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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. -
A Review of Electric Impedance Matching Techniques for Piezoelectric Sensors, Actuators and Transducers
Review A Review of Electric Impedance Matching Techniques for Piezoelectric Sensors, Actuators and Transducers Vivek T. Rathod Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA; [email protected]; Tel.: +1-517-249-5207 Received: 29 December 2018; Accepted: 29 January 2019; Published: 1 February 2019 Abstract: Any electric transmission lines involving the transfer of power or electric signal requires the matching of electric parameters with the driver, source, cable, or the receiver electronics. Proceeding with the design of electric impedance matching circuit for piezoelectric sensors, actuators, and transducers require careful consideration of the frequencies of operation, transmitter or receiver impedance, power supply or driver impedance and the impedance of the receiver electronics. This paper reviews the techniques available for matching the electric impedance of piezoelectric sensors, actuators, and transducers with their accessories like amplifiers, cables, power supply, receiver electronics and power storage. The techniques related to the design of power supply, preamplifier, cable, matching circuits for electric impedance matching with sensors, actuators, and transducers have been presented. The paper begins with the common tools, models, and material properties used for the design of electric impedance matching. Common analytical and numerical methods used to develop electric impedance matching networks have been reviewed. The role and importance of electrical impedance matching on the overall performance of the transducer system have been emphasized throughout. The paper reviews the common methods and new methods reported for electrical impedance matching for specific applications. The paper concludes with special applications and future perspectives considering the recent advancements in materials and electronics. -
Smith Chart Calculations
The following material was extracted from earlier edi- tions. Figure and Equation sequence references are from the 21st edition of The ARRL Antenna Book Smith Chart Calculations The Smith Chart is a sophisticated graphic tool for specialized type of graph. Consider it as having curved, rather solving transmission line problems. One of the simpler ap- than rectangular, coordinate lines. The coordinate system plications is to determine the feed-point impedance of an consists simply of two families of circles—the resistance antenna, based on an impedance measurement at the input family, and the reactance family. The resistance circles, Fig of a random length of transmission line. By using the Smith 1, are centered on the resistance axis (the only straight line Chart, the impedance measurement can be made with the on the chart), and are tangent to the outer circle at the right antenna in place atop a tower or mast, and there is no need of the chart. Each circle is assigned a value of resistance, to cut the line to an exact multiple of half wavelengths. The which is indicated at the point where the circle crosses the Smith Chart may be used for other purposes, too, such as the resistance axis. All points along any one circle have the same design of impedance-matching networks. These matching resistance value. networks can take on any of several forms, such as L and pi The values assigned to these circles vary from zero at the networks, a stub matching system, a series-section match, and left of the chart to infinity at the right, and actually represent more. -
Admittance, Conductance, Reactance and Susceptance of New Natural Fabric Grewia Tilifolia V
Sensors & Transducers Volume 119, Issue 8, www.sensorsportal.com ISSN 1726-5479 August 2010 Editors-in-Chief: professor Sergey Y. Yurish, tel.: +34 696067716, fax: +34 93 4011989, e-mail: [email protected] Editors for Western Europe Editors for North America Meijer, Gerard C.M., Delft University of Technology, The Netherlands Datskos, Panos G., Oak Ridge National Laboratory, USA Ferrari, Vittorio, Universitá di Brescia, Italy Fabien, J. Josse, Marquette University, USA Katz, Evgeny, Clarkson University, USA Editor South America Costa-Felix, Rodrigo, Inmetro, Brazil Editor for Asia Ohyama, Shinji, Tokyo Institute of Technology, Japan Editor for Eastern Europe Editor for Asia-Pacific Sachenko, Anatoly, Ternopil State Economic University, Ukraine Mukhopadhyay, Subhas, Massey University, New Zealand Editorial Advisory Board Abdul Rahim, Ruzairi, Universiti Teknologi, Malaysia Djordjevich, Alexandar, City University of Hong Kong, Hong Kong Ahmad, Mohd Noor, Nothern University of Engineering, Malaysia Donato, Nicola, University of Messina, Italy Annamalai, Karthigeyan, National Institute of Advanced Industrial Science Donato, Patricio, Universidad de Mar del Plata, Argentina and Technology, Japan Dong, Feng, Tianjin University, China Arcega, Francisco, University of Zaragoza, Spain Drljaca, Predrag, Instersema Sensoric SA, Switzerland Arguel, Philippe, CNRS, France Dubey, Venketesh, Bournemouth University, UK Ahn, Jae-Pyoung, Korea Institute of Science and Technology, Korea Enderle, Stefan, Univ.of Ulm and KTB Mechatronics GmbH, Germany -
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. -
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| = . -
S-Parameter Simulation and Optimization
S-parameter Simulation and Optimization ADS 2009 (version 1.0) Copyright Agilent Technologies 2009 Slide 5 - 1 S-parameters are Ratios Usually given in dB as 20 log of the voltage ratios of the waves at the ports: incident, reflected, or transmitted. S-parameter (ratios): out / in • S11 - Forward Reflection (input match - impedance) Best viewed on a • S22 - Reverse Reflection (output match - impedance) Smith chart. • S21 - Forward Transmission (gain or loss) These are easier • S12 - Reverse Transmission (leakage or isolation) to understand and simply plotted. Results of an S-Parameter Simulation in ADS • S-matrix with all complex values at each frequency point • Read the complex reflection coefficient (Gamma) • Change the marker readout for Zo • Smith chart plots for impedance matching • Results are similar to Network Analyzer measurements Next, ADS data ADS 2009 (version 1.0) Copyright Agilent Technologies 2009 Slide 5 - 2 Typical S-parameter data in ADS Transmission: S21 Reflection: S11 magnitude vs frequency Impedance on a Smith Chart Complete S-matrix with port impedance Note: Smith marker impedance readout is changed to Zo = 50 ohms. Smith chart basics... ADS 2009 (version 1.0) Copyright Agilent Technologies 2009 Slide 5 - 3 The Impedance Smith Chart simplified... This is an impedance chart transformed from rectangular Z. Normalized to 50 ohms, the center = R50+J0 or Zo (perfect match). For S11 or S22 (two-port), you get the complex impedance. Circles of constant Resistance 16.7 50 150 SHORT OPEN 25 50 100 Lines of constant Reactance (+jx above and -jx below) Zo (characteristic impedance) = 50 + j0 More Smith chart.. -
EEEE-816 Design and Characterization of Microwave Systems
EEEE-816 Design and Characterization of Microwave Systems Dr. Jayanti Venkataraman Department of Electrical Engineering Rochester Institute of Technology Rochester, NY 14623 March 2008 EE816 Design and Characterization of Microwave Systems I. Course Structure - 4 credits II. Pre-requisites – Microwave Circuits (EE717) and Antenna Theory (EE729) III. Course level – Graduate IV. Course Objectives Electromagnetics education has been rejuvenated by three emerging technologies, namely mixed signal circuits, wireless communication and bio-electromagnetics. As hardware and software tools continue to get more sophisticated, there is a need to be able to perform specific tasks for characterization and validation of design, working within the capabilities of test equipment, and the ability to develop corresponding analytical formulations There are two primary course objectives. (i) Design of experiments to characterize or measure specific quantities, working with the constraints of measurable quantities using the vector network analyzer, and in conjunction with the development of closed form analytical expressions. (ii) Design, construction and characterization of microstrip circuitry and antennas for a specified set of criteria using analytical models, and software tools and measurement techniques. Microwave measurement will involve the use of network analyzers, and spectrum analyzers in conjunction with the probe station. Simulated results will be obtained using some popular commercial EM software for the design of microwave circuits and antennas. -
S-Parameter Techniques – HP Application Note 95-1
H Test & Measurement Application Note 95-1 S-Parameter Techniques Contents 1. Foreword and Introduction 2. Two-Port Network Theory 3. Using S-Parameters 4. Network Calculations with Scattering Parameters 5. Amplifier Design using Scattering Parameters 6. Measurement of S-Parameters 7. Narrow-Band Amplifier Design 8. Broadband Amplifier Design 9. Stability Considerations and the Design of Reflection Amplifiers and Oscillators Appendix A. Additional Reading on S-Parameters Appendix B. Scattering Parameter Relationships Appendix C. The Software Revolution Relevant Products, Education and Information Contacting Hewlett-Packard © Copyright Hewlett-Packard Company, 1997. 3000 Hanover Street, Palo Alto California, USA. H Test & Measurement Application Note 95-1 S-Parameter Techniques Foreword HEWLETT-PACKARD JOURNAL This application note is based on an article written for the February 1967 issue of the Hewlett-Packard Journal, yet its content remains important today. S-parameters are an Cover: A NEW MICROWAVE INSTRUMENT SWEEP essential part of high-frequency design, though much else MEASURES GAIN, PHASE IMPEDANCE WITH SCOPE OR METER READOUT; page 2 See Also:THE MICROWAVE ANALYZER IN THE has changed during the past 30 years. During that time, FUTURE; page 11 S-PARAMETERS THEORY AND HP has continuously forged ahead to help create today's APPLICATIONS; page 13 leading test and measurement environment. We continuously apply our capabilities in measurement, communication, and computation to produce innovations that help you to improve your business results. In wireless communications, for example, we estimate that 85 percent of the world’s GSM (Groupe Speciale Mobile) telephones are tested with HP instruments. Our accomplishments 30 years hence may exceed our boldest conjectures.