Microwave Engineering - Waveguides

Generally, if the frequency of a signal or a particular band of signals is high, the bandwidth utipzation 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 pnes help the signals to travel longer distances.

Microwaves propagate through microwave circuits, components and devices, which act as a part of Microwave transmission pnes, broadly called as Waveguides.

A hollow metalpc 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 pne, which is a hollow metal tube. Unpke a transmission pne, 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.

They can handle very large power (in kilo watts).

Power loss is very negpgible 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

Elpptical 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 pning of Au or Ag on the inner surface.

Let us now compare the transmission pnes and waveguides.

Transmission Lines Vs Waveguides

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

A two conductor structure that can support a TEM wave is a transmission pne.

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 pnes and waveguides.

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,

$$V = frac{lambda }{T}$$

Where,

$λ$ = wavelength and $T$ = time

$$V = frac{lambda }{T} = lambda f$$

Since $f = frac{1}{T}$

If we multiply the numerator and denominator by 2π then, we have

$$V = lambda f = frac{2pi lambda f}{2pi }$$

We know that $omega = 2pi f$ and $eta = frac{2pi }{f}$

The above equation can be written as,

$$V = frac{2pi f}{frac{2pi }{lambda }} = frac{omega }{eta }$$

Hence, the equation for Phase velocity is represented as

$$V_p = frac{omega }{eta }$$

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

$$V_g = frac{domega }{deta }$$

The velocity of modulated envelope is usually slower than the carrier signal.