ECE 563 / TCOM 590Introduction 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 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

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 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

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

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• 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

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• 2- Use boundary conditions to solve for any constraints in our general solution for Ez and/or Hz

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