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Questions and Answers

What does a phasor represent in terms of sinusoidal functions?

  • Only phase angle
  • Frequency and amplitude
  • Real part only
  • Magnitude and phase (correct)

In the function $v(t) = A ext{cos}( heta + eta)$, how can it be expressed in phasor form?

  • V = A e^{j heta}
  • V = A + jeta
  • V = A e^{jeta}
  • V = A ext{cos} heta + jA ext{sin} heta (correct)

What is represented by the permittivity in electromagnetic material properties?

  • How efficiently a magnetic field is produced
  • How well a dielectric is insulated
  • How well a dielectric is polarized (correct)
  • How resistant a material is to electric flow

Which of the following statements about Maxwell's equations in phasor form is correct?

<p>They include time derivatives represented by complex numbers. (D)</p> Signup and view all the answers

Which property measures how well a magnetic material can be magnetized?

<p>Permeability (C)</p> Signup and view all the answers

What does the parameter $ heta$ represent in the equation $D= heta E$?

<p>Electric field intensity (C)</p> Signup and view all the answers

Which equation correctly represents the relationship between magnetic flux density and H-field intensity?

<p>B = $eta$H (C)</p> Signup and view all the answers

What property allows a material to easily store electric energy?

<p>High permittivity (A)</p> Signup and view all the answers

Which of the following is NOT a characteristic that distinguishes isotropic materials?

<p>Orientation dependent behavior (A)</p> Signup and view all the answers

What defines a homogeneous material?

<p>Consistent properties throughout (B)</p> Signup and view all the answers

What relationship does the equation $J = heta E$ illustrate?

<p>Current density and electric field intensity (D)</p> Signup and view all the answers

What does the term $E$ typically refer to in electromagnetic equations?

<p>Electric field intensity (A)</p> Signup and view all the answers

Which of the following describes a linear material?

<p>Response to field strength is proportional (D)</p> Signup and view all the answers

What characterizes a Transverse Electric Wave (TE)?

<p>No E-field in the direction of propagation (A)</p> Signup and view all the answers

Which of the following is NOT a type of transmission line mentioned?

<p>Coaxial cable (A)</p> Signup and view all the answers

In a Transverse Magnetic Wave (TM), which field is orthogonal to the direction of propagation?

<p>H-field only (D)</p> Signup and view all the answers

What is the purpose of the cutoff frequency in waveguides?

<p>To determine the mode of propagation (B)</p> Signup and view all the answers

Which option describes the configuration of a microstrip line?

<p>It consists of a dielectric substrate and two conductors (C)</p> Signup and view all the answers

What type of wave characteristic means neither the E-field nor H-field is in the direction of propagation?

<p>Transverse Electric and Magnetic (TEM) (A)</p> Signup and view all the answers

What is a defining feature of a coplanar waveguide?

<p>It uses two parallel conducting strips on the same plane (B)</p> Signup and view all the answers

Which transmission line is typically used in microwave applications?

<p>Microstrip line (D)</p> Signup and view all the answers

What does a voltage standing wave ratio (VSWR) of 1 indicate?

<p>There is a perfect match. (B)</p> Signup and view all the answers

What does a VSWR approaching infinity signify?

<p>Total reflection due to mismatch. (A)</p> Signup and view all the answers

In the context of return loss, what does a return loss of 0 dB indicate?

<p>Total reflection. (D)</p> Signup and view all the answers

What is indicated by a reflection coefficient ($\Gamma$) of 0?

<p>Perfect match. (C)</p> Signup and view all the answers

What happens when the load impedance ($Z_L$) is equal to the characteristic impedance ($Z_0$)?

<p>No standing waves are formed. (C)</p> Signup and view all the answers

If the reflection coefficient ($\Gamma$) is 1, what does this say about the reflection at the load?

<p>Total reflection occurs. (D)</p> Signup and view all the answers

What is the mathematical expression for calculating return loss?

<p>RL = -20 log10(\Gamma) (A)</p> Signup and view all the answers

What does the term 'matched condition' refer to in wave theory?

<p>A scenario with equal load and source impedances. (A)</p> Signup and view all the answers

Which of the following best describes 'standing waves'?

<p>Waves formed due to impedance mismatch. (C)</p> Signup and view all the answers

How can the voltage maximum ($V_{max}$) in a standing wave be expressed mathematically?

<p>$V_{max} = V_0 (1 + \Gamma)$ (A)</p> Signup and view all the answers

What is the result of a matched transmission line?

<p>Perfect energy transfer (A)</p> Signup and view all the answers

What does a high Return Loss (RL) indicate?

<p>Good impedance matching (C)</p> Signup and view all the answers

Which factor can lead to signal attenuation in a transmission line?

<p>Presence of resistance and conductance (D)</p> Signup and view all the answers

What does the term VSWR stand for?

<p>Voltage Standing Wave Ratio (A)</p> Signup and view all the answers

Which condition describes a lossy transmission line?

<p>Presence of resistance and conductance (A)</p> Signup and view all the answers

What is the relationship between Voltage Standing Wave Ratio (VSWR) and reflection coefficient (Gamma)?

<p>VSWR depends on the square of Gamma (C)</p> Signup and view all the answers

What happens to VSWR as Gamma approaches 0?

<p>VSWR approaches 1 (D)</p> Signup and view all the answers

Which of the following represents a mismatch in a transmission line?

<p>Gamma equals 0.5 (A)</p> Signup and view all the answers

What signifies a short termination in a transmission line?

<p>Reflection coefficient of 1 (B)</p> Signup and view all the answers

In terms of impedance, what does the term 'matched' specifically refer to?

<p>Load impedance equals characteristic impedance (A)</p> Signup and view all the answers

What characterizes a plane wave in the context of electromagnetic waves?

<p>It is constant in both magnitude and direction over a plane. (C)</p> Signup and view all the answers

What is the main purpose of boundary conditions in wave equations?

<p>To provide a unique solution. (C)</p> Signup and view all the answers

What is the representation of the angular frequency in wave mechanics?

<p>$ rac{2 ext{π}}{T}$ (A)</p> Signup and view all the answers

What does the Poynting vector represent in an electromagnetic field?

<p>The direction and magnitude of energy flow. (A)</p> Signup and view all the answers

What is true about the wave impedance in vacuum?

<p>It is defined as $Z_0 = 120 ext{π} ext{Ω}$. (B)</p> Signup and view all the answers

Which equation represents the relationship for electromagnetic fields in a wave?

<p>Both A and B are correct. (D)</p> Signup and view all the answers

What is the meaning of the term 'phase velocity' in the context of wave propagation?

<p>Speed of the wavefront. (A)</p> Signup and view all the answers

In the context of plane waves, what does the term 'wavefront' refer to?

<p>The surface over which the fields are constant. (D)</p> Signup and view all the answers

How is the wavelength related to frequency and angular frequency?

<p>$λ = rac{v}{f}$ (A)</p> Signup and view all the answers

What is not a characteristic of a plane wave?

<p>It perfectly represents real-world waves. (A)</p> Signup and view all the answers

What condition must be met for a wave equation to yield a unique solution?

<p>Boundary conditions must be provided. (C)</p> Signup and view all the answers

Which of the following parameters is not part of the wave impedance definition?

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

The intrinsic impedance in a vacuum is approximately:

<p>$377Ω$ (D)</p> Signup and view all the answers

What does the equation $ abla^2 E + ω^2 μ ε E = 0$ represent?

<p>The wave equation for electric fields. (D)</p> Signup and view all the answers

Flashcards

Phasor

A complex number representing the magnitude and phase of a sinusoidal quantity.

Time-Harmonic

Sinusoidal fields, currents, and voltages with a specific angular frequency 𝜔.

Permittivity (ε)

A material property describing how well a dielectric material polarizes in an electric field.

Permeability (µ)

A material property describing how well a material can be magnetized in a magnetic field.

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Conductivity

A material property indicating a conductor’s ability to conduct current without energy loss.

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Electric Flux Density (D)

The electric field strength per unit area. Measured in Coulombs per square meter.

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Electric Field Intensity (E)

Strength of an electric field. Measured in Volts per meter.

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Magnetic Flux Density (B)

The measure of magnetic field strength per unit area. Measured in Webers per square meter.

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Magnetic Field Intensity (H)

Strength of a magnetic field. Measured in Amperes per meter.

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Conductivity (σ)

Measure of a material's ability to conduct electrical current.

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Isotropic Material

Material properties are the same in all directions.

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Plane Wave

A transverse electromagnetic wave with constant magnitude and direction over a plane normal to its propagation direction.

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Wave Equation

Mathematical equation describing the propagation of waves, in this case, electromagnetic waves.

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Boundary Conditions

Specific conditions that a solution must meet at the boundaries of the system.

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Poynting Vector

A vector representing the power flow density of an electromagnetic field, calculated as the cross product of electric and magnetic fields.

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Phase Velocity

The speed at which a phase of a wave travels.

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Wavelength

The distance between two successive identical points (crests or troughs) in a wave.

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Frequency

The number of wave cycles per unit time.

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Angular Frequency

Frequency expressed in radians per second.

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Wave Number

A quantity representing how many waves there are per unit distance.

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Intrinsic Impedance

A characteristic impedance of a medium for electromagnetic waves.

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Transmission Line

A system that transmits electrical signals.

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TEM Wave

Transverse electromagnetic wave.

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Wave Impedance

The ratio of the electric field strength to the magnetic field strength in an electromagnetic wave.

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Amplitude

The maximum displacement in a wave.

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Period

The time it takes for a wave to complete one full cycle.

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What are the main types of transmission lines?

Transmission lines can be categorized as cable, waveguide, microstrip line, or coplanar waveguide. Each type has unique characteristics for signal transmission.

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What are planar transmission lines?

Planar transmission lines are a type of transmission line built on a flat plane, using a substrate material. Examples include stripline, microstrip line, coplanar waveguide, slot waveguide, and Substrate Integrated Waveguide (SIW).

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What are Microwave Circuits?

Microwave circuits use transmission line elements to create functional components like amplifiers, filters, and oscillators, operating at microwave frequencies.

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What does TEM wave mean?

A Transverse Electromagnetic (TEM) wave has both electric and magnetic fields perpendicular to the direction of propagation. This means the fields do not have a component along the direction the wave is traveling.

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What is a TE wave?

A Transverse Electric (TE) wave, also known as H-mode, has only the electric field perpendicular to the direction of propagation. The magnetic field can have a component along the direction of propagation.

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What is a TM wave?

A Transverse Magnetic (TM) wave, also known as E-mode, has only the magnetic field perpendicular to the direction of propagation. The electric field can have a component along the direction of propagation.

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What is cutoff frequency?

Cutoff frequency is the minimum frequency that a waveguide can support without significant attenuation. Below this frequency, the wave will not propagate effectively.

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What is the cutoff frequency formula for rectangular waveguides?

The cutoff frequency for a rectangular waveguide is calculated using the formula: f0 = (1/(2sqrt(με))) * sqrt((m/a)^2 + (n/b)^2). 'm' and 'n' are mode numbers, 'a' and 'b' are waveguide dimensions, and µ, ε are material permeability and permittivity.

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Transmission Line Termination

The condition at the end of a transmission line, determining how energy is reflected or absorbed.

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Open Circuit Termination

A transmission line ending with an infinite impedance, causing all energy to be reflected back.

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Short Circuit Termination

A transmission line ending with zero impedance, causing all energy to be reflected back, but with phase inversion.

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Matched Termination

A transmission line ending with an impedance equal to its characteristic impedance, resulting in no reflections.

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Voltage Standing Wave Ratio (VSWR)

A measure of the magnitude of voltage variations on a transmission line, indicating the degree of reflection.

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Return Loss

The ratio of reflected power to incident power, expressed in dB, indicating the amount of energy lost due to reflection.

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Gamma (Γ)

The reflection coefficient, representing the ratio of reflected voltage to incident voltage.

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Lossy Transmission Line

A transmission line that dissipates energy due to conductor resistance, dielectric losses, and radiation.

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Dispersive Transmission Line

A transmission line where different frequencies travel at different speeds, causing signal distortion.

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Good Transmission Line

A transmission line with low attenuation, low VSWR, and high return loss, ensuring effective energy transfer.

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Standing Wave

A wave pattern formed by the superposition of two waves traveling in opposite directions with the same frequency and amplitude. The wave appears stationary with points of maximum and minimum amplitude.

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What causes standing waves?

Standing waves are caused by the superposition of reflected and incident waves when there is an impedance mismatch at the load.

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Reflection Coefficient (Γ)

The ratio of reflected voltage to incident voltage in a transmission line. It indicates the amount of power reflected at a mismatch.

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Gamma (Γ) and VSWR Relationship

The reflection coefficient (Γ) is directly related to the VSWR. A higher Γ leads to a higher VSWR, indicating a greater impedance mismatch.

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Perfect Match

When the load impedance matches the characteristic impedance of the transmission line, there is no reflection and the VSWR is 1. All power is transmitted to the load.

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Total Reflection

When the load impedance is drastically different from the characteristic impedance, all power is reflected back, the VSWR approaches infinity, and there is a strong standing wave.

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Return Loss (RL)

The amount of power reflected back from a load due to mismatch, expressed in dB. A higher RL implies less power reflected.

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Relationship between RL and Γ

Return loss (RL) is directly related to the reflection coefficient (Γ). A higher Γ results in a lower RL indicating more reflected power.

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How does RL change with mismatch?

A perfect match (Γ = 0) results in infinite return loss (RL = +∞ dB) indicating no reflected power. Total reflection (Γ = 1) results in zero return loss (RL = 0 dB) indicating all power is reflected.

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Study Notes

Microwave Engineering & Special Topics in Passive Microwave Circuit Design

  • Course offered by the Electromagnetic Measurement & Application (EMMA) Lab, Department of Electrical and Information Engineering, SeoulTech.
  • Instructor: Jae-Young Chung.

Course Content

  • Electromagnetic (EM) Measurements: Broadband permittivity, permeability, shielding measurements; Antenna and RF component characterization; Conducted and radiated field measurements; Field tests.
  • EM Applications: Next-generation smartphone and base station antenna designs; Autonomous vehicle, military, and satellite antenna designs; High-frequency filters, power dividers, and controllers.
  • Course delivery is a blended format
    • In-class lectures on Mondays
    • Online video lectures on Fridays
    • Lecture materials (PPT slides) provided on Sundays
    • Online video materials on Thursdays
  • Learning materials are in eclass.
  • Students can utilize the Q&A bulletin board for course-related queries. Inquiries should be sent via email ([email protected]) if it is not related to the course or lecture.

Microwave Engineering Book

  • Any edition of Pozar's Microwave Engineering textbook is acceptable.

Homework

  • Homework assignments are included/planned.

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