Category: microwave Engineering

Microwave Engineering – Microwave Devices Just like other systems, the Microwave systems consists of many Microwave components, mainly with source at one end and load at the other, which are all connected with waveguides or coaxial cable or transmission line systems. Following are the properties of waveguides. High SNR Low attenuation Lower insertion loss Waveguide Microwave Functions Consider a waveguide having 4 ports. If the power is applied to one port, it goes through all the 3 ports in some proportions where some of it might reflect back from the same port. This concept is clearly depicted in the following figure. Scattering Parameters For a two-port network, as shown in the following figure, if the power is applied at one port, as we just discussed, most of the power escapes from the other port, while some of it reflects back to the same port. In the following figure, if V1 or V2 is applied, then I1 or I2 current flows respectively. If the source is applied to the opposite port, another two combinations are to be considered. So, for a two-port network, 2 × 2 = 4 combinations are likely to occur. The travelling waves with associated powers when scatter out through the ports, the Microwave junction can be defined by S-Parameters or Scattering Parameters, which are represented in a matrix form, called as “Scattering Matrix“. Scattering Matrix It is a square matrix which gives all the combinations of power relationships between the various input and output ports of a Microwave junction. The elements of this matrix are called “Scattering Coefficients” or “Scattering (S) Parameters”. Consider the following figure. Here, the source is connected through $i^{th}$ line while $a_1$ is the incident wave and $b_1$ is the reflected wave. If a relation is given between $b_1$ and $a_1$, $$b_1 = (reflection : : coefficient)a_1 = S_{1i}a_1$$ Where $S_{1i}$ = Reflection coefficient of $1^{st}$ line (where $i$ is the input port and $1$ is the output port) $1$ = Reflection from $1^{st}$ line $i$ = Source connected at $i^{th}$ line If the impedance matches, then the power gets transferred to the load. Unlikely, if the load impedance doesn”t match with the characteristic impedance. Then, the reflection occurs. That means, reflection occurs if $$Z_l neq Z_o$$ However, if this mismatch is there for more than one port, example $”n”$ ports, then $i = 1$ to $n$ (since $i$ can be any line from $1$ to $n$). Therefore, we have $$b_1 = S_{11}a_1 + S_{12}a_2 + S_{13}a_3 + …………… + S_{1n}a_n$$ $$b_2 = S_{21}a_1 + S_{22}a_2 + S_{23}a_3 + …………… + S_{2n}a_n$$ $$.$$ $$.$$ $$.$$ $$.$$ $$.$$ $$b_n = S_{n1}a_1 + S_{n2}a_2 + S_{n3}a_3 + …………… + S_{nn}a_n$$ When this whole thing is kept in a matrix form, $$begin{bmatrix} b_1\ b_2\ b_3\ .\ .\ .\ b_n end{bmatrix} = begin{bmatrix} S_{11}& S_{12}& S_{13}& …& S_{1n}\ S_{21}& S_{22}& S_{23}& …& S_{2n}\ .& .& .& …& . \ .& .& .& …& . \ .& .& .& …& . \ S_{n1}& S_{n2}& S_{n3}& …& S_{nn}\ end{bmatrix} times begin{bmatrix} a_1\ a_2\ a_3\ .\ .\ .\ a_n end{bmatrix}$$ Column matrix $[b]$ Scattering matrix $[S]$Matrix $[a]$ The column matrix $left [ b right ]$ corresponds to the reflected waves or the output, while the matrix $left [ a right ]$ corresponds to the incident waves or the input. The scattering column matrix $left [ s right ]$ which is of the order of $n times n$ contains the reflection coefficients and transmission coefficients. Therefore, $$left [ b right ] = left [ S right ]left [ a right ]$$ Properties of [S] Matrix The scattering matrix is indicated as $[S]$ matrix. There are few standard properties for $[S]$ matrix. They are − $[S]$ is always a square matrix of order (nxn) $[S]_{n times n}$ $[S]$ is a symmetric matrix i.e., $S_{ij} = S_{ji}$ $[S]$ is a unitary matrix i.e., $[S][S]^* = I$ The sum of the products of each term of any row or column multiplied by the complex conjugate of the corresponding terms of any other row or column is zero. i.e., $$sum_{i=j}^{n} S_{ik} S_{ik}^{*} = 0 : for : k neq j$$ $$( k = 1,2,3, … : n ) : and : (j = 1,2,3, … : n)$$ If the electrical distance between some $k^{th}$ port and the junction is $beta _kI_k$, then the coefficients of $S_{ij}$ involving $k$, will be multiplied by the factor $e^{-jbeta kIk}$ In the next few chapters, we will take a look at different types of Microwave Tee junctions. Learning working make money

Microwave Engineering – Rat-race Junction This microwave device is used when there is a need to combine two signals with no phase difference and to avoid the signals with a path difference. A normal three-port Tee junction is taken and a fourth port is added to it, to make it a ratrace junction. All of these ports are connected in angular ring forms at equal intervals using series or parallel junctions. The mean circumference of total race is 1.5λ and each of the four ports are separated by a distance of λ/4. The following figure shows the image of a Rat-race junction. Let us consider a few cases to understand the operation of a Rat-race junction. Case 1 If the input power is applied at port 1, it gets equally split into two ports, but in clockwise direction for port 2 and anti-clockwise direction for port 4. Port 3 has absolutely no output. The reason being, at ports 2 and 4, the powers combine in phase, whereas at port 3, cancellation occurs due to λ/2 path difference. Case 2 If the input power is applied at port 3, the power gets equally divided between port 2 and port 4. But there will be no output at port 1. Case 3 If two unequal signals are applied at port 1 itself, then the output will be proportional to the sum of the two input signals, which is divided between port 2 and 4. Now at port 3, the differential output appears. The Scattering Matrix for Rat-race junction is represented as $$[S] = begin{bmatrix} 0& S_{12}& 0& S_{14}\ S_{21}& 0& S_{23}& 0\ 0& S_{32}& 0& S_{34}\ S_{41}& 0& S_{43}& 0 end{bmatrix}$$ Applications Rat-race junction is used for combining two signals and dividing a signal into two halves. Learning working make money

Microwave Engineering – Directional Couplers A Directional coupler is a device that samples a small amount of Microwave power for measurement purposes. The power measurements include incident power, reflected power, VSWR values, etc. Directional Coupler is a 4-port waveguide junction consisting of a primary main waveguide and a secondary auxiliary waveguide. The following figure shows the image of a directional coupler. Directional coupler is used to couple the Microwave power which may be unidirectional or bi-directional. Properties of Directional Couplers The properties of an ideal directional coupler are as follows. All the terminations are matched to the ports. When the power travels from Port 1 to Port 2, some portion of it gets coupled to Port 4 but not to Port 3. As it is also a bi-directional coupler, when the power travels from Port 2 to Port 1, some portion of it gets coupled to Port 3 but not to Port 4. If the power is incident through Port 3, a portion of it is coupled to Port 2, but not to Port 1. If the power is incident through Port 4, a portion of it is coupled to Port 1, but not to Port 2. Port 1 and 3 are decoupled as are Port 2 and Port 4. Ideally, the output of Port 3 should be zero. However, practically, a small amount of power called back power is observed at Port 3. The following figure indicates the power flow in a directional coupler. Where $P_i$ = Incident power at Port 1 $P_r$ = Received power at Port 2 $P_f$ = Forward coupled power at Port 4 $P_b$ = Back power at Port 3 Following are the parameters used to define the performance of a directional coupler. Coupling Factor (C) The Coupling factor of a directional coupler is the ratio of incident power to the forward power, measured in dB. $$C = 10 : log_{10}frac{P_i}{P_f}dB$$ Directivity (D) The Directivity of a directional coupler is the ratio of forward power to the back power, measured in dB. $$D = 10 : log_{10}frac{P_f}{P_b}dB$$ Isolation It defines the directive properties of a directional coupler. It is the ratio of incident power to the back power, measured in dB. $$I = 10 : log_{10}frac{P_i}{P_b}dB$$ Isolation in dB = Coupling factor + Directivity Two-Hole Directional Coupler This is a directional coupler with same main and auxiliary waveguides, but with two small holes that are common between them. These holes are ${lambda_g}/{4}$ distance apart where λg is the guide wavelength. The following figure shows the image of a two-hole directional coupler. A two-hole directional coupler is designed to meet the ideal requirement of directional coupler, which is to avoid back power. Some of the power while travelling between Port 1 and Port 2, escapes through the holes 1 and 2. The magnitude of the power depends upon the dimensions of the holes. This leakage power at both the holes are in phase at hole 2, adding up the power contributing to the forward power Pf. However, it is out of phase at hole 1, cancelling each other and preventing the back power to occur. Hence, the directivity of a directional coupler improves. Waveguide Joints As a waveguide system cannot be built in a single piece always, sometimes it is necessary to join different waveguides. This joining must be carefully done to prevent problems such as − Reflection effects, creation of standing waves, and increasing the attenuation, etc. The waveguide joints besides avoiding irregularities, should also take care of E and H field patterns by not affecting them. There are many types of waveguide joints such as bolted flange, flange joint, choke joint, etc. Learning working make money

Microwave Engineering – Cavity Klystron For the generation and amplification of Microwaves, there is a need of some special tubes called as Microwave tubes. Of them all, Klystron is an important one. The essential elements of Klystron are electron beams and cavity resonators. Electron beams are produced from a source and the cavity klystrons are employed to amplify the signals. A collector is present at the end to collect the electrons. The whole set up is as shown in the following figure. The electrons emitted by the cathode are accelerated towards the first resonator. The collector at the end is at the same potential as the resonator. Hence, usually the electrons have a constant speed in the gap between the cavity resonators. Initially, the first cavity resonator is supplied with a weak high frequency signal, which has to be amplified. The signal will initiate an electromagnetic field inside the cavity. This signal is passed through a coaxial cable as shown in the following figure. Due to this field, the electrons that pass through the cavity resonator are modulated. On arriving at the second resonator, the electrons are induced with another EMF at the same frequency. This field is strong enough to extract a large signal from the second cavity. Cavity Resonator First let us try to understand the constructional details and the working of a cavity resonator. The following figure indicates the cavity resonator. A simple resonant circuit which consists of a capacitor and an inductive loop can be compared with this cavity resonator. A conductor has free electrons. If a charge is applied to the capacitor to get it charged to a voltage of this polarity, many electrons are removed from the upper plate and introduced into the lower plate. The plate that has more electron deposition will be the cathode and the plate which has lesser number of electrons becomes the anode. The following figure shows the charge deposition on the capacitor. The electric field lines are directed from the positive charge towards the negative. If the capacitor is charged with reverse polarity, then the direction of the field is also reversed. The displacement of electrons in the tube, constitutes an alternating current. This alternating current gives rise to alternating magnetic field, which is out of phase with the electric field of the capacitor. When the magnetic field is at its maximum strength, the electric field is zero and after a while, the electric field becomes maximum while the magnetic field is at zero. This exchange of strength happens for a cycle. Closed Resonator The smaller the value of the capacitor and the inductivity of the loop, the higher will be the oscillation or the resonant frequency. As the inductance of the loop is very small, high frequency can be obtained. To produce higher frequency signal, the inductance can be further reduced by placing more inductive loops in parallel as shown in the following figure. This results in the formation of a closed resonator having very high frequencies. In a closed resonator, the electric and magnetic fields are confined to the interior of the cavity. The first resonator of the cavity is excited by the external signal to be amplified. This signal must have a frequency at which the cavity can resonate. The current in this coaxial cable sets up a magnetic field, by which an electric field originates. Working of Klystron To understand the modulation of the electron beam, entering the first cavity, let”s consider the electric field. The electric field on the resonator keeps on changing its direction of the induced field. Depending on this, the electrons coming out of the electron gun, get their pace controlled. As the electrons are negatively charged, they are accelerated if moved opposite to the direction of the electric field. Also, if the electrons move in the same direction of the electric field, they get decelerated. This electric field keeps on changing, therefore the electrons are accelerated and decelerated depending upon the change of the field. The following figure indicates the electron flow when the field is in the opposite direction. While moving, these electrons enter the field free space called as the drift space between the resonators with varying speeds, which create electron bunches. These bunches are created due to the variation in the speed of travel. These bunches enter the second resonator, with a frequency corresponding to the frequency at which the first resonator oscillates. As all the cavity resonators are identical, the movement of electrons makes the second resonator to oscillate. The following figure shows the formation of electron bunches. The induced magnetic field in the second resonator induces some current in the coaxial cable, initiating the output signal. The kinetic energy of the electrons in the second cavity is almost equal to the ones in the first cavity and so no energy is taken from the cavity. The electrons while passing through the second cavity, few of them are accelerated while bunches of electrons are decelerated. Hence, all the kinetic energy is converted into electromagnetic energy to produce the output signal. Amplification of such two-cavity Klystron is low and hence multi-cavity Klystrons are used. The following figure depicts an example of multi-cavity Klystron amplifier. With the signal applied in the first cavity, we get weak bunches in the second cavity. These will set up a field in the third cavity, which produces more concentrated bunches and so on. Hence, the amplification is larger. Learning working make money

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. They can handle very large power (in kilo watts). 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. 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 All frequencies can pass through Only the frequencies that are greater than cut-off frequency can pass through Two conductor transmission One conductor transmission Reflections are less A wave travels through reflections from the walls 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” It has a return conductor to earth Return conductor is not required as the body of the waveguide acts as earth Bandwidth is not limited Bandwidth is limited Waves do not disperse Waves get dispersed 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 $beta = frac{2pi }{f}$ The above equation can be written as, $$V = frac{2pi f}{frac{2pi }{lambda }} = frac{omega }{beta }$$ Hence, the equation for Phase velocity is represented as $$V_p = frac{omega }{beta }$$ 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 $$V_g = frac{domega }{dbeta }$$ The velocity of modulated envelope is usually slower than the carrier signal. Learning working make money

Microwave Engineering Tutorial Job Search Of all the waves found in the electromagnetic spectrum, Microwaves are a special type of electromagnetic radiation that is used in many ways, from cooking simple popcorn to studying the nearby galaxies!! This tutorial will help readers get an overall knowledge on how Microwaves work and how we use them in several applications. Audience This tutorial will be helpful for all those readers who want to learn the basics of Microwave Engineering. The readers will gain knowledge on how Microwave signals are generated, controlled, transmitted, and measured. Prerequisites It is a simple tutorial written in a lucid way. We believe almost any reader having a basic knowledge of analog and digital communication can use this tutorial to good effect. Learning working make money

Avalanche Transit Time Devices The process of having a delay between voltage and current, in avalanche together with transit time, through the material is said to be Negative resistance. The devices that helps to make a diode exhibit this property are called as Avalanche transit time devices. The examples of the devices that come under this category are IMPATT, TRAPATT and BARITT diodes. Let us take a look at each of them, in detail. IMPATT Diode This is a high-power semiconductor diode, used in high frequency microwave applications. The full form IMPATT is IMPact ionization Avalanche Transit Time diode. A voltage gradient when applied to the IMPATT diode, results in a high current. A normal diode will eventually breakdown by this. However, IMPATT diode is developed to withstand all this. A high potential gradient is applied to back bias the diode and hence minority carriers flow across the junction. Application of a RF AC voltage if superimposed on a high DC voltage, the increased velocity of holes and electrons results in additional holes and electrons by thrashing them out of the crystal structure by Impact ionization. If the original DC field applied was at the threshold of developing this situation, then it leads to the avalanche current multiplication and this process continues. This can be understood by the following figure. Due to this effect, the current pulse takes a phase shift of 90°. However, instead of being there, it moves towards cathode due to the reverse bias applied. The time taken for the pulse to reach cathode depends upon the thickness of n+ layer, which is adjusted to make it 90° phase shift. Now, a dynamic RF negative resistance is proved to exist. Hence, IMPATT diode acts both as an oscillator and an amplifier. The following figure shows the constructional details of an IMPATT diode. The efficiency of IMPATT diode is represented as $$eta = left [ frac{P_{ac}}{P_{dc}} right ] = frac{V_a}{V_d}left [ frac{I_a}{I_d} right ]$$ Where, $P_{ac}$ = AC power $P_{dc}$ = DC power $V_a : & : I_a$ = AC voltage & current $V_d : & : I_d$ = DC voltage & current Disadvantages Following are the disadvantages of IMPATT diode. It is noisy as avalanche is a noisy process Tuning range is not as good as in Gunn diodes Applications Following are the applications of IMPATT diode. Microwave oscillator Microwave generators Modulated output oscillator Receiver local oscillator Negative resistance amplifications Intrusion alarm networks (high Q IMPATT) Police radar (high Q IMPATT) Low power microwave transmitter (high Q IMPATT) FM telecom transmitter (low Q IMPATT) CW Doppler radar transmitter (low Q IMPATT) TRAPATT Diode The full form of TRAPATT diode is TRApped Plasma Avalanche Triggered Transit diode. A microwave generator which operates between hundreds of MHz to GHz. These are high peak power diodes usually n+- p-p+ or p+-n-n+ structures with n-type depletion region, width varying from 2.5 to 1.25 µm. The following figure depicts this. The electrons and holes trapped in low field region behind the zone, are made to fill the depletion region in the diode. This is done by a high field avalanche region which propagates through the diode. The following figure shows a graph in which AB shows charging, BC shows plasma formation, DE shows plasma extraction, EF shows residual extraction, and FG shows charging. Let us see what happens at each of the points. A: The voltage at point A is not sufficient for the avalanche breakdown to occur. At A, charge carriers due to thermal generation results in charging of the diode like a linear capacitance. A-B: At this point, the magnitude of the electric field increases. When a sufficient number of carriers are generated, the electric field is depressed throughout the depletion region causing the voltage to decrease from B to C. C: This charge helps the avalanche to continue and a dense plasma of electrons and holes is created. The field is further depressed so as not to let the electrons or holes out of the depletion layer, and traps the remaining plasma. D: The voltage decreases at point D. A long time is required to clear the plasma as the total plasma charge is large compared to the charge per unit time in the external current. E: At point E, the plasma is removed. Residual charges of holes and electrons remain each at one end of the deflection layer. E to F: The voltage increases as the residual charge is removed. F: At point F, all the charge generated internally is removed. F to G: The diode charges like a capacitor. G: At point G, the diode current comes to zero for half a period. The voltage remains constant as shown in the graph above. This state continues until the current comes back on and the cycle repeats. The avalanche zone velocity $V_s$ is represented as $$V_s = frac{dx}{dt} = frac{J}{qN_A}$$ Where $J$ = Current density $q$ = Electron charge 1.6 x 10-19 $N_A$ = Doping concentration The avalanche zone will quickly sweep across most of the diode and the transit time of the carriers is represented as $$tau_s = frac{L}{V_s}$$ Where $V_s$ = Saturated carrier drift velocity $L$ = Length of the specimen The transit time calculated here is the time between the injection and the collection. The repeated action increases the output to make it an amplifier, whereas a microwave low pass filter connected in shunt with the circuit can make it work as an oscillator. Applications There are many applications of this diode. Low power Doppler radars Local oscillator for radars Microwave beacon landing system Radio altimeter Phased array radar, etc. BARITT Diode The full form of BARITT Diode is BARrier Injection Transit Time diode. These are the latest invention in this family. Though these diodes have long drift regions like IMPATT diodes, the carrier injection in BARITT diodes is caused by forward biased junctions, but not from the plasma of an avalanche region as in them. In IMPATT diodes, the carrier injection is quite

Microwave Engineering – Quick Guide Microwave Engineering – Introduction Electromagnetic Spectrum consists of entire range of electromagnetic radiation. Radiation is the energy that travels and spreads out as it propagates. The types of electromagnetic radiation that makes the electromagnetic spectrum is depicted in the following screenshot. Let us now take a look at the properties of Microwaves. Properties of Microwaves Following are the main properties of Microwaves. Microwaves are the waves that radiate electromagnetic energy with shorter wavelength. Microwaves are not reflected by Ionosphere. Microwaves travel in a straight line and are reflected by the conducting surfaces. Microwaves are easily attenuated within shorter distances. Microwave currents can flow through a thin layer of a cable. Advantages of Microwaves There are many advantages of Microwaves such as the following − Supports larger bandwidth and hence more information is transmitted. For this reason, microwaves are used for point-to-point communications. More antenna gain is possible. Higher data rates are transmitted as the bandwidth is more. Antenna size gets reduced, as the frequencies are higher. Low power consumption as the signals are of higher frequencies. Effect of fading gets reduced by using line of sight propagation. Provides effective reflection area in the radar systems. Satellite and terrestrial communications with high capacities are possible. Low-cost miniature microwave components can be developed. Effective spectrum usage with wide variety of applications in all available frequency ranges of operation. Disadvantages of Microwaves There are a few disadvantages of Microwaves such as the following − Cost of equipment or installation cost is high. They are hefty and occupy more space. Electromagnetic interference may occur. Variations in dielectric properties with temperatures may occur. Inherent inefficiency of electric power. Applications of Microwaves There are a wide variety of applications for Microwaves, which are not possible for other radiations. They are − Wireless Communications For long distance telephone calls Bluetooth WIMAX operations Outdoor broadcasting transmissions Broadcast auxiliary services Remote pickup unit Studio/transmitter link Direct Broadcast Satellite (DBS) Personal Communication Systems (PCSs) Wireless Local Area Networks (WLANs) Cellular Video (CV) systems Automobile collision avoidance system Electronics Fast jitter-free switches Phase shifters HF generation Tuning elements ECM/ECCM (Electronic Counter Measure) systems Spread spectrum systems Commercial Uses Burglar alarms Garage door openers Police speed detectors Identification by non-contact methods Cell phones, pagers, wireless LANs Satellite television, XM radio Motion detectors Remote sensing Navigation Global navigation satellite systems Global Positioning System (GPS) Military and Radar Radars to detect the range and speed of the target. SONAR applications Air traffic control Weather forecasting Navigation of ships Minesweeping applications Speed limit enforcement Military uses microwave frequencies for communications and for the above mentioned applications. Research Applications Atomic resonances Nuclear resonances Radio Astronomy Mark cosmic microwave background radiation Detection of powerful waves in the universe Detection of many radiations in the universe and earth’s atmosphere Food Industry Microwave ovens used for reheating and cooking Food processing applications Pre-heating applications Pre-cooking Roasting food grains/beans Drying potato chips Moisture levelling Absorbing water molecules Industrial Uses Vulcanizing rubber Analytical chemistry applications Drying and reaction processes Processing ceramics Polymer matrix Surface modification Chemical vapor processing Powder processing Sterilizing pharmaceuticals Chemical synthesis Waste remediation Power transmission Tunnel boring Breaking rock/concrete Breaking up coal seams Curing of cement RF Lighting Fusion reactors Active denial systems Semiconductor Processing Techniques Reactive ion etching Chemical vapor deposition Spectroscopy Electron Paramagnetic Resonance (EPR or ESR) Spectroscopy To know about unpaired electrons in chemicals To know the free radicals in materials Electron chemistry Medical Applications Monitoring heartbeat Lung water detection Tumor detection Regional hyperthermia Therapeutic applications Local heating Angioplasty Microwave tomography Microwave Acoustic imaging For any wave to propagate, there is the need of a medium. The transmission lines, which are of different types, are used for the propagation of Microwaves. Let us learn about them in the next chapter. Microwave Engineering – Transmission Lines A transmission line is a connector which transmits energy from one point to another. The study of transmission line theory is helpful in the effective usage of power and equipment. There are basically four types of transmission lines − Two-wire parallel transmission lines Coaxial lines Strip type substrate transmission lines Waveguides While transmitting or while receiving, the energy transfer has to be done effectively, without the wastage of power. To achieve this, there are certain important parameters which has to be considered. Main Parameters of a Transmission Line The important parameters of a transmission line are resistance, inductance, capacitance and conductance. Resistance and inductance together are called as transmission line impedance. Capacitance and conductance together are called as admittance. Resistance The resistance offered by the material out of which the transmission lines are made, will be of considerable amount, especially for shorter lines. As the line current increases, the ohmic loss $left ( I^{2}R : loss right )$ also increases. The resistance $R$ of a conductor of length “$l$” and cross-section “$a$” is represented as $$R = rho frac{l}{a}$$ Where $rho$ = resistivity of the conductor material, which is constant. Temperature and the frequency of the current are the main factors that affect the resistance of a line. The resistance of a conductor varies linearly with the change in temperature. Whereas, if the frequency of the current increases, the current density towards the surface of the conductor also increases. Otherwise, the current density towards the center of the conductor increases. This means, more the current flows towards the surface of the conductor, it flows less towards the center, which is known as the Skin Effect. Inductance In an AC transmission line, the current flows sinusoidally. This current induces a magnetic field perpendicular to the electric field, which also varies sinusoidally. This is well known as Faraday”s law. The fields are depicted in the following figure. This varying magnetic field induces some EMF into the conductor. Now this induced voltage or EMF flows in the opposite direction to the current flowing initially. This EMF flowing in the opposite direction is equivalently shown by a parameter known as Inductance, which is the property to oppose the

Discuss Microwave Engineering Of all the waves found in the electromagnetic spectrum, Microwaves are a special type of electromagnetic radiation that is used in many ways, from cooking simple popcorn to studying the nearby galaxies!! This tutorial will help readers get an overall knowledge on how Microwaves work and how we use them in several applications. Learning working make money

Microwave Engineering – E-Plane Tee An E-Plane Tee junction is formed by attaching a simple waveguide to the broader dimension of a rectangular waveguide, which already has two ports. The arms of rectangular waveguides make two ports called collinear ports i.e., Port1 and Port2, while the new one, Port3 is called as Side arm or E-arm. T his E-plane Tee is also called as Series Tee. As the axis of the side arm is parallel to the electric field, this junction is called E-Plane Tee junction. This is also called as Voltage or Series junction. The ports 1 and 2 are 180° out of phase with each other. The cross-sectional details of E-plane tee can be understood by the following figure. The following figure shows the connection made by the sidearm to the bi-directional waveguide to form the parallel port. Properties of E-Plane Tee The properties of E-Plane Tee can be defined by its $[S]_{3×3}$ matrix. It is a 3×3 matrix as there are 3 possible inputs and 3 possible outputs. $[S] = begin{bmatrix} S_{11}& S_{12}& S_{13}\ S_{21}& S_{22}& S_{23}\ S_{31}& S_{32}& S_{33} end{bmatrix}$ …….. Equation 1 Scattering coefficients $S_{13}$ and $S_{23}$ are out of phase by 180° with an input at port 3. $S_{23} = -S_{13}$…….. Equation 2 The port is perfectly matched to the junction. $S_{33} = 0$…….. Equation 3 From the symmetric property, $S_{ij} = S_{ji}$ $S_{12} = S_{21} : : S_{23} = S_{32} : : S_{13} = S_{31}$…….. Equation 4 Considering equations 3 & 4, the $[S]$ matrix can be written as, $[S] = begin{bmatrix} S_{11}& S_{12}& S_{13}\ S_{12}& S_{22}& -S_{13}\ S_{13}& -S_{13}& 0 end{bmatrix}$…….. Equation 5 We can say that we have four unknowns, considering the symmetry property. From the Unitary property $$[S][S]ast = [I]$$ $$begin{bmatrix} S_{11}& S_{12}& S_{13}\ S_{12}& S_{22}& -S_{13}\ S_{13}& -S_{13}& 0 end{bmatrix} : begin{bmatrix} S_{11}^{*}& S_{12}^{*}& S_{13}^{*}\ S_{12}^{*}& S_{22}^{*}& -S_{13}^{*}\ S_{13}^{*}& -S_{13}^{*}& 0 end{bmatrix} = begin{bmatrix} 1& 0& 0\ 0& 1& 0\ 0& 0& 1 end{bmatrix}$$ Multiplying we get, (Noting R as row and C as column) $R_1C_1 : S_{11}S_{11}^{*} + S_{12}S_{12}^{*} + S_{13}S_{13}^{*} = 1$ $left | S_{11} right |^2 + left | S_{11} right |^2 + left | S_{11} right |^2 = 1$ …….. Equation 6 $R_2C_2 : left | S_{12} right |^2 + left | S_{22} right |^2 + left | S_{13} right |^2 = 1$ ……… Equation 7 $R_3C_3 : left | S_{13} right |^2 + left | S_{13} right |^2 = 1$ ……… Equation 8 $R_3C_1 : S_{13}S_{11}^{*} – S_{13}S_{12}^{*} = 1$ ……… Equation 9 Equating the equations 6 & 7, we get $S_{11} = S_{22} $ ……… Equation 10 From Equation 8, $2left | S_{13} right |^2 quad or quad S_{13} = frac{1}{sqrt{2}}$ ……… Equation 11 From Equation 9, $S_{13}left ( S_{11}^{*} – S_{12}^{*} right )$ Or $S_{11} = S_{12} = S_{22}$ ……… Equation 12 Using the equations 10, 11, and 12 in the equation 6, we get, $left | S_{11} right |^2 + left | S_{11} right |^2 + frac{1}{2} = 1$ $2left | S_{11} right |^2 = frac{1}{2}$ Or $S_{11} = frac{1}{2}$ ……… Equation 13 Substituting the values from the above equations in $[S]$ matrix, We get, $$left [ S right ] = begin{bmatrix} frac{1}{2}& frac{1}{2}& frac{1}{sqrt{2}}\ frac{1}{2}& frac{1}{2}& -frac{1}{sqrt{2}}\ frac{1}{sqrt{2}}& -frac{1}{sqrt{2}}& 0 end{bmatrix}$$ We know that $[b]$ = $[S] [a]$ $$begin{bmatrix}b_1 \ b_2 \ b_3 end{bmatrix} = begin{bmatrix} frac{1}{2}& frac{1}{2}& frac{1}{sqrt{2}}\ frac{1}{2}& frac{1}{2}& -frac{1}{sqrt{2}}\ frac{1}{sqrt{2}}& -frac{1}{sqrt{2}}& 0 end{bmatrix} begin{bmatrix} a_1\ a_2\ a_3 end{bmatrix}$$ This is the scattering matrix for E-Plane Tee, which explains its scattering properties. Learning working make money