Microwave Passive Components (module-2).pptx

Electronics and communication engineering

1. Microwave Network Theory By Mr. Annappa. C Assistant Professor Department of ECE ( https://www.youtube.com/watch?v=_Y0MfLDi1Y0&t=360s ) (https://www.youtube.com/watch?v=R4jcZJM2GwE) (https://www.youtube.com/watch?v=gi_BfdZT1M8) (https://www.youtube.com/watch?v=QcHWzxG6TLU) E-PLANE (https://www.youtube.com/watch?v=5Q4TNOf1gMc) E- PLANE 17-06-2022 Department of ECE, Microwave and Antennas 1

2. Department of ECE VISION  To become a pioneer in developing competent professionals with societal and ethical values through transformational learning and interdisciplinary research in the field of Electronics and Communication Engineering.   MISSION  The department of Electronics and Communication is committed to:  M1 : Offer quality technical education through experiential learning to produce competent engineering professionals. M2 : Encourage a culture of innovation and multidisciplinary research in collaboration with industries/universities.   M3 : Develop interpersonal, intrapersonal, entrepreneurial and communication skills among students to enhance their employability.  M4 : Create a congenial environment for the faculty and students to achieve their desired goals and to serve society by upholding ethical values. 17-06-2022 Department of ECE, Microwave and Antennas 2

3. Department of ECE PROGRAM EDUCATIONAL OBJECTIVES (PEOS)  Upon completion of the program, graduates will be able to: PEO1 : Tackle complex engineering problems with the sound knowledge in Electronics and Communication Engineering. PEO2: Utilize their knowledge and skills to develop solutions in multi-disciplinary environments through collaborative research. PEO 3: Inculcate effective communication skills, teamwork and leadership for a successful career in industry and academia. PEO4: Exhibit professional ethics and social awareness in their professional career and engage in lifelong learning. PROGRAM SPECIFIC OUTCOMES (PSOs)    Upon graduation students will be able to: PSO1 : Apply the knowledge of leading-edge hardware and software tools to solve problems in the area of Embedded Systems, VLSI and IoT.   PSO2 : Apply the concepts of Signal and Image Processing to solve problems in communication systems 17-06-2022 Department of ECE, Microwave and Antennas 3

4. Department of ECE Course objectives: This course will enable students to: Describe the microwave properties and its transmission media Describe microwave devices for several applications Understand the basics of antenna theory Select antennas for specific applications Course Outcomes: At the end of the course, students will be able to: Describe the use and advantages of microwave transmission Analyze various parameters related to microwave transmission lines and waveguides Identify microwave devices for several applications Analyze various antenna parameters necessary for building an RF system Recommend various antenna configurations according to the applications 17-06-2022 Department of ECE, Microwave and Antennas 4

5. Department of ECE Text Books: 1. Microwave Engineering – Annapurna Das, Sisir K Das TMH Publication, 2nd, 2010. 2. Microwave Devices and circuits - Liao, Pearson Education. 3. Antennas and Wave Propagation, John D. Krauss, Ronald J Marhefka and Ahmad S Khan,4th Special Indian Edition , McGraw- Hill Education Pvt. Ltd., 2010. Reference Books: 1. Microwave Engineering – David M Pozar , John Wiley India Pvt. Ltd. 3rdEdn, 2008. 2. Microwave Engineering – Sushrut Das, Oxford Higher Education, 2ndEdn, 2015. 3. Antennas and Wave Propagation – Harish and Sachidananda : Oxford University Press, 2007. 17-06-2022 Department of ECE, Microwave and Antennas 5

6. MODULE-2 Microwave Network theory: Symmetrical Z and Y-Parameters for Reciprocal Networks, S matrix representation of Multi-Port Networks. (Text 1: 6.1, 6.2, 6.3) Microwave Passive Devices: Coaxial Connectors and Adapters, Attenuators, Phase Shifters, Waveguide Tees, Magic tees. (Text 1: 6.4.2, 6.4.14, 6.4.15, 6.4.16) L1, L2 17-06-2022 Department of ECE, Microwave and Antennas 6

7. Introduction A microwave network is formed when several microwave devices and components such as sources, attenuators, resonators, filters, amplifiers etc. are coupled by transmission line or waveguides for the desired transmission of microwave signal The point of intersection of two or more devices is called a junction For a low frequency network, a port is a pair of terminals, whereas for a microwave network, a port is a reference plane transverse to the length of the microwave transmission line or waveguide The measurable input and output variables for a two port network are voltage & current, which can be related in terms of the impedance Z-parameters or admittance Y-parameters or hybrid h-parameters or ABCD parameters 17-06-2022 Department of ECE, Microwave and Antennas 7

8. A Two – Port Network Impedance Parameters (Z) Impedance parameters are obtained by expressing port voltages and in terms of port currents and , , , are called Impedance parameters   17-06-2022 Department of ECE, Microwave and Antennas 8

9. Continued Matrix representation of Impedance parameters can be written as To measure or compute impedance parameters, we apply excitation at one port, make other port open. To get port 1 is exited, port 2 is open ( =0 ), to get , port 2 is exited, port 1 is open ( =0 ) , Input Impedance Forward transvers Impedance   17-06-2022 Department of ECE, Microwave and Antennas 9

10. Continued 3. , Reverse transverse Impedance 4. , Output Impedance Admittance Parameters Admittance parameters are obtained by expressing port currents and in terms of port voltages and , the resulting equations of admittance parameters are , , , are called admittance parameters   17-06-2022 Department of ECE, Microwave and Antennas 10

11. Continued The matrix representation of admittance parameters is given by To measure or compute admittance parameters, we apply excitation at one port, make other port shorted 1. , Input admittance 2. Forward transvers admittance 3. , Reverse transverse admittance 4. , Output admittance   17-06-2022 Department of ECE, Microwave and Antennas 11

12. Continued Hybrid Parameters The hybrid parameters are obtained in terms of mixture of port variables i.e these parameters express and in terms of and , , , are called hybrid parameters The matrix representation of hybrid parameters is   17-06-2022 Department of ECE, Microwave and Antennas 12

13. Continued To measure , , port 1 is exited, port 2 is shorted ( ) 1. , Input impedance 2. Forward current gain To measure , , port 2 is exited, port 1 is open ( ) 3. , Reverse voltage gain 4. , Output admittance   17-06-2022 Department of ECE, Microwave and Antennas 13

14. Continued ABCD Parameters ABCD Parameters are most suitable when cascading networks. Eg : Two transistor configuration 17-06-2022 Department of ECE, Microwave and Antennas 14

15. Continued 17-06-2022 Department of ECE, Microwave and Antennas 15

16. Continued 17-06-2022 Department of ECE, Microwave and Antennas 16

17. At Microwave frequency signal 17-06-2022 Department of ECE, Microwave and Antennas 17

18. Scattering Parameters Microwave circuits analysed using scattering or S- parameters. S – Parameters are power wave descriptors that permit us to define input-output relations of a network in terms of incident and reflected power waves with reference to the below figure, the incident normalized power wave and reflected normalized power wave are defines as 17-06-2022 Department of ECE, Microwave and Antennas 18

19. Continued 17-06-2022 Department of ECE, Microwave and Antennas 19

20. 17-06-2022 Department of ECE, Microwave and Antennas 20 S - Parameter for a Two Port Network with Mismatched Loop

21. 17-06-2022 Department of ECE, Microwave and Antennas 21 S - Parameter for a Two Port Network with Mismatched Loop Z L = load impedence Z g = Generator impedence Z = Charecteristic impedence transmission line

22. 17-06-2022 Department of ECE, Microwave and Antennas 22 S - Parameter for a Two Port Network with Mismatched Loop Γ 2 = a 2 / b 2 -------------(1) a 2 = b 2 Γ 2 b 1 = S 11 a 1 + S 12 a 2 = S 11 a 1 + S 12 b 2 Γ 2 -------------(2) b 2 = S 21 a 1 + S 22 a 2 = S 21 a 1 + S 22 b 2 Γ 2 -------------(3) From eqn (3) b 2 (1- S 22 Γ 2 ) = a 1 S 21 a 1 S 21 b 2 = ---------- -------------(4) 1- S 22 Γ 2 Substitute eqn (4) in eqn (2) S 12 Γ 2 a 1 S 21 b 1 = S 11 a 1 + ---------------- 1- S 22 Γ 2 S 12 Γ 2 S 21 b 1 = a 1 (S 11 + ------------ ) 1- S 22 Γ 2

23. 17-06-2022 Department of ECE, Microwave and Antennas 23 S - Parameter for a Two Port Network with Mismatched Loop For reciprocal networks ( S 12 = S 21 ) & for a mismatched load, input reflection coefficient ( Γ 1 ≠ S 11 ) b 1 S 2 12 Γ 2 Γ 1 = ---- = S 11 + ------------ -------------(5) Input reflection coefficient a 1 1- S 22 Γ 2 If the junction is lossless according to unitary property S 11 S 11 * + S 12 S 12 * = 1 -------------(6) S 22 S 22 * + S 12 S 12 * = 1 -------------(7) S 11 S 12 * + S 12 S 12 * = 0 -------------(8) Therefore , for a lossless , reciprocal two port network, terminated by a mismatched load, eqn (6) & (7) gives, | S 11 | = | S 22 | -------------(9) From eqn (6) | S 12 | = √(1 - | S 11 | 2 ) -------------(10)

24. 17-06-2022 Department of ECE, Microwave and Antennas 24 Comparision between |S|, |Z| & |Y| Matrices

25. 17-06-2022 Department of ECE, Microwave and Antennas 25 Comparision between |S|, |Z| & |Y| Matrices

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29. Microwave Passive Devices By Annappa C Assistant Professor Department of ECE, Atria IT 17-06-2022 Department of ECE, Microwave and Antennas 29

30. Coaxial Cables A length of coaxial cable is used for interconnecting several microwave components The outer conductor of the coaxial line is used to guide the signal & shield s the external or internal signal leakage through it The standard characteristic impedance ( Z ) of these cables are 50 ohms and 75 ohms 17-06-2022 Department of ECE, Microwave and Antennas 30

31. Continued Thre e types of coaxial cables with increasing order shielding i.e (1) flexible coaxial cable (2) semi-rigid coaxial cable and (3) rigid coaxial cable (1) Flexible coaxial cable use low-loss solid or foam polyethylene dielectrics The outer si n gal or double braid of the flexible cable is constructed for electromagnetic shielding by using knitted metal wire 17-06-2022 Department of ECE, Microwave and Antennas 31

32. Continued Rigi d cables will have air dielectric & conductors are supported by small dielectric spacers . dielectric spacers do not produce discontinuities to the signal flow. Semi - Rigid cables have solid dielectric & use a thin copper outer conductor so that it can be bent for convenient routing 17-06-2022 Department of ECE, Microwave and Antennas 32

33. Continued Coaxial cables are used in the frequency range from dc to microwaves The attenuation in coaxial cables increases with frequency, the upper frequency of operation is limited The shielding effectiveness of outer conductor is expressed in terms of transfer impedance of the cable, which is defined as Where = Longitudinal voltage induced per unit length on one side of the shield (outside) = Leakage current flowing on the other side (inside) of the shield . If both ends are terminated into matched loads, the load voltage will be , then   17-06-2022 Department of ECE, Microwave and Antennas 33

34. Coaxial Connectors and Adapters Coaxial cables are terminated or connected to other cables and components by means of shielded standard connectors The outer shield makes a 360 degree extremely low impedance joint to maintain shielding integrity These connectors are of various types depending on the frequency range & the cable diameter. Commonly used microwave connectors are Type N (male/female) BNC ( Bayonet Navy Connector) – (male/female) TNC (Threaded Navy connector) – (male/female) APC ( Amphenol precision Connector ) SMA (Sub – Miniature A) connectors 17-06-2022 Department of ECE, Microwave and Antennas 34

35. Continued 17-06-2022 Department of ECE, Microwave and Antennas 35 Type N Male Type N Female BNC Female BNC Male TNC Male TNC Female SMA Male & Female

36. Continued (1) T ype N (Navy) connector is a 50 & 75 ohm connector which was designed for military system applications during world war 2. It is suitable for flexible or rigid cables in the frequency range 1 – 18 GHz. (2) BNC ( Bayonet Navy Connector) – (male/female) The BNC is suitable for 0.25 inch 50 ohm or 75 ohm flexible cables used up to 1 GHz (3) TNC (Threaded Navy connector) – (male/female) The TNC is like BNC, except that the outer conductor has a thread to make firm contact with the surface to minimise radiation leakage at higher frequencies . These connecters are used upto 12 Ghz 17-06-2022 Department of ECE, Microwave and Antennas 36

37. Continued (4) SMA (Sub – Miniature A) connectors (male/female) The SMA Connectors are used for thin flexible or semi-rigid cables. The higher frequency is limited to 24 GHz because of generation of higher order modes beyond this limit (5) APC ( Amphenol precision Connector ) The APC - 7 is a very accurate 50 ohm, low VSWR connector which can operate up to 18 GHz which provide coupling without male or female configaration The APC - 3.5 is a high precision 50 ohm, low VSWR connector which can operate up to 34 GHz 17-06-2022 Department of ECE, Microwave and Antennas 37

38. Attenuators Attenuators are passive devices used to control power levels in a microwave system by partially absorbing the transmitted signal wave Attenuators are designed using resistive films Attenuators are classified into two types Fixed attenuator, Eg. Coaxial Fixed Attenuator Variable attenuator, Eg. Waveguide Attenuator Coaxial Fixed Attenuator A Coaxial fixed attenuator uses a film on the center conductor to absorb some of the power It contains a thin dielectric strip coated with resistive film & placed at the center of the waveguide parallel to the maximum E field 17-06-2022 Department of ECE, Microwave and Antennas 38

39. Continued Induced current on the resistive film due to the incident wave results in power dissipation, leading to attenuation of microwave energy The dielectric strip is tapered at both ends up to a length of more than half wavelength to reduce reflections 17-06-2022 Department of ECE, Microwave and Antennas 39

40. Continued Variable Type Attenuator A variable type attenuator can be constructed by moving the resistive vane by means of micrometre screw from one side of the narrow wall to the centre where the E field is maximum as shown in below figure. This is called Movable Vane Attenuator 17-06-2022 Department of ECE, Microwave and Antennas 40

41. Continued In case of Flap Attenuator by changing the depth of insertion of resistive vane at an E field maximum through a longitudinal slot at the middle of the broad wall as shown in below figure 17-06-2022 Department of ECE, Microwave and Antennas 41

42. Continued In both the cases a maximum of 90 dB attenuation is possible with VSWR of 1.05 The resistance card can be shaped to give a linear variation of attenuation with the depth of insertion Precision Variable Attenuator A precision variable type attenuator makes use of a circular waveguide section ( cw ) containing a very thin tapered resistive card (Rb), to both sides of which are connected axisymmetric sections of circular to rectangular waveguide tapered transitions (RCT & CRT) The centre circular section with the resistive card can be precisely rotated by 360 degrees with respect to the two fixed sections of circular to rectangular waveguide transitions 17-06-2022 Department of ECE, Microwave and Antennas 42

43. Continued The induced current on the resistive card R b due to the incident signal is dissipated as heat and produces attenuation of the transmitted signal 17-06-2022 Department of ECE, Microwave and Antennas 43

44. Continued The incident TE10 dominant wave in the rectangular waveguide is converted into a dominant TE11 mode in the circular waveguide A very thin tapered resistive card is placed perpendicular to the E field at the circular end of each transition section, so that it absorbs any component parallel to it. Therefore a pure TE11 mode is exited in the middle section 17-06-2022 Department of ECE, Microwave and Antennas 44

45. Continued If the resistive card at the centre section is kept at an angle θ relative to the E field direction, the component E cos θ parallel to the card gets absorbed while the component E sin θ is transmitted without attenuation This E sin θ , later appears as electric field component E θ in the rectangular output signal, thus the attenuation of incident wave is Or θ ) = -20log Thus precision rotary attenuator produces attenuation which depends only on the angle of rotation θ of the resistive card w.r.t the incident wave polarization   17-06-2022 Department of ECE, Microwave and Antennas 45

46. Phase Shifters Phase shifter is a device which provides variable insertion phase in a microwave signal path without altering the physical path length The phase of a microwave signal can be changed by inserting a low loss dielectric material or a ferrite material in the wave propagation path. Accordingly phase shifters are called dielectric phase shifters and ferrite phase shifters respectively Dielectric phase shifters are reciprocal phase shifters , ferrite phase shifters can be reciprocal as well as non-reciprocal phase shifters Phase shifters are characterised by low insertion loss & low VSWR 17-06-2022 Department of ECE, Microwave and Antennas 46

47. Dielectric Phase Shifters A dielectric phase shifter can be realized by placing a lossless dielectric slab within a waveguide parallel to E field & at the position of maximum E field. A differential phase change is produced due to the change of wave velocity through the dielectric slab compared to that through an empty waveguide in which   17-06-2022 Department of ECE, Microwave and Antennas 47

48. Continued Two ports are matched by reducing the reflections of the wave from the dielectric slab tapered at both ends as shown in figure The differential phase shift produced by the phase shifter is given by Where and are propagation constant, is the length of dielectric slab By adjusting the length , different phase shift can be produced The S-matrix of an ideal phase shifter can be expressed as   17-06-2022 Department of ECE, Microwave and Antennas 48

49. Precision Dielectric Rotary Phase Shifter A precision phase shifter can be designed as a rotary type as shown in the below figure 17-06-2022 Department of ECE, Microwave and Antennas 49

50. Continued It uses a section of circular waveguide containing a lossless dielectric plate of length called half wave (180 degrees) section This section can be rotated over 360 degrees precisely between two sections of circular to rectangular waveguide transitions, each containing lossless dielectric plates of length called quarter wave(90 degrees) sections oriented at an angle of 45 degrees The incident TE10 wave in the rectangular guide becomes a TE11 wave in the circular guide The middle half wave section produces a phase shift equal to twice its rotation angle θ with respect to the quarter wave section. The dielectric plates are tapered at both ends to reduce reflections due to discontinuity   17-06-2022 Department of ECE, Microwave and Antennas 50

51. Ferrite Phase Shifters Phase shift in a ferrite device is generated by magnetizing the ferrite inside the waveguide by RF current such that the phase constant in the propagating line alters due to change in permeability with magnetization Ferrite phase shifters may be latching or non – latching, the below diagram shows Ferrite twin-toroid phase shifter 17-06-2022 Department of ECE, Microwave and Antennas 51

52. Continued The twin toroid is a latching, nonreciprocal device. It uses either a closed magnetic circuit or a magnetic circuit with very small air gaps. The relative permeability of the ferrite is controlled by adjusting the magnetic flux level existing in the closed magnetic circuit The dielectric spacer is used to concentrate the RF energy in the centre of the waveguide 17-06-2022 Department of ECE, Microwave and Antennas 52

53. Waveguide 17-06-2022 Department of ECE, Microwave and Antennas 53

54. Waveguide Tees Waveguide tees are 3 port components They are used to connect branch or section of the waveguide in series or in parallel with the main waveguide transmission line for providing means of splitting , & also of combining power in a waveguide system The two types, E-plane (series) T & H-plane (shunt) T , are constructed as shown in the below diagram 17-06-2022 Department of ECE, Microwave and Antennas 54

55. Continued Waveguide tees are poorly matched devices Waveguide T’s are named according to the axis of the side arm which is parallel to the E field or H field in the collinear arms Because of symmetry & absence of non-linear elements in the junction, the S-matrix is symmetric i.e The general S-matrix of a T-junction is   17-06-2022 Department of ECE, Microwave and Antennas 55

56. WAVE GUIDE TEE JUNCTIONS A waveguide Tee is formed when three waveguides are interconnected in the form of English alphabet T . T hus waveguide tee is 3-port junction. The waveguide tees are used to connects a branch or section of waveguide in series or parallel with the main waveguide transmission line either for splitting or combining power in a waveguide system. 6/17/2022 M&A 56

57. Types There are basically 2 types of tees namely 1 ) . E - plane Tee junction : The axis of the side arm which is parellel to E plane in the colinear arm 2 ) . H -plane Tee junction : The axis of the side arm which is parellel to H plane in the colinear arm A combination of these two tee junctions is called a hybrid tee or “ Magic Tee”. 6/17/2022 M&A 57

58. E-plane Tee 6/17/2022 M&A 58 From concideration of symmetry & phase relationship of the waves in each of the arm. A wave incident at port 3 will result at port1 & port 2 , which are equal in magnitude but opposite in phase S 13 = - S 23 From symetrycity (ie S 13 = S 31 = - S 23 = - S 32 , S 12 = S 21 ) If 2 input waves are fed into ports 1 & 2 of the collinear arm, output wave at port 3 will be opposite in phase & substractive, Port 3 is called as difference arm . All diagonal elements of S matrix of a E plne T junction cannot be zero simeltaneously, Since tee junction cannot matched at all the 3 arms simeltaneously.  

59. E-plane Tee 6/17/2022 M&A 59 Concidering as matched port 3, S matrix can be derived as fallows. Denoting the incident & outgoing signal variables at ith port by ai & bi for input power at port3, the net input power to port 3 is |a 3 | 2 - |b 3 | 2 = |a 3 | 2 (1 - |S 33 | 2 ) --------(1) and out power is |b 1 | 2 + |b 2 | 2 = 2|a 3 | 2 |S 13 | 2 ---------- (2) since |S 31 | = |S 23 | by symmetry. since junction is lossless, from eqn (1) & (2) input power must be equal to the output power (1 - |S 33 | 2 ) = 2 |S 13 | 2

60. E-plane Tee 6/17/2022 M&A 60 By a suitable matching element we can make S 33 = 0 so that |S 13 | =1/√2 From symmetry charecteristics S 13 = S 31 = 1 / √2 S 23 = S 32 = -1 / √2 After matching the port 3, if one attemps to match either port 1 or 2 by similer method, The matching elements, such as tuning screws will interact with each other and matching at port 3 would be disturbed. Based on power concideration it can also be shown that S 11 = S 22 = 1/2 and S 12 = S 21 = 1/2 , S 33 = 0

61. E-plane Tee 6/17/2022 M&A 61 There fore, with matching at port 3, the S -matrix of a E -plane T can be expressed by real values with proper choices of refrence plane

62. H-plane Tee 6/17/2022 M&A 62 An H-plane tee is a waveguide tee in which the axis of its side arm is "shunting" the E field or parallel to the H field of the main guide If two input waves are fed to port 1 & 2 of the collinear arm, output wave at port 3 will be in phase & additive, (port 3 - H arm), input wave at port 3 will be equally divided into ports1 & 2 in phase, S 13 = S 23 From symetrycity (ie S 13 = S 31 = S 23 = S 32 , S 12 = S 21 ) Because the magnetic field loops get divided into two arms 1 & 2.  

63. H-plane Tee 6/17/2022 M&A 63 All diagonal elements of S matrix of a H plne T junction cannot be zero simeltaneously, Since tee junction cannot matched at all the 3 arms simeltaneously. for input power at port3, the net input power to port 3 is |a 3 | 2 - |b 3 | 2 = |a 3 | 2 (1 - |S 33 | 2 ) --------(1) and out power is |b 1 | 2 + |b 2 | 2 = 2|a 3 | 2 |S 13 | 2 ----------(2) since |S 31 | = |S 32 | by symmetry. since junction is lossless, from eqn (1) & (2) input power must be equal to the output power (1 - |S 33 | 2 ) = 2 |S 13 | 2

64. H-plane Tee 6/17/2022 M&A 64 By a suitable matching element we can make S 33 = 0 so that |S 13 | =1/√2 From symmetry charecteristics S 13 = S 31 = 1 /√2 S 23 = S 32 = 1 /√2 After matching the port 3, if one attemps to match either port 1 or 2 by similer method, The matching elements, such as tuning screws will interact with each other & matching at port 3 would be disturbed. Based on power concideration it can also be shown that S 11 = S 22 = 1/2 and S 12 = S 21 = -1/2 , S 33 = 0

65. H-plane Tee 6/17/2022 M&A 65

66. Problem : A 20 mW signal fed into one of collinear port1 of a lossless H plane T junction. Calulate the power delivered through each port when other ports are terminated in matched load. Solution : port 2 & port 3 are matched terminated, a2 = a3 = 0, S 11 = 1/2. The total effective power input to port 1 is P1 = |a1| 2 - |b1| 2 = |a1| 2 (1 - |b1| 2 /|a1| 2 ) P1 = |a1| 2 (1 - |S 11 | 2 ) = 20 (1 - 0.5 2 ) = 15 mW Power transmitted at port 3 is (S31 = 1/√2) P3 = |a1| 2 |S 31 | 2 = 20 * (1/√2) 2 = 10 mW Power transmitted at port 2 is (S21 = 1/2) P2 = |a1| 2 |S 21 | 2 = 20 * (0.5 2 ) = 5mW P1 = P2 + P3 6/17/2022 M&A 66

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69. HYBRIDE OR MAGIC TEE 6/17/2022 M&A 69 A magic tee is a combination of the E-plane tee and H -plane tee It has fallowing charecteristics when all ports are terminated with a matched loads. 1). If two waves of equal magnitude & inphase are fed into port 1 & 2, the output at port 3 (E- arm) is subtractive & becomes zero & total output will appear additively at port 4(H- arm), 2). A wave incident at port 3(E- arm) divides equally between port 1 & 2 but opposite in phase with no coupling to port 4 (H- arm) S 13 = - S 23 , S 13 = S 31 = 1/√2 = S 24 = S 42 S 43 = 0

70. HYBRIDE OR MAGIC TEE 6/17/2022 M&A 70 It has fallowing charecteristics when all ports are terminated with a matched loads. 3). A wave incident at port 4(H- arm) divedes equally between port 1 & 2 in phase, no coupling to port 3 (E -arm) Thus S 14 = S 41 = 1/√2 = S 24 = S 42 and S 34 = 0 4). A wave fed into one collinear port 1 or 2 , will not appear in the other collinear port 2 or 1 Hence two collinear ports are isolated from each other, making S 12 = S 21 = 0 --------- (1)

71. HYBRIDE OR MAGIC TEE 6/17/2022 M&A 71 Magic tee can be matched by putting screws suitably in the E & H arm without destroying the symmetry of the junctions. Therefore, for an ideal lossless magic-T matched at port 3 & 4, S 33 = S 44 = 0 The symmetry property at the junction for which S 14 = S 41 = S 24 = S 42 = S 31 = S 13 = - S 23 = - S 32 , S 34 = S 43 =0 S 12 = S 21 = 0 The S matrix for a magic T , matched at port 3 & 4

72. HYBRIDE OR MAGIC TEE 6/17/2022 M&A 72 From the unitary property applied to rows 1 & 2 |S 11 | 2 + |S 12 | 2 +| S 13 | 2 +|S 14 | 2 = 1 ------ (3) |S 12 | 2 + |S 22 | 2 +| S 13 | 2 +|S 14 | 2 = 1 ------ (4) Subtracting above two equations |S 11 | 2 - |S 22 | 2 = 0 or |S 11 | = |S 22 | ------ (5) From unitary property applied to rows 3 & 4 | S 13 | 2 + | S 13 | 2 = 1 2| S 13 | 2 = 1 or | S 13 | = 1/√2 -------(6) |S 14 | 2 + |S 14 | 2 = 1 2|S 14 | 2 = 1 or | S 14 | = 1/√2 ---------(7)

73. HYBRIDE OR MAGIC TEE 6/17/2022 M&A 73 From the unitary property applied to rows 1 & 2 |Substituting values in eqn (3) |S 11 | 2 + |S 12 | 2 + 1/2 + 1/ 2 = 1 or |S 11 | 2 + |S 12 | 2 = 0 ---------(8) Which is valid if S 11 = S 12 = 0 ------ (9) From eqn 5 & 9 S 22 = 0

74. APPLICATIONS OF MAGIC TEE 6/17/2022 M&A 74 E-H tuner : In an E-H tuner shon in fig. Both E & H arms are terminated by moveble shorts which act as E -plane & H plane stubs. The position of shorts can be adjusted so that a wide range of load impedence may be matched to reduce the VSWR of a waveguide system connected through the collinear arms.

75. APPLICATIONS OF MAGIC TEE 6/17/2022 M&A 75 Balanced mixer : In a Balanced microwave mixer configuaration, an incoming signal is fed to the E -arm & local oscillator signal is fed to H arm (fig). When these two signals enter the collinear arms, the crystal diodes placed in these arms produce the IF(Intermediate Frequency) signal or difference signal.

76. APPLICATIONS OF MAGIC TEE 6/17/2022 M&A 76

77. Problems on magic T 6/17/2022 M&A 77

78. APPLICATIONS OF MAGIC TEE The magic tee is commonly used for mixing, duplexing, and impedance measurements. Example, there are two identical radar transmitters in equipment stock. A particular application requires twice more input power to an antenna than either transmitter can deliver. A magic tee may be used to couple the two transmitters to the antenna in such a way that the transmitters do not load each other. The two transmitters should be connected to ports 3 & 4, respectively, as shown in Fig. 4-4-8. 6/17/2022 M&A 78

79. CONTI.. 6/17/2022 M&A 79

80. CONTI.. Transmitter 1, connected to port 3, causes a wave to emanate from port 1 & another to emanate from port 2; these waves are equal in magnitude but opposite in phase. Similarly, transmitter 2, connected to port 4, gives rise to a wave at port 1 and another at port 2, both equal in magnitude and in phase. At port 1 the two opposite waves cancel each other. At port 2 the two in-phase waves add together; so double output power at port 2 is obtained for the antenna as shown in Fig. 4-4-8. 6/17/2022 M&A 80