frequency radio waves are fairly arbitrary and are used variously between different fields of study. The term microwave generally refers to "alternating current signals with frequencies between 300 MHz (3×108 Hz) and 300 GHz (3×1011 Hz)."[1] Both IEC standard 60050 and IEEE standard 100 define "microwave" frequencies starting at 1 GHz (30 cm wavelength). Electromagnetic waves longer (lower frequency) than microwaves are called "radio waves". Electromagnetic radiation with shorter wavelengths may be called "millimeter waves", terahertz Page 1 radiation or even T-rays. -
Waveguides Waveguides, Like Transmission Lines, Are Structures Used to Guide Electromagnetic Waves from Point to Point. However
Waveguides Waveguides, like transmission lines, are structures used to guide electromagnetic waves from point to point. However, the fundamental characteristics of waveguide and transmission line waves (modes) are quite different. The differences in these modes result from the basic differences in geometry for a transmission line and a waveguide. Waveguides can be generally classified as either metal waveguides or dielectric waveguides. Metal waveguides normally take the form of an enclosed conducting metal pipe. The waves propagating inside the metal waveguide may be characterized by reflections from the conducting walls. The dielectric waveguide consists of dielectrics only and employs reflections from dielectric interfaces to propagate the electromagnetic wave along the waveguide. Metal Waveguides Dielectric Waveguides Comparison of Waveguide and Transmission Line Characteristics Transmission line Waveguide • Two or more conductors CMetal waveguides are typically separated by some insulating one enclosed conductor filled medium (two-wire, coaxial, with an insulating medium microstrip, etc.). (rectangular, circular) while a dielectric waveguide consists of multiple dielectrics. • Normal operating mode is the COperating modes are TE or TM TEM or quasi-TEM mode (can modes (cannot support a TEM support TE and TM modes but mode). these modes are typically undesirable). • No cutoff frequency for the TEM CMust operate the waveguide at a mode. Transmission lines can frequency above the respective transmit signals from DC up to TE or TM mode cutoff frequency high frequency. for that mode to propagate. • Significant signal attenuation at CLower signal attenuation at high high frequencies due to frequencies than transmission conductor and dielectric losses. lines. • Small cross-section transmission CMetal waveguides can transmit lines (like coaxial cables) can high power levels. -
Wave Guides Summary and Problems
ECE 144 Electromagnetic Fields and Waves Bob York General Waveguide Theory Basic Equations (ωt γz) Consider wave propagation along the z-axis, with fields varying in time and distance according to e − . The propagation constant γ gives us much information about the character of the waves. We will assume that the fields propagating in a waveguide along the z-axis have no other variation with z,thatis,the transverse fields do not change shape (other than in magnitude and phase) as the wave propagates. Maxwell’s curl equations in a source-free region (ρ =0andJ = 0) can be combined to give the wave equations, or in terms of phasors, the Helmholtz equations: 2E + k2E =0 2H + k2H =0 ∇ ∇ where k = ω√µ. In rectangular or cylindrical coordinates, the vector Laplacian can be broken into two parts ∂2E 2E = 2E + ∇ ∇t ∂z2 γz so that with the assumed e− dependence we get the wave equations 2E +(γ2 + k2)E =0 2H +(γ2 + k2)H =0 ∇t ∇t (ωt γz) Substituting the e − into Maxwell’s curl equations separately gives (for rectangular coordinates) E = ωµH H = ωE ∇ × − ∇ × ∂Ez ∂Hz + γEy = ωµHx + γHy = ωEx ∂y − ∂y ∂Ez ∂Hz γEx = ωµHy γHx = ωEy − − ∂x − − − ∂x ∂Ey ∂Ex ∂Hy ∂Hx = ωµHz = ωEz ∂x − ∂y − ∂x − ∂y These can be rearranged to express all of the transverse fieldcomponentsintermsofEz and Hz,giving 1 ∂Ez ∂Hz 1 ∂Ez ∂Hz Ex = γ + ωµ Hx = ω γ −γ2 + k2 ∂x ∂y γ2 + k2 ∂y − ∂x w W w W 1 ∂Ez ∂Hz 1 ∂Ez ∂Hz Ey = γ + ωµ Hy = ω + γ γ2 + k2 − ∂y ∂x −γ2 + k2 ∂x ∂y w W w W For propagating waves, γ = β,whereβ is a real number provided there is no loss. -
Uniform Plane Waves
38 2. Uniform Plane Waves Because also ∂zEz = 0, it follows that Ez must be a constant, independent of z, t. Excluding static solutions, we may take this constant to be zero. Similarly, we have 2 = Hz 0. Thus, the fields have components only along the x, y directions: E(z, t) = xˆ Ex(z, t)+yˆ Ey(z, t) Uniform Plane Waves (transverse fields) (2.1.2) H(z, t) = xˆ Hx(z, t)+yˆ Hy(z, t) These fields must satisfy Faraday’s and Amp`ere’s laws in Eqs. (2.1.1). We rewrite these equations in a more convenient form by replacing and μ by: 1 η 1 μ = ,μ= , where c = √ ,η= (2.1.3) ηc c μ Thus, c, η are the speed of light and characteristic impedance of the propagation medium. Then, the first two of Eqs. (2.1.1) may be written in the equivalent forms: ∂E 1 ∂H ˆz × =− η 2.1 Uniform Plane Waves in Lossless Media ∂z c ∂t (2.1.4) ∂H 1 ∂E The simplest electromagnetic waves are uniform plane waves propagating along some η ˆz × = ∂z c ∂t fixed direction, say the z-direction, in a lossless medium {, μ}. The assumption of uniformity means that the fields have no dependence on the The first may be solved for ∂zE by crossing it with ˆz. Using the BAC-CAB rule, and transverse coordinates x, y and are functions only of z, t. Thus, we look for solutions noting that E has no z-component, we have: of Maxwell’s equations of the form: E(x, y, z, t)= E(z, t) and H(x, y, z, t)= H(z, t). -
Lab 4: Prelab
ECE 445 Biomedical Instrumentation rev 2012 Lab 8: Active Filters for Instrumentation Amplifier INTRODUCTION: In Lab 6, a simple instrumentation amplifier was implemented and tested. Lab 7 expanded upon the instrumentation amplifier by improving circuit performance and by building a LabVIEW user interface. This lab will complete the design of your biomedical instrument by introducing a filter into the circuit. REQUIRED PARTS AND MATERIALS: Materials Needed 1) Instrumentation amplifier from Lab 7 2) Results from Prelab 3) Oscilloscope 4) Function Generator 5) DC Power Supply 6) Labivew Software 7) Data Acquisition Board 8) Resistors 9) Capacitors 10) Dual operational amplifier (UA747) PRELAB: 1. Print the Prelab and Lab8 Grading Sheets. Answer all of the questions in the Prelab Grading Sheet and bring the Lab8 Grading Sheet with you when you come to lab. The Prelab Grading Sheet must be turned in to the TA before beginning your lab assignment. 2. Read the LABORATORY PROCEDURE before coming to lab. Note: you are not required to print the lab procedure; you can view it on the PC at your lab bench. 3. For further reading consult class notes, text book and see Low Pass Filters http://www.electronics-tutorials.ws/filter/filter_2.html High Pass Filters http://www.electronics-tutorials.ws/filter/filter_3.html BACKGROUND: Active Filters As their name implies, Active Filters contain active components such as operational amplifiers or transistors within their design. They draw their power from an external power source and use it to boost or amplify the output signal. Operational amplifiers can also be used to shape or alter the frequency response of the circuit by producing a more selective output response by making the output bandwidth of the filter more narrow or even wider. -
DETERMINATION of the APPROPRIATE CUTOFF FREQUENCY in the DIGITAL FILTER DATA SMOOTHING PROCEDURE By
'DETERMINATION OF THE APPROPRIATE CUTOFF FREQUENCY IN THE DIGITAL FILTER DATA SMOOTHING PROCEDURE by BING YU B.S., Peking Institute of Physical Education, 1982 A MASTER'S THESIS Submitted in partial fulfillment of the requirements for the degree MASTER OF SCIENCE Department of Physical Education and Leisure Studies KANSAS STATE UNIVERSITY 1988 Approved by: Major Professo 3# AllSDfl 5327b7 ']cl ACKNOWLEDGEMENTS The author wishes to acknowledge the assistance and support of the entire graduate faculty of Kansas State University's Department of Physical Education and Leisure Studies. Special thanks go to committee members Dr. Stephan Konz and Dr. Kathleen Williams for their unique perspectives and editorial assistance. Most of all, I would like to thank my major professor, Dr. Larry Noble, for his integrity, his enthusiasm for knowledge, and the tremendous amount of time and assistance he has given me over the past two years. 11 DEDICATION This thesis is dedicated to my parents, Dr. Gou-Rei Yu and Ming-Hua Lu, to my wife Wei Li, to her parents, Dr. Ping Li and Dr. Xiu-Zhang Yu, and to all of the other folks of my family and her family for their understanding of my absence when my son Charlse Alan Yu was born. Their constant support and encouragement are deeply appreciated. 111 . CONTENTS ACKNOWLEDGMENTS ii DEDICATION iii LIST OF FIGURES vi LIST OF TABLES ix Chapter 1 INTRODUCTION 1 Statement Of The Problem 2 Definitions 3 2 REVIEW OF RELATED LITERATURE 7 The Nature Of Errors 7 Sources Of Errors 10 Data Smoothing Techniques Used In Sport Biomechanics 15 Finite difference technique 15 Least square polynomial approxination. -
CP27 Solution
Electric Circuits Prof. Shayla Sawyer Spring 2015 ECSE 2010 CP27 solution 1) Bode plots/Transfer functions a. Draw magnitude and phase bode plots for the transfer function s⋅() s+ 100 H s()= 0.01 ⋅ ()s+ 1E4 In your magnitude plot, indicate corrections at the poles and zeros. Step 1: Find poles, zeros Zeros: 0, 100 Poles: 1E4 Step 2: Define regions and find either H(j ω) or H(s) 100⋅ 0.01 − 4 = 1× 10 ⋅ 4 s< 100 1 10 0.01⋅ s⋅100 − 4 − 4 H s() = = 1⋅ 10 s +20db/dec slope 100⋅ 1⋅10 = 0.01 4 1⋅ 10 slope ends at 20⋅ log 0.01() −= 40 4 0.01 − 6 100< s < 10 = 1× 10 4 1⋅ 10 0.01⋅ s⋅s − 6 2 H s() = = 1⋅ 10 s 4 +40 db/dec slope 1⋅ 10 2 − 6 4 20log 10 ⋅()1⋅ 10 = 40 4 s> 10 0.01⋅ s⋅s +20db/dec H s() = = 0.01s s slope Step 3: Make corrections Correction at 100 is +3db because it is a ZERO^1! Correction at 10^4 is -3db because it is a POLE^1! 1 Electric Circuits Prof. Shayla Sawyer Spring 2015 ECSE 2010 CP27 solution s2 H ()s = 10 (s +100 )(s +10000 ) Phase plots 0.1 ωc1 = 10 ω = 10 j10⋅() j10+ 100 ∠ 0⋅ ∠90() ∠0() ∠H j10()= 0.01 ⋅ ∠ 90 ()10j+ 1E4 ∠0 ∠0 + ∠90 + ∠0 − ∠0 ⋅ 3 10 ωc1 = 10 3 ω = 10 3 3 3 j10 ⋅()j10 + 100 ∠ 0⋅ ∠90() ∠90() ∠H() j10 = 0.01 ⋅ ∠ 180 3 ∠0 ()10 j+ 1E4 ∠0 + ∠90 + ∠90 − ∠0 180− 45 = 135 2 Electric Circuits Prof. -
Microstrip Solutions for Innovative Microwave Feed Systems
Examensarbete LiTH-ITN-ED-EX--2001/05--SE Microstrip Solutions for Innovative Microwave Feed Systems Magnus Petersson 2001-10-24 Department of Science and Technology Institutionen för teknik och naturvetenskap Linköping University Linköpings Universitet SE-601 74 Norrköping, Sweden 601 74 Norrköping LiTH-ITN-ED-EX--2001/05--SE Microstrip Solutions for Innovative Microwave Feed Systems Examensarbete utfört i Mikrovågsteknik / RF-elektronik vid Tekniska Högskolan i Linköping, Campus Norrköping Magnus Petersson Handledare: Ulf Nordh Per Törngren Examinator: Håkan Träff Norrköping den 24 oktober, 2001 'DWXP $YGHOQLQJ,QVWLWXWLRQ Date Division, Department Institutionen för teknik och naturvetenskap 2001-10-24 Ã Department of Science and Technology 6SUnN 5DSSRUWW\S ,6%1 Language Report category BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB Svenska/Swedish Licentiatavhandling X Engelska/English X Examensarbete ISRN LiTH-ITN-ED-EX--2001/05--SE C-uppsats 6HULHWLWHOÃRFKÃVHULHQXPPHUÃÃÃÃÃÃÃÃÃÃÃÃ,661 D-uppsats Title of series, numbering ___________________________________ _ ________________ Övrig rapport _ ________________ 85/I|UHOHNWURQLVNYHUVLRQ www.ep.liu.se/exjobb/itn/2001/ed/005/ 7LWHO Microstrip Solutions for Innovative Microwave Feed Systems Title )|UIDWWDUH Magnus Petersson Author 6DPPDQIDWWQLQJ Abstract This report is introduced with a presentation of fundamental electromagnetic theories, which have helped a lot in the achievement of methods for calculation and design of microstrip transmission lines and circulators. The used software for the work is also based on these theories. General considerations when designing microstrip solutions, such as different types of transmission lines and circulators, are then presented. Especially the design steps for microstrip lines, which have been used in this project, are described. Discontinuities, like bends of microstrip lines, are treated and simulated.