1 TRANSMISSION LINES AND WAVEGUIDES Outline General Solutions for TEM, TE, and TM Waves Parallel Plate Waveguide Rectangular Waveguide Circular Waveguide Coaxial Line Surface Waves on a Grounded Dielectric Sheet Stripline Microstrip Line The Transverse Resonant Technique 10 Wave Velocities and Dispersion Transmission Line General two – conductor Tx Closed waveguide General Solutions for TEM, TE and TM Waves   Assume time harmonic fields with e-jt dependence and wave propagation along the z-axis The electric and magnetic field : Transverse components Longitudinal fields components Maxwell Equation Four Transverse Field Components  Cut-off wave number  Wave number:  Permittivity of material TEM Wave Transverse electromagnetic (TEM) waves are characterized by: Cut-off wave number : kc = Helmholtz Wave Equation for Ex For dependent, Laplace’s Equation TEM Wave (Cont.) Electric field can be expressed as the gradient of a Scalar potential also satisfies Laplace ‘s equation The voltage and current Wave Impedance 10 Some constants of Strip Line 53  Phase velocity:  Propagation constant:  Characteristic impedance: Characteristic Impedance 54 Attenuation due to Conductor Loss 55 Ex: Attenuation on Strip Line 56 Calculate the attenuation in dB/l at frequency of 10 GHz for a 50 Ω copper stripline conductor with b = 0.32 cm and er =2.2, tand =0.001 At 10 GHz the wave number is: Ex: Attenuation on Strip Line (Cont.) 57 The total attenuation constant is: Ex: Characteristic Impedance of Strip Line 58 Stripline with Outline 59 General Solutions for TEM, TE, and TM Waves Parallel Plate Waveguide Rectangular Waveguide Circular Waveguide Coaxial Line Surface Waves on a Grounded Dielectric Sheet Stripline Microstrip Line The Transverse Resonant Technique 10 Wave Velocities and Dispersion Microstrip Line 60     most popular types of planar transmission lines can be fabricated by photolithographic processes Easily miniaturized and integrated with both passive and active microwave devices The fields are quasi - TEM wave Effective Dielectric Constant 61 Characteristic Impedance 62 Attenuation Constant 63 Ex: Design of Microstrip Line 64 Design a microstrip line on a 0.5 mm alumina substrate for a 50 Ω characteristic impedance Find the length of the line required to produce a phase delay of 270 deg at 10 GHz and compute the total loss Ex: Design of Microstrip Line (Cont.) 65 Summary of Transmission Line 66 Onsite Homework & Homework 67  Home work: P 3.6, 3.19, 3.21, 3.22, [...]... Dielectric Loss 17 Outline 18 1 General Solutions for TEM, TE, and TM Waves 2 Parallel Plate Waveguide 3 Rectangular Waveguide 4 Circular Waveguide 5 Coaxial Line 6 Surface Waves on a Grounded Dielectric Sheet 7 Stripline 8 Microstrip Line 9 The Transverse Resonant Technique 10 Wave Velocities and Dispersion Parallel Plate Waveguide 19  Parallel plate waveguide is the simplest type of waveguide that can... Vector 28 Attenuation 29 30 Outline 31 1 General Solutions for TEM, TE, and TM Waves 2 Parallel Plate Waveguide 3 Rectangular Waveguide 4 Circular Waveguide 5 Coaxial Line 6 Surface Waves on a Grounded Dielectric Sheet 7 Stripline 8 Microstrip Line 9 The Transverse Resonant Technique 10 Wave Velocities and Dispersion Rectangular Waveguide 32  Earliest type of transmission line  Use for couplers, detectors,... for Analyzing a TEM Line 11 1.Solve Laplace’s equation, for (x, y) The solution will contain several unknown constants 2 Find these constants by applying the boundary conditions for the known voltages on the conductors 3 Compute 𝑒 and 𝐸 from (3.13) and (3.1a) Compute ℎ and 𝐻from (3.18) and (3.1b) 4 Compute V from (3.15) and I from (3.16) 5 The propagation constant is given by (3.8), and the characteristic... TE & TM Line 16 1 Solve the reduced Helmholtz equation, (3.21) or (3.25), for hz or ez The solution will contain several unknown constants and the unknown cutoff wave number, kc 2 Use (3.19) or (3.23) to find the transverse fields from hz or ez 3 Apply the boundary conditions to the appropriate field components to find the unknown constants and kc 4 The propagation constant is given by (3.6) and the... 9 The Transverse Resonant Technique 10 Wave Velocities and Dispersion Rectangular Waveguide 32  Earliest type of transmission line  Use for couplers, detectors, isolators, attenuators, and slotted lines  Wave band: 1~220 GHz Support TE & TM waves  TE Mode 33 TE mode solution can be obtained by solving Laplace’s equation: Solution for TE Mode 34 Solution for TE Mode 35 Constants 36 ... 8 Microstrip Line 9 The Transverse Resonant Technique 10 Wave Velocities and Dispersion Parallel Plate Waveguide 19  Parallel plate waveguide is the simplest type of waveguide that can support TE, TM and TEM TEM Mode 20 TEM mode solution can be obtained by solving Laplace’s equation: The boundary condition for : There is no variation in x, the solution is: Electromagnetic Field for TEM Mode 21 TM Mode ...Outline General Solutions for TEM, TE, and TM Waves Parallel Plate Waveguide Rectangular Waveguide Circular Waveguide Coaxial Line Surface Waves on a Grounded Dielectric Sheet Stripline Microstrip... Plate Waveguide Rectangular Waveguide Circular Waveguide Coaxial Line Surface Waves on a Grounded Dielectric Sheet Stripline Microstrip Line The Transverse Resonant Technique 10 Wave Velocities and. .. 30 Outline 31 General Solutions for TEM, TE, and TM Waves Parallel Plate Waveguide Rectangular Waveguide Circular Waveguide Coaxial Line Surface Waves on a Grounded Dielectric Sheet Stripline