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Transcript

ECE 563 / TCOM 590 Introduction to Microwaves and E&M Review September 2, 2004 M. Black Brief Microwave History • Maxwell (1864-73) – integrated electricity and magnetism – set of 4 coherent and self-consistent equations – predicted electromagnetic wave propagation • Hertz (1886-88) – experimentally confirmed Maxwell’s equations – oscillating electric spark to induce similar oscillations in a distant wire loop (=10 cm) Brief Microwave History • Marconi (early 20th century) – parabolic antenna to demonstrate wireless telegraphic communications – tried to commercialize radio at low frequency • Lord Rayleigh (1897) – showed mathematically that EM wave propagation possible in waveguides • George Southworth (1930) – showed waveguides capable of small bandwidth transmission for high powers Brief Microwave History • R.H. and S.F. Varian (1937) – development of the klystron • MIT Radiation Laboratory (WWII) – radiation lab series - classic writings • Development of transistor (1950’s) • Development of Microwave Integrated Circuits – microwave circuit on a chip – microstrip lines • Satellites, wireless communications, ... Microwave Applications – – – – – – – – – – Wireless Applications TV and Radio broadcast Optical Communications Radar Navigation Remote Sensing Domestic and Industrial Applications Medical Applications Surveillance Astronomy and Space Exploration Radar System Comparison Radar Characteristic tracking accuracy identification volume search adverse weather perf. perf. in smoke, dust, ... wave mmwave optical poor fair good poor fair good good fair poor good fair poor good good fair Microwave Engr. Distinctions · 1 - Circuit Lengths: · Low frequency ac or rf circuits · · · · time delay, t, of a signal through a device t = L/v « T = 1/f where T=period of ac signal but f=v so 1/f= /v so L «, I.e. size of circuit is generally much smaller than the wavelength (or propagation times or phase shift 0) · Microwaves: L · propagation times not negligible · Optics: L» Microwave Distinctions · 2 - Skin Depth: · degree to which electromagnetic field penetrates a conducting material · microwave currents tend to flow along the surface of conductors · so resistive effect is increased, i.e. · R RDC a / 2 , where – = skin depth = 1/ ( f o cond)1/2 – where, RDC = 1/ ( a2 cond) – a = radius of the wire • R waves in Cu >R low freq. in Cu Microwave Engr. Distinctions · 3 - Measurement Technique · At low frequencies circuit properties measured by voltage and current · But at microwaves frequencies, voltages and currents are not uniquely defined; so impedance and power are measured rather than voltage and current Circuit Limitations • Simple circuit: 10V, ac driven, copper wire, #18 guage, 1 inch long and 1 mm in diameter: dc resistance is 0.4 m, L=0.027μH – – – – – f = 0; XL = 2 f L 0.18 f 10-6 =0 f = 60 Hz; XL 10-5 = 0.01 m f = 6 MHz; XL 1 f = 6 GHz; XL 103 = 1 k So, wires and printed circuit boards cannot be used to connect microwave devices; we need transmission lines, waveguides, striplines, and microstrip High-Frequency Resistors • Inductance and resistance of wire resistors under high-frequency conditions (f 500 MHz): – – – – – L/RDC a / (2 ) R /RDC a / (2 ) where, RDC = /( a2 cond) a = radius of the wire = skin depth = 1/ ( f o cond)-1/2 Reference: Ludwig & Bretchko, RF Circuit Design High Frequency Capacitor • Equivalent circuit consists of parasitic lead conductance L, series resistance Rs describing the losses in the the lead conductors and dielectric loss resistance Re = 1/Ge (in parallel) with the Capacitor. • Ge = C tan s, where – tan s = (/diel) -1 = loss tangent Reference: Ludwig & Bretchko, RF Circuit Design Reference: Ludwig & Bretchko, RF Circuit Design Transit Limitations • Consider an FET • Source to drain spacing roughly 2.5 microns • Apply a 10 GHz signal: – T = 1/f = 10-10 = 0.10 nsec – transit time across S to D is roughly 0.025 nsec or 1/4 of a period so the gate voltage is low and may not permit the S to D current to flow Ref: text by Pozar Wireless Communications Options • Sonic or ultrasonic - low data rates, poor immunity to interference • Infrared - moderate data rates, but easily blocked by obstructions (use for TV remotes) • Optical - high data rates, but easily obstructed, requiring line-of-sight • RF or Microwave systems - wide bandwidth, reasonable propagation Cellular Telephone Systems (1) • Division of geographical area into nonoverlapping hexagonal cells, where each has a receiving and transmitting station • Adjacent cells assigned different sets of channel frequencies, frequencies can be reused if at least one cell away • Generally use circuit-switched public telephone networks to transfer calls between users Cellular Telephone Systems (2) • Initially all used analog FM modulation and divided their allocated frequency bands into several hundred channels, Advanced Mobile Phone Service (AMPS) – both transmit and receive bands have 832, 25 kHz wide bands. [824-849 MHz and 869-894 MHz] using full duplex (with frequency division) • 2nd generation uses digital or Personal Communication Systems (PCS) Satellite systems • Large number of users over wide areas • Geosynchronous orbit (36,000 km above earth) – fixed position relative to the earth – TV and data communications • Low-earth orbit (500-2000 km) – reduce time-delay of signals – reduce the need for large signal strength – requires more satellites • Very expensive to maintain & often needs line-of sight Global Positioning Satellite System (GPS) • 24 satellites in a medium earth orbit (20km) • Operates at two bands, L1 at 1575.42 and L2 at 1227.60 MHz , transmitting spread spectrum signals with binary phase shift keying. • Accurate to better that 100 ft and with differential GPS (with a correcting known base station), better than 10 cm. Frequency choices • availability of spectrum • noise (increases sharply at freq. below 100 MHz and above 10 GHz) • antenna gain (increases with freq.) • bandwidth (max. data rate so higher freq. gives smaller fractional bandwidth) • transmitter efficiency (decreases with freq.) • propagation effects (higher freq, line-of sight) Propagation • Free space power density decreases by 1/R2 • Atmospheric Attenuation • Reflections with multiple propagation paths cause fading that reduces effective range, data rates and reliability and quality of service • Techniques to reduce the effects of fading are expensive and complex Antennas • RF to an electromagnetic wave or the inverse • Radiation pattern - signal strength as a function of position around the antenna • Directivity - measure of directionality • Relationship between frequency, gain, and size of antenna, = c/f – size decreases with frequency – gain proportional to its cross-sectional area \ 2 – phased (or adaptive) array - change direction of beam electronically Math Review Misalkan A dan B interseksi on vectors A B A B cos : scalar atau dot product, projeksi satu vecto r terhadap lainnya A B A B sin C Perubahan yg didefisika n oleh partial /x menghasilk an x y z x y z Untuk systems coordinate berikutnya jika sebuah field memiliki scalar u u(x, y, z) bervariasi dalam ruang (Space) u u u z ; gradient : rate of change y x u z y x Ax Ay Az ; Divergence : net outward flow A z y x Ay Ax ) z ; Curl or ROT (Russian) ( A) z ( y x rotation (pusaran daun yg mengalir di sungai) A A 0; u 0 or curl of gradient 0 A ( B C ) ( A B) C ; ( C ) ( ) C 0 or div of curl 0 A ds ( A)dV ; Divergence theorem v s A d ( A)ds; Stokes (batu) theorem s Maxwell’s Equations D B 0 E B / t H J D / t • • • • Gauss No Magnetic Poles Faraday’s Laws Ampere’s Circuit Law Characteristics of Medium Constitutive Relationships D E, ro , Dielectric Permitivit y B H, or, Magnetic Permeabili ty Jc E, J Jc Jv, Jv Convective Current Assumption s J 0, in the medium itself, not so on surfaces , , scalars except ferrites, plasma E, H proportion al to exp(j t - z) where j, attentuati on constant phase constant, z direction of propagatio n Fields in a Dielectric Materials Assume D oE P, and non magnetic, so o and J 0 (D electric flux or displaceme nt density) P dipole moment density e oE, e dielectric suceptibil ity D o(1 e )E E o(1 e ) j , for good dielectric (3 or 4 orders of magnitude) accounts for loss in the medium (heat) negative due to entergy conservati on 0 Fields in a Conductive Materials J J c E, where E fields vary as e jt H J D E E E jE t t )E ( j j( j))E j j( j j )E [ j ( )]E where is the effective conductivi ty effective loss tangent tan j( Wave Equation Consider /t j E -jH, H jE ( E) ( E) - 2 E ( jH) ( j )( j )E 2 E - 2 E; similarly 2 H - 2 H; define : k 2 propagatio n constant of waves in medium described by and General Procedure to Find Fields in a Guided Structure • 1- Use wave equations to find the z component of Ez and/or Hz – – – – – note classifications TEM: Ez = Hz= 0 TE: Ez = 0, Hz 0 TM: Hz = 0, Ez 0 HE or Hybrid: Ez 0, Hz 0 General Procedure to Find Fields in a Guided Structure • 2- Use boundary conditions to solve for any constraints in our general solution for Ez and/or Hz n̂ E 0, or E t 0 on surface of perfect conductor n̂ E s / n̂ H J s n̂ H 0, or H n 0 on surface of perfect conductor where n̂ normal to the surface of conductor Plane Waves in Lossless Medium 2 E k 2 E 0, where k ω is real since and are real in a lossless medium E E x and /x /y 0 2E x 2 jkz jkz k E 0 E ( z ) E e E e x x 2 z or in the time domain : E x (z, t ) E (cos( t kz)) E (cos( t kz)) ω t kz constant moving in the z direction Phase Velocity Fixed phase point trav els at a velocity dz d t - constant vp ( ) dt dt k k in free space v p 1 o o 1 c 3 108 m/sec Wavelength : distance between 2 successive maxima (t - kz) - (t - k(z )) 2 k 2 2v p v p or v p f k f in free space : v p f c Wave Impedance H By Maxwell' s eqn : E - jH t E x 0; so ẑ E x x̂ ŷ x y z z jkE e jkz jkE e jkz jH y k Hy ( E e jkz E e jkz ) where or E/H k Plane Waves in a Lossy Medium E jH and H jE E E j( H) j( jE E ) E ( E) 2 E 2 2 E (1 j )E 0 2 (1 j ) 2 wave number , now complex j j (1 j ) note 0, 0 and j and k Wave Impedance in Lossy Medium as before E E x x̂ and /x /y 0 Ex 2 2 E x 0 E x (z) E e z E e z z z z j z z e e e time domain e cos(t z) 2 j z Hy (E e E e z ) j where wave impedance with losses Plane Waves in a good Conductor practical case j j / j j 2 / (1 j) / 2 / 2 s 1 / 2 / skin depth at 10 GHz, s 1m for most metals (Al, Cu, Ag, Au) at microwave frequencie s, currents flow on the surface Energy and Power A source of electromag netic energy sets up fields that store electric and magnetic energy and carry power that may be transmitt ed or dissipated as loss We 1 / 4 Re E D *dv / 4 E E *dv v v Wm 1 / 4 Re H B*dv / 4 H H *dv v v Ps power generated by sources Po P 2 j( Wm We ) Po 1 / 2 Re E H ẑds power transmitt ed * s