Microwave Engineering V. S. Bagad Technical Publications Pune®i Microwave Enginerring ISBN 9788184313604 Al rights reserved with Technical Publications. No part of this book should be reproduced in any form, Electronic, Mechanical, Photocopy oF ony information storage and ‘eirieval systom without prior permission in writing, from Technical Publications, Pune Published by = ‘Technical Publications Pune” 1, Aait Residency, 419, Shaniwar Peth, Pune - 411 030, nds Printers : Vikram Printers 34, Parvati Industrial Estate Pune-Satara Road, Pune - 411008.Table of Contents 1.1 Microwave Spactrum and Bands .......cuc.scessstesuseien 11.1 Microwave Frequencies . 1.1.2 Electromagnetic Field po 1.1.3 Popegaion of lecomagnaie Waves . tT 1.2 Applications of Microwave ... 1.3 Rectangular Waveguides ..... 1.3.1 Modes of Propagation. 192 Nomevistance of TEM Made 1.3.3 Solutions of Wave Equations in Rectangular Co-ordinaias =. 1.3.4 Field Equations for TE Mode... 1.3.8 Field Patter in Waveguide . 1.3.6 Waveguide Parameters . 1.3.7 Comparison of TE and TM Modes . 1.3.8 Boundary Conditions for TE Made 1.3.9 Boundary Concittons for TM Moda 1.4 Power Transmitted in Waveguide .. 4.5 Power Loss in Waveguide ..... 1.5.1 Power Loss in Dielectric Filing 1.5.2 Power Loss in Waveguide Walls ....... 1-23 1.5.3 Misaligned Waveguide Sectons ......., ce 1-2 1.6 Waveguide Excitation ........c0sssuussssasssss 1-23 1.7 Comparison of Waveguide and Co-axial Cable 1-25 1.8 Advantages of Waveguide Over Co-axial Cable... 1-25 Solved Examples .......c.ccscscceesceesesceeeseesimnscesimneesieaeseeen 12 26 Points to Remember 1-40 sep cater eecueinen! princess Soto GAREReview Questions... 2.1 Propagation of TE Wave in Circular Waveguide... 2.4.1 Boundary Conditions / Characteristic Equations 2.1.2 Dominant and Degenerate Modes: 2.4.3 Impossibility of TEM Mode 2.2.1.1 Higher Onder Modes in Strip Lines 2.2.1.2 Losses in Strip Lines 22.4.3 Excitation of Strip Lines. 2.2.2 Microstrip Lines... 22.2.1 Effective Dielectric Constant 2.2.2.2 Characteristic Impedance (Z,) 2.2.2.3 Losses in Microstrip Lines (2.2.2.4 Q-factor of Microstrip . . 2.2.2.5 Limitations of Microstrip... ss ss ‘Comparison of Stripline and Microstrip 225 Slot bins 224 Coplanar Lines ..... 2.2.5 Advantages of Planar Transmission Lines: 2.2.6 Disadvantages of Pianar Transmission Lines . 2.3 Cavity Resonators...... ae 2.3.1 Rectangular Cavity Resonator... . 2.3.2 Q-Factor of Cavity Resonator... . 2.3.3 Applications af Cavity Resonator. . 2.3.4 Re-entrant Cavity 2.3.5 Excitation of Cavity Resonator... - Solved Examples... Points to Remember 2-22 Review Questions 2-22 tS SESE RIESE Pl ab SEES3.14 Seattering Parameters 3.1.2 Scattering Matrix... _ wees - . 2... 3-5 1.1.3 Scattering Matrix Representation for Multiport Network 311.5 Properties of $-Parametors... we $4.6 S.Parametors of» Two Pot Notun ih Mamatched Load ee 2. 3-10 3.1.7. Comparison between ($], (2), and [Y| Matrices... co 3.1.8 Relations of Z, 3.2 Waveguide Tees... 4216-Plane Toe. 3.23 Magic Tee... sees 3.3 Waveguide Couplings... 8.3.4 Coupling Loops .. 3.4 Microwave Attenuators . ‘3.4.1 Fixed Attenuator . 3.4.2 Variable Attenuator. .. . 3.5 Waveguide Comers, Bends and Twists... 3.6 Waveguide Transitions ... 3.6.1 Rectangular to Circular Waveguide Te Transition. 3.6.2 Circular to Rectangular Waveguide Transition : ceeteeeeteeees £163 Ton botween Cosa Gabi and Rectannder Wavoguido vee eceeeeeeesees 9229 3.7 Tuning Screws .... 3.8 Directional Couplers....... 3.8.1 Directional Coupler Parameters 3.8.2 Two Hole Directional Coupler. 3.8.3 Multihole Directional Coupler 3.8.4 Bathe Hole Directional Coupler 3.9 Waveguide Flanges . «3-37 3.10 Matched Terminations .... siseeereerenseenetessereseimeraneessees 87 BB 3.10.4 Standard Mis-matehes =... cee eee teens 3-40 Figo ego raeMicrowave Engineering 2-12 Circular Waveguides The propagating fields in slot lines are concentrated in the dielectric regions at the gap between the two adjacent conductors. The magnetic fields has a strong component in the propagation direction. Therefore, the primary transmission mode is not TEM but TE. This characteristics is more when the system requires the incorporation of non-reciprocal ferrite components. Fig. 2.2.7 shows field patterns of slot line E Lines Hines Fig. 2.2.7 Field pattern of slot lines The magnetic field has beth longitudinal and transverse components, the propagating mode is TE. The characteristic impedance Zo at’ slot lines are proportional to the width of the slot and frequency. Advantage of slot line over micrdstrip line is that the active and passive somponents can easily be shunt mounted to the line from the top while in microstrip series mounting is possible. 2.2.4 Coplanar Lines The coplanar lines consists of a thin metal strip with ground planes on either side. It combines some of the advantages of microstrip and slot lines. For example, series and shunt connections are easily achieved in coplanar line. Fig. 2.2.8 shows coplanat lines. Ground planes ‘Center strip Dielectric substrate (c,) Fig. 2.2.6 Coplanar lines:Microwave Engineering Circular Waveguides © The propagating modes in coplanar lines are TE modes. As a significant magnetic field component is present, nonreciprocal ferrite components can be realized, 2.2.5 Advantages of Planar Transmission Lines . Major advantages of planar transmission lines are 1. Compact in size 2. Light in weight 3. Highly reliable 4. Better reproducibility 5. Longer life 6. Low cost 7. Basy access to component mounting (exception is strip line) 8. Characteristic impedance can be controlled by adjusting, dimension of strip. 2.2.6 Disadvantages of Planar Transmission Lines * There are few disadvantages of planar transmission lines. 1. As the size of strip is small, power handling capability is lower. 2. Because of open structure, radiation losses are more. 2.3 Cavity Resonators * A cavity resonator is a metallic enclosure formed by shorting two ends of a section of a waveguide. Cavity resonator confines the electromagnetic energy. The stored electric and magnetic field components inside the cavity determines the equivalent inductance and capacitance. Within the cavity, various TE, and TMyy, Modes are possible. A very high value of Q can be obtained with these resonator. © In microwave applications the commonly used cavity resonators are 1. Rectangular cavity resonator 2. Circular cavity resonator 3, Re-entrant cavity resonatorMicrowave Engineering 2-14 Circular Waveguides. 2.3.1 Rectangular Cavity Resonator * In a rectangular waveguide section if the short circuit is placed at two ends. The resultant configuration is called a rectangular cavity resonator in which the signal bounces back and forth between the opposite walls, Fig. 2.3.1 shows rectangular cavity resonator, Fig. 2.3.1 Rectangular cavity resonator If m = number of half-wave periodicity in the x-direction n = number of half wave periodicity in the y-direction Pp = number of half wave periodicity in the z-direction ‘Then for both modes ic. TE,,.. and TM,,,,, the resonant frequency f, is expressed by (ey +8 Because for air : B= band B= % (hy &) V2 = Therefore, 2.3.2 Q-Factor of Cavity Resonator * Qfactor is the measure of the frequency selectivity of a circuit, Q is defined as Maximum energy stored during a cycle Q = 25) erage energy discipated per cycleMicrowave Engineering 2.45 Circular Waveguides where o, = Energy stored in cavity P,_ = Average power loss in cavity o, = 2 1" FT * The average power loss can be divided into three parts - i) Power loss in walls (Pw) ii) Power loss in dielectric (P,,) ) Power loss due to loading of coupled device (P, gsspting) + PL = Pie + Pra + Pe coupling For loaded circuit os Qa = 4 w+ Pld + Preoupling. a. G2" O where Q, = Qfactor of wall Q-factor of dielectric Q-factor of coupling Q, is unloaded Q factor Since Qy >> Qu, and where K = Coupling coefficientMicrowave Engineering 2-16 Circular Waveguides * There can be three values of coupling coefficient i) Critical coupling When resonator and generator are matched, then K = 1 Q for loaded circuit is given by - Qe Qs ii) Over coupling : K > 1 Here cavity terminals are at maximum voltage, and the impedance at maxi voltage is standing wave ratio (p) Le. K =p. aq = a T+p ) Under coupling : K < 4 Here cavity terminals are of minimum voltage and the impedance is equal to reciprocal of SWR (3) ie. K 1 P Qu PL pri The relationship of coupling coefficient K and SWR is shown in the Fig. 2.3.2. Under coupled Critically SWRip) Wedd » on Over coupled Coupling coefficient (i) Fig. 2.3.2 Coupling coefficient Vs SWRMicrowave Engineering 2-47 2.3.3 Applications of Cavity Resonator + In microwaves the cavity resonators are devices. Few of them are explained below. 1) Microwave filters : ae . Movable plunger Fig. 2.3.3 Cavity resonator in notch filter 2) Wavemeter : Circular Waveguides: used in microwave measuring In notch (narrow band) filters the use of cavity resonator is shown in Fig. 2.3.3. In notch filter shown in the Fig. 2.3.3 the cavity dimensions are flexible ie. it can be changed by plunger screw movement when — incoming signal frequency is equal ta resonant frequency. Thus energy stored in the cavity can also be varied, Therefore it acts as noteh filter or band pass filter, Screw ‘Waveguide Cavity Fig. 2.3.4 Cavity resonator In wavemeterMicrowave Engineering 2-18 Circular Waveguides Wavemeter is used for measuring frequency. Cavity dimensions are changed by screw when incoming signal frequency in waveguide matches with resonant frequency of cavity, the cavity absorbs power and output of waveguide is minimum, A calibrated micrometer scale gives directly the frequency. Fig. 23.4 shows the arrangement of wavemeter. 3) Microwave signal generation Cavity resonators are used in Reflex Klystron and Magnetron for generation of microwave signal 4) Radar systems Cavity resonators are employed in Duplexers of Radar systems. 2.3.4 Re-entrant Cavity In order to maintain resonance at operating frequency and for efficient energy transfer into the cavity resonator, the inductance and. capacitance must be reduced. The re-entrant cavities are specially designed to meet this requirement. Re-entrant cavity is one in which metallic boundaries extend into the interior of cavity, One of the commonly used reentrant cavity is co-axial cavity. In this not only inductance is reduced but resistance losses are also reduced and shelf shielding enclosure prevents radiation losses. Fig. 2.3.5 shows co-axial re-entrant cavity Fig. 2.3.5 Co-axlal re-entrant cavity Re-entrant cavities are used in Klystrons and other microwave tubes. 2.3.5 Excitation of Cavity Resonator In order to excite a particular mode, the cavity must be properly coupled to an external source. Different coupling methods are used in microwave filters and wavemetersMicrowave Engineering (A) Loop Coupling Rectangular cavity Fig. 2.3.6 Loop coupled cavity magnetic flux lines. (B) Probe Coupling Co-axial line Rectangular cavity Fig. 2.3.7 Probe coupled cavity (C) Aperture Coupling Apertyre 1 iris Fig. 2.3.8 Aperture coupled cavity resonator Circular Waveguides A rectangular cavity that is loop coupled to a co-axial line is shown in Fig. 23.6. The loop size is very small and the current in the loop can be considered to be constant. The conduction current in the loop produces a linking magnetic field. The loop is capable of exciting any cavity mode. The plane of the loop is placed perpendicular to the A rectangular cavity that is probe coupled to a co-axial line is shown in Fig. 2.3.7. Any cavity mode having an electric field component parallel to the probe can be excited by this coupling arrangement. In aperture coupling cavity resonator is excited by a generator by means of a small centred hole in the transverse wall. Such type of coupling is also called as iris coupling. Fig. 2.3.8 shows iris/aperture coupling. A magnetic field component that is parallel to the lang dimension of the slot will be coupled through the aperture.Microwave Engineering 2-20 Circular Wavequides Solved Examples map Example 2.1: A metal box is 3x4x5 cm in dimensions, filled with air. Calculate the resanant frequency of the cavity for TE 102. = Sem = 3x10%m Solution; Given a b = 4cm=4x107m d = 5ems5x1l0?m m= 1 n=0 p=2 Resonant frequency for rectangular cavity is given by a mm Example 2.2: Calculate the lowest resonant frequency of @ rectangular cavity resonator with dimensions a = 2 cm, b= I cm and d = 3.0m Solution : The dominant mode for rectangular waveguide is TE, mode and lowest frequency can be obtained when p = I(ie. lowest value). Therefore the TEj,, mode will give the lowest resonant frequency i.e. m = 1, n= 0 and p=1 Given : a = 2cm, b = lem, d =3cm. Resonant frequency for rectangular cavity is given by,Microwave Engineering 2-21 Circular Waveguides _ 3x10@ fy fe ay 3) . f, = 9GHz » Ans. mm Example 2.3: A rectangular cavity resonator 10x 8% 6 em. Compute the following: @) Resonant frequency b) Resonant frequency of dominant mode for a dielectric filled cavity of e, = 3, For TE, mode Solution : a = 10cm=010m b = 8cm= 008 m c = 6cm=0.06m m = 1 n=l pel f, = 34 GHz w Ans. (b) Resonant frequency with filled dielectric is given by f = 2GHz . Ans.Microwave Engineering 2-22 Circular Waveguides Points to Remember 1, The principal mode of propagation in coaxial line is TEM. Hence it does not have cut-off frequency. 2. Strip line consists of a central conductor strip and two ground plates. The dominant mode in strip line is TEM. 3, Microstrip line consists of a conductor strip and a ground plane. The electromagnetic wave propagates in quasi TEM mode. 4. Three types of losses taking place in microstrip. i) Dielectric loss ii) Ohmic loss iii) Radiation loss 5. Slot lines consists of two conducting planes separated by a slot. The electromagnetic waves propagates in TE mode. 6. Coplanar lines consists of a thin metal strip with ground planes on either side. The propagating modes in coplanar lines are TE modes. 7. A cavity resonator is a metallic enclosure formed by shorting two ends of a section of a waveguide. Review Questions. L. Explain the construction and field pattern of strip line. 2. Write a note on higher order modes im strip lines. 3. Briefly explain how the strip lines are excited. 4. Describe the construction and field pattern for microstrip line. 5. Elaborate different lasses taking place in microstrip line. 6. What are the limitations of microstrip line ? 2. Compare strip line and microstrip line & Explain the construction and field pattern for slot lines. 9. Write @ note on coplanar fines. 10, Give advantages and disadvantages of planar transmission lime. 11. Explain cavity resonator. 12, Deduce Q factor for cavity resonator, 13. Briefly explain the applications of cavity resonator. QoogWaveguide Components and Applications - I 3.1 Microwave Network . A microwave network consists of microwave devices and components (sources, attenuators, resonators, filters, amplifiers etc.) are coupled by transmission lines or waveguides. The point of intersection of two or more signals is called as junction. In electronic circuits operating at low frequency, a port is a pair of terminals while for a microwave frequency a port is a reference plane transverse to the length of the microwave transmission line or waveguide. The variables at low frequencies are voltages and currents. The variables {voltages and currents) are related interms of ABCD parameters, Z-parameters, Y-parameters or h-parameters in matrix forms Consider a generalized two-port linear network as shown in Fig. 3.1.1. Two Port % Hee i fg Fig. 3.1.1 Two port network The relationship between variables and parameters is given by following matrices. 41, ABCD parameters / chain matrix : ie] [e alle (3-1)Microwave Engineering 3-2 Waveguide Components and Applications - | 2. Z-parameters / impedance parameters : Mil _ [Zu Ze fh V2} [2n 222} [le 3. ¥-parameters / admittance parameters : fa]. [Ye Ya] [Ve th] * [yn Yn] [ve 4. h-parameters / hybrid parameters : Vi] _ fin he] fh Te} [har haz | LV2 Limitations of ABCD, Z, Y and h-Parameters. * Problems arise in the measurement of these parameters at microwave frequencies. These measurements involve terminating the networks in open and short circuits and subsequent measurement of voltages and currents. Firstly it is difficult to achieve good quality open and short circuits at frequencies above 1 GHz, and terminating, active devices in this way, can damage the devices due to the total reflection of power back into the device. * Another problem arises in the measurement of voltages and currents at microwave frequencies and often they can only be derived from measurable quantities such as VSWR reflection coefficient, power etc. The easiest parameters to measure are incident and reflected power and the optimum test conditions are when the two port is terminated in matched loads. + For describing and analyzing a microwave network the input-output parameters are defined by scattering matrix. Scattering matrix is also known as S-matrix. Since at microwave frequencies measuring voltage, current and impedance is difficult instead of transmission coefficient, reflection coefficient, standing wave ratio can be measured accurately. Hence, the conventional methods of using Z, Y, h and ABCD parameters are not applicable at microwave: frequencies. Scattering matrix is widely used to analyze the microwave’ networks. Also scattering matrix can be applied to multiport networks which is common in microwave application. 3.1.4 Scattering Parameters + First consider a general transmission line as shown in Fig. 3.1.2. Here V; and ¥; are the incident and reflected voltages at the load port. lv. Incident power P,Microwave Engineering 3-3 | Waveguide Components and Applications -1 wat . Zo Power delivered to the load . Me Reflected power P; Vel? rh z Load reflection coefficient Ze Fig. 3.1.2 Generalised transmission line _ ¥e_Z.-Zo Zi +Zo Now replace the source and line by its Thevenin equivalent as shown in Fig. 3.1.3 If we now define variables a and b such that a= tT and b= Val 2Re (Zs) 2Re(Z.)" Where * denotes complex conjugate and Re represents the real part, then we find that the power available from the source is Pa = fal? and the power delivered to the load is R= |aP-/b/ Where |b|? is the power which is scattered or reflected by the load. a and b are termed the generalised incident and reflected scattering variables or power waves. They have dimensions of power. = The scattering parameters S of the load is defined as- s = b.V-S1 4 -Z a W+Z,1 2 +ZyMicrowave Engineering 3-4 Waveguide Components and Applications -| This is a very similar form to that of the generalised reflection coefficient. Note that $ is defined interms of 7,. Fig. 3.1.3 Thevenin equivalent of Fig. 3.1.2 * Now consider the generalised two port circuit shown in the Fig. 3.1.4. The set of linear equations describing the behaviour of the circuit using the power waves as variables is : by = Sy ay +Sy2 a2 bz = Sn ar +Sx a2 ‘or in matrix form fb} = [5] a) where [5] is known as the scattering matrix. where be fr and (| a=], az and the scattering matrix is defined by, Su Sa s [ese] => abe Su = a and Sas and with a, = 0(V, =0) = be abe Sa = 32 and Sp = So S;, and Sz2 represents the generalised input and output reflection coefficients.Microwave Engineering 3-5 Waveguide Components and Applications -1 * It should be noted at this point that these generalised S-parameters are defined interms of the reference impedances at the ports and so a set of values is meaningless without knowledge of the reference impedances associated with each port. However, almost without exception, S-parameters are defined with reference to the characteristic impedance of the network or system in which they are considered. Fig. 3.1.4 Two port for power wave definition 3.1.2 Scattering Matrix © It is a matrix which shows a linear relationship between coefficients of the ports « Scattering matrix is a useful analytical technique for studying multiport microwave networks. Its elements relate forward and reverse travelling waves at the various ports of the network. The elements of this matrix are called scattering coefficients or scattering parameters, in short it is abbreviated as S-parameters. These S-parameters are complex numbers, For a two port network the equations of S-parameters are given as, by = Sy ay +S az bz = Sy ai +Sm ar Reflection coefficient at port-1 when port-2 is terminated with matched load ie. a: = 0 Attenuation of wave travelling from port-2 to port-1. Attenuation of wave travelling from port-1 to port-2Microwave Engineering 3-6 Waveguide Components and Applications - | terminated with a matched load a; Sn = Bl Reflection coefficient at port-2 when port-1 is ar ato Here a represents normalised incident wave and b represents normalised reflected wave at the corresponding ports. Su Se Sn Sa The diagonal elements of the scattering matrix are reflection coefficient and the off diagonal elements are transmission coefficient. Scattering matrix s 3.1.3 Scattering Matrix Representation for Multipart Network * For a multiport (say n) microwave function, equations of S-parameters are expressed as: by = Spay +Siz a2 +53 ag ++ Sin an bp = Snap +Sx az +8 a3 ¢....4+S2n an by = Sai An +52 02 +Sp3 3 +... Son dn * Above equations can be represented by nxn mat for n-port microwave junction is represented as by Su Si + Sin | [ar by Sa Sa The scattering matrix ba} [Sm Sa — Sm |lan 3.1.4 Losses in Network * In microwave circuits it is sometimes necessary to represent various losses in terms of S-parameters when the ports are terminated with matched load. ‘Consider two port network as shown in Fig. 3.15. Let P, is power fed at port-1. P, és power reflected at port-1, P, is qutput power at port-2.Microwave Engineering 3-7 Waveguide Components and Applications -1 ty Ip Me Vy V2 Port - 1 Pot-2 —e —a, —_—) — Fig. 3.1.5 Then insertion loss, transmission loss, reflection loss, return loss associated with two port network is given as, a) Insertion loss. Insertion loss (dB) = 10 log Z 2 Insertion loss (4B) = 10 log [21 [ba] Insertion loss (dB) = 20 log Bal q Insertion loss (dB) = 20 log —!— |S. | b) Transmission loss Transmission loss is also called as attenuation loss. ‘Transmission loss (dB) = 10 log © = 2 Transmission loss (dB) = 10 log Ss a ¢) Reflection loss R -F 1 = 10 log —~—. 1-]$n[" Reflection loss (dB) = 10 logMicrowave Engineering 3-8 Waveguide Components and Applications - | d) Return loss Return loss (dB) = 10 log a Return loss (4B) = 20 log in 7 1 [sn] Return loss (4B) = 20 log 3.1.5 Properties of S-Parameters © Scattering parameters are complex quantities. In microwave network the S-parameters show following properties. 4) Symmetry Property « The symmetry property states that if a microwave junction satisfies a reciprocity condition, the junction is a linear passive circuit and the S-parameters are equal to their corresponding, transposes. 5 = 5 or s=s! Where ST is the transpose of S. Example 1: Consider S-matrix of a two port network, _ [Su Se S= fe =| Su Sa st= [es Sn By symmetry property, Sa = Sn Example 2: Consider 3 x 3 S-matrix, Su Sa Sia) S=|Sn Sn Sx] | Sn Sx Su}Microwave Engineering Waveguide Components and Applications - | Su Sa Su S'=|S2 Sn Su Sis Su Sa By symmetry property, Si2 = Sx Sis = Sa Sm = Se + The symmetry property results from the fact that the transmission of energy from port-1 to port-2 is exactly equal in magnitude to the transmission of energy (in reverse direction) from port-2 to port-1, provided that the network is bilateral and there are no losses in it. 2) Unity Property / Unitary Property * Unity property states that “the sum of the products of each term of any row or column of S-matrix multiplied by its complex conjugate is unity." ss For j= 1,23.. 3) Zero Property * Zero property states that "the sum of the product of each term of any row or column multiplied by the complex conjugate of the corresponding terms of any other row is zero. Six Si, = 0 For k= 4) Phase Shift Property «If any of the terminal planes (k'* port) is moved away from the junction by an electric distance B,, |,, each of the coefficient S; involving k will be multiplied by the factor e-Pk, * A change in the specified location of the terminal planes of an arbitrary junction will affect only the phase of the scattering coefficient of the junction. Ss = 6S,Microwave Engineering 3-40 Waveguide Components and Applications -1 on 0 wu. O Where, 6 =| 0 62 .. 0 Ove see Onn bu = bor = Oy CPMEfor k = 1,2, 3,0. 3.1.6 5-Parameters of a Two Port Network with Mismatched Load * In a transmission line, two port network is formed when there is discontinuity between the input and output port eg. waveguide step junction, transitions of signal. During propagation of microwave signal from one port to other evanescent modes are excited, which contains reactive energy. The evanescent modes decay with propagation. The terminal reference plane are chosen beyond the effect of evanescent. * For a two port network terminated by normalized load and source impedances. t= 2 s Zy [E es By) Now S-parameter equations ae by = Sia; +512 a2 by = Sm ai+Sy a2 Substituting value of a2 =t2 bz by = Sy a) +S bz tz bz = Sn ai+Sy b2t2 The input reflection coefficient is given as, br ar 1sMicrowave Engineering 3-41 Waveguide Components and Applications -| Sig Sate ue Sut Toga For a reciprocal network Siz =Sz 3.1.7 Comparison between [S], [Z], and [Y] Matrices + [5]. [Z] and [Y] matrices give the unique intrinsic properties of the device with the circuit characteristics at test frequency. Also one matrix can be represented interms of other matrix. The common properties of [S], [Z] and [Y] matrices are - 1. Number of elements in each matrices are equal. 2. For a reciprocal device the matrices exhibits reciprocity properties, eg. Zy = Zj or Sij = Si 3. If a matrix is symmetrical, its equivalent matrix is also symmetrical. 4. Few properties of S-matrix are proved to be advantageous aver the [Z] and [¥] matrices such as - a} Unitary property b) When reference plane is changed, the S-coefficients changes only in phase. c) By knowing the matrix coefficients, all the measurement parameters can be calculated such a direct correspondance is not possible with [Z] and [Y] matrices. 3.1.8 Relations of Z, Y and ABCD with S-Parameters For a two-port network the relationship between variables and parameters are given as, Et Ml 2) Rearranging and comparing above two matrices we get, Za Za il) Z-paramoters A=Microwave Engineering 3-12 Waveguide Components and Applications -1 _ Zu 22-2 Zn) Zn _ -Zn Zu = fe sie Rearranging and comparing with ABCD parameter matrix. iii) Y-parameters _D Yn + & _ LA Yo = -= 1 Ye = 5 Ya = c+AD Wy) S-matrix bi] _ [Sn Sz] far br} [Sa S| aa gs, = CADBIC+D) nS (A-B+E-D) Sp = 2 2(AD+BO) 2 (A-B+C-D) Sa = —— 2. at” (A =B+C=D) Sq = TASB+C+D) (A-B+C-DyMicrowave Engineering 3-13 Waveguide Componants and Applications -| iam Example 3.1.1: Express S-parameters interms of impedance when two transmission lines are joined with character impedances Z, and Z>. Solution : Assuming matched input and output impedances. The reflection coefficient at input side. and Sa &- 2B The S-matrix can be written as, 3.2 Waveguide Tees © Waveguide tee junctions are used to split the line power into two or combine the power from two lines with proper consideration of the phase. The junctions that are widely encountered in the microwave techniques are E-plane, H-plane tee and magic tee. 3.2.1 E-Plane Tee + An E-plane tee is designed by fastening a piece of similar waveguide to the broader wall of a waveguide section. The fastened waveguide is called auxiliary arm. It is parallel to the plane of the electric field of the dominantMicrowave Engineering 3-14 Waveguide Components and Applications - | mode TE,, in the main waveguide as shown in Fig. 3.2.1. Hence this type of junction is called E-plane Tee. Fig. 323 shows the propagation of electromagnetic fields in an E-plane Tee when the dominant mode TE, is incident on the symmetrical port-3. While passing through the junction the electric lings of force bend and as a result af this, fields of opposite polarity emerge from the two arms. Fig. 3.2.1 E-plane tee + If the fields of opposite polarity are fed into the two arms 1 and 2, the fields in the symmetrical arm 3 are added as shown in Fig. 3.2.1 * If the fields of same polarity are fed inta the two side arms _there emerge out the Fig. 3.2.2 Transmission line symmetric arm in opposite phase and equivalent of E-plane tee therefore cancel out the effect of each other as shown in Fig. 3.2.3. ¥ Pot @ Input TE 10 Output — Output port pot Fig. 3.2.3 E-field of TE,, mode with input at port-3Microwave Engineering 3-15 Waveguide Components and Applications -| Analysis of E-Plane Tee using S-Matrix ‘Consider a three port microwave junctions having a scattering matrix given by Si Sz Ss [S] = |S Sx Sx (3.2.1) Su Sa Se Suppose the junction is perfectly matched, there are no reflections at the ports. This is matrix notation implies : Sy = Sy =Sy=0 = AB.2.2) Since [8] is symmetric and unitary, we have, Spy = Sy weA3.2.3la)) Sy, = Sy +f3.2.3(b)} Sy = Sy +(3.2.3(C)) Si Sf, +5253, +51355, (3.2.4) For a loss-less junction, we have, Su Sf, +5283, +5055, = 1 (3.2.5 (a)) Sy 53, +5228}, +5238}, = 1 +(3.2.5 (b)) Sy Sj, #5325, + S83 = 1 -AB.2.5 ()) From equation (3.2.2) and (3.2.4), Su +53, = 0 -A3.2.6) By using equation (3.2.2) and (3.2.5 (a)), we find 182|? = 1 [83/7 = 1+ [Sp]? (3.2.7) In case of E-plane tee, the outputs at ports-1 and 2 are out of phase by 180° with an input at port-3. The scattering coefficient is given by, Sa = Sey =~ Sis ---(3.28) If port-3 is perfectly matched to the junction, S, = 0 3.2.9) With above properties, from equations (3.23) and (3.2.9), the scattering matrix becomes : Si Sz Ss [S} = |Si2 Sm -Sis --(3.2.10) Ss -Su 0Microwave Engineering 3-16 Waveguide Components and Applications - 1 From unitary property, [S] -[S*] = 1 From (3.2.10), we can write the scattering matrix as, Su Sa Sa [8,2 8) Sa] fo 0 jSe Sx Ss |/5, Sb Sy }=/0 1 0 [Sa Sis Si, =8j, 0 | oo1 By multiplying R, C, : (Sul? * [Sa]? * 18:5 e(B.2.11) By multiplying R, Cy : [Sia]? + 1Ss21? * [Sia]? -(3.2.12) By multiplying R, C, : [S317 + [S317 = 1 23.2.1) By multiplying R, C; : $583, -Ss Sf, = 0 Sy (Si -Sh) = 0 of S,=S, From (3.2.11) and (3.2.12), we get, Sn = Sn - 3.2.15) From equation (3.2.13) we get, + A3.2.04) 5, = # A216) By using the values of equations (3.2.14) to (3.2.16) in equation (3.2.11), we get, 2 2,1, Sul? + [Sul +3 = 1 1 21Sulh= 5 > ISul? -AB247) From equations (3.2.14), (3.2.16) and (3.2.17), the scattering matrix of equation (3.2.10) becomes, [s] = (3.2.18) g]enic in 1Microwave Engineering 3-17 Waveguide Components and Applications - | The scattering matrix is defined as, {b] is} = LOL [s} fal [B] = {5} fa (3.2.19) Where b is output port and a is input port. 1oioa by 2 2 2 | fa b,}=}2 2 1} Ia (3.2.20) 2 3 7 |" 82! bs 1 1 as v2 2 _i,i1 1 b= Fat gat em G22) 1, il L b= Fat Emm (8.2.22) 1 1 by = ana (3.2.23) There are three cases arises in E-plane tee : Case 1: * When an input at port-3 equally divides between port-l and port2 but introduces a phase shift of 180° between two output. Hence E-plane tee acts as a 3 dB splitter. a = %=0, a 40 From equation (3.2.21) to (3.2.23), output is : 1 1 b= ae bo aga by Case 2: Equal inputs at port-1 and 2 result in no output. a = aza a= 0 From equation (3.2.21) to (3.2.23),Microwave Engineering 3-48 Waveguide Components and Applications - 1 b, = b, = a-—a=0 ieb,=0 Case 3: When input at port-1 is non zero and at ports-2 and 3, it is zero, then output is a, #0, a, =0,a,=0 = a bea ; a= > : ar 3.2.2 H-Plane Tee An H-plane tee is obtained by fastening the auxiliary waveguide perpendicular to narrow arm of the waveguide section. The auxiliary arm should lie in the H-plane of the dominant mode TE,y mode in the main waveguide as shown in Fig. 3.24. When a wave incident in the symmetrical side arm ie. Port-3, then it splits into two equal inphase waves in two main arms ie. Port-l and port-2 as shown in Fig. 3.24. ‘The reason for the two waves being inphase is that while passing, through the Fig. 3.2.5 Transmission line equivalent of H-plane tee comer a PotMicrowave Engineering 3-19 Waveguide Components and Applications -| H-junetion the electric field does not suffer any bending and the junction splits one wave into two ports. + If two waves are fed from two side arms 1 and 2, these are added at a auxiliary arm at port-3 as shown in Fig, 3.25. * When a wave incident in the side arm ray at port-I, then it is again divided symmetrically into two arms port-2 and port-3 as shown in Fig. 3.2.5. Analysis of H-plane tee using S-Matrix * In H-plane tee, there are also 3 possible inputs and three outputs. So scattering matrix is given by, [Se S2 Sal] [S] = |S Sn Sx | oo(9.2.24) [Su Se Sus | For symmetric plane, scattering coefficients 5,, and S.y must be equal Sis = Sas 43.2.25) From the symmetric properties : Si = Sy Sa = Sav Sy = Se 3.2.26) The port-3 is perfectly matched, then 0 (3.2.27) By using properties of equations (3.2.25) to (3.2.27), the scattering matrix of equation (3.2.24) can be rewritten as, Su Sz Sis (S] = |S Sx Ss + AB.2.28) Si Sis 0 From unitary property = Is}[S*] = 1 Si $2 Ss] {Si Sh Sh] [1 90 Sn Sm Ss] |Si, Sz 5 |=|0 1 0 Ss Ss 0] |s $3 0} lo 01 Maltiplying R, C,, we get, 81, “Sf, +512 Sf, +8 Sf, = 1Microwave Engineering 3-20 Waveguide Components and Applications -1 And |Sy[? + [Sp [? + [S317 =1 43.2.29) By multiplying R, C, : [Sip]? + [Sa]? + [5,3]? = 1 (3.2.30) From equations (3.2.29) and (3.2.30) : ISul? = [Sp/? Sy = Sy (3.2.31) By multiplying R, C,, we get, [S317 + [S317 = 1 = 2 (S5[?=1 (3.2.32) By multiplying R; C, Sy 5}, +Sis 8}, = 0 Sp (Si, +8),) = 0 Since S,, #0 Sj, +Si, = 0 Si, = -Sh $1 = -Su (3.2.33) By using values of (3.2.32) and (3.2.33) in (3.2.39), 2 2,1_ WSnl?+ [S12 +5 = 1 1 222 218i? = 5 1 Sy, = = ey From equations (3.2.31) and (3.2.32), 1 Sa = -3 Sn = 5Microwave Engineering 3-24 Waveguide Components and Applications -1 By using above calculated values in the S - matrix of equation (3.2.29) written as : 1 _1 1 2°37 _/.2 1 1 = |-3 3 5 Lio v2 2 The output of the three different ports is calculated by using equation (3.2.20), Quad by 202 V2\fa o}=|2 2 Th | 2 Lbs Lad VP lss v2 V2 b, = ta-ta44 (3.2.34(a)) 1 = FU Za yw ol bp = -Lattasrta +GB.2.34(b) ne ght htm 1 1 be = tae (8. 2 te (3.2.34(c)) There are two cases arises in H-plane tee : Case 1: When the input applied to the port-3 only, a; #0, a,=a,=0 then output from equations (3.2.34), = 33 bee = 43 by = b, = 0 ‘The input power divides between port-1 and port-2. It is also a 3 dB splitter. 3 dB splitter : If P,, P, and P, are different ports of E or H-plane tee, then total output power is written as, Py, = Pi+P, If input power at port P, is equal to port P, ie. P= Py then total power : P, = 2P,Microwave Engineering 3-22 Waveguide Components and Applications -| The amount of power coming out of port P, or port P, due to the input at port Py. Case 2: a, = a=0 a, = 0 = 28482 2 SB. b, = 5 at 3 5 0 be = 54548 = r0 by = Sh BR 2 2B Power output at port-3 is addition of power at port-l and port-2 and in same phase. 3.2.3 Magic Tee * A magic tee is a combination of an E-plane and H-plane tee, It acts as a 4-port hybrid circuit. It is also called as Hybrid tee. Fig. 32.6 shows magic tee. Collinear arm Hearn Fig. 3.2.6 Magic tee (Hybrid tee) Characteristics of magic tea 1. If two waves of equal magnitude and the same phase are fed into port-1 and port-2, the output will be zero at port-3 and additive at port-4. 2. If a wave is fed into port-4, it will be divided equally between port-1 and port-2 of the collinear arms and will not appear at port-3. Su = Sa =1/¥2, Su = Sq = 1/2 and Sy =0Microwave Engineering 3-23 Waveguide Components and Applications -1 3. If a wave is fed into port-3, it will produce an output of equal magnitude and opposite phase at port-1 and port-2. The output at port-4 is zero. Sis = Sn = 1/ V2, So = Sp = 1/2 and Sy =0 4. If wave is fed into one of the collinear arms at port-1 or port-2, it will not appear in the other collinear arm at port-2 or port-1 because the E-arm causes a phase delay while the H-arm causes a phase lead. S2 = Su =0 Magic tee is symmetrical about an imaginary plane bisecting arms port-3 and port. * If port-1 and 2 are terminated in matched loads and no reflections take place inside the junction, entrance of power through either port 3 or 4 results in equal power delivery to arm 1 and 2. Reflections may take place due to severe discontinuities in the junction Effects of reflections 1. Only a portion of the power that approaches the junction through port-3 or 4 is delivered to port-1 and 2. 2. Power is not divided equally between port-1 and 2, when power enters through port-3 or 4 3. Balance does not exist between port1 and 2 ie. some power transmits directly from port-1 to port-2. Reflections must, therefore, be avoided or compensated. By virtue of above properties discussed above, a magic tee has several applications. Applications of magic tee 1. As an isolator. 2. As a matching device 3. As a phase shifter. 4. As duplexer. 5. As mixer, S-matrix for magic tee is a 4 x 4 matrix Si Sa Sa Sis Sn Sn Sn Sa Ss, Sm Ss Sa} Sa Se Ss Su] (S] = But S, = 0, Sp=0 SyMicrowave Engineering 3-24 Waveguide components and Applications -1 8, = 0, S250, Sy=0, Sy=0 and Sia = Soe S13 = - Ss For port-3 and port-4 matched ©. Smatrix becomes 0 0 Sy 0 0 Sp is} = 61 Sa Sz 0 Sa Se 0 0 0 Sis oud 10 0 -Ss 0-11 “{|Six -Sa 0 -10 0 Sis Sia 0 1 0 0 3.3. Waveguide Couplings * Ih order to produce field intensities of desired mode in the waveguide a probe or loop coupling device is commonly used. The waveguides are excited from microwave signal source through a co-axial cable. © The inner conductor of the co-axial cable is projected inside the waveguide. This inner conductor acts as an electric dipole. The dipole is oriented so as to excite the electric field intensity of the mode and the coupling loop so as to generate the magnetic field intensity of the desired mode, the TEia mode Co-axial cable Fig. 3.3.1 Co-axial to waveguide adapterMicrowave Engineering 3-25 Waveguide components and Applications -1 with the probe at the centre from the broad wall or perpendicular to the maximum E-field. Fig. 3.3.1 shows co-axial to waveguide adapter. By choosing proper values of L and D, the input impedance of the probe can be adjusted to the characteristic impedance of co-axial line feed. 3.3.1 Coupling Loops In order to excite a particular mode, the waveguide must be properly coupled to an external source. Different coupling methods are used in microwave fillers and wavemeters A rectangular waveguide that is loop coupled to a co-axial line is shown in Fig. 3.3.2. The loop size is very small and the current in the loop can be considered to be constant. The conduction current in the loop produces a linking magnetic field. Co-axial line The loop is capable of exciting any mode. The plane of the loop is placed perpendicular to the magnetic flux lines. Fig. 3.3.2 Loop coupling 3.4 Microwave Attenuators A device used to control the amount of microwave power transferred from one point to another on a microwave transmission system is called microwave attenuator. Microwave attenuators control the flow of microwave power either by reflecting it or absorbing it. Attenuators can be classified as fixed or variable type. 3.4.1 Fixed Attenuator Fixed attenuator consists of a dissipative element called pad which is placed in a waveguide. The pad is placed in such a way that its plane is parallel to the electric field, for this two thin metal rods are used. The pad is tapered for providing a gradual transition from the waveguide medium to the absorbing medium of pad. This also reduces the reflections. Fig. 3.4.1 shows side view of fixed attenuator in a waveguide.Microwave Engineering 3-26 Waveguide components and Applications -1 Power Thin i absorbing a pas AEA (ZEZENZEZEIA VEIT Fig. 3.4.1 Fixed attenuator © The amount of power that a fixed attenuator can absorb depends on- i) Strength of dielectric field. ii) Location of pad within waveguide. iii) Area of pad. iv) Frequency of operation. v) Pad material used for power absorption. Fixed attenuators are used where fixed amount of attenuation is required. 3.4.2 Variable Attenuator * Variable attenuator provides continuous attenuation. The amount of attenuation introduced is controlled by the depth of insertion of absorbing plate inside the waveguide. Por this a knob and gear assembly is used. The Fig. 3.4.2 Variable attenuatorMicrowave Engineering 3-27 Waveguide components and Applications -| knob can be calibrated suitably. The maximum attenuation will be offered when the pad extends all the way across the guide. Fig. 3.4.2 shows variable attenuator. 3.5 Waveguide Corners, Bends and Twists © Change of direction of guides are often required in microwave applications. For changing the direction through an angle, waveguide corners, bends and twists are used. Use of corner and bends will create discontinuities in the guide therefore standing wave ratio will be increased because of reflections. In order to minimize the reflections in the bend, its length (L) is made several wavelengths. Generally the length (L) of bends or comers is odd multiple of quarter wavelengths. * IEA, = Wavelength in waveguide, then length ‘Where n= 0,1,2,3,.. Sharper the bend greater will be the reflections and losses. Fig. 3.5.1 shows various waveguide corners, bends and twists. Fig. 3.5.1 Waveguide bends, corners and twist Twistowave Engineering 3-32 Waveguide components and Applications - 1 The losses introduced by well designed matching screw are small hence the susceptance for quarter wavelength insertion tends to infinite value. + The disadvantage of screw tuning is the requirement of a slot in the wall of the waveguide 3.8 Directional Couplers * Directional coupler is used to measure the unidirectional power being delivered to a load by sampling technique. In sampling technique, only a known fraction of power in foeward wave is measured. From this fractional power, the total power can be measured. There are no reflections at the junction of these four port. * Directional coupler is a four port waveguide junction, Fig. 3.8.1. shows directional coupler structure using waveguide. Auxiliary output Matched termination ‘Ausiliary arm Port Pont-2 Hole’ at 2a Main’ arm Fig. 3.8.1 Directional coupler * Directional coupler measures power in auxiliary waveguide arm in one direction. Symbolic representation of directional coupler is shown in Fig. 3.8.2 Main waveguides. Porte ® Port-2 Port:3 ° © Port-4 Auxiliary waveguide Fig. 3.8.2 Directional coupler symbolMicrowave Engineering 3-33 Waveguide components and Applications - | 3.8.1 Directional Coupler Parameters © The performance of a directional coupler is measured interms of four basic parameters. i) Coupling Factor (C) if) Directivity (D) iii) Isolation (I) iv) Return loss (R) i) Coupling factor (C) © The coupling factor is a measure of how much of incident power is being sampled. It is the ratio of power levels in main and auxiliary waveguides. The coupling factor is denoted by C Main waveguide Incident power Py Forward coupled power Pa ‘waveguide Fig. 3.8.3 * Let the incident power is A, in main waveguide and the power coupled in the auxiliary waveguide in forward direction is Py. Then, Cas) = 10 togno( F} ii) Directivity (D) © The directivity is a measure of how well the directional coupler distinguishes between the forward and reverse travelling power. It is the ratio of forward coupled power at auxiliary waveguide to the reverse power at auxiliary waveguide. It is denoted by D. «Let the power coupled in the auxiliary waveguide in forward direction is P, and the reverse power at auxiliary port is P3.Microwave Engineering 3-34 Waveguide components and Applications - | Reverse Forward power ‘coupled power Py Pa Auxiliary waveguide Fig. 3.8.4 (P Then, Daw, = 10 togiol $) iii) Isolation (I) * The isolation measures the directive properties of directional coupler. It is defined as the ratio of incident power at main waveguide (P1) to the reverse power at auxiliary waveguide (P3). It is denoted by 1 Then, l=10 tos) dB 3 iv) Return loss (R) * Return loss is defined as the ratio of power incident to the power transmitted in the main arm. It is also denoted as insertion loss. r) ‘Then, og (7 Where P, is the received power from the port where power is transmitted. 3.8.2 Two Hole Directional Coupler «By making holes in the common wall between two waveguides power can transfer between the guides. Using two or more holes allows the design of a directional coupler, where the power transfer from one guide to the second occurs preferentially in one direction of propagation in the second guide. The two hole coupler is shown in the Fig. 3.8.5.Microwave Engineering 3-35 Waveguide components and Applicatigns -| eee ee Port-2 Port-1 T stots ¥ sit — i! Ports AS A Portes P, = Input port P, - Output port P, - Isolated port P,- Coupled port Fig. 3.8.5 Two hole directional coupler + Two hole directional coupler consists of twe guides with two (holes) common between them. These two apertures holes are at a distance of 2.,/4. + Energy is coupled through the slots from the main to the coupled guide. Because the slots are a quarter-wavelength a part, the energy in the coupled guide will cancel in one direction and reinforce in the other direction. * Consider a wave propagating from port-1 to port-2. When the wave -passes slot a energy is radiated into the coupled guide, where it radiates in both directions. The main guide wave continues to propagate toward slot b. Part of the wave couples through slot b into the other guide. As before the coupled wave propagates in both directions in the other guide. The portion that propagates towards portd is in phase with slot a energy and thus reinforces the signal. But the prtion that propagates from slat b back towards slot a is phase shifted 180% Thus the port-3 signals from slots a and b are out of phase by 180° and cancel each other. We can label port 1 the input, port-2 the output, port-3 the isolated port and port-4 the coupled port. «The spacing between slots a and b is critical because it is necessary to effect a 180° phase shift in the a-b-b-a path. 3.8.3. Multihole Directional Coupler * Multihole directional coupler operates on the same basic principles as two hole er — ex coupler. The coupling array holes are t t 1 separated by a distance 1,/4. Fig. 3.8.6 shows multihole directional coupler. Fig. 3.8.6 4-Hole directional couplerMicrowave Engineering 3-36 Waveguide components and Applications - I 3.8.4 Bathe Hole Directional Coupler LF LT wa feef Main | Mainguide Fig. 3.8.7 Bathe hole directional coupler * Bathe hole directional coupler consists of two rectangular waveguides coupled by means of circular aperture located at the center of common broad edge. S-Matrix of a Directional Coupler ince in a directional coupler all four ports are completely matched. Therefore the diagonal elements of S-matrix are zeros and Sy = Sx = Sy = 5,4 = 0 It may be noted that there is no coupling between port-1 and port-3 and between port-2 and port-4 Therefore Hence the S-matrix of directional coupler becomes 0 Sy O Su Si 0 Sy 0 0 Sy O Sy Sa 0 Sy 0 | S= From the zero property of the S-matrix, we get, S,. St, +Sa2 8}, = 0 (3.8.1) Sy Sy +Su Sh = 0 -3.8.2) Also from the unity property of the S-matrix, we get Si 8h +S Si, = 0 3.8.3) We can rewrite the equations (3.8.1) and (3.8.2) as follows, [Sal ISiel = [Sab 131Microwave Engineering 3-41 Waveguide components and Applications -! 3.11 Waveguides Irisis © Irises are fixed or adjustable projections from the walls of waveguide. Irises are also known as windows. Irises are used for impedance matching purposes. * When a dominant wave is incident on such structure, higher order waves are excited in order to satisfy boundary condition of zero tangential electric field on irises. These higher order modes die down at a distance less than 2/4 and store teactive energy. Depending on the type of energy inductive or capacitive characteristics may be obtained, when magnetic energy is stored resulting in inductive characteristics and when electric energy is stored results in capacitive characteristics. * The normalized susceptances of the irises are varying with the iris dimensions. These reactive impedances are used to cancel the opposite reactance in the mismatched load, Hence they can be used as impedance matching element Types of Irises * There are three basic forms of irises - i) Inductive Iris ii) Capacitive Iris iii) Resonant Iris 3.11.1 Inductive Iris Conducting diaphragms extending into a waveguide from side walls have the effect of adding an inductive susceptance across the waveguide at the point at which . diaphragms are placed. In the 2 uz rt SEE De LE Mee LZ magnetic field some energy is Sexo SEEN stored and hence there is an ae increased inductance at that point Projections from of the waveguide. Such an side walls of guide element, therefore called an inductive iris. The amount of normalized inductive susceptance added is a function of the window insertion distance (J). Fig. 3.11.1 shows inductive iris in a waveguide. Fig. 3.11.4 Inductive iris‘Microwave Engineering 3-42 Waveguide components and Applications - I 3.11.2 Capacitive Iris * Conducting diaphragms extending into the waveguide from top and bottom walls produces effect of capacitive susceptance shunted across the waveguide at that point. Fig. 3.11.2 shows capacitiv Waveguide walls LE . Fig. 3.11.2 Capacitive iris «It is obvious that the potential which earlier had existed between top and bottom walls of waveguide now exists between surfaces that are closer and therefore the capacitance has increased at that point. * Capacitive windows are not used extensively because of the possibility of voltage breakdown which ultimately places limit on the power that can be transmitted through the waveguide. 3.11.3 Resonant Iris * A conducting diaphragm as shown in Fig. 3.11.3 gives the effect of a parallel tuned LC circuit connected across the guide at the point where diaphragm is placed. An equivalent circuit of resonant iris is also shown. The reactances introduced form a circuit that is parallel resonant. re Resonant itis Equivalent circuit Fig. 3.11.3 * Since the impedance of iris is very high for dominant mode and the shunting effect is also negligible, other modes are attenuated considerably. Therefore, resonant window acts a3 a made filter or band pass filter.