TOPIC 2

WAVEGUIDE AND COMPONENTS COURSE LEARNING OUTCOME (CLO) CLO1 • Explain clearly the generation of , the effects of microwave radiation and the propagation of electromagnetic in a and its accessories CLO2 • Apply given mathematical equations or Smith Chart to solve problem related to microwave propagation. CLO3 • Handle systematically the related microwave communication equipment in performing the assigned practical work.

Understand the characteristic of waveguide Upon completion of this topic, students should be able to: 1. Define a) Critical (cut-off) b) Critical (cut-off) 2. Explain the following terminologies: Group velocity, Phase velocity, propagation wavelength, waveguide characteristic impedance 3. Calculate the item no.1 and no. 2 for rectangular and circular waveguide

Rectangular Waveguide

With;

a = broad dimension

b = narrow dimension

x = length waveguide

Dimensions of the waveguide which determines the operating frequency range

Dimensions of the waveguide which determines the operating frequency range:

1. The size of the waveguide determines its operating frequency range. 2. The frequency of operation is determined by the dimension ‘a’. 3. This dimension is usually made equal to one – half the wavelength at the lowest frequency of operation, this frequency is known as the waveguide cutoff frequency. 4. At the cutoff frequency and below, the waveguide will not transmit energy. At above the cutoff frequency, the waveguide will propagate energy. Circular waveguide

r = radius x = length waveguide

Characteristic of waveguide

• are basically a device ("a guide") for transporting electromagnetic energy from one region to another.

• They are capable of directing power precisely to where it is needed, can handle large amounts of power and function as a high-pass filter.

• The waveguide acts as a high pass filter in that most of the energy above a certain frequency (the cutoff frequency) will pass through the waveguide, whereas most of the energy that is below the cutoff frequency will be attenuated by the waveguide.

Critical (cut-off) Frequency, Fc • The cutoff frequency is the frequency at which all lower frequencies are attenuated by the waveguide, and above the cutoff frequency all higher frequencies propagate within the waveguide. • The cutoff frequency defines the high-pass filter characteristic of the waveguide: above this frequency, the waveguide passes power, below this frequency the waveguide attenuates or blocks power.

• The cutoff frequency depends on the shape and size of the cross section of the waveguide. The larger the waveguide is, the lower the cutoff frequency for that waveguide is. The formula for the cutoff frequency of a rectangular cross sectioned waveguide is given by:

- permeability - permittivity Rectangular Waveguide • Let us consider a rectangular waveguide with interior dimensions are a x b, • Waveguide can support TE and TM modes. – In TE modes, the electric field is transverse to the direction of propagation. – In TM modes, the magnetic field that is transverse and an electric field component is in the propagation direction. • The order of the mode refers to the field configuration in the guide, and is given by m and n integer subscripts, TEmn and TMmn. – The m subscript corresponds to the number of half- wave variations of the field in the x direction, and – The n subscript is the number of half-wave variations in the y direction.

Location of Modes Rectangular Waveguide

• A particular mode is only supported above its cutoff frequency. The cutoff frequency is given by

2 2 2 2 1 m   n  c  m   n  f    cmn         22a   b     a   b  8 rr where c  3 10 m/s

Rectangular Waveguide

Formula Dominant Mode

• The dominant mode is the mode with lowest cutoff frequency.

• It’s always TE10 • The order of the next modes change depending on the dimensions of the guide.

Group and Phase velocity How fast is the wave traveling? • Velocity is a reference distance divided by a reference time. • Group velocity is the velocity at which the energy of the wave propagates. This means that the wave moves at the speed of vg. • Phase velocity is the speed of movement of a point of constant phase in a continous wave. • Group and phase velocities have the same value in free space and in parallel wire transmission lines.

Group and Phase velocity The Phase velocity

This is the velocity at which the overall shape of the wave’s amplitudes, or the wave ‘envelope’, propagates. (= signal velocity)

Here, phase velocity = group velocity (the medium is non- dispersive) Group velocity Dispersion: phase/group velocity depends on frequency

Black dot moves at phase velocity. Red dot moves at group velocity.

This is normal dispersion (refractive index decreases with increasing λ) Rectangular Waveguide

Need to find the fields components of the em wave inside the waveguide

Ez Hz Ex Hx Ey Hy

We’ll find that waveguides don’t support TEM waves

• The m and n represent the mode of propagation and indicates the number of variations of the field in the x and y directions • Note that for the TM mode, if n or m is zero, all fields are zero.

Variation of wave impedance

• Wave impedance varies with frequency and mode

Rectangular Waveguide - Wave Propagation

Wave Guide Impedance

Wave feature impedance for TE mode is ZTE = 377 2    1      with;  0  • ZTE = characteristic impedance for TE mode • 377 = free space feature impedance •  = free space wavelength • 0 = wavelength cut. Wave Guide Impedance

Wave feature impedance for TM mode is ZTM =  2 377 1 ( ) 0 where; • ZTM = characteristic impedance for TM mode • 377 = free space feature impedance •  = free space wavelength • 0 = wavelength cut. Question Waveguide

The circular waveguide is used in many special applications in microwave techniques. It has the advantage of greater power – handling capacity and lower attenuation for a given cutoff wavelength. However, the disadvantage of somewhat greater size and weight. The polarization of the transmitted wave can be altered due to the minor irregularities of the wall surface of the circular guide, whereas the rectangular wave guide the polarization is fixed Description

The wave of lowest frequency or the dominant mode in the circular waveguide is the TE11 mode. The first subscript m indicates the number of full – wave variations of the radial component of the electric field around the circumference of the waveguide. The second subscript n indicates the number of half – wave variations across the diameter. The field configurations of TE mode in the circular waveguide is shown in11 the diagram below

Applications of circular waveguide  Rotating joints in radars to connect the horn feeding a parabolic reflector (which must rotate for tracking)

 TE01 mode suitable for long distance waveguide transmission above 10 GHz.  Short and medium distance broad band communication (could replace / share coaxial and microwave links)

• From the cutoff frequencies or the cutoff , the phase velocity, the group velocity, the guide wavelength and the wave impedance of each mode can be found using the same equations as those for the rectangular waveguide.

Cut Off Wavelength Example 1

Example 2 Solution