Transmission Lines Quiz
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Questions and Answers

Which of the following is NOT a factor that contributes to power loss in a transmission line?

  • Conductor loss
  • Radiation loss
  • Capacitance loss (correct)
  • Dielectric heating loss
  • What is the main reason why conductor loss increases with frequency?

  • Increased capacitance at higher frequencies
  • Increased radiation from the conductors at higher frequencies
  • Skin effect causing current to flow mostly on the surface of conductors (correct)
  • Increased current flow at higher frequencies
  • How does the characteristic impedance of a transmission line affect conductor loss?

  • Higher characteristic impedance leads to higher conductor loss (correct)
  • Characteristic impedance only affects conductor loss at high frequencies
  • Characteristic impedance has no effect on conductor loss
  • Lower characteristic impedance leads to higher conductor loss
  • Why does the center of a conductor become irrelevant for EM wave propagation above 100 MHz?

    <p>The current flow is completely concentrated on the outside surface of the conductor (B)</p> Signup and view all the answers

    What is the relationship between the ac resistance and dc resistance of a conductor, as described in the context?

    <p>Ac resistance is directly proportional to dc resistance, with a factor called the resistance ratio (D)</p> Signup and view all the answers

    What is the velocity factor of a transmission line, as described in the context?

    <p>The ratio of the velocity of propagation of the signal in the transmission line to the speed of light in a vacuum (C)</p> Signup and view all the answers

    Which of these is NOT a transmission line characteristic that impacts the velocity of propagation?

    <p>Conductor diameter (A)</p> Signup and view all the answers

    In the context, what is the primary reason for using a larger-diameter wire for a transmission line?

    <p>To decrease the attenuation of the signal (C)</p> Signup and view all the answers

    What is the Q factor for short-circuited /4 sections?

    <p>About 10,000 (B)</p> Signup and view all the answers

    What happens when a load is purely inductive or purely capacitive?

    <p>The SWR is infinite. (D)</p> Signup and view all the answers

    What is the purpose of a transmission-line stub?

    <p>To remove the reactive component to match the transmission line. (A)</p> Signup and view all the answers

    Who developed the Smith chart?

    <p>Philip H. Smith (C)</p> Signup and view all the answers

    What frequency response does a high-grade inductor and capacitor provide compared to short-circuited sections?

    <p>Inferior quality (A)</p> Signup and view all the answers

    What is the primary characteristic of a transmission line that must be minimized?

    <p>Attenuation of the signal (C)</p> Signup and view all the answers

    What type of waves do transmission lines primarily propagate?

    <p>Transverse electromagnetic waves (A)</p> Signup and view all the answers

    How is a transverse wave defined in relation to its direction of propagation?

    <p>The displacement is perpendicular to the direction of propagation (D)</p> Signup and view all the answers

    Which of the following statements about electromagnetic waves is true?

    <p>They consist of E and H fields that are perpendicular to each other. (B)</p> Signup and view all the answers

    What happens to the behavior of transmission lines when propagating high-frequency signals?

    <p>It behaves more peculiarly and becomes more involved. (D)</p> Signup and view all the answers

    What separates the conductors in a transmission line?

    <p>An insulator or dielectric (D)</p> Signup and view all the answers

    Which type of signal can transmission lines propagate?

    <p>Both low-frequency AC and high-frequency signals (C)</p> Signup and view all the answers

    What is space quadrature in the context of electromagnetic waves?

    <p>The 90° angle between the E and H fields at all points (B)</p> Signup and view all the answers

    What occurs when a finite line is terminated in a purely resistive load equal to Zo?

    <p>Energy is dissipated in the load. (B)</p> Signup and view all the answers

    Which factor dominates in determining the characteristic impedance at extremely low frequencies?

    <p>Resistance (B)</p> Signup and view all the answers

    How can the characteristic impedance of a two-wire parallel transmission line with an air dielectric be determined?

    <p>From its physical dimensions. (A)</p> Signup and view all the answers

    What is true about the input impedance of an infinitely long line at radio frequencies?

    <p>It is purely resistive and equal to Zo. (D)</p> Signup and view all the answers

    What is the effect of terminating a transmission line with a load equal to Z?

    <p>The line behaves like an infinite line. (A)</p> Signup and view all the answers

    What describes a non-resonant line?

    <p>There are no reflected waves. (C)</p> Signup and view all the answers

    In what units is the propagation constant commonly expressed?

    <p>Decibels per unit length (B)</p> Signup and view all the answers

    For an infinitely long transmission line, what happens to the incident power as it propagates?

    <p>All incident power is dissipated. (A)</p> Signup and view all the answers

    What happens to the total voltage at the shorted end of a transmission line under a short-circuit load condition?

    <p>The total voltage is zero. (C)</p> Signup and view all the answers

    In a transmission line terminated in a short, how does the current standing wave behave?

    <p>It is reflected back without phase reversal. (D)</p> Signup and view all the answers

    What is the result of an open-circuit load condition at the end of a transmission line?

    <p>The energy reflects back to the load. (A)</p> Signup and view all the answers

    What characterizes the voltage standing wave in a transmission line terminated in an open?

    <p>It is reflected back as if it were to continue. (C)</p> Signup and view all the answers

    What occurs to the sum of the incident and reflected voltage waveforms at the open end of a transmission line?

    <p>It is maximum at the open. (D)</p> Signup and view all the answers

    When using a shorted quarter wavelength section of a transmission line, it ideally behaves like which type of circuit?

    <p>Parallel LC circuit. (C)</p> Signup and view all the answers

    Why are open-circuit sections of transmission lines seldom used in applications?

    <p>They tend to radiate a significant amount of energy. (B)</p> Signup and view all the answers

    What happens to a shorted transmission line section that is less than a quarter wavelength?

    <p>It behaves like a pure inductance. (C)</p> Signup and view all the answers

    What is the characteristic impedance of a transmission line given by?

    <p>Zo = (L/C)^1/2 (B)</p> Signup and view all the answers

    Which condition must be met for maximum power transfer in a transmission line?

    <p>The load must be purely resistive and equal to the characteristic impedance. (D)</p> Signup and view all the answers

    What happens to energy in an infinitely long transmission line connected to a source?

    <p>The line can store energy indefinitely without dissipation. (A)</p> Signup and view all the answers

    The characteristic impedance (Zo) of a transmission line is dependent on which of the following factors?

    <p>The inductance and capacitance distributed along the line. (A)</p> Signup and view all the answers

    Why do manufacturers often provide the impedance of transmission cables?

    <p>To avoid the need for impedance measurements in practice. (C)</p> Signup and view all the answers

    What is NOT a characteristic of the characteristic impedance?

    <p>It is influenced by the impedance of connected loads. (B)</p> Signup and view all the answers

    What condition results in a resistive characteristic impedance for a finite-length transmission line?

    <p>Using a purely resistive load that matches the surge impedance. (C)</p> Signup and view all the answers

    How can an impedance meter or bridge be useful in transmission line applications?

    <p>To measure the inductance and capacitance of the transmission line. (A)</p> Signup and view all the answers

    Flashcards

    What is a transmission line?

    A system that transmits electrical energy between two points.

    What is a transverse wave?

    A type of wave where the displacement of the wave is perpendicular to the direction it's traveling.

    What is an electromagnetic wave?

    A type of wave that is generated by the movement of an electric charge. It consists of both electric and magnetic fields.

    What is a Transverse Electromagnetic (TEM) wave?

    A type of electromagnetic wave that travels on a transmission line, with electric and magnetic fields perpendicular to each other.

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    What is attenuation in a transmission line?

    The ability of a transmission line to carry a signal without losing too much energy.

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    What is radiation in a transmission line?

    The unwanted emission of radio waves from a transmission line.

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    What is space quadrature?

    The relationship between the electric and magnetic fields in space in a TEM wave, where they are at right angles to each other.

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    Why are high frequency signals more complex on a transmission line?

    The behavior of transmission lines becomes more complex when carrying high frequency signals compared to low frequencies.

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    Characteristic Impedance

    The impedance seen looking into a line of n such sections is determined from the following expression: For extremely low frequencies, the resistances dominate. For extremely high frequencies, the inductance and capacitance dominate.

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    Characteristic Impedance (Two-Wire & Coaxial)

    The characteristic impedance of a two-wire parallel transmission line with an air dielectric can be determined from its physical dimensions. The characteristic impedance of a concentric coaxial cable can also be determined from its physical dimensions.

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    Infinite Line Characteristics

    The input impedance of an infinitely long line at radio frequencies is resistive and equal to Zo. Electromagnetic waves travel down the line without reflections; such a line is called non-resonant. The ratio of voltage to current at any point along the line is equal to Zo. The incident voltage and current at any point along the line are in phase.

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    Matched Load

    Line losses on a non-resonant line are minimum per unit length. Any transmission line that is terminated in a purely resistive load equal to Z acts like an infinite line.

    ✓Zi = Zo ✓There are no reflected waves. ✓V and I are in phase. ✓There is maximum transfer of power from source to load.

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    Propagation Constant

    Sometimes called propagation coefficient, is used to express the attenuation (signal loss) and the phase shift per unit length of a transmission line. Used to determine the reduction in voltage or current with distance as a TEM wave propagates down a transmission line. For an infinitely long line, all of the incident power is dissipated in the resistance of the wire as the wave propagates down the line. With an infinitely long line or a line that looks infinitely long, such as a finite line terminated in a matched load (Za = ZL), no energy is returned or reflected back toward the source.

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    Velocity of Propagation

    The speed at which an electromagnetic wave propagates through a transmission line.

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    Velocity Factor

    The ratio of the velocity of propagation in a transmission line to the speed of light in a vacuum.

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    Conductor Loss

    The loss of power in a transmission line due to the resistance of the conductors.

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    Skin Effect

    The phenomenon where the current flow in a conductor is concentrated near the surface at higher frequencies.

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    Resistance Ratio

    The ratio of the AC resistance of a conductor to its DC resistance.

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    Transmission Line Losses

    The attenuation experienced by a signal as it travels along a transmission line.

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    Attenuation

    A measure of the power loss in a transmission line.

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    Output Power

    The power delivered to the load after passing through a transmission line.

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    Short-circuited λ/4 section

    A section of transmission line with a length equal to one-quarter of the wavelength of the signal being transmitted.

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    Stub matching

    A type of impedance matching technique that uses a short section of transmission line to cancel out reactive component of the load impedance.

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    Smith Chart

    A specialized graphical tool used to solve transmission line problems visually. It represents complex impedance as a point on a circular graph.

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    Quality factor (Q)

    A measure of the ability of a circuit to store energy. A high Q factor indicates that the circuit can store more energy than it dissipates.

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    Reflection Coefficient

    The ratio of the reflected power to the incident power. A value of 1 indicates all power is reflected, while 0 indicates all power is transmitted.

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    Characteristic Impedance (Zo)

    The impedance seen looking into an infinitely long transmission line, or a finite length terminated by a resistive load equal to its own value.

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    Matched Impedance

    The condition where maximum power is transferred from the source to the load, with no energy reflected back.

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    Infinitely Long Transmission Line

    A transmission line with infinite length stores energy indefinitely, acting like a resistor dissipating all incoming energy.

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    Energy Storage in Transmission Lines

    The ability of a transmission line to store energy in its inductance and capacitance.

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    Characteristic Impedance Formula

    The ratio of inductance (L) to capacitance (C) of a transmission line, with units of ohms.

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    Impedance Seen by RF Generator

    The resistance seen by an RF generator connected to a transmission line.

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    Reflected Energy

    A condition where the energy from the source is reflected back towards the source, instead of being fully absorbed by the load.

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    Transmission Line Matching

    The process of adjusting the load impedance to match the characteristic impedance of the transmission line, minimizing reflected energy.

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    Short-Circuited Transmission Line

    A shorted transmission line, where the load impedance is zero, causes the voltage wave to be reflected back with a 180-degree phase shift. The reflected wave cancels out the incident wave at the short, resulting in zero voltage at that point.

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    Voltage Reflection on a Shorted Line

    Voltage waves on a shorted transmission line are reflected back with a 180-degree phase shift, effectively canceling out the incident wave at the short.

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    Current Reflection on a Shorted Line

    Current waves on a shorted transmission line are reflected back without a phase shift, adding to the incident wave at the short.

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    Open-Circuited Transmission Line

    An open-circuit transmission line, with an infinitely high load impedance, causes the voltage wave to be reflected back without a phase shift. This leads to a maximum voltage at the open end.

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    Voltage Reflection on an Open Line

    Voltage waves on an open transmission line are reflected back without a phase shift, reinforcing the incident wave at the open end.

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    Current Reflection on an Open Line

    Current waves on an open transmission line are reflected back with a 180-degree phase shift, effectively canceling out the incident wave at the open end.

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    Shorted Quarter-Wavelength Line

    A shorted quarter-wavelength transmission line acts like a parallel LC circuit, effectively creating an open circuit at the resonant frequency.

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    Transmission Line as Inductance/Capacitance

    Shorted transmission line sections can create inductance or capacitance depending on their length. Sections shorter than a quarter-wavelength act as inductors, while sections longer than a quarter-wavelength act as capacitors.

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    Study Notes

    Transmission Lines

    • Transmission lines are metallic conductor systems used to transfer electrical energy from one point to another.
    • They consist of two or more conductors separated by an insulator (e.g., a pair of wires).
    • Transmission lines can be short (a few inches) or long (thousands of miles).
    • Transmission lines propagate various signals: DC, low-frequency AC (e.g., 60 cycle power, audio), and high-frequency AC (e.g., intermediate and radio frequencies).

    Primary Requirements

    • Two primary requirements for transmission lines are:
      • Minimum attenuation of the signal.
      • No radiation of the signal as radio energy.
    • All transmission lines and connectors are designed with these requirements in mind.

    Transmission Line Behavior

    • Low-frequency signals propagate predictably along transmission lines.
    • High-frequency signals exhibit more complex and somewhat peculiar behavior, relevant to lumped constant circuits and systems.

    Transverse Electromagnetic (TEM) Waves

    • Propagation of electrical power along a transmission line occurs in the form of TEM waves.
    • A TEM wave is an oscillatory motion where the vibration of a particle excites similar vibrations in nearby particles.
    • The TEM wave propagates primarily through the non-conductor (dielectric) separating the two conductors.
    • A transverse wave's displacement direction is perpendicular to its propagation direction.

    Types of Transmission Lines

    • Transmission lines can be classified as balanced or unbalanced.
      • Balanced lines: both conductors carry current 180° out of phase with each other's current.
      • Unbalanced lines: one wire is grounded, and the other carries all the current.
    • Currents in balanced lines flow in opposite directions and have equal magnitudes with respect to ground.

    Parallel-Conductor Transmission Lines

    • Open-wire line: simple arrangement of two parallel wires, separated by air with nonconductive spacers.
    • Distance between conductors is generally between 2 and 6 inches.
    • Twin-lead (ribbon cable): similar to open-wire but spacers are replaced with a solid dielectric.
      • Typical distance between conductors is 5/16 in.
    • Twisted-pair cable: two insulated conductors twisted together, often in units.
      • Various sheathing types based on intended use.
      • Different pitch twisting reduces interference between pairs.
    • Shielded cable pair: two wires enclosed in a conductive metal braid, which acts as a shield, to reduce radiation.

    Coaxial (Concentric) Transmission Lines

    • Parallel-conductor transmission lines are suitable for low frequencies but unsuitable for high frequencies.
    • Coaxial cables are used for high-frequency applications, reducing losses and isolating transmission paths.
    • Consists of a center conductor surrounded by a concentric outer conductor.
    • The outer conductor provides excellent shielding at high frequencies but is generally grounded in unbalanced applications.
    • Two common types of coaxial cable:
      • Air-filled rigid: using a tubular outer conductor, a spacer, and air as the insulating material.
      • Solid flexible: a braided, flexible outer conductor covering a solid inner conductor.

    Connectors

    • Most transmission lines terminate in a connector that connects the cable to a device or another cable.
      • Ordinary AC power plugs/outlets are basic types of connectors.
      • Special connectors are used with parallel lines and coaxial (often labeled by N-Type, SMA, PL-259, RCA etc.)
      • Connectors are essential for maintain the cable's physical and electrical properties.

    Transmission-Line Equivalent Circuit

    • Transmission line characteristics are determined by its electrical and physical properties (e.g., wire diameter, insulator, and conductor spacing).
    • The primary electrical constants are series dc resistance (R), series inductance (L), shunt capacitance (C), and shunt conductance (G).
      • Resistance and inductance occur along the line.
      • Capacitance and conductance occur between the conductors.
    • These constants are distributed parameters.
    • In simplified circuits; inductance, resistance, and capacitance are lumped together (into larger lumps) to represent a distributed line.
    • The shunt leakage resistance is often negligible and ignored.
      • For short line segments, the resistance of the conductors can also be ignored.

    Characteristic Impedance

    • For maximum power transfer, a transmission line must be terminated in a purely resistive load equal to its characteristic impedance.
    • Zo is a totally independent complex ac quantity expressed in ohms (and often referred to as surge impedance).
    • Can't be measured directly but needed for good design.
    • Can be determined from physical dimensions for certain types of lines.
    • For extremely low frequencies; resistance dominates impedance calculations
    • For extremely high frequencies; inductance and capacitance dominate impedance calculations

    Velocity Factor

    • Velocity constant is the ratio of the actual speed/velocity of propagation through a given medium to the speed of propagation in free space.
    • (Speed/velocity of propagation in media) / (speed of propagation in free space)
    • The velocity factor is approximately 1 / sqrt(εr), where εr is the relative dielectric constant of the material.
    • The dielectric constant (εr) affects the velocity of propagation in a transmission line.

    Electrical Length

    • Electrical length of a transmission line is a ratio of its physical length to the wavelength of the signal propagating along the line.
    • Represented in degrees (º) and/or radians (rad).

    Transmission Line Losses

    • Transmission lines experience various losses.
      • Conductor: (I^2)R loss, directly proportional to current and line length.
        • Skin effect increases this loss at higher frequencies.
      • Radiation: electrostatic and electromagnetic fields around conductors produce radiation losses.
        • Proper shielding can reduce this loss.
      • Dielectric heating: difference of potential between conductors generates heat in the dielectric material.
        • Generally, losses less noticeable with air dielectrics.
      • Coupling: connections and discontinuities in a transmission line cause energy loss.
      • Corona: arcing occurs between conductors at high voltages, damaging the line.
    • Various formulas and ways of calculating total loss.

    Incident and Reflected Waves

    • Transmission lines are bidirectional.
    • Power/voltage/current propagate from source and load, incident power goes to load, reflected power from load.
    • Incident and reflected waves cause standing waves.

    Resonant and Non-resonant Lines

    • Non-resonant lines: have no reflected power/voltage/current.
    • Power/voltage/current are constant along the line.
    • Resonant lines: significant reflected components, and energy alternates between magnetic and electric fields of a transmission line.

    Reflection Coefficient

    • Reflection coefficient (Γ) is a ratio of reflected voltage/current to incident voltage/current.
    • This coefficient is indicative of a mismatch between the load and transmission line.
    • Has mathematical formulas to represent it.

    Standing Waves

    • Standing waves result from interference of reflected and incident waves in a transmission line.
    • These waves have minima and maxima (nodes and antinodes) spaced by half a wavelength.
    • Math Formulas to represent it

    Standing-Wave Ratio (SWR)

    • SWR is the ratio of maximum voltage or current to minimum.
    • Represents a mismatch between load and line characteristic impedance.
    • Math formulas to represent it.

    Return Loss

    • Return loss (RL) is the ratio of power in reflected wave to incident wave.
    • Low return loss is better and more efficient.
    • Math formulas to represent it

    Transmission Loss (TL)

    • A measure of loss in a transmission line.
    • Has mathematical formulas to represent it based on SWR and reflection coefficient

    Exercises

    • Specific scenarios are provided where students should calculate mismatch loss or determine characteristic impedance given various line properties and conditions from provided formulas.

    Transmission Line Applications

    • Applications include simulations of inductance, capacitance, & resonance (using shorted and open sections).
    • Specific values/lengths of short/open lines can be used to simulate pure inductance and capacitance.
    • Smith chart use for visualizing these applications.

    Stub Matching

    • Useful technique for matching transmission lines to loads using a shorter section of a transmission line called a "stub."
    • Essentially a way to tune/match susceptance of a load in a transmission line - often using short or open transmission line segments.
    • Provides a different way to improve impedance matching.

    The Smith Chart

    • A graphical tool that simplifies calculations and analysis/diagnostics/design involving transmission lines.
    • A method used to quickly solve common transmission line problems.
      • A complex graph providing quick solutions for transmission line calculations.

    References

    • List of references (textbooks and other resources)

    Thank You

    • Thank you note. Note references might be part of the references section rather than here.

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