DOCSLIB.ORG

For Most Practical Waveguides the Loss Associated with Dielectric Loss

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
For Most Practical Waveguides the Loss Associated with Dielectric Loss Adapted from notes by ECE 5317-6351 Prof. Jeffery T. Williams Microwave Engineering Fall 2019 Prof. David R. Jackson Dept. of ECE Notes 7 Waveguiding Structures Part 2: Attenuation ε,, µσ 1 Attenuation on Waveguiding Structures For most practical waveguides and transmission lines the loss associated with dielectric loss and conductor loss is relatively small. To account for these losses we will make this approximation: αα≈+cd α Attenuation constant Attenuation constant due due to conductor loss to dielectric loss (ignore dielectric loss) (ignore conductor loss) 2 Attenuation due to Dielectric Loss: αd Lossy dielectric ⇒ complex permittivity ⇒ complex wavenumber k σ εε= − j c ω σ k=ω µε = kk µε = µε(1 − j tan δ ) =−−εε′jj ′′ c00 rrc rr d ω =εε′ − ′′ k= k′ − jk ′′ ccj εc′′ =εc′ 1 − j εc′ =εδ′ (1 − j tan ) Note: kk′ = Re{ } cd =εε0 r (1 − j tan δ ) Note : εεrc′ is denoted as r . (e.g., ε r = 2.1 for Teflon). 3 Dielectric Attenuation for TEM Mode TEM mode: kkz = where kk= 0 µεrr (1− j tan δd ) Assume a small dielectric loss in medium: tanδ << 1 Use 1−zz ≈ 1 − /2 for z<< 1 ⇒≈kk0 µεrr(1 − j( tan δd) / 2) kk′ ≈ 0 µεrr 1 kk′′ ≈ µεtan δ 2 0 rr d 4 Summary of Dielectric Attenuation TEM mode kzd=−=βα jk β =Re(kk) = ′ αd =−=Im(kk) ′′ β≈ k0 µεrr 1 α≈ k µεtan δ d 2 0 rr d k=−= k′ jk ′′ k0 µεrr 1 −j tan δd 5 Dielectric Attenuation for Waveguide Mode An exact general expression for the dielectric attenuation: 22 kzd=−=−βα j kk c k=−= k′ jk ′′ k0 µεrr 1 −j tan δd Remember: The value kc is always real, regardless of whether the waveguide filling material is lossy or not. Note: The radical sign denotes the principal square root: −<ππarg( z) < 6 Dielectric Attenuation for Waveguide Mode (cont.) Approximation for the wavenumber of a waveguide mode : 22 kzd=−=−βα j kk c 22 =k0 µεrr(1 −− jk tan δd ) c 2 22 =(k00µεrr −− k c) jk µεrrtan δ d Assume a small dielectric loss: 2 22 k00µεrrtan δ d<< kk µε rr − c Then use: 11zz a− z = a1/ −( za) ≈ a 1 − =a − for z<< a 22a a 7 Approximate Dielectric Attenuation (cont.) Hence, we have: 2µε δ 221jk0 rr tan d We assume here that we kkz≈( 0 µεrr −− k c) 2 kk22µε − are above cutoff. ( 0 rr c) This gives us: 22 β≈−(kk0 µεrr c) k 2µεtan δ α ≈ 0 rr d d 2β 8 Summary of Dielectric Attenuation Waveguide mode (TMz or TEz) 22 kzd=−=−βα j kk c 22 β =Re kk − c 22 αdc=−−Im kk 22 β≈−kk0 µεrr c k 2µεtan δ α ≈ 0 rr d d 2β k=−= k′ jk ′′ k0 µεrr 1 −j tan δd 9 Attenuation due to Conductor Loss Assuming a small amount of conductor loss: We can assume that the fields of the lossy guide are approximately the same as those for lossless guide, except with a small amount of attenuation. ⇒ We can use a “perturbation” method to determine αc . Notes: . Dielectric loss does not change the shape of the fields at all in a waveguide or transmission line, since the boundary conditions remain the same (PEC). Conductor loss does disturb the fields slightly. 10 Surface Resistance This is a very important concept for calculating loss at a metal surface. x εµ, ε,, µσ z Note: The tangential fields determine the power going into εµ, the metal. Plane wave in a good conductor Note: In this figure, z is the direction normal to the metal surface, not the axis of the waveguide. Also, the electric field is assumed to be in the x direction for simplicity. 11 Surface Resistance (cont.) σ Assume 1 (for the metal) ωε The we have (for the metal): 1/2 1/2 σ σ µσ1− j ωµσ kj=ω µε − ≈− ωµ j = ω =(1 −j ) ω ωω2 2 Hence ωµσ k=−≈ k′ jk ′′ (1 −j) 2 Therefore ωµσ kk′≈≈ ′′ 2 12 Surface Resistance (cont.) ωµσ kk′≈≈ ′′ 2 1 Denote δ ≡=d “skin depth” = “depth of penetration” p k′′ e−1 ≈ 0.37 (For z = δ, fields are down to 37% Note : of their values at the surface.) Then we have 2 δ =d = At 3 GHz, the p ωµσ skin depth for copper is about 1 1.2 microns. kk′≈≈ ′′ δ 13 Surface Resistance (cont.) Frequency δ 2 1 [Hz] 6.6 [cm] δ = 10 [Hz] 2.1 [cm] ωµσ 100 [Hz] 6.6 [mm] 1 [kHz] 2.1 [mm] 10 [kHz] 0.66 [mm] Example: copper (pure) 100 [kHz] 0.21 [mm] −7 µµ=0 =4 π × 10 [H/m] 1 [MHz] 66 [µm] σ =5.8 × 107 [S/m] 10 [MHz] 20.1 [µm] 100 [MHz] 6.6 [µm] 1 [GHz] 2.1 [µm] Note: 10 [GHz] 0.66 [µm] × 7 A value of 3.0 10 [S/m] is often 100 [GHz] 0.21 [µm] assumed for “practical” copper. 14 Surface Resistance (cont.) x S z Fields evaluated on this plane 2 Pd = time-average power dissipated / m on S 11* P =Re(E × H ) ⋅= zˆ Re( EH* ) d 22x yz=0 15 Surface Resistance (cont.) Inside conductor: EHxy=η where µ µ µ ωµ η ==≈=j εσσσ “Surface resistance (Ω)” c ε −−jj ωω ωµ 1+ j ωµ Rs ≡ = 2σ 2 σ ωµ =(1 + j ) “Surface impedance (Ω)” 2σ Zss=(1 + jR) =(1 + jR ) s = Zs Note: To be more general: Note: Ets= ZnH( ˆ × t) EE xx= HH nˆ = outward normal yyz=0, air plane wave in metal 16 Surface Resistance (cont.) eff nˆ J s Conductor Ets= ZnH( ˆ × t) Et = tangential electric field at surface Ht = tangential magnetic field at surface nˆ = outward unit normal to conductor surface “Effective surface current” Hence we have eff Jst≈×( nHˆ ) eff Et≈ ZJ ss For the “effective” surface current density we imagine the The surface impedance gives us the ratio of the actual volume current density to tangential electric field at the surface to the be collapsed into a planar effective surface current flowing on the object. surface current. 17 Surface Resistance (cont.) Summary for a Good Conductor Ets= ZnH( ˆ × t) (fields at the surface) eff Et≈ ZJ ss (effective surface current) Zss=(1 + jR ) ωµ 1 R = = s 2σ σδ 2 δ = ωµσ 18 Surface Resistance (cont.) Frequency Rs 1 [Hz] 2.61×10-7 [Ω] ωµ 1 10 [Hz] 8.25×10-7 [Ω] Rs = = 2σ σδ 100 [Hz] 2.61×10-6 [Ω] 1 [kHz] 8.25×10-6 [Ω] Example: copper (pure) 10 [kHz] 2.61×10-5 [Ω] 100 [kHz] 8.25×10-5 [Ω] µµ= =4 π × 10−7 [H/m] 0 1 [MHz] 2.61×10-4 [Ω] σ =5.8 × 107 [S/m] 10 [MHz] 8.25×10-4 [Ω] 100 [MHz] 0.00261 [Ω]6.6 1 [GHz] 0.00825 [Ω] Note: 10 [GHz] 0.0261 [Ω] A value of 3.0×107 [S/m] is often assumed for “practical” copper. 100 [GHz] 0.0825 [Ω] 19 Surface Resistance (cont.) Returning to the power calculation, we have: 11** 12 Pd = Re(EHx yz )=0= Re((ZHs y00) H y) = R s H y0 22 2 1 2 In general, P = RH d2 st0 eff For a good conductor, Jst≈× nHˆ 0 This gives us the power dissipated per 1 2 Hence eff square meter of conductor surface, if we Pd= RJ ss know the effective surface current density 2 flowing on the surface. eff PEC eff PEC PEC limit: JJss→ Perturbation method : Assume that JJss≈ 20 Perturbation Method for αc −2α z Power flow along the guide: Pz()= Pe0 Power P0 @ z = 0 is calculated from the lossless case. dP( z) Power loss (dissipated) per unit length: P = − (∆P = −∆ Pz( )) l dz abs flow −2αz ⇒=Pl () z 2αα Pe0 = 2 P () z Pz( ) P (0) ⇒ α =ll = Note: α α 2Pz () 2 P0 = c for conductor loss 21 Perturbation Method: Waveguide Mode There is a single Pl (0) αc = conducting 2P0 boundary. S C z 1 * P0 =Re E ×⋅ H zˆ dS ∫∫2 For these calculations, we S z=0 neglect loss when we determine the fields and currents. R 2 P(0) = s Jd ls2 ∫ C z=0 Js = nHˆ × On PEC conductor Surface resistance of ωµ R = metal conductors: s 2σ 22 Perturbation Method: TEM Mode There are two S Pl (0) αc = conducting 2P0 boundaries. z 1 * P0 =Re E ×⋅ H zˆ dS ∫∫2 S z=0 For these calculations, we 1 2 neglect loss when we determine = ZI 2 0 the fields and currents. lossless (ZZ00= ) 1122 P(0) = RJ d+ RJ d l 22∫∫ss11ss CC12zz=00= Js = nHˆ × On PEC conductor Surface resistance of ωµ R =(σσ = or σ) metal conductors: s 2σ 12 23 Wheeler Incremental Inductance Rule The Wheeler incremental inductance rule gives an S alternative method for calculating the conductor attenuation on a transmission line (TEM mode): z It is useful when you have a formula for Z0. RZs ∂ 0 The formula is applied for each conductor αc = and the conductor attenuation from each of 2Z0η ∂ the two conductors is then added. In this formula, (for a given conductor) is the distance by which the conducting boundary is receded away from the field region. The top plate of a PPW line E E is shown being receded. H. Wheeler, “Formulas for the skin-effect,” Proc. IRE, vol. 30, pp. 412-424, 1942. 24 Calculation of R for TEM Mode From αc we can calculate R (the resistance per unit length of the transmission line): i( zt, ) Rz∆ Lz∆ i( z+∆ zt, ) Pl (0) αc = 2P0 + + v( zt, ) Gz∆ Cz∆ v( z+∆ zt, ) - 1 2 - P= ZI z 02 00 1 2 P(0) = RI Assume conductor loss only.
Load more

Recommended publications
  • Basic PCB Material Electrical and Thermal Properties for Design Introduction
    1 Basic PCB material electrical and thermal properties for design Introduction: In order to design PCBs intelligently it becomes important to understand, among other things, the electrical properties of the board material. This brief paper is an attempt to outline these key properties and offer some descriptions of these parameters. Parameters: The basic ( and almost indispensable) parameters for PCB materials are listed below and further described in the treatment that follows. dk, laminate dielectric constant df, dissipation factor Dielectric loss Conductor loss Thermal effects Frequency performance dk: Use the design dk value which is assumed to be more pertinent to design. Determines such things as impedances and the physical dimensions of microstrip circuits. A reasonable accurate practical formula for the effective dielectric constant derived from the dielectric constant of the material is: -1/2 εeff = [ ( εr +1)/2] + [ ( εr -1)/2][1+ (12.h/W)] Here h = thickness of PCB material W = width of the trace εeff = effective dielectric constant εr = dielectric constant of pcb material df: The dissipation factor (df) is a measure of loss-rate of energy of a mode of oscillation in a dissipative system. It is the reciprocal of quality factor Q, which represents the Signal Processing Group Inc., technical memorandum. Website: http://www.signalpro.biz. Signal Processing Gtroup Inc., designs, develops and manufactures analog and wireless ASICs and modules using state of the art semiconductor, PCB and packaging technologies. For a free no obligation quote on your product please send your requirements to us via email at [email protected] or through the Contact item on the website.
    [Show full text]
  • Agilent Basics of Measuring the Dielectric Properties of Materials
    Agilent Basics of Measuring the Dielectric Properties of Materials Application Note Contents Introduction ..............................................................................................3 Dielectric theory .....................................................................................4 Dielectric Constant............................................................................4 Permeability........................................................................................7 Electromagnetic propagation .................................................................8 Dielectric mechanisms ........................................................................10 Orientation (dipolar) polarization ................................................11 Electronic and atomic polarization ..............................................11 Relaxation time ................................................................................12 Debye Relation .................................................................................12 Cole-Cole diagram............................................................................13 Ionic conductivity ............................................................................13 Interfacial or space charge polarization..................................... 14 Measurement Systems .........................................................................15 Network analyzers ..........................................................................15 Impedance analyzers and LCR meters.........................................16
    [Show full text]
  • Application Note: ESR Losses in Ceramic Capacitors by Richard Fiore, Director of RF Applications Engineering American Technical Ceramics
    Application Note: ESR Losses In Ceramic Capacitors by Richard Fiore, Director of RF Applications Engineering American Technical Ceramics AMERICAN TECHNICAL CERAMICS ATC North America ATC Europe ATC Asia [email protected] [email protected] [email protected] www.atceramics.com ATC 001-923 Rev. D; 4/07 ESR LOSSES IN CERAMIC CAPACITORS In the world of RF ceramic chip capacitors, Equivalent Series Resistance (ESR) is often considered to be the single most important parameter in selecting the product to fit the application. ESR, typically expressed in milliohms, is the summation of all losses resulting from dielectric (Rsd) and metal elements (Rsm) of the capacitor, (ESR = Rsd+Rsm). Assessing how these losses affect circuit performance is essential when utilizing ceramic capacitors in virtually all RF designs. Advantage of Low Loss RF Capacitors Ceramics capacitors utilized in MRI imaging coils must exhibit Selecting low loss (ultra low ESR) chip capacitors is an important ultra low loss. These capacitors are used in conjunction with an consideration for virtually all RF circuit designs. Some examples of MRI coil in a tuned circuit configuration. Since the signals being the advantages are listed below for several application types. detected by an MRI scanner are extremely small, the losses of the Extended battery life is possible when using low loss capacitors in coil circuit must be kept very low, usually in the order of a few applications such as source bypassing and drain coupling in the milliohms. Excessive ESR losses will degrade the resolution of the final power amplifier stage of a handheld portable transmitter image unless steps are taken to reduce these losses.
    [Show full text]
  • Dielectric Loss
    Dielectric Loss - εr is static dielectric constant (result of polarization under dc conditions). Under ac conditions, the dielectric constant is different from the above as energy losses have to be taken into account. - Thermal agitation tries to randomize the dipole orientations. Hence dipole moments cannot react instantaneously to changes in the applied field Æ losses. - The absorption of electrical energy by a dielectric material that is subjected to an alternating electric field is termed dielectric loss. - In general, the dielectric constant εr is a complex number given by where, εr’ is the real part and εr’’ is the imaginary part. Dept of ECE, National University of Singapore Chunxiang Zhu Dielectric Loss - Consider parallel plate capacitor with lossy dielectric - Impedance of the circuit - Thus, admittance (Y=1/Z) given by Dept of ECE, National University of Singapore Chunxiang Zhu Dielectric Loss - The admittance can be written in the form The admittance of the dielectric medium is equivalent to a parallel combination of - Note: compared to parallel an ideal lossless capacitor C’ with a resistance formula. relative permittivity εr’ and a resistance of 1/Gp or conductance Gp. Dept of ECE, National University of Singapore Chunxiang Zhu Dielectric Loss - Input power: - Real part εr’ represents the relative permittivity (static dielectric contribution) in capacitance calculation; imaginary part εr’’ represents the energy loss in dielectric medium. - Loss tangent: defined as represents how lossy the material is for ac signals. Dept of ECE, National University of Singapore Chunxiang Zhu Dielectric Loss The dielectric loss per unit volume: Dept of ECE, National University of Singapore Chunxiang Zhu Dielectric Loss - Note that the power loss is a function of ω, E and tanδ.
    [Show full text]
  • A Comprehensive Guide to Selecting the Right Capacitor for Your Specific Application
    CAPACITOR FUNDAMENTALS EBOOK A Comprehensive Guide to Selecting the Right Capacitor for Your Specific Application 2777 Hwy 20 (315) 655-8710 [email protected] Cazenovia, NY 13035 knowlescapacitors.com CAPACITOR FUNDAMENTALS EBOOK TABLE OF CONTENTS Introduction .................................. 2 The Key Principles of Capacitance and How a Basic Capacitor Works .............................. 3 How Capacitors are Most Frequently Used in Electronic Circuits ............................. 6 Factors Affecting Capacitance .................. 9 Defining Dielectric Polarization .................. 11 Dielectric Properties ........................... 15 Characteristics of Ferroelectric Ceramics ......................... 19 Characteristics of Linear Dielectrics .............. 22 Dielectric Classification ......................... 24 Test Parameters and Electrical Properties .......... 27 Industry Test Standards Overview. 32 High Reliability Testing .......................... 34 Visual Standards For Chip Capacitors ............. 37 Chip Attachment and Termination Guidelines ...... 42 Dissipation Factor and Capacitive Reactance ..... 49 Selecting the Right Capacitor for Your Specific Application Needs ............................ 51 1 CAPACITOR FUNDAMENTALS EBOOK INTRODUCTION At Knowles Precision Devices, our expertise in capacitor technology helps developers working on some of the world’s most demanding applications across the medical device, military and aerospace, telecommunications, and automotive industries. Thus, we brought together our top engineers
    [Show full text]
  • LOSSY CAPACITORS 1 Dielectric Loss
    Chapter 3—Lossy Capacitors 3–1 LOSSY CAPACITORS 1 Dielectric Loss Capacitors are used for a wide variety of purposes and are made of many different materials in many different styles. For purposes of discussion we will consider three broad types, that is, capacitors made for ac, dc, and pulse applications. The ac case is the most general since ac capacitors will work (or at least survive) in dc and pulse applications, where the reverse may not be true. It is important to consider the losses in ac capacitors. All dielectrics (except vacuum) have two types of losses. One is a conduction loss, representing the flow of actual charge through the dielectric. The other is a dielectric loss due to movement or rotation of the atoms or molecules in an alternating electric field. Dielectric losses in water are the reason for food and drink getting hot in a microwave oven. One way of describing dielectric losses is to consider the permittivity as a complex number, defined as = − j = ||e−jδ (1) where = ac capacitivity = dielectric loss factor δ = dielectric loss angle Capacitance is a complex number C∗ in this definition, becoming the expected real number C as the losses go to zero. That is, we define C∗ = C − jC (2) One reason for defining a complex capacitance is that we can use the complex value in any equation derived for a real capacitance in a sinusoidal application, and get the correct phase shifts and power losses by applying the usual rules of circuit theory. This means that most of our analyses are already done, and we do not need to start over just because we now have a lossy capacitor.
    [Show full text]
  • A Review of Degradation Behavior and Modeling of Capacitors: Preprint
    A Review of Degradation Behavior and Modeling of Capacitors Preprint Anunay Gupta,1 Om Prakash Yadav,1 Douglas DeVoto,2 2 and Joshua Major 1 North Dakota State University 2 National Renewable Energy Laboratory Presented at the American Society of Mechanical Engineers (ASME) 2018 International Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Microsystems (InterPACK 2018) San Francisco, California August 27–30, 2018 NREL is a national laboratory of the U.S. Department of Energy Conference Paper Office of Energy Efficiency & Renewable Energy NREL/CP-5400-71386 Operated by the Alliance for Sustainable Energy, LLC October 2018 This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. Contract No. DE-AC36-08GO28308 A Review of Degradation Behavior and Modeling of Capacitors Preprint Anunay Gupta,1 Om Prakash Yadav,1 Douglas DeVoto,2 2 and Joshua Major 1 North Dakota State University 2 National Renewable Energy Laboratory Suggested Citation Anunay Gupta, Om Prakash Yadav, Douglas DeVoto, and Joshua Major. 2018. A Review of Degradation Behavior and Modeling of Capacitors: Preprint. Golden, CO: National Renewable Energy Laboratory. NREL/CP-5400-71386. https://www.nrel.gov/docs/fy19osti/71386.pdf. NREL is a national laboratory of the U.S. Department of Energy Conference Paper Office of Energy Efficiency & Renewable Energy NREL/CP-5400-71386 Operated by the Alliance for Sustainable Energy, LLC October 2018 This report is available at no cost from the National Renewable Energy National Renewable Energy Laboratory Laboratory (NREL) at www.nrel.gov/publications. 15013 Denver West Parkway Golden, CO 80401 Contract No.
    [Show full text]
  • Table of Contents
    NOVACAP TECHNICAL BROCHURE Table of Contents A. INTRODUCTION ................................................................................................ 2 B. CAPACITOR APPLICATIONS ......................................................................... 3 C. THE BASIC CAPACITOR ................................................................................. 4 D. CAPACITANCE ................................................................................................... 5 E. FACTORS AFFECTING CAPACITANCE ...................................................... 5 F. DIELECTRIC BEHAVIOR ................................................................................. 7 G. DIELECTRIC PROPERTIES ......................................................................... 13 H. FERROELECTRIC CERAMICS.................................................................... 20 I. LINEAR DIELECTRICS ................................................................................... 24 J. CLASSES OF DIELECTRICS ......................................................................... 25 K. TEST PARAMETERS AND ELECTRICAL PROPERTIES...................... 29 L. INDUSTRY TEST STANDARDS..................................................................... 35 M. HIGH RELIABILITY TESTING .................................................................... 37 N. VISUAL STANDARDS FOR CHIP CAPACITORS ..................................... 40 O. CHIP USER GUIDELINES ............................................................................... 46 1 NOVACAP
    [Show full text]
  • Permittivity and Measurements 3693
    PERMITTIVITY AND MEASUREMENTS 3693 00 0 PERMITTIVITY AND MEASUREMENTS tan de ¼ e =e . Mechanisms that contribute to the dielectric loss in heterogeneous mixtures include polar, electronic, atomic, and Maxwell–Wagner responses [7]. At RF and V. K OMAROV microwave frequencies of practical importance and cur- S. WANG rently used for applications in material processing (RF J. TANG Washington State University 1–50 MHz and microwave frequencies of 915 and 2450 MHz), ionic conduction and dipole rotation are domi- nant loss mechanisms [8]: 1. INTRODUCTION 00 00 00 00 s e ¼ ed þ es ¼ ed þ ð2Þ Propagation of electromagnetic (EM) waves in radio e0o frequency (RF) and microwave systems is described mathematically by Maxwell’s equations with corres- where subscripts ‘‘d’’ and ‘‘s’’ stand for contributions due to ponding boundary conditions. Dielectric properties of dipole rotation and ionic conduction, respectively; s is the lossless and lossy materials influence EM field distri- ionic conductivity in S/m of a material, o is the angular bution. For a better understanding of the physical frequency in rad/s, and e0 is the permittivity of free space processes associated with various RF and microwave or vacuum (8.854 Â 10–12 F/m). Dielectric lossy materials devices, it is necessary to know the dielectric properties convert electric energy at RF and microwave frequencies of media that interact with EM waves. For telecommuni- into heat. The increase in temperature (DT) of a material cation and radar devices, variations of complex dielectric can be calculated from [9] permittivity (referring to the dielectric property) over a wide frequency range are important.
    [Show full text]
  • Dielectric Loss and Ferroelectric Hysteresis
    SEPTEMBER 2018 I SS U E #117 TECHNICALTIDBITS MATERION PERFORMANCE ALLOYS DIELECTRIC LOSS AND FERROELECTRIC HYSTERESIS Last month we made the observation that the per- The amount of energy converted to heat during a polar- mittivity of an ideal capacitor is equal to the relative ization cycle is known as the dissipation factor (Df), permittivity (dielectric constant, abbreviated loss tangent or tan ( ), with being the loss angle. Dk or r) multiplied by the permittivity constant The derivation of the loss angle and the tangent thereof δ δ At a Loss! – A brief ( 0). This is true for direct current (DC) conditions, or can be a bit esoteric unless you are an electrical engi- ε discussion on energy lost for ideal, lossless dielectric materials. However, nature neer. Technical Tidbits always tries to strike a balance rarelyε presents us with ideal materials or conditions, between oversimplification (with a risk of inaccuracy) as waste heat in materials so we have to consider real-world cases. and getting too in depth for introductory material due to the presence of (getting lost in the weeds). However, if you are comfort- changing electric fields. As discussed last month, under the influence of an able with phasors as well as real and imaginary parts of externally applied electric field, the electric dipoles current and capacitance, then feel free to research on. in a polarizable material will align themselves with the field, if they are free to rotate or move, and if they Under AC conditions, all realistic dielectric materials will have enough time to do so. Of course, such movement have losses.
    [Show full text]
  • Planar Transmission Line Method for Char- Acterization of Printed Circuit Board Di- Electrics
    Progress In Electromagnetics Research, PIER 102, 267{286, 2010 PLANAR TRANSMISSION LINE METHOD FOR CHAR- ACTERIZATION OF PRINTED CIRCUIT BOARD DI- ELECTRICS J. Zhang CISCO Systems, Inc. CA, USA M. Y. Koledintseva Missouri University of Science & Technology Rolla, MO, USA G. Antonini Department of Electrical Engineering University of L'Aquila Poggio di Roio, 67040 AQ, Italy J. L. Drewniak Missouri University of Science & Technology Rolla, MO 65401, USA A. Orlandi Department of Electrical Engineering University of L'Aquila Poggio di Roio, 67040 AQ, Italy K. N. Rozanov Institute for Theoretical and Applied Electromagnetics Russian Academy of Sciences Moscow 125412, Russia Corresponding author: M. Y. Koledintseva ([email protected]). 268 Zhang et al. Abstract|An e®ective approach to characterize frequency-dispersive sheet materials over a wide RF and microwave frequency range based on planar transmission line geometries and a genetic algorithm is proposed. S-parameters of a planar transmission line structure with a sheet material under test as a substrate of this line are measured using a vector network analyzer (VNA). The measured S-parameters are then converted to ABCD matrix parameters. With the assumption of TEM/quasi-TEM wave propagation on the measured line, as well as reciprocity and symmetry of the network, the complex propagation constant can be found, and the corresponding phase constant and attenuation constant can be retrieved. Attenuation constant includes both dielectric loss and conductor loss terms. At the same time, phase term, dielectric loss and conductor loss can be calculated for a known transmission line geometry using corresponding closed- form analytical or empirical formulas.
    [Show full text]
  • Planar Transmission Lines
    Adapted from notes by ECE 5317-6351 Prof. Jeffery T. Williams Microwave Engineering Fall 2018 Prof. David R. Jackson Dept. of ECE Notes 11 Waveguiding Structures Part 6: Planar Transmission Lines w ε0 ε r h 1 Planar Transmission Lines w w b ε h r εr Microstrip Stripline w w εr g g h εr g g h Coplanar Waveguide (CPW) Conductor-backed CPW s s εr h εr h Slotline Conductor-backed Slotline 2 Planar Transmission Lines (cont.) w w w w ε h εr s h r s Coplanar Strips (CPS) Conductor-backed CPS . Stripline is a planar version of coax. Coplanar strips (CPS) is a planar version of twin lead. 3 Stripline . Common on circuit boards ε,, µσd b . Fabricated with two circuit boards w . Homogenous dielectric (perfect TEM mode) TEM mode (also TE & TM Modes) Field structure for TEM mode: Electric Field Magnetic Field 4 Stripline (cont.) . Analysis of stripline is not simple. TEM mode fields can be obtained from an electrostatic analysis (e.g., conformal mapping). A closed stripline structure is analyzed in the Pozar book by using an approximate numerical method: b w b /2 ε,, µσd a ab>> 5 Stripline (cont.) Conformal mapping solution (S. Cohn): Exact solution: 30π Kk ( ) Z0 = K = complete elliptic Kk()′ integral of the first kind π /2 1 Kk( ) ≡ dθ ∫ 22 0 1− k sin θ π w k = sech 2b π w k′ = tanh 2b 6 Stripline (cont.) Curve fitting this exact solution: η b Z = 0 ln( 4) 0 ε ln(4) Note : = 0.441 4 r wb+ π e π Effective width Fringing term w 0 ;for ≥ 0.35 wwe b = − 2 bbww 0.35− ;for 0.1≤≤ 0.35 bb 1bb /2 η η b ideal 0 The factor of 1/2 in front is from the parallel Note: Z0 =η = = 24ww4w ε r combination of two ideal PPWs.
    [Show full text]