11: Transmission Lines
- Page ID
- 22733
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 11.1: Introduction
- This page explains the behavior of plane waves between two infinitely conducting metal planes, detailing boundary conditions where the tangential electric field \(E\) and normal magnetic field \(H\) are zero due to Maxwell's equations. It highlights that energy travels at light speed in this setup and discusses the limitations of using parallel planes compared to hollow pipes for wave transmission, noting practical applications like strip-lines and coaxial cables.
- 11.2: Strip-lines
- This page covers the characteristics of electric and magnetic fields in strip-line transmission lines, noting that electric fields have an x-component and magnetic fields have a y-component. It explains the use of Maxwell's equations to derive relationships between these fields and wave functions, highlighting how pulses can be transmitted without distortion.
- 11.3: Co-axial Cables
- This page explores the use of cylindrical coordinates to analyze electromagnetic fields in a coaxial cable through Maxwell's equations, highlighting the radial electric field and angular magnetic field components. It derives equations connecting these fields, focusing on voltage and current pulses.
- 11.4: Transmission Lines in General
- This page focuses on lossless transmission lines, emphasizing their inductance (L) and capacitance (C) per unit length, which are vital for signal propagation. It provides equations illustrating the relationship between voltage and current changes along the line, drawing parallels to earlier established equations.
- 11.5: A Terminated Line
- This page covers the behavior of transmission line pulses at discontinuities and terminations. It illustrates scenarios involving pulse collisions, cancellation, and reflections at open circuits and short circuits, examining how reflection coefficients impact this behavior. Additionally, the interaction of voltage pulses with capacitors and inductors is explained, highlighting the resulting potential changes and the mathematical relationships governing these reflections.
- 11.6: Sinusoidal Signals on a Terminated Line
- This page covers the behavior of transmission lines linking signal generators to loads, focusing on voltage and current waves in phasor notation, and key parameters like characteristic and load impedances. It highlights the differences in impedances seen from the generator versus the load, particularly for long cables.
- 11.7: The Slotted Line
- This page explains how a slotted line measures electric field strength and analyzes load impedance via Voltage Standing Wave Ratio (VSWR). It describes the relationship between voltage minima positions and load types; specifically, how they differ for inductive versus capacitive loads. The phase angle θ is derived from these minima, aiding in identifying load characteristics.
- 11.8: Transmission Line with Losses
- This page examines voltage and current behavior on lossless transmission lines and their relation to Maxwell's equations, emphasizing the role of frequency-dependent dielectric constants and losses in conductors. It explains how load impedance affects signal propagation and presents examples of co-axial cable attenuation at various frequencies.
Thumbnail: 3-phase high-voltage lines. (CC BY-SA 3.0; Jeffrey G. Katz via Wikipedia)