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MICRO

Unit - 2Microwave Components 2.1 Multi port junctions: Construction and Operation of E-plane, H-planeMicrowave multiport junctions are the devices that are used to split or combine microwave power. The important parts of microwave junctions are ports, arms, and junction regions. Ports are openings to which the source or load is connected. Arms are pieces of the transmission lines or waveguides with which the junction device is fabricated. The junction region is the common space where all the arms of the device meet each other.A microwave circuit is a combination of several microwave devices that are connected in a way so as to achieve the desired transmission of microwave signals. In general, a microwave junction is an interconnection of two or more microwave components as shown below,

A port is said to be perfectly matched to the junction if nothing out of the power incident at the port is reflected back to the port by the junction. Two ports are said to be perfectly isolated if nothing out of the power incident at one port appears at the other port. When an input from a microwave source is fed to port 1, it spreads all of its power into ports 2, 3, 4, and some of the power is reflected back to port 1 due to the existence of a mismatch between the port and that junction. Low-frequency circuits can be described by Z, Y, h, and ABCD parameters, and these parameters are related in terms of currents and voltages. However, at microwave frequencies, instead of currents and voltages, we talk of travelling waves with their associated powers.Microwave TEE JunctionsWaveguide Tees are used for the purpose of connecting a branch or a section of a waveguide in a series or parallel to the main waveguide. The intersection of waveguides in the shape of the English capital letter “T” is called a T junction. E-plane Tee and H-plane Tee are examples of three-port waveguide T junctions. Normal reciprocal three-port junctions has one drawback, that is, lack of isolation between the output ports. This results in dependence of the power consumed at one port on the termination at the other output port. This lack of isolation between the output ports limits the usefulness of the three port junctions, particularly in power monitoring and divider applications.E-plane Tees: E-plane Tee is a voltage or series junction. A side arm is attached to a waveguide by cutting a rectangular slot along the broader dimension of waveguide as shown.

If the E-plane junction is completely symmetrical and if waves enter through the side arm, the waves that leave the main arms are equal in magnitude and opposite in phase. Since the electric field lines change their direction when they come out of ports 1 and 2, it is called an E-plane Tee. Any signal that is to be split or any two signals which are to be combined will be fed to the E arm.As power dividerIf the amplitude of the input wave at port 3 is A, the amplitudes of the waves at ports 1 and 2 are same and equal to A/√2. They are out of phase when its collinear arms lengths are same. When the power incident at port 3 is P, the powers that appear at ports 1 and 2 are P/2 each.

The amount of power coming out of ports 1 and 2 in decibels is=

That is why it is called a 3dB splitter. As power combinerWhen equal input signals are given at both the collinear ports,the output signal appears at the side arm port whose power is the sum of the powers of the input signals provided the collinear arm lengths are same and the sources are out of phase. The output power is zero. When the sources are equal, in the phase and collinear arms lengths are same.H-plane Tee: H-plane Tee is a current, shunt, or parallel junction. Since the axis of the side arm is parallel to the plane of the H field of the main waveguide, it is called a H-plane Tee. A rectangular slot is cut along the narrow dimension of a long waveguide, and a side arm is attached as shown

As power dividerThey are in phase when its collinear arm lengths are same. If the amplitude of the input wave at port 3 is A, the amplitudes of the waves at ports 1 and 2 are same and equal to A/√2. It is called a 3db splitter, because when the power incident at port3 is P, the powers that appear at ports 1 and 2 are P/2 each. As power combiner When equal input signals are given at both the collinear ports, the output signal appears at the side arm whose power is the sum of the powers of the input signals provided the collinear arm lengths are same and the sources are in phase. The output power is zero. When the sources are equal, in the out of phase and collinear arms the lengths are same. Comparison of E-plane Tee with H-plane Tee:1. In an E-plane Tee, the axis of its side arm is parallel to the electric field of the main waveguide whereas in an H-plane Tee, the axis of its side arm is parallel to the magnetic field or shunting the electric field of the main waveguide. 2. The E-plane Tee is also called a series Tee whereas an H-plane Tee is also called a parallel or shunt Tee. 3. When the power is fed at port (3), that is, at the side arm, the resulting power is equally divided between port (1) and (2), but a phase shift of 180° is introduced between the two outputs whereas when the power is fed to a H-plane Tee at port (3),that is, at the side arm, the resulting power is equally divided between port (1) and port (2) within phase. 4. When the equal input power is fed to both ports (1) and (2), no output is obtained at port (3) whereas when the equal input power is fed to H-plane Tee to both ports (1) and (2), the maximum power (i.e., addition of two inputs) is obtained at port (3).5. When the input signal is applied at any one of the collinear ports i.e., port (1) or port (2), the resulting power is obtained at port (3) whereas when the input is applied to H-plane Tee at any one of the collinear ports i.e., port (1) or port (2), the resulting power is obtained at port (3). 2.2 Magic Tee and Directional CouplersThe combination of an E-plane Tee and an H-plane Tee is called as Magic Tee. A Magic Tee can be formed by attaching arms to the slots made in the broad and narrow walls of a waveguide. It is also called as hybrid tee in which the power distributes equally between the output ports. The outputs may have 0° or 180° phase difference. Magic Tee is a 3db hybrid coupler which is also called as an anti-symmetric coupler. If one of the coplanar arms is terminated, then the power delivered to another coplanar arm is independent of terminated port. The hybrid (Magic) Tee Junction with its equivalent circuit is shown below,

Characteristics:Let us consider two waves whose magnitude and phase are equal. If we feed these waves to ports 1 and 2, the outputs at port 3 and port 4 will be zero and additive respectively. The power distributes equally at ports 1 and 2 if a wave is incident at port 4 and no power will appear at port 3.The power at ports 1 and 2 appears with an equal magnitude and the opposite phase if a wave is incident at port 3 and no power will appear at port 4. If a wave is incident on any one of the coplanar arms i.e., port 1 or port 2, then no power will appear at other coplanar arm i.e., port 2 or port 1. This is due to the occurring of phase delay and phase advance in E arm and H arm respectively. In Magic Tee the imaginary plane bisects arms 3 and 4 symmetrically. There will not be any reflections in the junction, if ports 1 and 2 are terminated with matched loads. Since all the ports are the collinear arm ports in Magic Tee, they are perfectly matched to the junction, and the E and H arm ports are decoupled individually The signal distributes equally between the E and H arms, if signal is incident on collinear arm and output signal is given as,

A signal into the H arm splits equally between the collinear arms,the outputs being in phase, equidistant from the junction. A signal into the E arm splits equally between the collinear arms, the outputs being out of phase, equidistant from the junction. For signals into both collinear arms. 1. The signal output from the E arm is equal to 1/√2 times the phasor difference of the input signals. (Difference arm) 2. The signal output from the H arm is equal to 1/√2 times the phasor sum of the input signals. (Sum arm)Advantages of magic tee :Due to the decoupling property of output ports, the power delivered to one of the output ports becomes independent of the termination at the other output port. In the E- or H-plane Tee, the power division between ports depends on terminations existing at the respective output ports; but in Magic Tee (in which all the ports are perfectly matched), power division between the ports is independent of terminations. Disadvantages of magic tee :There is an impedance mismatch at the junctions, when a signal is applied to any arm of the Magic Tee. Because of this impedance mismatch the flow of energy in the output arms is affected by reflections. These reflections cause the following two disadvantages of Magic Tee: When all the energy that is fed into the junction does not reach the load due the reflections, it results in power loss. The standing waves that are produced due to reflections can result in internal arcing. Thus, it results in reduction of the maximum power that a Magic Tee can handle.Applications of magic tee :Depending on the above explained properties, a magic tee has many applications as follows :As an isolator As a matching device As a phase shifter As a duplexer As a mixer As a measurement of impedanceDirectional CouplerIn some applications such as radar, very often we need to check the exact frequency/power applied to the antenna or that is radiated into space. Directional couplers allow us to sample or monitor the frequency level and/or power level of a given signal as it goes from one point to another. The directional coupler is a 4–port reciprocal device. Direction couplers consist of two transmission lines and a mechanism for coupling signals between them. Let us understand the meaning of the two terms (viz coupler and directional) in the directional coupler. Coupler: A coupler is a device that consists of two waveguides which are placed very close to each other (as shown in the figure). Thus, a portion of energy traveling in waveguide A will be coupled on waveguide B.

We can make this coupler directional by using a specific length (L) of the transmission line.Directional: The term directional means the energy is passed in one direction only, and no energy passes in the reverse direction. The directional property is obtained by using a specific length (L) of a transmission line, that is, a quarter wavelength (λ/4). A λ/4 transmission line offers high impedance at one end and low impedance at the other end. Therefore, the specific length (L = λ/4 or (2n + 1) λ/4) makes a coupler directional over a certain band of frequency (as shown in the figure).

Power flow in a directional coupler :The power incident at port 1 (input) is split between two other ports ( port 4 (coupled) and port 2 (output)), and no power appears from port 3 (isolated). Power flow in a directional coupler is shown in the figure. Pi or P1 = power incident at port 1 Pf or P2 = forward power or output power at port 2Pb or P3 = reflected power at isolated port 3 in secondary waveguide Pfc or P4 = forward coupled power in the secondary waveguide, that is, at port 4

The properties of an ideal directional coupler are as follows: In an ideal directional coupler, all the four ports are perfectly matched and also ports1,3 and ports 2, 4 are perfectly isolated. A portion of the wave is coupled to port 4 but not coupled to port 3 which is traveling from port 1 to port 2. Similarly, a portion of the wave travelling from port 2 to port 1 is coupled to port 3 but not to port 4. Likewise, the portion of the wave traveling from port 4 to port 3 is coupled to port 1 but not to port 2. Similarly, a portion of the wave traveling from port 3 to port 4 is coupled to port 2 but not to port 1 The coupling between port 1 and port 4 is similar to that between port 2 and port 3, and the degree of coupling depends on the structure of the coupler. The outputs are always in phase quadrature; that is, they exhibit a phase difference of 90o. For this reason, a directional coupler is called a quadrature-type hybrid.Types of directional couplers: There are two types of directional couplers; both are four-port components and are reciprocal. Two-hole directional coupler and Single-hole or Bethe-hole directional coupler Two-Hole Directional Couplers:The two-hole directional coupler is mostly used in all applications. The directional coupler consists of two waveguides referred to as a main waveguide with ports 1 and 2 and an auxiliary waveguide with ports 3 and 4. When a power is applied at port 1 of the main waveguide, the output is taken at port 2 of the main waveguide. A fraction of the power is coupled into port 4 of the auxiliary waveguide, and no power flows in port 3 of the auxiliary waveguide. Since the device is reciprocal, the power incident in port 3 of the auxiliary waveguide flows in port 4, a fraction of the power couples in port 2, and no power flows in port 1 of the main waveguide.

Functional Operation of 2 Hole Directional Coupler :To have the directional property of a coupler, the spacing between the centers of two holes should be L = (2n+1)λ/4, where ‘n’ is any positive integer. The hole acts as a slot antenna. A portion of the wave energy entering into port 1 passes through holes and radiates into the secondary guide. Forward waves in the secondary guide are added at port 4 and are in a similar phase. Waves travelling from a

c and from a

c have similar path lengths. Backward waves in the secondary waveguide are out of phase and are cancelled at port 3. Waves travelling from paths a

d and a

d have a difference of two wave components, one coupled out immediately from ‘a’ and the other from ‘b’, are 180° out of phase at ‘d’; therefore, waves traveling toward port 3 vanish. Bethe-hole Directional Couplers:This is the simplest form of a waveguide directional coupler. In the Bethe-hole coupler, two waveguides are placed one above the other. A hole is located at the center of a common broad wall of two waveguides. The two waveguides are placed at an angle, θ as shown in the figure,

The input is incident at port 1 of the main waveguide (i.e. lower waveguide). The mode of propagation is the TE10 mode. If the hole (or aperture) is small compared with the propagating signal wavelength (λ), the hole acts similar to an electric dipole that is normal to the aperture plane. This dipole moment is a function of the normal component of the electric field in the main waveguide and the tangential component of the exciting magnetic field at the aperture. Due to radiation from this dipole, coupling to the auxiliary guide is achieved. The electric dipole radiates symmetrically in both directions longitudinally as shown in the figure,

However, the magnetic field dipole radiates asymmetrically in longitudinal directions. In the auxiliary waveguide, both Hy and Hz components are present in the direction of propagation (port 4) as shown in the figure below. The Hy and Hz fields are in the opposite direction and have different magnitudes; whereas the Hy component will be present in port 3 (coupled port).

By varying the angle between the waveguides, the magnitudes of Hy and Hz components at port 4 can be made equal. This leads to the zero magnetic field at the output port of the auxiliary waveguide, and power is coupled only at port 3 (coupled port).Applications of Directional Couplers:Directional couplers are extensively used in systems that measure the amplitude and phase of travelling waves. The major applications are as follows: Power monitoring and source levellingSWR measurements In unidirectional power measurements In reflectometers Unidirectional wave launching Isolation of signal sources 2.3 Ferrites Components: Ferrite Composition and CharacteristicsA device that is composed of material which has useful magnetic properties and, simultaneously, it provides high resistance to current flow is a ferrite. The electron movement within the atoms of the material results in the magnetic property of that material. There are two types of motions of Electrons: (1) Orbital movement of the electrons around the nucleus of the atom; (2) Movement of the electron about its own axis, called electron spin. The different types of electron movement are shown in the figure below. Movement of the electrons within the atom causes the current to flow. Therefore, the magnetic field is generated. Under the influence of the applied external magnetic field, the electron spin axes within some materials, such as iron or nickel, can be caused to align. Therefore, magnetic fields get added.

In the case of ferrites, electrons try to balance between two forces. They are as follows: (1) A force that holds the atoms together (i.e. orbital motion of the electrons about the nucleus); (2) An external static magnetic field. Interaction of these two forces causes the electrons to wobble on their axis (as shown in figure below). Ferrite action depends on the behaviour of electrons due to the influence of the external field. This result is wobble frequency. Electrons that wobble also have natural resonant wobble frequency. It varies with the strength of the applied field.

2.4 Faraday RotationIf a linearly polarized wave is made to pass through a ferrite rod and if it is influenced by the magnetic field, the axis of polarization gets tilted in clockwise direction. This is because the frequency of the microwave energy is much greater than the electron wobble frequency ( shown in the figure ). This is known as the Faraday rotation effect. The strength of the magnetic field and the geometry of ferrite is the basis for the amount of tilt. The direction of the Faraday rotation depends on whether the signal frequency is smaller or larger than the resonance frequency.

( Rotation of signal due to ferrite ) The phase shift of the resultant wave is given by( β+ - β-)

and the tilt angle is given by

Where β + and β - are phase constants of the components Ex and Ey. Hence, as the wave propagates to the distance of ‘l’ in a ferrite, the tilt angle of the polarization vector changes. This is called Faraday rotation. A typical change is 100° per centimeter at 10 GHz. The tilt angle θ rotates in the same direction with respect to the coordinate system, if the direction of propagation is reversed. Thus the tilt angle does not return from θ to 0°, but its value becomes twice the tilt angle. Therefore, the Faraday rotation is a non-reciprocal phenomenon. Composition and Characteristics of Ferrites:Ferrites are non-metallic materials with resistivities and dielectrics. They provide high resistance to current flow. Characteristics of Ferrites: Ferrite materials are a mixture of metallic oxide and ferric oxide (MeOFe2O3) where Me is any divalent such as Mn+2, Zn+2, Cd+2, and Ni+2. Ferrites have strong magnetic properties. In microwave devices ferrites are most suitable to reduce the reflected power, for modulation purposes, and in switching circuits. Ferrites are used up to 100 GHz as they have high resistivity. The non-reciprocal property is also exhibited by Ferrites. Their resistivities are around 1014 times greater than metals. The dielectric constant of ferrite materials is around 10 to 15. These materials have relative permeabilities of the order of 1000. One widely used ferromagnetic material is Yttrium-Iron-Garnet [Y3Fe2(FeO4)3] or YIG (Yttrium iron garnet) in short.Microwave gyrator, isolator, and circulator use the principle of Faraday rotation. So, these are ferrite components. 2.5 Construction and Operation of GyratorA gyrator is a two-port non-reciprocal ferrite device having a relative phase difference of 180° when wave is transmitting from port 1 to port 2 and a 0° phase shift when wave is transmitting from port 2 to port 1.

It has a circular waveguide propagating the dominant mode (TE11), which changes over to a rectangular waveguide with the dominant mode (TE10) at both ends. The circular waveguide consists of a thin, circular ferrite rod which is tapered at both the ends to reduce the attenuation and is supported by polyfoam. This also helps for smooth rotation of the polarized wave. A dc magnetic field is generated by permanent magnet which is placed around the waveguide for appropriate operation of ferrites (as shown in the figure below. To this waveguide’s input end a 90° twisted rectangular waveguide is attached.

The plane of polarization of incident wave rotates by 90° when it enters port 1. This is because of waveguide’s twist. The wave again experiences a faraday rotation of 90° due to ferrite rod. So the wave coming out of port 2 will have a total phase shift of 180° with respect to the input wave entered the port 1. In the same way when TE10 mode signal is incident at port 2 it experiences a faraday rotation of 90° in anti-clock wise direction. It again rotates back by 90° because of twist in the waveguide. So the resultant phase shift when wave comes out of port 1 is 0°. Hence we can conclude that, the wave enters port 1 experiences a phase shift of 180° but the same wave when incident on port 2 does not undergo any change in the phase shift. 2.6 Isolator and CirculatorAn isolator is a unilateral, two-port nonreciprocal transmission device. It is used to isolate one component from reflections of other components in the transmission line. The flow of power can be from input to output, but cannot be the other way. Hence, the bad effects of changing load impedance can be reduced by the use of the isolator on a signal source. Ferrites are used as the main material in isolators. The function of an isolator is shown in the figure below,

An ideal isolator is one which absorbs the power fully for propagation in one direction and provides lossless transmission in the opposite direction. In the figure, the microwave energy is fed through port 1 of the isolator, and a load is connected through port 2 of the isolator. The isolator allows the energy to travel through it and to reach the load with minimum attenuation and provides maximum attenuation to the energy travelling from load to source. Therefore, isolators are used to improve the frequency stability of the microwave generators, such as klystrons and magnetrons, in which the reflection from the load affects the generating frequency. The figure below shows the Faraday rotation isolator. The isolator consists of a piece of circular waveguide supporting the dominant TE11 mode with transitions to a standard rectangular guide supporting the TE10 mode at both ends. A thin pencil-shaped ferrite is located inside the circular guide, supported by polyfoam, and the waveguide is surrounded by a permanent magnet that generates a magnetic field in the ferrite core.

Two resistive plates are placed in x-z plane at the ends of rectangular waveguide as shown in the figure. The transition from rectangular to circular waveguide results in 45° phase shift. The plane of polarization of the wave can be rotated by 45° by the DC magnetic field, which is applied longitudinally to the ferrite rod. The degree of rotation depends on the applied dc magnetic field and on the length and diameter of the ferrite rod. If TE10 wave is incident on the isolator’s left end which is perpendicular to the input resistive card, then the wave passes through the ferrite rod without attenuation. The operation of isolator based on Faraday rotation is explained below. A TE10 wave passes from port 1 through the resistive card without attenuation. The wave is shifted by 45° due to twist in the anti-clockwise direction after coming out of the card. Then, because of the ferrite rod, there is a shift of another 45° in the clock-wise direction. Hence, the polarization of the wave at port 2 will be same as at port 1 where there is no attenuation. As the plane of polarization of the wave is perpendicular to the plane of the resistive card, when the TE10 wave is fed from port 2, it passes from the resistive card placed near port 2. This wave suffers a phase shift of 45° in clock-wise direction due to the ferrite rod and again rotates by 45° in the same direction due to the twist. Now, the input card absorbs the wave as the plane of polarization of the wave is parallel to the input resistive card. Therefore, zero output will appear at port 1. In reverse transmission, the typical performance of these isolators is about 20 to 30 dB isolation and in forward transmission is about 1 dB insertion loss. Faraday Rotation-Based Circulator:The most important ferrite component is a circulator. A circulator is conceptually similar to the isolator, except that it is a multiport device. The circulator is also a unilateral device; i.e., power flows in only one direction. The main application of the circulator is in connection with multiple isolation in radars, parametric amplifiers, and so on. It is a nonreciprocal device in which the ports are arranged in such a way that the electromagnetic energy which is entering a certain port is coupled to an adjacent port and not coupled to the other ports. The three-port symmetrical devices are commonly used as circulators. The figure below represents a three-port circulator’s circuit symbol.

A signal applied to port 1 emerges from port 2 with a loss if all ports of a circulator are matched. This loss is called the insertion loss, which is given in decibels is given by,Insertion Loss, IL(dB) = 10log10(

A small part of the input signal emerges from port 3. Assuming that port 2 is terminated by a matched load Isolation can also be defined as the ratio of that emerging signal to the input signal. Isolation is given in decibels as below.I(dB) = 10 log10(

The circulator is a three-port network that can be used to prevent reflection at the antenna from returning to the source. 2.7 Strip Lines: Structural Details and Applications of Strip LinesThe hollow single conductor transmission lines are known as “waveguides” and two coaxial cylindrical conductors based transmission lines are known as “coaxial lines”. Transmission lines which are printed or etched out on substrates (dielectric material) are known as planar transmission lines. The planar transmission lines are important as these are widely used in microwave integrated circuits. Some of the important planar transmission lines are:Microstrip line Stripline Slotline Coplanar lineSTRIPLINEStripline or tri-plate is a planar transmission line and can be seen as an extended version of microstrip line. It is basically a sandwich structure in which ground planes are available on the both sides of the substrate while the metal strip remains at the mid of the substrate. This configuration provides a homogenous medium to the electromagnetic wave as compared to the microstrip line which remains uncovered. The basic stripline configuration is shown in the figure below,

The stripline is etched out on one side of the grounded substrate and then covered by another grounded substrate. Specific bonding films are used to attach two grounded substrates of same height. This process is complex and requires extreme care while fabricating stripline. The field configuration inside the stripline is shown in the figure. The fields are confined within the substrate, hence TEM mode can be achieved for stripline configuration and the effective dielectric constant of the medium is equal to the relative dielectric constant of the dielectric substrate.

(a) Effective dielectric constant: The effective dielectric constant (ɛeff) of the medium for strip line configuration is same as relative dielectric constant of the substrate dielectric material, hence it is expressed as:ɛeff = ɛr(b) Phase velocity and guide wavelength: As we know that the phase velocity and guide wavelength depend upon the relative dielectric constant of the medium through which the EM wave is travelling. Hence in case of stripline configuration, the phase velocity (vp) and guide wavelength (l) are expressed as:

where, λ0 = free space wavelength, c = velocity of light in vacuum. (c) Characteristic impedance: The characteristic impedance of a stripline depends upon the trace width (W), total height of the substrate (h) and trace thickness (t). For small trace thickness (t), the characteristic impedance of stripline for a given trace width (W) and substrate height (h) can be given as:

where,

(d) Attenuation: The total attenuation in a stripline configuration can be calculated as the sum of dielectric loss and conductor loss. The dielectric loss in a stripline is same as of TEM lines and can be expressed as:

where, k = wave number = 2p/l tan δ = loss tangent of the dielectric. The loss due to conductor can be given by Perturbation model and comes out as:

where, Rs = skin resistance Z0 = characteristic impedance Advantages of StriplineGood electromagnetic shielding, because the stripline is covered by substrate and ground planes. Low attenuation losses. Wide bandwidth with no lower cut-off frequency as it supports TEM wave. Better isolation between adjacent traces or lines due to non interfering nature.Disadvantages of StriplineComplex and expensive to fabricate as it is a sandwich configuration. The stripline trace width (W ) is smaller for the given impedance and substrate height as compared to microstrip line trace width. The tuning of stripline circuits are quite complex because tuning destroys the symmetry of stripine which in turn affects the mode of propagation of electromagnetic wave in stripline. 2.8 Microstrip LineA microstrip line as shown in the figure below, is most widely used planar transmission line. The microstrip line is evolved from two conductor transmission lines in which both the conducting surfaces are parallel to each other and separated by the substrate. The characteristic parameters of a microstrip line

are dependent upon the strip width (W), substrate height or thickness (h) and dielectric constant of substrate (ɛ). From the figure, it is clear that the metal strip on the top of the substrate is not completely covered by the substrate, hence the wave propagating through microstrip line doesn’t encounter a homogenous medium. It indicates that in a microstrip line the electromagnetic wave can’t propagate in pure transverse electromagnetic (TEM) mode. The mode of propagation in microstrip line is termed as “quasi-TEM” mode. The fields’ configurations in a microstrip line are shown in the figure. The magnetic field is shown in closed loops while the electric field is starting from microstrip trace and going upto ground plane.

( Field configuration in a microstrip line.) Electromagnetic wave in microstrip line encounters two mediums. One is air and the other one is substrate. To analyse the wave propagation throughout the microstrip line, it is assumed that the EM wave encounters a homogenous medium having the effective dielectric constant (eeff).Generalised formulae are given as:(a) Effective dielectric constant:The effective dielectric constant (ɛeff) of the medium for microstrip configuration is expressed as:

(1) By the Eq. (1) , it is clear that 1 <ɛeff<ɛr (b) Phase velocity and guide wavelength:The phase velocity and guide wavelength depend upon the relative dielectric constant of the medium through which the EM wave is travelling. Hence in case of microstrip configuration, the phase velocity (vp) and guide wavelength (l) are written as:

(2) and

(3)where, λ0 = free space wavelength, c = velocity of light in vacuum. (c) Characteristic impedance:The characteristic impedance of a microstrip transmission line is the function of the ratio of trace width (W) and substrate height (h). For different ratios of W/h, characteristic impedance of a microstrip line can be given as:

(4) (d) Attenuation :The attenuation in a microstrip configuration is caused by dielectric loss (ad) and conductor loss (ac). Hence, these types of attenuation are defined in terms of their respective coefficients (in neper/m) which is given as:

(5)where, β0 = = propagation constant = 2p /λ0and tanδ = loss tangent of the dielectric=

where, Rs = surface resistance, Z0 = characteristic impedance.Microstrip lines can be configured in many ways. Some of the important configurations are: (a) Inverted microstrip line (b) Suspended microstrip line (c) Shielded microstrip line In inverted microstrip line configuration, the ground plane and the microstrip line lie on the same side but separated by air. The height (h) includes the substrate thickness and the air gap between microstrip trace and ground plane. The suspended microstrip line is the reciprocal of the inverted microstrip line. In suspended microstrip line, the ground plane and microstrip trace lie opposite to each other. The air gap is kept between the substrate and the ground plane.

( Inverted microstrip line,)

( suspended microstrip line )

( shielded microstrip line )Shielded microstrip line is similar to the basic microstrip line configuration except the metallic enclosure. The metallic enclosure covers the whole microstrip line configuration. In most of the practical applications, the microstrip line is shielded to reduce electromagnetic interference (EMI). This is the most realistic microstrip configuration because all the microstrip line based circuits are required to be protected from the environment.Advantages of microstrip line Microstrip offers smallest size for microwave circuits. Easy to fabricate. Disadvantages of microstrip line Unwanted radiations from microstrip lines due to the uncovered structure. High attenuation losses. Poor isolation among adjacent lines. 2.9 Parallel Strip LineA parallel strip line consists of two perfectly parallel strips separated by a perfect dielectric slab of uniform thickness, as shown in the figure below.

The plate width is ‘w’ and the separation distance is ‘d’ and the relative dielectric constant of the slab is ‘ɛrd’ . Characteristic ImpedanceThe characteristic impedance of a lossless parallel strip line is given by

The phase velocity along a parallel strip line is given by

The character impedance of a lossy parallel strip line a microwave frequencies is approximated as,

Attenuation LossesThe propagation constant of a parallel strip line at microwave frequencies can be expressed by,

for R

Thus the attenuation and phase constants are given by,

2.10 Coplanar Strip LineThe coplanar waveguide (CPW) is a planar transmission line widely used for microwave integrated circuits. It consists of a conductor strip at the centre and two ground planes located at equal distance on either sides of the centre conductor. The centre conductor and the two ground planes lie in the same plane. The construction of a coplanar waveguide is shown in the figure below,

In coplanar stripline, most of the electromagnetic energy is confined within the dielectric. The leakage of the electromagnetic energy in air can be controlled by taking substrate height (h) twice of the gap width (S). At low frequencies, CPW supports quasi-TEM mode and at high frequencies, it supports TE mode of electromagnetic wave propagation. In CPW, the effective dielectric constant is same as of slotline. The characteristic impedance of a CPW is generally not much affected by substrate thickness and mainly depends upon strip width (W) and slot space (S). The lowest range for characteristic impedance can be obtained by maximum strip width and minimum slot space.Advantages of CPW Low dispersion because less field density fringes out in air. Simple realisation because etching process is required in a single plane. Broadband performance because it doesn’t require via holes for series and shunt circuit elements. Disadvantages of CPW CPW is costly to fabricate because in order to suppress higher order modes, gold ribbons are used as “bridges” at every l/4 distance or less. Poor heat sinking capability. Relatively thicker substrates are required. 2.11 Shielded Strip Line

A partially shielded strip line has its strip conductor embedded in a dielectric medium and its bottom ground planes have no connection, as shown in the figure above.The characteristic impedance of a wide strip is given by,

Where, K=

t=the strip thicknessd=the distance between the two ground planes

Reference Books1. M. Kulkarni, “Microwave and Radar engineering”, 3rd edition, Umesh Publications.2. ML Sisodia& GS Raghuvamshi, “Microwave Circuits and Passive Devices”Wiley, 1987.3. M L Sisodia& G S Raghuvanshi, “Basic Microwave Techniques and Laboratory Manual”, New Age International (P) Limited, Publishers.

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