課程大綱 Introduction of Electromagnetic Theory (1) Transmission Line Theory (2) Transmission Line (3, 10.5) Microwave Network Analysis (4) Impedance Matching and Tuning (5) Microwave resonators (6) ps. 括弧中之數字代表所對應教科書之章節

教學目標 以傳輸線理論為基礎，學習微波電路設計所需之基本原理和技巧，包括微波網路及諧振器分析和阻抗匹配方法，以期應用在微波被動式與主動式元件及電路系統設計上。

教科書 D.M. Pozar, Microwave Engineering, 3nd. Ed. John Wiley & Sons, 2005. 參考資料 Lecture Note by Prof. T.S. Horng, E.E. Dept. NSYSU. T.C. Edwards and M.B. Steer, Foundations of Interconnect and Microstrip Design, 3nd. Ed. John Wiley & Sons, 2000.

考試重點(Open Book) 評分標準 簡答題 重點敘述 課本內容之Point of Interest 設計及計算題 範例及問題 習題 期中考 40% 期末考 40% 二次(模擬)作業 20%

名詞解釋 The term microwave (微波) refers to alternating current signals with frequencies between 300 MHz (3108 Hz) and 30 GHz (31010 Hz), with a corresponding electrical wavelength between 1 m and 1 cm. (Pozar defines the range from 300 MHz to 300 GHz) The term millimeter wave (毫米波) refers to alternating current signals with frequencies between 30 GHz (31010 Hz) to 300 GHz (31011 Hz), with a corresponding electrical wavelength between 1 cm to 1 mm. The term RF (射頻) is an abbreviation for the “Radio Frequency”. It refers to alternating current signals that are generally applied to radio applications, with a wide electromagnetic spectrum covering from several hundreds of kHz to millimeter waves.

Microwave Applications

Functional Block Diagram of a Communication System Input signal (Audio, Video, Data) Input Transducer Transmitter Wire or Wireless Channel Output signal (Audio, Video, Data) Output Transducer Receiver Electrical System

Antenna and Wave Propagation Microwave & Millimeter Wave Satellite communication Ionsphere Sky Wave Repeaters(Terrestrial communication) 50Km@25fts antenna Direct Wave Surface Wave Receiving Antenna Transmitting Antenna Earth

Wireless Electromagnetic Channels RF Microwave Millimeter Wave

Natural and manmade sources of background noise

Absorption by the atmosphere Remote sensing: 20 or 55 GHz Spacecraft Communication: 60 GHz Communication Windows: 35.94and 135 GHz , below 10 GHz

IEEE Standard C95.1-1991 recommended power density limits for human exposure to RF and microwave electromagnetic fields

Popular Wireless Transmission Frequencies

Popular Wireless Applications

Wireline and Fiber Optic Channels RF Millimeter wave Microwave Wireline Coaxial Cable Waveguide Fiber 1 kHz 10 kHz 100 kHz 1 MHz 10 MHz 100 MHz 1 GHz 10 GHz 100 GHz 1014 Hz 1015 Hz

Guided Structures at RF Frequencies Conventional Transmission Lines and Waveguides Planar Transmission Lines and Waveguides Good for Long Distance Communication Good for Microwave Integrated Circuit (MIC) Applications

Theory l >>  l <<  l   Conventional Circuit Theory Microwave Engineering Optics l >>  l <<  l   Wireline Coaxial Cable Waveguide Fiber 1 kHz 10 kHz 100 kHz 1 MHz 10 MHz 100 MHz 1 GHz 10 GHz 100 GHz 1014 Hz 1015 Hz Transmission Line

RF & Microwave Background Build-Up RF and Microwave ICs and Systems RF and Microwave Active and Nonlinear Components Goal for this course RF and Microwave Passive Components Transmission Line Impedance Matching Microwave Network Microwave Resonator Circuit Theory, Electronics, Electromagnetics

Electromagnetic Theory Chapter 1 Electromagnetic Theory

History of Microwave Engineering J.C. Maxwell (1831-1879) formulated EM theory in 1873. O. Heaviside (1850-1925) introduced vector notation and provided an analysis foundation for guided waves and transmission lines from 1885 to 1887. H. Hertz (1857-1894) verified the EM propagation along wire experimentally from 1887 to 1891 G. Marconi (1874-1937) invented the idea of wireless communication and developed the first practical commercial radio communication system in 1896. E.H. Armstrong (1890-1954) invented superheterodyne architecure and frequency modulation (FM) in 1917. N. Marcuvitz, I.I. Rabi, J.S. Schwinger, H.A. Bethe, E.M. Purcell, C.G. Montgomery, and R.H. Dicke built up radar theory and practice at MIT in 1940s (World War II). ps. The names underlined were Nobel Prize winners. Maxell (English) Heaviside (English) Hertz (German) Marconi (Italian, NL 1909, in recognition of their contributions to the development of wireless telegraphy) Armstrong (USA) I.I. Rabi (USA, NL, 1944, for his resonance method for recording the magnetic properties of atomic nuclei) J.S. Schwinger (USA, NL, 1965, for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles) H.A. Bethe (USA, NL, 1967, for his contributions to the theory of nuclear reactions, especially his discoveries concerning the energy production in stars) E.M Purcell (USA, NL, 1952, for their development of new methods for nuclear magnetic precision measurements and discoveries in connection therewith).

Maxwell’s Equations Equations in point (differential) form of time-varying Equations in integral form Generally, EM fields and sources vary with space (x, y, z) and time (t) coordinates.

Time-Harmonic Fields When steady-state condition is considered, phasor representations of Maxwell’s equations can be written as : (time dependence by multiply e -jt ) Where MKS system of units is used, and E : electric field intensity, in V/m. H : magnetic field intensity, in A/m. D : electric flux density, in Coul/m2. B : magnetic flux density, in Wb/m2. M : (fictitious) magnetic current density, in V/m2. J : electric current density, in A/m2. ρ: electric charge density, in Coul/m3. ultimate source of the electromagnetic field. Q : total charge contained in closed surface S. I : total electric current flow through surface S.

where 0 = 8.85410-12 farad/m is the permittivity of free space. In free space In istropic materials (e.g. Crystal structure and ionized gases) where 0 = 8.85410-12 farad/m is the permittivity of free space. μ0 = 410-7 Henry/m is the permeability of free space. Question : 2(6) equations are not enough to solve 4(12) unknown field components Constitutive Relations Complex and  where Pe is electric polarization, Pm is magnetic polarization, e is electric susceptibility, and m is magnetic susceptibility. The negative imaginary part of  and  account for loss in medium (heat).

where  is conductivity (conductor loss), ω’’ is loss due to dielectric damping, (ω’’ + ) can be seen as the total effective conductivity,  is loss angle. In a lossless medium,  and  are real numbers. Microwave materials are usually characterized by specifying the real permittivity, ’=r0,and the loss tangent at a certain frequency. It is useful to note that, after a problem has been solved assuming a lossless dielectric, loss can easily be introduced by replaced the real  with a complex .

Example1.1 : In a source-free region, the electric field intensity is given as follow. Find the signal frequency? Solution :

Boundary Conditions Fields at a dielectric interface Fields at the interface with a perfect conductor (Electric Wall) It is analogous to the relations between voltage and current at the end of a short-circuited transmission line. Magnetic Wall boundary condition (not really exist) It is analogous to the relations between voltage and current at the end of a open-circuited transmission line.

Helmholtz (Vector) Wave Equation In a source-free, linear, isotropic, and homogeneous medium Solutions of above wave equations Plane wave in a lossless medium is defined the wavenumber, or propagation constant , of the medium; its unit are 1/m. is wave impedance, intrinsic impedance of medium. In free space, 0=377.

In wave equations, j k  for following conditions. is phase velocity, defined as a fixed phase point on the wave travels. In free space, vp=c=2.998108 m/s. is wavelength, defined as the distance between two successive maximum (or minima) on the wave. In wave equations, j k  for following conditions. Plane wave in a general lossy medium Good conductor Condition: (1)  >>ω or (2) ’’>>’ is skin depth or penetration depth, defined as the amplitude of fields in the conductor decay by an amount 1/e or 36.8%, after traveling a distance of one skin depth.