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

3. Brief Microwave History
Maxwell ( )
integrated electricity and magnetism
set of 4 coherent and self-consistent equations
predicted electromagnetic wave propagation
Hertz ( )
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 accuracy poor fair good
identification poor fair good
volume search good fair poor
adverse weather perf. good fair poor
perf. in smoke, dust, good good fair

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 = = 0.10 nsec
transit time across S to D is roughly 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. [ MHz and 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 ( 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 and L2 at 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. Maxwell’s Equations Gauss No Magnetic Poles Faraday’s Laws
Ampere’s Circuit Law

31. Characteristics of Medium Constitutive 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