RESONATORS AND WAVEGUIDES BY: P. Vijaya & Niraja

Microwaves Microwaves are the electromagnetic waves with wavelengths ranging from as long as a few centimeter to as short as one millimeter and with frequencies ranging from 1GHz to 1000 GHz. Microwaves include the entire SHF band (3 to 30 GHz).

Electromagnetic Waves Frequency Bands Frequency Range Uses VLF 3-30KHz Used for long distance Communication. LF 30-300KHz Used For Marine Communication. MF 300-3000KHz Used for Radio broadcasting. HF 3-30MHz For long distance Communication VHF 30-300MHz FM Radio, Television broadcasting. UHF 300-3000MHz For short distance communication. SHF 3-30GHz Satellite/Space communication. EHF 30-300GHz Radar, Space communication.

Advantage of Microwaves 1. Larger Bandwidth 2. Better Directive Properties 3. Lower Power Requirement 4. Fading effect

Frequency-Wavelength A definite relationship exists between the frequency (f) and the corresponding wavelength (λ) of electromagnetic waves .The product of these two i.e. (f) and (λ) gives the velocity of propagation of electro-magnetic waves and it is equal to the velocity of light . This is expressed as c = f * λ c= velocity of light. (approx. 3* 108 m/sec ).

Applications Of Microwaves 1.Communication : Microwaves is used in broadcasting and Telecom. transmission, due to their short wavelength, highly directional antennas are smaller . Mobile phone networks, like GSM, use the low microwave/UHF frequencies around 1.8 and 1.9GHz .

Microwaves are used in television signal to transmit a signal from a remote location to a television station from a specially equipped van. Microwave are used for comm. from one point to another via satellite. Satellite TV either operates in the C band for the traditional large dish fixed satellite service or Ku band for direct –broadcast satellite.

2. Remote Sensing : The most important application of remote sensing is RADAR, that uses a transmitter to illuminate an object and a receiver to detect its position and velocity. Another class of remote sensing is radio astronomy .It is a sub-class of astronomy that studies celestial objects at radio frequencies.

3.Heating Application Baking : The heating property of microwaves are used for baking, cooking using microwave oven. In microwave oven ,the food is heated directly by microwave radiations without heating the container. The cooking time very small as compare to conventional heating

Concentrating : Permits concentration of heat sensitive solution and slurries at relatively low temperatures. Also applicable to highly corrosive or viscous solutions Drying : microwaves are used for drying the solids. Drying is uniform throughout the product moisture present in the product is evaporated out .Drying is at relatively low temp.

Enzyme Inactivation : The enzyme inactivation can be achieved by rapid and uniform heating which can control and terminate enzyme reactions. Precooking : Microwaves are ideal for precooking the food items because there is no overcooking of the surface and cooking losses are negligible i.e is nutrients in the food are not lost.

Parameters Of Microwaves System Frequency Characteristics : Microwaves are very short frequency radio waves that have many of the characteristics of light waves they travel in line of sight paths and can be reflected and focused . By focusing these ultra high radio waves into a narrow beam, their energies are concentrated and relatively low transmitting power is required for reliable transmission over long distance .

System Capacity : Microwaves communication systems are used to carry telephony, television and data signals. Majority of the system carry multi- channel telephone signals (base band ). Individual telephone channels , 4KHz wide are multiplexed together in a multiplexer equipment to get the base band. At microwave due to high bandwidth capacity is more.

Microwave Frequency Bands As already mentioned ,microwave is an electromagnetic wave ranging from approximately 1GHz in frequency, but older usage includes lower frequencies . Most common applications are within the range1 to 40GHz.

Letter Designation Frequency Range L band 1 to 2 GHz S band 2 to 4 GHz C band 4 to 8 GHz X band 8 to 12 GHz Ku band 12 to 18 GHz K band 18 to 26.5 GHz Ka band 26.5 to 40 GHz Millimeter (mm) 40 to 300 GHz Sub –Millimeter 300 to above (GHz)

Classification of Microwaves on the basis of Frequency bands : 1. L-band: L-band (20-cm radar long band) is a portion of the microwave band of the electromagnetic spectrum ranging roughly from 0.39 to 1.55 GHz. It is used by some communication satellite and by terrestrial. 2. S-band: S-band or 10 cm. radar short band, is the part of microwave band of the electromagnetic spectrum ranging roughly from 1.55 to 5.2 GHz. It is used by weather radar and some communication satellites

3. C-band: C-band (“ Compromise” band) is a portion of electromagnetic spectrum in the microwave range of frequencies ranging from 4 to 6 GHz. 4. X-band: The X-band (3 cm radar spot band) of the microwave band of the electromagnetic spectrum roughly ranges from 5.2 to 10.9 GHz. It is used by some communication satellite and X-band radar. 5. Ku-band: The Ku-band (Kurz-under band) is a portion of electromagnetic spectrum in the microwave range of frequency range 11 to 18 GHz. It’s primarily used for satellite communication.

6. K-band: It is a portion of the EM wave spectrum in the microwave range of frequency range between 12 to 40 GHz. The K comes from Kurz. K-band between 18 to 26.5GHz is absorbed easily by water vapour. 7. Ka-band: The Ka-band ( Kurz-above band is a portion of the K-band) of the microwave band of the electromagnetic spectrum. Ka-band roughly ranges from 18 to 40 GHz.

Rectangular Waveguides

Waveguide to coax adapter Waveguide component Waveguide to coax adapter Rectangular waveguide Waveguide bends E-tee

Dr. Sandra Cruz-Pol More waveguides Electromagnetics, waveguides

Uses To reduce attenuation loss High frequencies High power Dr. Sandra Cruz-Pol Uses To reduce attenuation loss High frequencies High power Can operate only above certain frequencies Acts as a High-pass filter Normally circular or rectangular We will assume lossless rectangular Electromagnetics, waveguides

Dr. Sandra Cruz-Pol Rectangular WG 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 Electromagnetics, waveguides

Rectangular Waveguides: Fields inside Dr. Sandra Cruz-Pol Rectangular Waveguides: Fields inside Using phases & assuming waveguide filled with lossless dielectric material and walls of perfect conductor, the wave inside should obey. Electromagnetics, waveguides

Then applying on the z-component

Fields inside the waveguide Dr. Sandra Cruz-Pol Fields inside the waveguide Electromagnetics, waveguides

Dr. Sandra Cruz-Pol Substituting Electromagnetics, waveguides

Dr. Sandra Cruz-Pol Other components From Faraday and Ampere Laws we can find the remaining four components: *So once we know Ez and Hz, we can find all the other fields. Electromagnetics, waveguides

Modes of propagation From these equations we can conclude: Dr. Sandra Cruz-Pol Modes of propagation From these equations we can conclude: TEM (Ez=Hz=0) can’t propagate. TE (Ez=0) transverse electric In TE mode, the electric lines of flux are perpendicular to the axis of the waveguide TM (Hz=0) transverse magnetic, Ez exists In TM mode, the magnetic lines of flux are perpendicular to the axis of the waveguide. HE hybrid modes in which all components exists Electromagnetics, waveguides

TM Mode Boundary conditions: From these, we conclude: Dr. Sandra Cruz-Pol TM Mode Boundary conditions: From these, we conclude: X(x) is in the form of sin kxx, where kx=mp/a, m=1,2,3,… Y(y) is in the form of sin kyy, where ky=np/b, n=1,2,3,… So the solution for Ez(x,y,z) is Electromagnetics, waveguides

Dr. Sandra Cruz-Pol TM Mode Substituting Electromagnetics, waveguides

TMmn Other components are Dr. Sandra Cruz-Pol Electromagnetics, waveguides

Dr. Sandra Cruz-Pol TM modes 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. See applet by Paul Falstad Electromagnetics, waveguides

TM Cutoff The cutoff frequency occurs when Evanescent: Propagation: Dr. Sandra Cruz-Pol TM Cutoff The cutoff frequency occurs when Evanescent: Means no propagation, everything is attenuated Propagation: This is the case we are interested since is when the wave is allowed to travel through the guide. Electromagnetics, waveguides

Dr. Sandra Cruz-Pol Cutoff attenuation Propagation of mode mn fc,mn The cutoff frequency is the frequency below which attenuation occurs and above which propagation takes place. (High Pass) The phase constant becomes Electromagnetics, waveguides

Phase velocity and impedance Dr. Sandra Cruz-Pol Phase velocity and impedance The phase velocity is defined as And the intrinsic impedance of the mode is Electromagnetics, waveguides

Summary of TM modes Wave in the dielectric medium Inside the waveguide Dr. Sandra Cruz-Pol Summary of TM modes Wave in the dielectric medium Inside the waveguide Electromagnetics, waveguides

Related example of how fields look: Dr. Sandra Cruz-Pol Related example of how fields look: Parallel plate waveguide - TM modes m = 1 m = 2 m = 3 x z a Ez 0 a x Electromagnetics, waveguides

TE Mode Boundary conditions: From these, we conclude: Dr. Sandra Cruz-Pol TE Mode Boundary conditions: From these, we conclude: X(x) is in the form of cos kxx, where kx=mp/a, m=0,1,2,3,… Y(y) is in the form of cos kyy, where ky=np/b, n=0,1,2,3,… So the solution for Ez(x,y,z) is Electromagnetics, waveguides

Dr. Sandra Cruz-Pol Substituting Note that n and m cannot be both zero because the fields will all be zero. Electromagnetics, waveguides

TEmn Other components are Dr. Sandra Cruz-Pol Electromagnetics, waveguides

Cutoff The cutoff frequency is the same expression as for the TM mode Dr. Sandra Cruz-Pol Cutoff attenuation Propagation of mode mn fc,mn The cutoff frequency is the same expression as for the TM mode But the lowest attainable frequencies are lowest because here n or m can be zero. Electromagnetics, waveguides

Dr. Sandra Cruz-Pol 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. Electromagnetics, waveguides

Waveguides Pipe through which waves propagate Can have various cross sections Rectangular Circular Elliptical Can be rigid or flexible Waveguides have very low loss

Modes Waves can propagate in various ways Time taken to move down the guide varies with the mode Each mode has a cutoff frequency below which it won’t propagate Mode with lowest cutoff frequency is dominant mode

Mode Designations TE: transverse electric Electric field is at right angles to direction of travel TM: transverse magnetic Magnetic field is at right angles to direction of travel TEM: transverse electromagnetic Waves in free space are TEM

Rectangular Waveguides Dominant mode is TE10 1 half cycle along long dimension (a) No half cycles along short dimension (b) Cutoff for a = c/2 Modes with next higher cutoff frequency are TE01 and TE20 Both have cutoff frequency twice that for TE10

Cutoff Frequency For TE10 mode in rectangular waveguide with a = 2 b

Usable Frequency Range Single mode propagation is highly desirable to reduce dispersion This occurs between cutoff frequency for TE10 mode and twice that frequency It’s not good to use guide at the extremes of this range

Example Waveguide RG-52/U Internal dimensions 22.9 by 10.2 mm Cutoff at 6.56 GHz Use from 8.2-12.5 GHz

Group Velocity Waves propagate at speed of light c in guide Waves don’t travel straight down guide Speed at which signal moves down guide is the group velocity and is always less than c

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Phase Velocity Not a real velocity (>c) Apparent velocity of wave along wall Used for calculating wavelength in guide For impedance matching etc.

Characteristic Impedance Z0 varies with frequency

Guide Wavelength Longer than free-space wavelength at same frequency

Summary of TE modes Wave in the dielectric medium Inside the waveguide Dr. Sandra Cruz-Pol Summary of TE modes Wave in the dielectric medium Inside the waveguide Electromagnetics, waveguides

Variation of wave impedance Dr. Sandra Cruz-Pol Variation of wave impedance Wave impedance varies with frequency and mode h hTE h’ hTM fc,mn Electromagnetics, waveguides

Group velocity, vg Is the velocity at which the energy travels. Dr. Sandra Cruz-Pol Group velocity, vg Is the velocity at which the energy travels. It is always less than u’ Electromagnetics, waveguides

Dr. Sandra Cruz-Pol Group Velocity As frequency is increased, the group velocity increases.   Electromagnetics, waveguides

Dr. Sandra Cruz-Pol Power transmission The average Poynting vector for the waveguide fields is where h = hTE or hTM depending on the mode [W/m2] [W] Electromagnetics, waveguides

Attenuation in Lossy waveguide Dr. Sandra Cruz-Pol Attenuation in Lossy waveguide When dielectric inside guide is lossy, and walls are not perfect conductors, power is lost as it travels along guide. The loss power is Where a=ac+ad are the attenuation due to ohmic (conduction) and dielectric losses Usually ac >> ad Electromagnetics, waveguides

Attenuation for TE10 Dielectric attenuation, Np/m Dr. Sandra Cruz-Pol Attenuation for TE10 Dielectric attenuation, Np/m Conductor attenuation, Np/m Dielectric conductivity! Electromagnetics, waveguides