EP 603 Microwave Devices CHAPTER 2 WAVEGUIDE AND
![EP 603 Microwave Devices CHAPTER 2 WAVEGUIDE AND COMPONENTS - Propagation mode of Electromagnetic EP 603 Microwave Devices CHAPTER 2 WAVEGUIDE AND COMPONENTS - Propagation mode of Electromagnetic](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-1.jpg)
![2. 1 Propagation Mode of EM Wave 2. 1 Propagation Mode of EM Wave](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-2.jpg)
![Transverse Electromagnetic (TEM) • The electric field, E and the magnetic field, H are Transverse Electromagnetic (TEM) • The electric field, E and the magnetic field, H are](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-3.jpg)
![Transverse Electric (TE) • The electric field, E is transverse to the direction of Transverse Electric (TE) • The electric field, E is transverse to the direction of](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-4.jpg)
![Transverse Magnetic (TM) • The magnetic field, H is transverse to the direction of Transverse Magnetic (TM) • The magnetic field, H is transverse to the direction of](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-5.jpg)
![Cont. Cont.](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-6.jpg)
![Poynting Vector • It determines that the power radiation is away from the antenna Poynting Vector • It determines that the power radiation is away from the antenna](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-7.jpg)
![Cont. • It represents the power in watts per square meter of the electromagnetic Cont. • It represents the power in watts per square meter of the electromagnetic](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-8.jpg)
![Example 1 1. If E-field propagates in the direction of +ve x-axis and Hfield Example 1 1. If E-field propagates in the direction of +ve x-axis and Hfield](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-9.jpg)
![Boundary Condition • It refers to the conditions that E-field and H-field within a Boundary Condition • It refers to the conditions that E-field and H-field within a](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-10.jpg)
![Cont. • Since E-field causes a current flow that in turn produces Hfield, both Cont. • Since E-field causes a current flow that in turn produces Hfield, both](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-11.jpg)
![Spherical Wave • Is a sphere of constant phase moving away from the antenna Spherical Wave • Is a sphere of constant phase moving away from the antenna](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-12.jpg)
![Cont. • At a given distance from an antenna radiating an electromagnetic wave, the Cont. • At a given distance from an antenna radiating an electromagnetic wave, the](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-13.jpg)
![Plane Wave • A small part of the sphere that appears as a flat Plane Wave • A small part of the sphere that appears as a flat](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-14.jpg)
![2. 2 Waveguide & Transmission Line • Waveguide: hollow metal tube used to guide 2. 2 Waveguide & Transmission Line • Waveguide: hollow metal tube used to guide](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-15.jpg)
![Cont. Transmission Line Coaxial Line Stripline Microstrip Waveguides Rectangular Circular Ridge Flexible Cont. Transmission Line Coaxial Line Stripline Microstrip Waveguides Rectangular Circular Ridge Flexible](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-16.jpg)
![Rectangular Waveguide • It consists of a hollow rectangular waveguide (rectangular cross section) that Rectangular Waveguide • It consists of a hollow rectangular waveguide (rectangular cross section) that](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-17.jpg)
![Cont. • It is a standard convention to have the longest side of the Cont. • It is a standard convention to have the longest side of the](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-18.jpg)
![Circular Waveguide • It consists of a hollow, round (circular cross section) metal pipe Circular Waveguide • It consists of a hollow, round (circular cross section) metal pipe](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-19.jpg)
![Cont. • The structure of such a circular waveguide with inner radius a, is Cont. • The structure of such a circular waveguide with inner radius a, is](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-20.jpg)
![Ridge Waveguide • It is formed with a rectangular ridge projecting inward from one Ridge Waveguide • It is formed with a rectangular ridge projecting inward from one](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-21.jpg)
![Cont. Ridged Waveguide Using Metal Bar Singled Ridged Waveguide Double Ridged Waveguide Cont. Ridged Waveguide Using Metal Bar Singled Ridged Waveguide Double Ridged Waveguide](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-22.jpg)
![Coaxial Line • Coaxial line: an electrical cable with an inner conductor surrounded by Coaxial Line • Coaxial line: an electrical cable with an inner conductor surrounded by](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-23.jpg)
![Cont. Cont.](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-24.jpg)
![Strip Line • It consists of a thin conducting strip of width W that Strip Line • It consists of a thin conducting strip of width W that](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-25.jpg)
![Cont. Outer Conductor E-field Dielectric Ground plane w Inner Conductor H-field Cont. Outer Conductor E-field Dielectric Ground plane w Inner Conductor H-field](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-26.jpg)
![Microstrip • It consists of a conducting strip separated from a ground plane by Microstrip • It consists of a conducting strip separated from a ground plane by](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-27.jpg)
![Cont. Cont.](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-28.jpg)
![Flexible Waveguide • It is used for bends, twists or in applications where certain Flexible Waveguide • It is used for bends, twists or in applications where certain](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-29.jpg)
![Cont. • The H bend of Figure (a) is used to turn a 90° Cont. • The H bend of Figure (a) is used to turn a 90°](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-30.jpg)
![2. 3 Characteristic of Waveguide • Critical (cut-off) frequency, fc(Hz): the lowest frequency for 2. 3 Characteristic of Waveguide • Critical (cut-off) frequency, fc(Hz): the lowest frequency for](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-31.jpg)
![Cont. • Phase velocity (vp, m/s): a) The velocity at which the wave changes Cont. • Phase velocity (vp, m/s): a) The velocity at which the wave changes](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-32.jpg)
![Cont. • Propagation wavelength in the waveguide (λg, m/s): a)Wavelength of travelling wave that Cont. • Propagation wavelength in the waveguide (λg, m/s): a)Wavelength of travelling wave that](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-33.jpg)
![Rectangular Waveguide TE/TM Calculations • Dominant mode (mode with lowest cutoff frequency) for rectangular Rectangular Waveguide TE/TM Calculations • Dominant mode (mode with lowest cutoff frequency) for rectangular](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-34.jpg)
![Cont. Cont.](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-35.jpg)
![Example 1. For a rectangular waveguide with a width of 3 cm and a Example 1. For a rectangular waveguide with a width of 3 cm and a](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-36.jpg)
![Circular Waveguide TE/TM Calculations • Dominant mode for circular waveguide is TE 1, 1. Circular Waveguide TE/TM Calculations • Dominant mode for circular waveguide is TE 1, 1.](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-37.jpg)
![Cont. Cont.](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-38.jpg)
![Cont. Cont.](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-39.jpg)
![Example 1. For a circular waveguide with a radius of 1 cm and a Example 1. For a circular waveguide with a radius of 1 cm and a](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-40.jpg)
- Slides: 40
![EP 603 Microwave Devices CHAPTER 2 WAVEGUIDE AND COMPONENTS Propagation mode of Electromagnetic EP 603 Microwave Devices CHAPTER 2 WAVEGUIDE AND COMPONENTS - Propagation mode of Electromagnetic](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-1.jpg)
EP 603 Microwave Devices CHAPTER 2 WAVEGUIDE AND COMPONENTS - Propagation mode of Electromagnetic Wave - Microwave Waveguide & Transmission Line -Characteristic of Waveguide - Methods of Propagation Modes/ Excitation in Waveguides - Discontinuities in Waveguide Components - Attenuation in Waveguide Components
![2 1 Propagation Mode of EM Wave 2. 1 Propagation Mode of EM Wave](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-2.jpg)
2. 1 Propagation Mode of EM Wave
![Transverse Electromagnetic TEM The electric field E and the magnetic field H are Transverse Electromagnetic (TEM) • The electric field, E and the magnetic field, H are](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-3.jpg)
Transverse Electromagnetic (TEM) • The electric field, E and the magnetic field, H are oriented transverse to the direction of propagation of wave. • Exists in plane waves and transmission lines (2 conductors). • No cut-off frequency. y Ey Direction of Travel Hz Hz z x
![Transverse Electric TE The electric field E is transverse to the direction of Transverse Electric (TE) • The electric field, E is transverse to the direction of](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-4.jpg)
Transverse Electric (TE) • The electric field, E is transverse to the direction of propagation of wave and the magnetic field, H has components transverse and in the direction of the wave. • Exists in waveguide modes. y Ey Hx Hy z H Direction of travel x
![Transverse Magnetic TM The magnetic field H is transverse to the direction of Transverse Magnetic (TM) • The magnetic field, H is transverse to the direction of](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-5.jpg)
Transverse Magnetic (TM) • The magnetic field, H is transverse to the direction of propagation of wave and the electric field, E has components transverse and in the direction of the wave. • Exists in waveguide modes. y Ey E Ex Hz z Direction of travel x
![Cont Cont.](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-6.jpg)
Cont.
![Poynting Vector It determines that the power radiation is away from the antenna Poynting Vector • It determines that the power radiation is away from the antenna](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-7.jpg)
Poynting Vector • It determines that the power radiation is away from the antenna (the E and H field are perpendicular to each other). • Can be expressed mathematically as: H where ; P = power, W/m² E E = electric field, V/m H = magnetic field, A/m V
![Cont It represents the power in watts per square meter of the electromagnetic Cont. • It represents the power in watts per square meter of the electromagnetic](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-8.jpg)
Cont. • It represents the power in watts per square meter of the electromagnetic wave and the velocity of its wave is equal to the speed of light. • Steps to sketch the direction of e. m. wave propagation according to Poynting vector: a) Determine the direction of propagation. b) Refer to the electric and magnetic field orientation. c) Sketch the em wave propagation base on step no. 2.
![Example 1 1 If Efield propagates in the direction of ve xaxis and Hfield Example 1 1. If E-field propagates in the direction of +ve x-axis and Hfield](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-9.jpg)
Example 1 1. If E-field propagates in the direction of +ve x-axis and Hfield propagates in the direction of +ve y-axis, sketch the direction of the electromagnetic wave propagation.
![Boundary Condition It refers to the conditions that Efield and Hfield within a Boundary Condition • It refers to the conditions that E-field and H-field within a](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-10.jpg)
Boundary Condition • It refers to the conditions that E-field and H-field within a waveguide must meet before energy travels down the waveguide. • There are 2 conditions that must be met: a)For an electric field to exist at the surface of a conductor, it must be perpendicular to the conductor. An electric field CANNOT exist parallel to a perfect conductor. a)For a varying magnetic field to exist, it must form closed loops in parallel with the conductors and be perpendicular to the electric field. • Energy travelling down a waveguide is similar to the electromagnetic waves travel in free space. The difference is that the energy in a waveguide is confined to the physical limits of the guide.
![Cont Since Efield causes a current flow that in turn produces Hfield both Cont. • Since E-field causes a current flow that in turn produces Hfield, both](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-11.jpg)
Cont. • Since E-field causes a current flow that in turn produces Hfield, both fields always exist at the same time in a waveguide. • If one field satisfies one of these boundary conditions, it must also satisfy the other since neither field can exist alone.
![Spherical Wave Is a sphere of constant phase moving away from the antenna Spherical Wave • Is a sphere of constant phase moving away from the antenna](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-12.jpg)
Spherical Wave • Is a sphere of constant phase moving away from the antenna with a velocity equal to the speed of light in a direction determined by Poynting vector. • Radiates in all direction uniformly. Isotropic source (source of e. m. wave radiation: radiates in all direction uniformly) Circular curve form a straight line.
![Cont At a given distance from an antenna radiating an electromagnetic wave the Cont. • At a given distance from an antenna radiating an electromagnetic wave, the](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-13.jpg)
Cont. • At a given distance from an antenna radiating an electromagnetic wave, the phase of the electric field at that instant of time would be the same over the surface of the sphere. H field P points outward H E field E Wavefront at a given instant of time Direction of wavefront
![Plane Wave A small part of the sphere that appears as a flat Plane Wave • A small part of the sphere that appears as a flat](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-14.jpg)
Plane Wave • A small part of the sphere that appears as a flat surface with the electric field, E and the magnetic field, H be at right angles (90˚) to each other and are straight lines. E H
![2 2 Waveguide Transmission Line Waveguide hollow metal tube used to guide 2. 2 Waveguide & Transmission Line • Waveguide: hollow metal tube used to guide](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-15.jpg)
2. 2 Waveguide & Transmission Line • Waveguide: hollow metal tube used to guide e. m. energy from one point to another or through which e. m. waves propagate. • Typically one enclosed conductor filled with an insulating medium. • The transmission of e. m. energy along waveguide travels at velocity slower than e. m. energy traveling through free space. • Transmission line: Two or more conductors separated by some insulating medium.
![Cont Transmission Line Coaxial Line Stripline Microstrip Waveguides Rectangular Circular Ridge Flexible Cont. Transmission Line Coaxial Line Stripline Microstrip Waveguides Rectangular Circular Ridge Flexible](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-16.jpg)
Cont. Transmission Line Coaxial Line Stripline Microstrip Waveguides Rectangular Circular Ridge Flexible
![Rectangular Waveguide It consists of a hollow rectangular waveguide rectangular cross section that Rectangular Waveguide • It consists of a hollow rectangular waveguide (rectangular cross section) that](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-17.jpg)
Rectangular Waveguide • It consists of a hollow rectangular waveguide (rectangular cross section) that can propagate TM and TE modes but not TEM since only one conductor is present. • The wall of the guides are conductors and therefore reflection from them may take place. • Applications: high-power systems, millimeter wave applications, satellite systems, precision test applications.
![Cont It is a standard convention to have the longest side of the Cont. • It is a standard convention to have the longest side of the](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-18.jpg)
Cont. • It is a standard convention to have the longest side of the waveguide along x-axis [a (width) > b (length)]
![Circular Waveguide It consists of a hollow round circular cross section metal pipe Circular Waveguide • It consists of a hollow, round (circular cross section) metal pipe](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-19.jpg)
Circular Waveguide • It consists of a hollow, round (circular cross section) metal pipe that supports TE and TM waveguide modes. • Applications: used in transmission of circularly polarized waves, to connect components having circular cross-section (e. g. : isolators or attenuators) to rectangular waveguide.
![Cont The structure of such a circular waveguide with inner radius a is Cont. • The structure of such a circular waveguide with inner radius a, is](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-20.jpg)
Cont. • The structure of such a circular waveguide with inner radius a, is shown below:
![Ridge Waveguide It is formed with a rectangular ridge projecting inward from one Ridge Waveguide • It is formed with a rectangular ridge projecting inward from one](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-21.jpg)
Ridge Waveguide • It is formed with a rectangular ridge projecting inward from one or both of the wide walls in a rectangular waveguide. • Ridge is used to concentrate the electric field across the ridge and to lower the cutoff frequency of TE 10 mode. • Applications: attractive for UHF and low microwave ranges.
![Cont Ridged Waveguide Using Metal Bar Singled Ridged Waveguide Double Ridged Waveguide Cont. Ridged Waveguide Using Metal Bar Singled Ridged Waveguide Double Ridged Waveguide](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-22.jpg)
Cont. Ridged Waveguide Using Metal Bar Singled Ridged Waveguide Double Ridged Waveguide
![Coaxial Line Coaxial line an electrical cable with an inner conductor surrounded by Coaxial Line • Coaxial line: an electrical cable with an inner conductor surrounded by](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-23.jpg)
Coaxial Line • Coaxial line: an electrical cable with an inner conductor surrounded by a flexible insulating layer, surrounded by a conducting shield (outer conductor). • Microwaves travel through the flexible insulation layer. • Applications: feed lines connecting radio transmitter and receivers with their antennas, computer network (internet) connections and distributing cable television(signal).
![Cont Cont.](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-24.jpg)
Cont.
![Strip Line It consists of a thin conducting strip of width W that Strip Line • It consists of a thin conducting strip of width W that](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-25.jpg)
Strip Line • It consists of a thin conducting strip of width W that is centered between two wide conducting ground planes. • Dielectric material is placed on both sides of the strip conductor. • Applications: used inside of the microwave devices themselves (e. g. : microwave integrated circuitry).
![Cont Outer Conductor Efield Dielectric Ground plane w Inner Conductor Hfield Cont. Outer Conductor E-field Dielectric Ground plane w Inner Conductor H-field](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-26.jpg)
Cont. Outer Conductor E-field Dielectric Ground plane w Inner Conductor H-field
![Microstrip It consists of a conducting strip separated from a ground plane by Microstrip • It consists of a conducting strip separated from a ground plane by](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-27.jpg)
Microstrip • It consists of a conducting strip separated from a ground plane by a dielectric layer known as the substrate. • A conductor of width W is printed on a thin, grounded dielectric substrate of thickness h and relative permittivity ᵋ r. • Applications: used inside of the microwave devices themselves (e. g. : microwave integrated circuitry).
![Cont Cont.](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-28.jpg)
Cont.
![Flexible Waveguide It is used for bends twists or in applications where certain Flexible Waveguide • It is used for bends, twists or in applications where certain](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-29.jpg)
Flexible Waveguide • It is used for bends, twists or in applications where certain criteria may not be fulfilled by normal waveguides. • Figure below shows some of the flexible waveguides:
![Cont The H bend of Figure a is used to turn a 90 Cont. • The H bend of Figure (a) is used to turn a 90°](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-30.jpg)
Cont. • The H bend of Figure (a) is used to turn a 90° corner. • The E bend Figure (b) also completes a 90° turn in either an upward or downward direction. • The twist of Figure (c) is used to effect a shift in the polarization of the wave.
![2 3 Characteristic of Waveguide Critical cutoff frequency fcHz the lowest frequency for 2. 3 Characteristic of Waveguide • Critical (cut-off) frequency, fc(Hz): the lowest frequency for](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-31.jpg)
2. 3 Characteristic of Waveguide • Critical (cut-off) frequency, fc(Hz): the lowest frequency for which a mode will propagate in a waveguide. • Critical (cut-off) wavelength, λc (m/cycle): the largest wavelength that can propagate in the waveguide without any / minimum attenuation (or the smallest free space wavelength that is just unable to propagate in the waveguide). • Group velocity (vg, m/s): a) The velocity at which a wave propagates. b) Refers to the velocity of a group of waves. c) It is also the velocity at which information signals or energy is propagated.
![Cont Phase velocity vp ms a The velocity at which the wave changes Cont. • Phase velocity (vp, m/s): a) The velocity at which the wave changes](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-32.jpg)
Cont. • Phase velocity (vp, m/s): a) The velocity at which the wave changes phase. b) It is the apparent velocity of the wave (i. e. : max electric intensity point). c) vp always equal to or greater than vg (vp ≥ vg). d) It may exceed the velocity of light (velocity in free space). • In theory: c < vg ≤ vp. • The relationship between vg, vp and speed of light, c is given by: c 2 = vg + vp
![Cont Propagation wavelength in the waveguide λg ms aWavelength of travelling wave that Cont. • Propagation wavelength in the waveguide (λg, m/s): a)Wavelength of travelling wave that](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-33.jpg)
Cont. • Propagation wavelength in the waveguide (λg, m/s): a)Wavelength of travelling wave that propagates down the waveguide. b)λg will be greater in the waveguide than in free space (λo). • Waveguide characteristic impedance (Zo, Ω): a)It depends on the cut-off frequency, which in turn is determined by the guide dimension. b)It is also closely related to the characteristic impedance of free space (377 Ω). c)Generally, Zo > 377 Ω.
![Rectangular Waveguide TETM Calculations Dominant mode mode with lowest cutoff frequency for rectangular Rectangular Waveguide TE/TM Calculations • Dominant mode (mode with lowest cutoff frequency) for rectangular](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-34.jpg)
Rectangular Waveguide TE/TM Calculations • Dominant mode (mode with lowest cutoff frequency) for rectangular waveguide is TE 1, 0. • A waveguide acts as a high-pass filter in that it passes only those frequencies above the cutoff frequency.
![Cont Cont.](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-35.jpg)
Cont.
![Example 1 For a rectangular waveguide with a width of 3 cm and a Example 1. For a rectangular waveguide with a width of 3 cm and a](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-36.jpg)
Example 1. For a rectangular waveguide with a width of 3 cm and a desired frequency of operation of 6 GHz (for dominant mode), determine: a) Cut-off frequency b) Cut-off wavelength c) Group velocity d) Phase velocity e) Propagation wavelength in the waveguide f) Characteristic impedance 2. Repeat Example 1 for a rectangular waveguide with a width of 2. 5 cm and a desired frequency of operation of 7 GHz.
![Circular Waveguide TETM Calculations Dominant mode for circular waveguide is TE 1 1 Circular Waveguide TE/TM Calculations • Dominant mode for circular waveguide is TE 1, 1.](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-37.jpg)
Circular Waveguide TE/TM Calculations • Dominant mode for circular waveguide is TE 1, 1. • For TE 1, 1 mode, x’ 11 = 1. 841 (solution of Bessel function equation).
![Cont Cont.](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-38.jpg)
Cont.
![Cont Cont.](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-39.jpg)
Cont.
![Example 1 For a circular waveguide with a radius of 1 cm and a Example 1. For a circular waveguide with a radius of 1 cm and a](https://slidetodoc.com/presentation_image_h/97ef87995d7df17d76be86bc2c61271d/image-40.jpg)
Example 1. For a circular waveguide with a radius of 1 cm and a desired frequency of operation of 10 GHz (for dominant mode), determine: a) Cut-off frequency b) Cut-off wavelength c) Group velocity d) Phase velocity e) Propagation wavelength in the waveguide f) Characteristic impedance 2. Repeat Example 1 for a circular waveguide with a radius of 2. 5 cm and a desired frequency of operation of 7 GHz.
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