Microwave Engineering - Waveguides

Generally, if the frequency of a signal or a particular band of signals is high, the bandwidth
utilization is high as the signal provides more space for other signals to get accumulated.
However, high frequency signals can't travel longer distances without getting attenuated. We
have studied that transmission lines help the signals to travel longer distances.
Microwaves propagate through microwave circuits, components and devices, which act as a part
of Microwave transmission lines, broadly called as Waveguides.
A hollow metallic tube of uniform cross-section for transmitting electromagnetic waves by
successive reflections from the inner walls of the tube is called as a Waveguide.
The following figure shows an example of a waveguide.

A waveguide is generally preferred in microwave communications. Waveguide is a special form

of transmission line, which is a hollow metal tube. Unlike a transmission line, a waveguide has
no center conductor.
The main characteristics of a Waveguide are −
 The tube wall provides distributed inductance.
 The empty space between the tube walls provide distributed capacitance.
 These are bulky and expensive.

Advantages of Waveguides

Following are few advantages of Waveguides.

 Waveguides are easy to manufacture.

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  They can handle very large power in kilowatts.
 Power loss is very negligible in waveguides.
 They offer very low loss low value of alpha−attenuation.
 When microwave energy travels through waveguide, it experiences lower losses than a
coaxial cable.

Types of Waveguides

There are five types of waveguides.

 Rectangular waveguide
 Circular waveguide
 Elliptical waveguide
 Single-ridged waveguide
 Double-ridged waveguide
The following figures show the types of waveguides.

The types of waveguides shown above are hollow in the center and made up of copper walls.
These have a thin lining of Au or Ag on the inner surface.

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Let us now compare the transmission lines and waveguides.

Transmission Lines Vs Waveguides

The main difference between a transmission line and a wave guide is −

 A two conductor structure that can support a TEM wave is a transmission line.
 A one conductor structure that can support a TE wave or a TM wave but not a TEM
wave is called as a waveguide.
The following table brings out the differences between transmission lines and waveguides.

Transmission Lines Waveguides

Supports TEM wave Cannot support TEM wave

Only the frequencies that are greater than cut-off

All frequencies can pass through
frequency can pass through

Two conductor transmission One conductor transmission

A wave travels through reflections from the walls

Reflections are less
of the waveguide

It has a characteristic impedance It has wave impedance

Propagation of waves is according to "Circuit theory" Propagation of waves is according to "Field

theory"

Return conductor is not required as the body of the

It has a return conductor to earth
waveguide acts as earth

Bandwidth is not limited Bandwidth is limited

Waves do not disperse Waves get dispersed

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Phase Velocity

Phase Velocity is the rate at which the wave changes its phase in order to undergo a phase shift
of 2π radians. It can be understood as the change in velocity of the wave components of a sine
wave, when modulated.
Let us derive an equation for the Phase velocity.
According to the definition, the rate of phase change at 2π radians is to be considered.
Which means, λ / T hence,
V=λ/T
Where,
λ = wavelength and T = time
V=λ/T=λf
Since f=1/T
If we multiply the numerator and denominator by 2π then, we have
V=λf=2πλf/2π
We know that ω=2πf and β=2π/f
The above equation can be written as,
V=2πf/2π/λ=ω/β
Hence, the equation for Phase velocity is represented as
Vp=ω/β

Group Velocity

Group Velocity can be defined as the rate at which the wave propagates through the waveguide.
This can be understood as the rate at which a modulated envelope travels compared to the
carrier alone. This modulated wave travels through the waveguide.
The equation of Group Velocity is represented as
Vg=dω/dβ
The velocity of modulated envelope is usually slower than the carrier signal.
Mode:
Many different field configurations can be found to have no tangential component of electric
field at the walls. each such configuration is known as modes.
Dominant Mode:

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Different modes have different cut off wavelengths, the particular mode for which the cutoff
wavelength is greatest is termed as dominant mode.
Modes of propagation in a Waveguide:

When an electromagnetic wave is transmitted through a waveguide. Then it has two field
components that oscillate mutually perpendicular to each other. Out of the two one is electric
field and the other is a magnetic field.

The figure below represents the propagation of an electromagnetic wave in the z-direction with
the two field components:

The propagation of wave inside the waveguide originates basically 2 modes. However, overall
basically 3 modes exist, which are as follows:

 Transverse Electric wave:

In this mode of wave propagation, the electric field component is totally transverse to the
direction of wave propagation whereas the magnetic field is not totally transverse to the direction
of wave propagation. It is abbreviated as TE mode.

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It is possible to propagate several modes of electromagnetic waves within a waveguide. The
physical dimensions of a waveguide determine the cutoff frequency for each mode. If the
frequency of the impressed signal is above the cutoff frequency for a given mode, the
electromagnetic energy can be transmitted through the guide for that particular mode with
minimal attenuation. Otherwise the electromagnetic energy with a frequency below cutoff for
that particular mode will be attenuated to a negligible value in a relatively short distance.

Figure 1: E- field variation in a rectangular guide

The dominant mode in a particular waveguide is the mode having the lowest cutoff frequency.
For rectangular waveguide this is the TE 10 mode. The TE (transverse electric) signifies that all
electric fields are transverse to the direction of propagation and that no longitudinal electric
field is present. There is a longitudinal component of magnetic field and for this reason the
TEmn waves are also-called Hmnwaves. The TE designation is usually preferred.
Figure 1 shows a graphical depiction of the E field variation in a waveguide for the TE 10 TE20,
and TE30 modes. As can be seen, the first index indicates the number of half wave loops across
the width of the guide and the second index, the number of loops across the height of the guide
- which in this case is zero.
It is advisable to choose the dimensions of a guide in such a way that, for a given input signal,
only the energy of the dominant mode can be transmitted through the guide. For example, if for
a particular frequency, the width of a rectangular guide is too large, then the TE 20 mode can
propagate causing a myriad of problems. For rectangular guides of low aspect ratio the
TE20 mode is the next higher order mode and is harmonically related to the cutoff frequency of
the TE10 mode. It is this relationship together with attenuation and propagation considerations
that determine the normal operating range of rectangular waveguide.
Another type of waveguide commonly used in EW systems is the “double ridge” rectangular
waveguide. The ridges in this waveguide increase the bandwidth of the guide at the expense of
higher attenuation and lower power-handling capability.

 Transverse Magnetic wave:

In this mode of wave propagation, the magnetic field component is totally transverse to the
direction of wave propagation while the electric field is not totally transverse to the direction of
wave propagation. It is abbreviated as TM mode.

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  Transverse electromagnetic wave:
In this mode of wave propagation, both the field components i.e., electric and magnetic fields are
totally transverse to the direction of wave propagation. It is abbreviated as TEM mode.

It is to be noted here that, TEM mode is not supported in waveguides. As for the TEM mode,
there is a need for the presence of two conductors and we already know that a waveguide is a
single hollow conductor.

Now, the question arises why do we need two conductors for the TEM mode to take place?

The answer to the above question is that, in a TEM mode, both electric and magnetic field are
totally transverse to the direction of wave propagation.

In the case of two separate conductors this is possible because, from the inner conductor, the
electric field generates and terminates at the outer one. And at this particular conductor, a current
source must be present in order to generate a magnetic field. But, as we have already discussed
that waveguide is a single conductor transmission media. This is the reason why TEM mode is
not supported in waveguides.

Parameters of a Waveguide:

 Cut-off wavelength: It the maximum signal wavelength of the transmitted signal that can be
propagated within the waveguide without any attenuation. This means up to cut-off wavelength,
a microwave signal can be easily transmitted through the waveguide. It is denoted by λ c.

 Group velocity: Group velocity is the velocity with which wave propagates inside the
waveguide. If the transmitted carrier is modulated, then the velocity of the modulation envelope
is somewhat less as compared to the carrier signal.
This velocity of the envelope is termed as group velocity. It is represented by Vg.

 Phase velocity: It is the velocity with which the transmitted wave changes its phase during
propagation. Or we can say it is basically the velocity of a particular phase of the propagating
wave. It is denoted by Vp.

 Wave Impedance: It is also known as the characteristic impedance. It is defined as the ratio of
the transverse electric field to that of the transverse magnetic field during wave propagation at
any point inside the waveguide. It is denoted by Zg.

Advantages of waveguides

1. In waveguides, the power loss during propagation is almost negligible.

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2. Waveguides have the ability to manage large-signal power.
3. As waveguides possess a simple structure thus their installation is somewhat easy.

Disadvantages of waveguides

1. Its installation and manufacturing cost is high.

2. Waveguides are generally rigid in nature and hence sometimes causes difficulty in applications
where tube flexibility is required.
3. It is somewhat large in size and bulkier as compared to other transmission lines.
It is noteworthy in the case of waveguides that their diameter must have some certain value in
order to have proper signal propagation. This is so because if its diameter is very small and the
wavelength of the signal to be propagated is large (or signal frequency is small) then it will not
be propagated properly.
So, the signal frequency must be greater than the cutoff frequency in order to have a proper
signal transmission.