Smith Chart Calculations
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Smith Chart Tutorial
Frank Lynch, W4FAL Smith Charts Frank A. Lynch W 4FA L Page 1 24 April 2008 “SCARS” http://smithchart.org Frank Lynch, W4FAL Smith Chart History • Invented by Phillip H. Smith in 1939 • Used to solve a variety of transmission line and waveguide problems Basic Uses For evaluating the rectangular components, or the magnitude and phase of an input impedance or admittance, voltage, current, and related transmission functions at all points along a transmission line, including: • Complex voltage and current reflections coefficients • Complex voltage and current transmission coefficents • Power reflection and transmission coefficients • Reflection Loss • Return Loss • Standing Wave Loss Factor • Maximum and minimum of voltage and current, and SWR • Shape, position, and phase distribution along voltage and current standing waves Page 2 24 April 2008 Frank Lynch, W4FAL Basic Uses (continued) For evaluating the effects of line attenuation on each of the previously mentioned parameters and on related transmission line functions at all positions along the line. For evaluating input-output transfer functions. Page 3 24 April 2008 Frank Lynch, W4FAL Specific Uses • Evaluating input reactance or susceptance of open and shorted stubs. • Evaluating effects of shunt and series impedances on the impedance of a transmission line. • For displaying and evaluating the input impedance characteristics of resonant and anti-resonant stubs including the bandwidth and Q. • Designing impedance matching networks using single or multiple open or shorted stubs. • Designing impedance matching networks using quarter wave line sections. • Designing impedance matching networks using lumped L-C components. • For displaying complex impedances verses frequency. • For displaying s-parameters of a network verses frequency. -
W5GI MYSTERY ANTENNA (Pdf)
W5GI Mystery Antenna A multi-band wire antenna that performs exceptionally well even though it confounds antenna modeling software Article by W5GI ( SK ) The design of the Mystery antenna was inspired by an article written by James E. Taylor, W2OZH, in which he described a low profile collinear coaxial array. This antenna covers 80 to 6 meters with low feed point impedance and will work with most radios, with or without an antenna tuner. It is approximately 100 feet long, can handle the legal limit, and is easy and inexpensive to build. It’s similar to a G5RV but a much better performer especially on 20 meters. The W5GI Mystery antenna, erected at various heights and configurations, is currently being used by thousands of amateurs throughout the world. Feedback from users indicates that the antenna has met or exceeded all performance criteria. The “mystery”! part of the antenna comes from the fact that it is difficult, if not impossible, to model and explain why the antenna works as well as it does. The antenna is especially well suited to hams who are unable to erect towers and rotating arrays. All that’s needed is two vertical supports (trees work well) about 130 feet apart to permit installation of wire antennas at about 25 feet above ground. The W5GI Multi-band Mystery Antenna is a fundamentally a collinear antenna comprising three half waves in-phase on 20 meters with a half-wave 20 meter line transformer. It may sound and look like a G5RV but it is a substantially different antenna on 20 meters. -
A Polarization Approach to Determining Rotational Angles of a Mortar
A POLARIZATION APPROACH TO DETERMINING ROTATIONAL ANGLES OF A MORTAR by Muhammad Hassan Chishti A thesis submitted to the Faculty of the University of Delaware in partial fulfillment of the requirements for the degree of Master of Science in Electrical and Computer Engineering Summer 2010 Copyright 2010 Muhammad Chishti All Rights Reserved A POLARIZATION APPROACH TO DETERMINING ROTATIONAL ANGLES OF A MORTAR by Muhammad Hassan Chishti Approved: __________________________________________________________ Daniel S. Weile, Ph.D Professor in charge of thesis on behalf of the Advisory Committee Approved: __________________________________________________________ Kenneth E. Barner, Ph.D Chair of the Department Electrical and Computer Engineering Approved: __________________________________________________________ Michael J. Chajes, Ph.D Dean of the College of Engineering Approved: __________________________________________________________ Debra Hess Norris, M.S Vice Provost for Graduate and Professional Education This thesis is dedicated to, My Sheikh Hazrat Maulana Mufti Muneer Ahmed Akhoon Damat Barakatuhum My Father Muhammad Hussain Chishti My Mother Shahida Chishti ACKNOWLEDGMENTS First and foremost, my all praise and thanks be to the Almighty Allah, The Beneficent, Most Gracious, and Most Merciful. Without His mercy and favor I would have been an unrecognizable speck of dust. I am exceedingly thankful to my advisor Professor Daniel S. Weile. It is through his support, guidance, generous heart, and mentorship that steered me through this Masters Thesis. Definitely one of the smartest people I have ever had the fortune of knowing and working. I am really indebted to him for all that. I would like to thank the Army Research Labs (ARL) in Aberdeen, MD for providing me the funding support to perform the research herein. -
Smith Chart Examples
SMITH CHART EXAMPLES Dragica Vasileska ASU Smith Chart for the Impedance Plot It will be easier if we normalize the load impedance to the characteristic impedance of the transmission line attached to the load. Z z = = r + jx Zo 1+ Γ z = 1− Γ Since the impedance is a complex number, the reflection coefficient will be a complex number Γ = u + jv 2 2 2v 1− u − v x = r = 2 2 ()1− u 2 + v2 ()1− u + v Real Circles 1 Im {Γ} 0.5 r=0 r=1/3 r=1 r=2.5 1 0.5 0 0.5 1 Re {Γ} 0.5 1 Imaginary Circles Im 1 {Γ} x=1/3 x=1 x=2.5 0.5 Γ 1 0.5 0 0.5 1 Re { } x=-1/3 x=-1 x=-2.5 0.5 1 Normalized Admittance Y y = = YZ o = g + jb Yo 1− Γ y = 1+ Γ 2 1− u 2 − v2 g 1 u + + v2 = g = 2 ()1+ u 2 + v2 1+ g ()1+ g − 2v 2 b = 2 1 1 2 2 ()u +1 + v + = ()1+ u + v b b2 These are equations for circles on the (u,v) plane Real admittance 1 Im {Γ} 0.5 g=2.5 g=1 g=1/3 1 0.5 0 0.5Re {Γ} 1 0.5 1 Complex Admittance 1 Im {Γ} b=-1 b=-1/3 b=-2.5 0.5 1 0.5 0 0.5Re {Γ 1} b=2.5 b=1/3 0.5 b=1 1 Matching • For a matching network that contains elements connected in series and parallel, we will need two types of Smith charts – impedance Smith chart – admittance Smith Chart • The admittance Smith chart is the impedance Smith chart rotated 180 degrees. -
Smith Chart • Smith Chart Was Developed by P
Smith Chart • Smith Chart was developed by P. Smith at the Bell Lab in 1939 • Smith Chart provides an very useful way of visualizing the transmission line phenomenon and matching circuits. • In this slide, for convenience, we assume the normalized impedance is 50 Ohm. Smith Chart and Reflection coefficient Smith Chart is a polar plot of the voltage reflection coefficient, overlaid with impedance grid. So, you can covert the load impedance to reflection coefficient and vice versa. Smith Chart and impedance Examples: The upper half of the smith chart is for inductive impedance. The lower half of the is for capacitive impedance. Constant Resistance Circle This produces a circle where And the impedance on this circle r = 1 with different inductance (upper circle) and capacitance (lower circle) More on Constant Impedance Circle The circles for normalized rT = 0.2, 0.5, 1.0, 2.0 and 5.0 with Constant Inductance/Capacitance Circle Similarly, if xT is hold unchanged and vary the rT You will get the constant Inductance/capacitance circles. Constant Conductance and Susceptance Circle Reflection coefficient in term of admittance: And similarly, We can draw the constant conductance circle (red) and constant susceptance circles(blue). Example 1: Find the reflection coefficient from input impedance Example1: Find the reflection coefficient of the load impedance of: Step 1: In the impedance chart, find 1+2j. Step 2: Measure the distance from (1+2j) to the Origin w.r.t. radius = 1, which is read 0.7 Step 3: Find the angle, which is read 45° Now if we use the formula to verify the result. -
Impedance Matching
Impedance Matching Advanced Energy Industries, Inc. Introduction The plasma industry uses process power over a wide range of frequencies: from DC to several gigahertz. A variety of methods are used to couple the process power into the plasma load, that is, to transform the impedance of the plasma chamber to meet the requirements of the power supply. A plasma can be electrically represented as a diode, a resistor, Table of Contents and a capacitor in parallel, as shown in Figure 1. Transformers 3 Step Up or Step Down? 3 Forward Power, Reflected Power, Load Power 4 Impedance Matching Networks (Tuners) 4 Series Elements 5 Shunt Elements 5 Conversion Between Elements 5 Smith Charts 6 Using Smith Charts 11 Figure 1. Simplified electrical model of plasma ©2020 Advanced Energy Industries, Inc. IMPEDANCE MATCHING Although this is a very simple model, it represents the basic characteristics of a plasma. The diode effects arise from the fact that the electrons can move much faster than the ions (because the electrons are much lighter). The diode effects can cause a lot of harmonics (multiples of the input frequency) to be generated. These effects are dependent on the process and the chamber, and are of secondary concern when designing a matching network. Most AC generators are designed to operate into a 50 Ω load because that is the standard the industry has settled on for measuring and transferring high-frequency electrical power. The function of an impedance matching network, then, is to transform the resistive and capacitive characteristics of the plasma to 50 Ω, thus matching the load impedance to the AC generator’s impedance. -
Beyond the Smith Chart
IMAGE LICENSED BY GRAPHIC STOCK Beyond the Smith Chart Eli Bloch and Eran Socher he topic of impedance transformation and Since CMOS technology was primarily and ini- matching is one of the well-established tially developed for digital purposes, the lack of and essential aspects of microwave engi- high-quality passive components made it practically neering. A few decades ago, when discrete useless for RF design. The device speed was also radio-frequency (RF) design was domi- far inferior to established III-V technologies such as Tnant, impedance matching was mainly performed us- GaAs heterojunction bipolar transistors (HBTs) and ing transmission-lines techniques that were practical high-electron mobility transistors (HEMTs). The first due to the relatively large design size. As microwave RF CMOS receiver was constructed at 1989 [1], but design became possible using integrated on-chip com- it would take another several years for a fully inte- ponents, area constraints made LC- section match- grated CMOS RF receiver to be presented. The scal- ing (using lumped passive elements) more practical ing trend of CMOS in the past two decades improved than transmission line matching. Both techniques are the transistors’ speed exponentially, which provided conveniently visualized and accomplished using the more gain at RF frequencies and also enabled opera- well-known graphical tool, the Smith chart. tion at millimeter-wave (mm-wave) frequencies. The Eli Bloch ([email protected]) is with the Department of Electrical Engineering, Technion— Israel Institute of Technology, Haifa 32000, Israel. Eran Socher ([email protected]) is with the School of Electrical Engineering, Tel-Aviv University, 69978, Israel. -
The DBJ-1: a VHF-UHF Dual-Band J-Pole
By Edison Fong, WB6IQN The DBJ-1: A VHF-UHF Dual-Band J-Pole Searching for an inexpensive, high-performance dual-band base antenna for VHF and UHF? Build a simple antenna that uses a single feed line for less than $10. wo-meter antennas are small com- dipole because it is end fed; this results antenna on my roof since 1992 and it has pared to those for the lower fre- in virtually no disruption to the radiation been problem-free in the San Francisco Tquency bands, and the availability pattern by the feed line. fog. of repeaters on this band greatly extends The basic configuration of the ribbon the range of lightweight low power The Conventional J-Pole J-Pole is shown in Figure 1. The dimen- handhelds and mobile stations. One of the I was introduced to the twinlead ver- sions are shown for 2 meters. This design most popular VHF and UHF base station sion of the J-Pole in 1990 by my long-time was also discussed by KD6GLF in QST.1 antennas is the J-Pole. friend, Dennis Monticelli, AE6C, and I That antenna presented dual-band reso- The J-Pole has no ground radials and was intrigued by its simplicity and high nance, operating well at 2 meters but with it is easy to construct using inexpensive performance. One can scale this design to a 6-7 dB deficit in the horizontal plane at materials. For its simplicity and small size, one-third size and also use it on UHF. UHF when compared to a dipole. -
Design and Fabrication of a Micro-Strip Antenna for Wi-Max Applications
MEE08:29 DESIGN AND FABRICATION OF A MICRO-STRIP ANTENNA FOR WI-MAX APPLICATIONS Tulha Moaiz Yazdani Munawar Islam This thesis is presented as part of Degree of Master of Science in Electrical Engineering Blekinge Institute of Technology October 2008 Blekinge Institute of Technology School of Engineering Department: Signal Processing Supervisor: Dr. Mats Pettersson Examiner: Dr. Mats Pettersson - ii - UAbstract Worldwide Interoperability for Microwave Access (Wi-Max) is a broadband technology enabling the delivery of last mile (final leg of delivering connectivity from a communication provider to customer) wireless broadband access (alternative to cable and DSL). It should be easy to deploy and cheaper to user compared to other technologies. Wi-Max could potentially erase the suburban and rural blackout areas with no broadband Internet access by using an antenna with high gain and reasonable bandwidth Microstrip patch antennas are very popular among Local Area Network (LAN), Metropolitan Area Network (MAN), Wide Area Network (WAN) technologies due to their advantages such as light weight, low volume, low cost, compatibility with integrated circuits and easy to install on rigid surface. The aim is to design and fabricate a Microstrip antenna operating at 3.5GHz to achieve maximum bandwidth for Wi-Max applications. The transmission line model is used for analysis. S-parameters (S11 and S21) are measured for the fabricated Microstrip antenna using network analyzer in a lab environment. The fabricated single patch antenna brings out greater bandwidth than conventional high frequency patch antenna. The developed antenna also is found to have reasonable gain. - iii - - iv - UAcknowledgement It is a great pleasure to express our deep and sincere gratitude to our supervisor Dr. -
36 Smith Chart and VSWR
36 Smith Chart and VSWR Generator Transmission line I d ( ) Wire 2 + Load Z + g V d Zo • Consider the general phasor expressions - ( ) ZL F = Vg - Wire 1 l d V +ejβd(1 − Γ e−j2βd) 0 + jβd −j2βd L |V (d)|max V (d)=V e (1 + ΓLe ) and I(d)= |V (d)| Zo describing the voltage and current variations on TL’s in sinusoidal |V (d)|min dmax steady-state. dmin – Complex addition displayed Unless ΓL =0,thesephasorscontainreflectedcomponents,which graphically superposed on a means that voltage and current variations on the line “contain” Smith Chart standing waves. SmithChart 1 .5 2 In that case the phasors go through cycles of magnitude variations as a function of d,andinthevoltagemagnitudeinparticular(seemargin) .2 z(dmaxx!5) ( d) Γ(d) varying as 1+Γ =VSWR .2 .5 1 2 r!5 + −j2βd + 0 VSWR |V (d)| = |V ||1+ΓLe | = |V ||1+Γ(d)| 1 Γ(dmax)=|ΓL| takes maximum and minimum values of ".2 x!"5 + + |V (d)|max = |V |(1 + |ΓL|) and |V (d)|min = |V |(1 −|ΓL|) ".5 "2 "1 at locations d = dmax and dmin such that |1+Γ(d)| maximizes for d = dmax −j2βdmax −j2βdmin Γ(dmax)=ΓLe = |ΓL| and Γ(dmin)=ΓLe = −|ΓL|, |1+Γ(d)| minimizes for d = dmin and such that Γ(dmin)=−Γ(dmax) λ d − d is an odd multiple of . max min 4 1 Generator Transmission line I d – These results can be most easily understood and verified graphi- ( ) Wire 2 + Load cally on a SC as shown in the margin. + Zg Z - V (d) o ZL F = Vg - Wire 1 l d • We define a parameter known as voltage standing wave ratio,or 0 |V (d)|max VSWR for short, by |V (d)| |V (d)|min dmax |V (dmax)| 1+|ΓL| VSWR − 1 VSWR ≡ = ⇔|ΓL| = . -
Electronic Science Electrodynamics and Microwaves 17. Stub Matching
1 Module 17 Stub Matching Technique in Transmission Lines 1. Introduction 2. Concept of matching stub 3. Mathematical Basis for Single shunt stub matching 4 .Designing of single stub using Smith chart 5. Series single stub 6. Concept of Double stub matching 7. Mathematical Basis for Double Stub Matching 8. Design of Double stub using Smith Chart: 9. Summary Objectives After completing this module, you will be able to 1. Understand the concept of matching stub and different types of it. 2. Understand the mathematical principle behind the stub matching technique. 3. Design single stub and double stub using Smith chart. 4. Know about advantages and limitations of stub matching technique. Electrodynamics and Microwaves Electronic Science 17. Stub Matching Technique in Transmission Lines 2 1. Introduction In the earlier modules , we have discussed about how matching networks and QWT can be used for matching the load impedance with the lossless transmission line. Both these techniques suffer from some drawbacks .Especially the losses like, insertion loss, mismatch loss are of much more prominent losses. There is another technique known as “Stub Matching Technique” to match the load impedance with the Characteristic impedance of the given transmission line so as to have zero reflection coefficient. The technique is marvelous and the designing can be done using Smith chart in a very simple way. Let us discuss it with adequate details rather qualitatively avoiding mathematical rigor in it. 2. Concept of Matching Stub A section of a transmission line having small length is called as a stub. Two types’ namely single stub and double stub comprising of one or two stubs are in common use. -
ANTENNA THEORY Analysis and Design CONSTANTINE A
ANTENNA THEORY Analysis and Design CONSTANTINE A. BALANIS Arizona State University JOHN WILEY & SONS New York • Chichester • Brisbane • Toronto • Singapore Contents Preface xv Chapter 1 Antennas 1 1.1 Introduction 1 1.2 Types of Antennas 1 Wire Antennas; Aperture Antennas; Array Antennas; Reflector Antennas; Lens Antennas 1.3 Radiation Mechanism 7 1.4 Current Distribution on a Thin Wire Antenna 11 1.5 Historical Advancement 15 References 15 Chapter 2 Fundamental Parameters of Antennas 17 2.1 Introduction 17 2.2 Radiation Pattern 17 Isotropic, Directional, and Omnidirectional Patterns; Principal Patterns; Radiation Pattern Lobes; Field Regions; Radian and Steradian vii viii CONTENTS 2.3 Radiation Power Density 25 2.4 Radiation Intensity 27 2.5 Directivity 29 2.6 Numerical Techniques 37 2.7 Gain 42 2.8 Antenna Efficiency 44 2.9 Half-Power Beamwidth 46 2.10 Beam Efficiency 46 2.11 Bandwidth 47 2.12 Polarization 48 Linear, Circular, and Elliptical Polarizations; Polarization Loss Factor 2.13 Input Impedance 53 2.14 Antenna Radiation Efficiency 57 2.15 Antenna as an Aperture: Effective Aperture 59 2.16 Directivity and Maximum Effective Aperture 61 2.17 Friis Transmission Equation and Radar Range Equation 63 Friis Transmission Equation; Radar Range Equation 2.18 Antenna Temperature 67 References 70 Problems 71 Computer Program—Polar Plot 75 Computer Program—Linear Plot 78 Computer Program—Directivity 80 Chapter 3 Radiation Integrals and Auxiliary Potential Functions 82 3.1 Introduction 82 3.2 The Vector Potential A for an Electric Current Source