EC-307

RF and Microwave Engineering

 Unit 2
Waveguides and Resonators: Rectangular and Circular
Waveguides. Mode structures, Cut-off frequency,
Propagation characteristics, Wall current, Attenuation
constant, and Waveguide excitations. Waveguide
Resonators-Rectangular & Cylindrical; Resonant
frequencies, Mode structures, Q factor, Co-axial Resonators;
Excitation & Coupling of cavities, Design of resonators

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Waveguides
❖ A hollow metallic tube of a uniform cross-section for transmitting electromagnetic
waves by successive reflections from the tube’s inner walls is called a waveguide.

❖ In other words, Waveguides are the structures that guide electromagnetic waves to a
targeted destination. They transmit energy in one direction with minimum loss.

❖ Microwaves propagate through microwave circuits, components, and devices, which

are part of Microwave transmission lines, broadly called Waveguides.

❖ A waveguide is generally preferred in microwave communications. A waveguide is a

special form of a transmission line, which is a hollow metal tube. Unlike the
transmission line, the waveguide has no center conductor.

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ADVANTAGES OF WAVEGUIDES:
❖ Waveguides are easy to manufacture.

❖ They can handle very large power (in kilowatts).

❖ Power loss is very negligible in waveguides.

❖ They offer very low loss (low value of α-attenuation).

❖ The microwave energy, when it travels through the

waveguide, experiences lower losses than a coaxial cable.

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Types of waveguides:
❖ Rectangular waveguide

❖ Circular waveguide

❖ Elliptical waveguide

❖ Single ridged waveguide

❖ Double ridged waveguide

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Transmission Lines Vs Waveguides:

The main difference between a transmission line and

a waveguide is−

❖ A transmission line is a two-conductor structure that

can support a TEM wave.

❖ A one-conductor structure that can support a TE wave

or a TM wave but not a TEM wave is called a
waveguide.

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Rectangular Waveguides
❑ Rectangular waveguides are one of the earliest types of transmission lines.

❑ They are used in many applications. Many components, such as isolators, detectors,
attenuators, couplers, and slotted lines, are available for various standard waveguide
bands between 1 GHz to above 220 GHz.

❑ A rectangular waveguide supports TM and TE modes but not TEM waves because
we can not define a unique voltage since there is only one conductor in a
rectangular waveguide.

❑ The shape of a rectangular waveguide is shown. A material with permittivity ɛ and

permeability µ fills the inside of the conductor.

❑ A rectangular waveguide can not propagate below some certain frequency. This
frequency is called the cut-off frequency. Here, we will discuss TM mode
rectangular waveguides and TE mode rectangular waveguides separately.

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 ❑ A material with permittivity ɛ and
permeability µ fills the inside of the
conductor.

The main characteristics of a Waveguide are −

• The tube wall provides distributed inductance.

• The empty space between the tube walls provides distributed capacitance.
• These are bulky and expensive.

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Modes of Waveguides

• The propagation of electromagnetic waves through a waveguide

depends on the type of electromagnetic wave and the medium inside
it.

• Wave Propagation takes different modes depending on the

distribution of electric and magnetic fields with respect to the
direction of propagation.

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Modes of Waveguides
Looking at waveguide theory, it is possible to calculate that there are a
number of formats in which an electromagnetic wave can propagate
within the waveguide. These different types of waves correspond to the
different elements within an electromagnetic wave.

❑ TE mode: This waveguide mode is dependent upon the transverse

electric waves, also sometimes called H-waves, characterized by
the fact that the electric vector (E) is always perpendicular to the
direction of propagation. In TE wave, only the E-field is purely
transverse to the direction of propagation, and the magnetic field is
not purely transverse i.e., Ez=0, Hz≠0.

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Modes of Waveguides
❑ TM mode: Transverse magnetic waves, also called E-waves, are
characterized by the fact that the magnetic vector (H-vector) is
always perpendicular to the direction of propagation. In the TM
wave, only the H-field is purely transverse to the direction of
propagation, and the Electric field is not purely transverse, i.e.,
Ez≠0, Hz=0.

❑ TEM mode: The Transverse electromagnetic wave can not be

propagated within a waveguide, but is included for completeness. It
is the mode that is commonly used within coaxial and open wire
feeders. The TEM wave is characterized by the fact that both the
electric vector (E-vector) and the magnetic vector (H-vector) are
perpendicular to the direction of propagation. In this, neither
electric nor magnetic fields are purely transverse to the direction of
propagation, i.e., Ez = 0, Hz = 0
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Solution of Wave Equation in rectangular coordinates

Rectangular coordinates

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Solution of Wave Equation in rectangular coordinates

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Solution of Wave Equation in rectangular coordinates

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Solution of Wave Equation in rectangular coordinates

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Solution of Wave Equation in rectangular coordinates

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Solution of Wave Equation in rectangular coordinates

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TE mode in Rectangular Waveguide

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TE mode in Rectangular Waveguide

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TE mode in Rectangular Waveguide

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TE mode in Rectangular Waveguide

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TE mode in Rectangular Waveguide

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TE mode in Rectangular Waveguide

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TE mode in Rectangular Waveguide

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TE mode in Rectangular Waveguide

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TE mode in Rectangular Waveguide

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TM mode in Rectangular Waveguide

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TM mode in Rectangular Waveguide

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TM mode in Rectangular Waveguide

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TM mode in Rectangular Waveguide

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TE and TM mode in rectangular waveguide

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Power Transmission in Rectangular Waveguide

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Power Transmission in Rectangular Waveguide

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Power Losses in Rectangular Waveguide

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Power Losses in Rectangular Waveguide
When the electric and magnetic field propagate through a lossy waveguide,

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Power Losses in Rectangular Waveguide
Surface Resistance of the guide:

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Excitation of modes in Rectangular Waveguide

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Solution of Wave Equation in Circular Coordinates

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Solution of Wave Equation in Circular Coordinates

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Solution of Wave Equation in Circular Coordinates

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Solution of Wave Equation in Circular Coordinates

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TE Mode in Circular Waveguide

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TE Mode in Circular Waveguide

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TE Mode in Circular Waveguide

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TE Mode in Circular Waveguide

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TE Mode in Circular Waveguide

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TE Mode in Circular Waveguide

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TM Mode in Circular Waveguide

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TM Mode in Circular Waveguide

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TM Mode in Circular Waveguide

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TE and TM mode in circular waveguide

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TEM Mode in Circular Waveguide

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TEM Mode in Circular Waveguide

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TEM Mode in Circular Waveguide

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Power Transmission in Circular/Coaxial Waveguide

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Power Transmission in Circular/Coaxial Waveguide

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Power Transmission in Circular/Coaxial Waveguide

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Power Losses in Circular/Coaxial Waveguide

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Excitation of Modes in Circular/Coaxial Waveguide

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