ECE 563 / TCOM 590 Introduction to Microwaves and E&M Review

1. ECE 563 / TCOM 590Introduction to Microwavesand E&M Review September 2, 2004 M. Black

3. 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)

4. 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

5. 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, ...

6. 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

7. Radar System Comparison Radar Characteristicwave mmwave optical tracking accuracypoorfairgood identification poorfairgood volume searchgoodfairpoor adverse weather perf. goodfairpoor perf. in smoke, dust, ...goodgoodfair

8. 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» 

9. 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

10. 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

11. 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

12. 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

13. Reference: Ludwig & Bretchko, RF Circuit Design

14. 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

15. Reference: Ludwig & Bretchko, RF Circuit Design

16. Reference: Ludwig & Bretchko, RF Circuit Design

17. 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

18. Ref: text by Pozar

19. 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

20. Cellular Telephone Systems (1) • Division of geographical area into non-overlapping 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

21. 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)

22. 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

23. 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.

24. 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)

25. 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

26. 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

30. Gauss No Magnetic Poles Faraday’s Laws Ampere’s Circuit Law Maxwell’s Equations

31. Characteristics of MediumConstitutive Relationships

32. Fields in a Dielectric Materials

33. Fields in a Conductive Materials

34. Wave Equation

35. 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

36. 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

37. Plane Waves in Lossless Medium

38. Phase Velocity

39. Wave Impedance

40. Plane Waves in a Lossy Medium

41. Wave Impedance in Lossy Medium

42. Plane Waves in a good Conductor

43. Energy and Power