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

September 2, 2004 M. Black

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**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)

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**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

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**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, ...

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**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

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**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

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**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»

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**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

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**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

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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

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**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

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**Reference: Ludwig & Bretchko, RF Circuit Design**

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**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

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**Reference: Ludwig & Bretchko, RF Circuit Design**

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**Reference: Ludwig & Bretchko, RF Circuit Design**

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**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

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Ref: text by Pozar

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**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

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**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

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**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)

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**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

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**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.

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**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)

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**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

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**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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**Maxwell’s Equations Gauss No Magnetic Poles Faraday’s Laws**

Ampere’s Circuit Law

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**Characteristics of Medium Constitutive Relationships**

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**Fields in a Dielectric Materials**

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**Fields in a Conductive Materials**

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Wave Equation

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**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

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**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

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**Plane Waves in Lossless Medium**

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Phase Velocity

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Wave Impedance

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**Plane Waves in a Lossy Medium**

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**Wave Impedance in Lossy Medium**

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**Plane Waves in a good Conductor**

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Energy and Power

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