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Radio Frequency Integrated Circuits and Systems

Dr K.J. Vinoy

Associate Professor

ECE Dept, IISc, Bangalore


Brief Outline• Overview/Scope

• Challenges to be addressed

• Course schedule

• Important issues

– Importance of Home/Lab works

– Software tools

– Final Project

– Final Exam

• Grading Policy

• Text books

• Other useful references

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Radio Frequency Integrated Circuits and Systems

• Overview

– There is a demand for a course on the present technology for Telecommunications.

– Course on Microwave Systems Engineering was introduced in 2005.

– Topics covered included • microwave engineering fundamentals• basic concepts of passive and active circuits • antennas • numerical electromagnetic techniques.

• Reasons for change of title (2008)

– Software tool• Since 2006 we started using ADS for this course • New licenses are now available (total of 7)• IC-CAP available for device modeling

– Earlier offerings had stress on computational techniques

– New research in RF CMOS circuits

– New courses on MEMS, micro systems fabrication etc.

• New topics added

– A systems perspective to circuit design

– Topics on RF CMOS circuit design


Why study Electromagnetics• Electromagnetics explain why electrons and protons behave as they do, and

thus why resistors, capacitors, inductors, transistors and ultimately all electrical gadgets work.

• Electromagnetics is relevant in a wide range of topics taught under electrical, electronics, telecommunication, and computer engineering.

– Radio, TV, Cellular telephones, Computers, Electric Machinery, Particle Accelerators, Electrostatic precipitators, Magnets, Superconductors

– Lightning, Magnets, Light, Radiowaves

• Bottom line: It is wise to be fundamentally sound across the breadth of your profession

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Why study Electromagnetics• Opportunity to study things that vary in space AND time

– We learn a lot of phenomenon with ordinary differential equations.

– Maxwell's equations are fascinating because they account for variation in space as well as time.

– Many of us study/research because of a burning curiosity about the physical world.

– The study of electromagnetics is vibrant enough to keep you going for a lifetime.

• Where is this relevant

– To better understand modern communications and computer systems.

– To be able to design and analyze electromagnetics-based devices such as antenna systems, fiber optics systems and microwave systems

• If you Master Electromagnetics

– You can solve a lot of issues your colleagues are eager to avoid

– Address a lot research problems of today’s world


Technology Impact

Device Concepts

Computational Techniques for design & Modeling

Raw Materials

Process Technologies

Systems

Components & subsystems

ComputersIT gadgets Mobile phones

SmallerCheaperWidespread

Benefits to the Society

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Relevant Electromagnetic Spectrum• Radio Frequency Spectrum

– HF 3-30 MHz 100m-10m– VHF 30-300 MHz 10m - 1m– UHF 300-1000 MHz 1m-30cm

– L-Band 1-2 GHz 30cm-15cm– S-Band 2-4 GHz 15cm-7.5cm– C-Band 4-8 GHz 7.5cm-4.5cm– X Band 8-12 GHz 4.5cm-2.5cm– Ku-Band 12-18 GHz 2.5cm-1.67cm– K-Band 18-26.5 GHz 1.67cm-1.13cm– Ka-band 26.5-40 GHz 1.13cm-7.5mm– Q band 30 - 50 GHz 1 cm – 6mm– U band 40 - 60 GHz 7.5mm – 5mm– V band 50 - 75 GHz 6 mm – 4mm– E band 60 - 90 GHz 5 mm – 3.33 mm– W band 75 - 110 GHz 4 mm – 2.7 mm– F band 90 - 140 GHz 3.33mm – 2.14 mm– D band 110 - 170 GHz 2.7mm – 1.76 mm

– Sub-millimeter: >300GHz < 1mmwave bands

||| | Microwave bands|||

1 MHz = 106 Hz1 GHz = 109 Hz = 1000 MHz

||| Presently called RF||↓

||| (30-300 GHz)| Millimeter bands ||||


Frequency Spectra for Radio Communications

• The most POPULAR frequency bands during the last 50+ years…

• The ‘primary’ bands jump 10x in every ten years…

2010200019901980197019601950

~MHzRadios

100s MHzTelevision

1000s MHzMobile phones

WiFi/WLAN

10s GHz??

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Perspective: What is Microwave Engineering?

• Microwave engineering is a study of wave-material interactions at microwave frequencies

– Size of component is of the order of a wavelength

– Unlike audio or optical frequencies

• At microwave frequencies

– Many materials (or, material systems) behave differently

– Most devices do not perform as good

– Different/ new approaches are required for circuit design

– New components are required for miniaturization and/or multi-function capabilities

– There can be significant interaction between elements in a system

• Typical Design Specifications

– Early microwave engineering: Low volume, high specs

– Present: High volume, less critical/agile specs

• There is a distinctive trend towards multidisciplinary approaches to research


Emerging Areas

Device TechnologyMaterials technologiesDesign ApproachesComputational techniques

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New Opportunities / Challenges• Wireless communications systems require antennas.

– Small, multifunctional antennas

– Space based communications

– Optical communications

• High speed circuits in modern PCs

– PCs are fast becoming microwave devices.

– Many chips are already operating at GHz

• Semiconductor Technology leveraging on Mechanical Microsystems

– RF MEMS

– Sub-millimeterwave systems

• Advancements in Theoretical Studies

– Metamaterials in circuits, antennas, and other components

• Electromagnetic interference and compatibility EMI/EMC

– Interaction with human tissues is yet to be completely understood

With ideas from www.eas.asu.edu/~holbert/wise/EE-program-2001.ppt

http://www.who.int/peh-emf/about/WhatisEMF/en/


“Local” Challenges• Inadequate preparation at UG level

• Familiarization of new text books and software tools

• Tricks of the technology & thumb rules

• Use of Greeks, often for different purposes

• General skepticism

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Course Objectives• Understand why RF Design is ‘different’

– Learn RF circuit Design softwares and characterization systems

• Revise EM fundamentals

• Explore New/emerging possibilities

• Try out some things…


Course Schedule

15Test 18-Feb

2Practice Exercise 4: Use ADS/AWR to design a simple 2-way equal power divider; fabricate & test

Analysis of 3 and 4 port circuits, couplers etc.

Passive microwave circuits; power dividers 1-Feb

1Practice Exercise 3: Learn ADS/AWR; Use this to analyze a simple circuit; design a transissionline for 50 ohm

microwave network analysis, ABCD-, S-, X-parameters

Microstrip and Coplanar waveguide implementations25-Jan

2Practice Exercise 2: Use Smith Chart to design Single stub tuning circuit

smith chart, impedance matching

Review of Transmission line Theory, terminated transmission lines18-Jan

1Practice Exercise 1: Use Maxwell Equations to derive the wave impedance of free space.

Introduction to Maxwell Eqn, Wave eqn, Wave propagation

Introduction to wireless systems, personal communication systems, High frequency effects in circuits and systems.11-Jan

Points TopicWeek

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Course Schedule-2

15Test 2

Micromachined varactors, inductors and filters8-Mar

MEMS technologies and components for RF applications: RF MEMS switches

Switching devices and circuits1-Mar

2Practice Exercise 7: Use ADS/AWR to analyze a filter with periodic structure; obtain its k-beta diagram using Matlab/script programs OR Transmissionline component using CRLH concepts

Theory of microwave metamaterials, CRLH Transmission lines; Applications

Microwave filters with Periodic structures 22-Feb

2Practice Exercise 6: Use ADS/AWR to design a passive RF filter; implement using realistic lumped and distributed components

Design of microwave filters: insertion loss method

resonant structures using distributed transmission lines, components and interconnects at high frequencies15-Feb

1Practice Exercise 5: Learn netlist & EM modeling in ADS/AWR to design tuning circuits for a given frequency

Series and parallel RLC circuits

8-Feb


Course Schedule-3

4Practice Exercise 11: Use ADS/AWR to design a microstrip antenna; Fabricate & test

Systems aspects in wireless trans-receiver design

Design of typical Wire and Planar antennas for Wireless systems5-Apr

Introduction to microwave antennas, definitions and basic principles

Oscillators, linear oscillators, tuned oscillators, negative resistance oscillators29-Mar

2Practice Exercise 10: Test and anlysis of LNA

LNA design, designs based on impedance match noise performance, linearity, noise and large signal performance; noise and distortion,

CMOS circuit design for RF applications; Feedback systems, phase locked loops22-Mar

2Practice Exercise 9: Use ADS/AWR to design/analyze a LNA

Power amplifier design, Various classes of power amplifiers

Basics of high frequency amplifier design, device technologiesbiasing techniques, simultaneous tuning of 2 port circuits15-Mar

1Practice Exercise 8: Expt with RF Lab Kit

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Why is this course 2:1• Microwave engineering is about designing circuits that work!

– Many conventional theories fail at high frequencies

– More of it next week!

– Learn from experience

• Today’s software tools are highly pervasive

• Yet real experience comes by burning your own fingers

• All are expected to be able to design, fabricate and test some circuit component by the end of this course

• By the end of the course you will be asked to take an example from published recent literature and

– Redesign with materials available in the Lab.

– Study the effects of various parameters

– Fabricate by self or outside (if time permits)

– Measure in the Lab

• All cost will be born by the Lab.

• As a training towards this several home/lab work experiments are planned during the semester


Grading Policy• Home/Lab work

– All practice Exercises should be submitted as soft copies.

– Scope, objectives, screen grab of project schematics, simulation results and conclusions are required in all reports

– Last date for valid submission is the Wednesday after it is announced

– Penalty for late submission: 1st day 25%; 2nd day 60%; 3rd day 90%; no credits if submitted later than Saturday; Negative marks (2x) if not submitted or proved to be copied.

– Exercises have a total credit of 20 points

• Tests– 2 tests have a total of 30 points

• Final Project – The final project is based on a recent paper relevant to the course and/or research

– Fabrication and test is compulsory for this. Active circuits are not usually preferred due to unavailability of components.

– The report should briefly explain the original work, and highlight modifications/extensions attempted during the present work

– Total of 20 points• Novelty/technical content etc: 5• Presentation & report 15

• Final Exam– Has 30 points

• Relative grading is not feasible in a small class D40-50

C51-65

B66-80

A81-90

S91-100

GradeMarks

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Course Material• Text books

– DM Pozar Microwave and RF Wireless Systems

– TH Lee The design of CMOS Radio Frequency Integrated Circuits*

– D.M. Pozar, Microwave Engineering, John Wiley*

– VK Varadan, K.J. Vinoy, K.A. Jose, RF MEMS and Their Applications

• Other reference books– MNO Sadiku, Elements of Electromagnetics 3rd Ed., Oxford Univ. Press*

– R.E. Collin Foundations for Microwave Engineering John Wiley*

– C.A. Balanis, Antenna Theory: Analysis and Design, John Wiley*

– JD Kraus, MJ Marhefka , Antennas for all Applications, Tata McGraw Hill*

– I Bahl, Lumped Elements for RF and Microwave Circuits, Artech House

– I. Bahl & P. Bartia, Microwave Solid State Circuit Design, Wiley Inter Science, 2003.

– K Chang Radio Frequency Circuit design Wiley Inter Science, 2003

• Websites– To be updated

• Volunteer needed– There is a request to bring out a set of lecture notes for several courses at IISc during the centenary

year.

– I request participation from 1 or 2 of you in this regard.

* Indian reprint editions are available to many of these

books.


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Introduction to Wireless Systems• GPS

• GSM/CDMA

• Bluetooth

• WiFi

• WLAN

• RFID

• DBS

Dr Vijay Nair, Intel Corp., IEEE MTT-DML


Wireless Personal Area Network• A personal area network (PAN) is a computer network used for

communication among computer devices (including telephones and PDAs) close to one person.

• The reach of a PAN is typically a few meters.

• PANs can be used for communication among the personal devices themselves (intrapersonal communication), or for connecting to a higher level network and the Internet (an uplink).

• Personal area networks may be wired with computer buses such as USB and FireWire.

• A wireless personal area network (WPAN) can also be made possible with network technologies such as IrDA, Bluetooth, or UWB.

Note: Most information in this and the following ~10 slides are from Wikipedia

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Bluetooth• Bluetooth is an industrial specification for wireless personal area

networks (PANs).

• The specification is based on frequency-hopping spread spectrum technology.

• Provides a way to connect and exchange information between devices such as mobile phones, laptops, PCs, printers, digital cameras, and video game consoles over a secure, globally unlicensed short-range radio frequency.

• The Bluetooth specifications are developed and licensed by the Bluetooth Special Interest Group.

• Bluetooth vs. Wi-Fi in networking

– Both are versions of unlicensed spread spectrum technology.

– Use the same frequency range, but employ different multiplexing schemes.

– For different applications

– Wi-Fi provides higher throughput and covers greater distances, but requires more expensive hardware and higher power consumption.

– Bluetooth is often thought of as wireless USB, whereas Wi-Fi is wireless Ethernet (both with much lower bandwidth than the cable systems).

• Recent development: Wibree

– Wibree is a digital radio technology (open standard) designed for ultra low power consumption (button cell batteries) within a short range (10 meters) based around low-cost transceiver microchips in each device.

– Expected use cases include watches displaying Caller ID information, sports sensors monitoring heart rate during exercise, as well as medical devices

~1 m.1 mW (0 dBm)Class 3

~10 m.2.5 mW (4 dBm)Class 2

~100 m.100 mW (20 dBm)Class 1

Range (approx.)

Max. Power (mW/dBm)Class

53 - 480 Mbit/s

WiMedia Alliance(proposed)

3 Mbit/sVersion 2.0 + EDR

1 Mbit/sVersion 1.2

Data RateVersion


Zigbee• ZigBee is the name of a specification for a suite of high level communication

protocols using small, low-power digital radios based on the IEEE 802.15.4 standard for wireless personal area networks (WPANs), such as wireless headphones connecting with cell phones via short-range radio.

• The technology is intended to be simpler and cheaper than other WPANs, such as Bluetooth.

• ZigBee operates in ISM radio bands: 868 MHz in Europe, 915 MHz in countries such as USA and Australia, and 2.4 GHz in most jurisdictions worldwide.

• Targets RF applications requiring a low data rate, long battery life, and secure networking.

• ZigBee defines a general-purpose, inexpensive, self-organizing, mesh network that can be used for industrial control, embedded sensing, medical data collection, smoke and intruder warning, building automation, home automation, etc.

• The resulting network will use very small amounts of power so individual devices might run for a year or two using the originally installed battery.

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Competition: EnOcean• EnOcean GmbH is a spin-off company of Siemens AG founded in 2001,

• It is a technology supplier of self-powered modules (transmitters, receivers, transceivers, energy converter) to several companies which develop and manufacture products used in building automation (light, shading, hvac), industrial automation, and automotive industry (replacement of the conventional battery in tyre pressure sensors).

• The technology is based on the efficient exploitation of slightest changes in the environmental energy using the principles of energy harvesting. In order to transform such energy fluctuations into usable electrical energy, electromagnetic, piezogenerators, solar cells, thermocouples, and other energy converters are used.

• Products (such as sensors and radio switches) are battery-less and are engineered to operate maintenance-free.

• RF energy is only transmitted for the 1's on the data

• The frequency used is 868.3 MHz

• Packets of data are transmitted at 120 kbit/s with the packet being 14 bytes long with a four byte data payload.

• The signals of these sensors and switches can be transmitted across a distance up to 300 m.

• Three packets are sent at pseudo-random intervals reducing the possibility of packet collisions to a very low figure.

• Every device has a unique 32-bit serial number, so local interference is avoided by 'training in' receivers to the transmitters required to operate them.


WiFi• A wireless technology brand-owned by the Wi-Fi Alliance intended to improve the

interoperability of wireless local area network products based on the IEEE 802.11 standards.

• Wi-Fi also allows connectivity in peer-to-peer (wireless ad-hoc network) mode, which enables devices to connect directly with each other.

• Applications

– Internet and VoIP phone access,

– gaming

– network connectivity for televisions, DVD players, and digital cameras.

• Wi-Fi allows LANs to be deployed without cabling for client devices, typically reducing the costs of network deployment and expansion. Useful in spaces where cables cannot be run, such as outdoor areas and historical buildings.

• A typical Wi-Fi home router using 802.11b or 802.11g with a stock antenna mighthave a range of 32 m (120 ft) indoors and 95 m (300 ft) outdoors.

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Wireless Local Area Network (WLAN)• Links two or more computers without using wires.

• WLAN utilizes spread-spectrum or OFDM modulation technology based on radio waves to enable communication between devices in a limited area, also known as the basic service set.

• Advantages

– This gives users the mobility to move around within a broad coverage area and still be connected to the network.

– The wireless nature allows users to access network resources from nearly any convenient location within their primary networking environment (home or office).

– With the emergence of public wireless networks, users can access the internet even outside their normal work environment.

– Users connected to a wireless network can maintain a nearly constant affiliation with their desired network as they move from place to place.


Key Disadvantages in WLAN• Security:

– For proper reception with these antennas within reasonable range, the WLAN transceiver utilizes a fairly considerable amount of power.

– To combat this consideration, wireless networks users usually choose to utilize various encryption technologies available such as Wi-Fi Protected Access (WPA).

• Range: – The typical range of a common 802.11g network with standard equipment is ~10’s m.

– To obtain additional range, repeaters or additional access points required.

• Reliability: – Subject to a wide variety of interference, as well as complex propagation effects (such as multipath, or

especially in this case Rician fading).

– Usually, modulation is achieved by phase-shift keying (PSK) or quadrature amplitude modulation (QAM), causing interference and other propagation effects.

– Important network resources such as servers are rarely connected wirelessly.

• Speed: – The speed on most wireless networks (~ 1-108 Mbit/s) is slow compared to the slowest common wired

networks (100 Mbit/s - several Gbit/s).

– Additionally, there are performance issues caused by TCP and its built-in congestion avoidance.

– Newer standards such as 802.11n are addressing this limitation and will support peak throughputs in the range of 100-200 Mbit/s.

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WiMAX• Worldwide Interoperability for Microwave Access

• WiMAX is a technology aimed at providing wireless data over long distances in a variety of ways, from point-to-point links to full mobile cellular type access.

• It is based on the IEEE 802.16 standard, which is also called WirelessMAN.

• The WiMAX forum describes WiMAX as “a standards-based technology enabling the delivery of last mile wireless broadband access as an alternative to cable and DSL.”

• The bandwidth and reach of WiMAX make it suitable for the following potential applications:

– Connecting Wi-Fi hotspots with each other and to other parts of the Internet.

– Providing a wireless alternative to cable and DSL for last mile broadband access.

– Providing high-speed data and telecommunications services.

– Providing a diverse source of Internet connectivity as part of a business continuity plan.

• Frequencies

– In the USA, the biggest segment available is around 2.5 GHz. Elsewhere in the world, with 2.3 GHz probably being most important in Asia.

– Some countries in Asia like India, Vietnam and Indonesia will use a mix of 3.3 GHz and other frequencies.

Comparison with Wi-Fi•WiMAX is a long-range system (kms) uses (un)licensedspectrum Different 802.16 standards provide different types of access, from mobile (analogous to access via a cellphone) to fixed (an alternative to wired access, where the end user's wireless termination point is fixed in location.)

•Wi-Fi is a shorter range system, typically hundreds of meters, that uses unlicensed spectrum to provide access to a network, typicall. Typically Wi-Fi is used by an end user to access their own network, which may or may not be connected to the Internet.

•QoS mechanisms: WiMAX uses a mechanism based on setting up


Global System for Mobile communications• GSM: originally from Groupe Spécial Mobile

• Most popular standard for mobile phones in the world (~82%)

• international roaming

• considered a second generation (2G) mobile phone system

• GSM also pioneered SMS (now supported on other mobile standards)

• Frequency bands– Mostly 900 MHz or 1800 MHz bands.

– Canada and USA use 850 and 1900 MHz bands

– 400 and 450 MHz frequency bands are assigned in some Scandinavian countries

• 900/1800 Band:– uplink frequency: 890–915 MHz,

– downlink frequency: 935–960 MHz.

– This 25 MHz bandwidth is subdivided into 124 carrier frequency channels

– Time division multiplexing is used to allow eight full-rate or sixteen half-rate speech channels per RF channel.

– There are eight radio timeslots (giving eight burst periods) grouped into a TDMA frame.

– Half rate channels use alternate frames in the same timeslot. The channel data rate is 270.833 kbit/s, and the frame duration is 4.615 ms.

– The transmission power in the handset is limited to a maximum of 1 watt in GSM1800/1900.

– GSM has used a variety of voice codecs (usually based on linear predictive coding (LPC)) to squeeze 3.1 kHz audio into between 5.6 (half rate) and 13 (full rate) kbit/s.

– The modulation used in GSM is Gaussian minimum-shift keying (GMSK). In GMSK, the signal is first smoothed with a Gaussian low-pass filter prior to being fed to a frequency modulator, which greatly reduces the interference to neighboring channels (adjacent channel interference).

GSM / UMTS (3GPP) Family2G

* GSM* GPRS* EDGE (EGPRS)

o EDGE Evolution* HSCSD

3G* UMTS (3GSM)* HSPA

o HSDPAo HSUPAo HSPA+

* UMTS-TDDo TD-CDMAo TD-SCDMA

* FOMAPre-4G

* UMTS Revision 8o LTEo HSOPA (Super 3G)

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Global Positioning System (GPS)• Application

– Maps on the go

• Key facts

– Global Positioning System (GPS) a fully functional Global Navigation Satellite System (GNSS).

– Uses a constellation of at least 24 Medium Earth Orbit satellites that transmit precise microwave signals, the system enables a GPS receiver to determine its location, speed, direction, and time.

– Other similar systems are the Russian GLONASS (incomplete as of 2007), the upcoming European Galileo positioning system, the proposed COMPASS navigation system of China, and IRNSS of India.

– Following the shoot-down of Korean Air Lines Flight 007 in 1983, GPS has been made available for public use, become a widely used aid to navigation worldwide, and a useful tool for map-making, land surveying, commerce, and scientific uses.

– GPS also provides a precise time reference used in many applications including scientific study of earthquakes, and synchronization of telecommunications networks.

http://en.wikipedia.org/wiki/Global_Positioning_System


GPS• Frequencies used by GPS include

– L1 (1575.42 MHz): • Mix of Navigation Message, coarse-acquisition (C/A) code and encrypted precision P(Y) code, plus the new

L1C on future Block III satellites.– L2 (1227.60 MHz):

• P(Y) code, plus the new L2C code on the Block IIR-M and newer satellites.– L3 (1381.05 MHz):

• Used by the Nuclear Detonation (NUDET) Detection System Payload (NDS) to signal detection of nuclear detonations and other high-energy infrared events. Used to enforce nuclear test ban treaties.

– L4 (1379.913 MHz): • Being studied for additional ionospheric correction.

– L5 (1176.45 MHz): • Proposed for use as a civilian safety-of-life (SoL) signal (planned for 2008)

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Direct broadcast satellite (DBS)• DBS refers to satellite television broadcasts intended for home reception, also

referred to as direct-to-home signals.

• DTH refers to services carried by lower power satellites which required larger dishes (1.7m diameter or greater) for reception.

• DBS typically requires smaller (0.9m dishes). Uses higher powered satellites

• The term DBS now covers both analog and digital television and radio reception, and is often extended to other services provided by modern digital television systems, including video-on-demand and interactive features.

• Modern satellite providers in the United States use high power Ku-band transmissions using circular polarization, which result in small dishes, and digital compression (hence bringing in an alternative term, Digital Satellite System)

• European Ku band DBS systems operate > 10.7 GHz.

• DD Direct Plus is a free Direct to Home (DTH) service that provides satellite television and audio programming, owned by Doordarshan.


Local Multipoint Distribution Service (LMDS)

• LMDS is a broadband wireless access technology governed by the IEEE and is outlined by the 802 LAN/MAN Standards Committee through the efforts of the IEEE 802.16.1 Task Group.

• LMDS commonly operates on microwave frequencies across the 26GHz and 29GHz bands. In the United States, frequencies from 31.0 through 31.3 GHz are also considered LMDS frequencies.

• LMDS was conceived as a broadband, fixed wireless, point-to-multipoint technology for utilization in the last mile.

• Throughput capacity and reliable distance of the link depends on common radio link constraints and the modulation method used - either phase-shift keying or amplitude modulation. In general deployment links of up to 5 miles (8 km) from the base station are possible, but distance is typically limited to about 1.5 miles due to rain fading attenuation constraints.

• Point-to-point systems are also capable of using the LMDS frequencies and can reach slightly farther distances due to increased antenna gain.

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RF ID• Radio-frequency identification (RFID) is an automatic identification method, relying on storing and remotely retrieving data using devices

called RFID tags or transponders.

• An RFID tag is an object that can be applied to or incorporated into a product, animal, or person for the purpose of identification using radio waves.

• Some tags can be read from several meters away and beyond the line of sight of the reader.

• Most RFID tags contain at least two parts.

– One is an integrated circuit for storing and processing information, modulating and demodulating a (RF) signal and can also be used for other specialized functions.

– The second is an antenna for receiving and transmitting the signal.

– A technology called chipless RFID allows for discrete identification of tags without an integrated circuit, thereby allowing tags to be printed directly onto assets at lower cost than traditional tags.

• RFID use is in

– enterprise supply chain management,

– improving the efficiency of inventory tracking and management.

• Types

– Passive tags require no internal power source, thus being pure passive devices (they are only active when a reader is nearby to power them). To communicate, tags respond to queries generating signals that must not create interference with the readers, as arriving signals can be very weak and must be told apart. Backscattering (far field) or load modulation (near field) techniques can be used to manipulate the reader's field.

– Active RFID tags have their own internal power source, which is used to power IC and broadcast the signal to the reader. Active tags are typically much more reliable than passive tags due to their ability to conduct a "session" with a reader. Active tags transmit at higher power levels than passive tags, allowing them to be more effective in "RF challenged" environments like water, metal or at longer distances, generating strong responses from weak requests. They are generally bigger and more expensive to manufacture, and their potential shelf life is much shorter. Many active tags have practical ranges of hundreds of meters, and a battery life of up to 10 years.

– Semi-passive tags are similar to active tags in that they have their own power source, but the battery only powers the microchip and does not broadcast a signal. The RF energy is reflected back to the reader like a passive tag. An alternative use for the battery is to store energy from the reader to emit a response in the future, usually by means of backscattering. The battery-assisted receive circuitry of semi-passive tags lead to greater sensitivity than passive tags, typically 100 times more. Semi-passive tags have three main advantages 1) Greater sensitivity than passive tags 2) Better battery life than active tags. 3) Can perform active functions (such as temperature logging) under its own power, even when no reader is present


Typical Communication System

Nguen et al, 1998 IEEE

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Selection of frequencies: Atmospheric attenuation

http://www.microwaves101.com/encyclopedia/frequency.cfm


Some useful bands System Frequency range RFID systems 125 to 134 kHz

13.56 MHz UHF (400 to 930 MHz) 2.45 GHz 5.8 GHz

FM radio 88 to 108 MHz Broadcast television, channels 7-13 174 to 220 MHz Remote keyless entry (RKE) systems, tire pressure monitoring systems (TPMS)

315 or 433 MHz

UHF television (channels 14-83) 470 to 890 MHz Cell phones (GSM) 824 to 960 MHz

1710 to 1990 MHz Industrial, medical & scientific (ISM) band 902 to 928 MHz

2400 to 2483.5 MHz 5.725 to 5.85 GHz

Global positioning system (GPS) 1227.6 MHz (L2 band, 20 MHz wide) 1575.42 MHz (L1 band, 20 MHz wide)

Shared wireless data protocols (Bluetooth, 802.11b):

2402 to 2495 MHz

Microwave ovens 2450 MHz Satellite radio downlink 2330 to 2345 MHz 802.11a wireless local area network (WLAN) 5.15 to 5.25 GHz (lower band) 5.25 to 5.35

GHz (middle band) 5.725 to 5.825 (upper band)

Direct broadcast satellite TV downlink (Europe)

11.7 to 12.5 GHz

Automotive radar, distance sensors 24 GHz 4G (fourth generation wireless) 59 to 64 GHz (U.S. general wireless)

65 to 66 GHz (Europe, mobile broadband) Automotive radar, adaptive cruise control 76 to 77 GHz E-band

76 GHz, 81 to 86 GHz and 92 to 95 GHz

http://www.microwaves101.com/encyclopedia/frequency.cfm

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Overview• What is electromagnetics

• A bit of history

– Early Indian contributions

• Electromagnetic field theory

– Maxwell Equations


In the beginning…• Electromagnetics started with the experimental observations of

– (i) forces between electric charges;

– (ii) forces between conductors carrying electric currents

www.eie.polyu.edu.hk/~em/em05pdf/1%20Transmission%20Line.pdf

21


What is Electromagnetics• An electromagnetic (EM) field is generated when charged particles, such

as electrons, are accelerated.

– All electrically charged particles are surrounded by electric fields.

– Charged particles in motion produce magnetic fields.

• When the velocity of a charged particle changes, an EM field is produced.

– EM fields are typically generated by an AC current in electrical conductors.

• Electromagnetic fields were first discovered in the 19th century

• Physicists noticed that electric arcs (sparks) could be reproduced at a distance, with no connecting wires in between.

– to communicate over long distances without wires.

– The first radio transmitters made use of electric arcs.

– The beginning of WIRELESS COMMUNICATION.

http://searchsmb.techtarget.com/sDefinition/0,,sid44_gci212055,00.html


Electromagnetic Radiations• Electromagnetic radiation is a stream of photons (massless particles traveling in a

wave-like pattern) moving at the speed of light.

• Each photon contains a certain amount (or bundle) of energy.

• The only difference between the various types of electromagnetic radiation is the amount of energy found in the photons.

• Radio waves have photons with low energies, and gamma-rays are the most energetic.

http://imagine.gsfc.nasa.gov/docs/science/know_l1/emspectrum.html

22


Representation of EM Radiations• The electromagnetic spectrum can be expressed in terms of energy,

wavelength, or frequency.

– Frequency is measured in cycles per second (which is called a Hertz),

– Wavelength is measured in meters,

– Energy is measured in electron volts

• Each way of thinking about the EM spectrum is related to the others in a precise mathematical way.

• Use whichever units are easiest

– Radio/microwave: use wavelengths [m/cm/mm] or frequencies [kHz/MHz/GHz]

– Infrared/optical: use wavelength [um/nm]

– ultraviolet, X-ray, and gamma-ray: energies [eV]• lengths have become too tiny to think about any more. • Ultraviolet radiation: a few electron volts (eV) to a about 100 eV. • X-ray photons have energies in the range 100 eV to 100,000 eV (or 100 keV). • Gamma-rays: photons with energies greater than 100 keV


Bit of HistoryBenjamin Franklin (1706-1790) Boston. In the 1740's electricity was a fashionable subject, Franklin began to investigate electrical phenomena. Franklin invented many terms still used in discussing electricity (positive, negative, battery, conductor, etc.)This triboelectric machine is based on a rotating glass sphere rubbing against a silk cloth. Charge is the transferred to a metallic sphere on the other side.

Charles-Augustin de Coulomb (1736-1806), French military civil engineer. He discovered that the torsion characteristics of long fibers made them ideal for the sensitive measurement of magnetic and electric forces. He was familiar with Newton's inverse-square law and in the period 1785-1791 he showed that electrostatic forces obey the same rule.

Luigi Galvani (1737-1798) Italian physician who, in the 1770's, began to investigate thenature and effects of electricity in animal tissue and of muscular stimulation by electrical means. In 1786, he obtained muscular contractions in a frog by touching its nerves with a pair of scissors during an electrical storm.

Alessandro Giuseppe Antonio Anastasio Volta (1745-1827) a professor at the University of Pisa. Volta began experimenting in 1794 with metals and found that currnet can be produced using. His invention and demonstration of the electric battery in 1800 provided the first continuous electric power source

These history pages and photos are from http://www.ece.umd.edu/~taylor/frame1.htm

23


Pierre-Simon Laplace (1749-1827) A letter on the principles of mechanics written to d'Alembert gained him a professorship at the École Militaire. His discovery that the attractive force of a mass upon a particle could be obtained directly by differentiating a single potential function laid the mathematical foundation for the analysis of heat, magnetism, and electricity.

Siméon-Denis Poisson (1781-1849) In Paris at the École Polytechnique, Laplace and Lagrange were his instructors, and lifelong friends. Poisson's work concerned the application of mathematics to electricity and magnetism, and other areas of physics.

Hans Christian Ørsted (1777-1851), a professor at the University of Copenhagen. In 1820 he was performing a classroom demonstration of the heating effect of electric currents when he observed the deflection of a nearby compass. He discovered a connection between electricity and magnetism.

George Green (1793-1841) In 1828 he privately published "An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism" in which he extended the work of Poisson to obtain a general method of solution for the potential.

Georg Simon Ohm (1789-1854) German physicist. Discovered the law that the current flow through a conductor is proportional to the voltage and inversely proportional to the resistance. Current flowing through the metal bar in the center cylinder deflects a magnetized needle suspended above it. The deflection angle is proportional to the current. The source of electric potential is a thermocouple. The ends of the thermocouple are heated by steam and cooled by ice-water in the small containers on the tripods.



André-Marie Ampère (1775-1836) He had flashes of inspiration which he would pursue to their conclusion. After Ørsted's discovery in 1820 that a magnetic needle is deflected by a varying nearby current, he worked on the theory of this phenomenon, formulating the law of electromagnetism (Ampère's law) that describes mathematically the magnetic force between two circuits.

Jean-Baptiste Biot (1774-1862) along with Félix Savart formulated the Biot-Savart law of magnetic fields. In 1804 he took part in the first balloon ascension for scientific research and showed that the terrestrial magnetic field does not vary appreciably with altitude.

Augustin-Jean Fresnel (1788-1827) He became involved in optics and pioneered in establishing the wave theory of light. The wave theory of light led Fresnel into the Fresnel mirrors (canted to produce an interference pattern), the Fresnel rhomb (produces elliptical polarization using internal reflection), and the Fresnel lens, which uses a stepped geometry to produce focussing. Fresnel lenses are used in automobile headlights and large glass Fresnel lenses are used in lighthouses and have been instrumental in the prevention of shipwrecks.


24


Karl Friedrich Gauss (1777-1855) overturned the theories and methods of 18th-century mathematics. Beginning in 1830, Gauss worked closely with Weber. They organized a worldwide system of stations for systematic observations of terrestrial magnetism. The most important result of their work in electromagnetism was the development, by others, of telegraphy.

Wilhelm Eduard Weber (1804-1891), a German physicist, who with his friend Gauss investigated terrestrial magnetism, also established a system of absolute electrical units. His work on the ratio between the electrodynamic and electrostatic units was crucial to Maxwell's electromagnetic theory of light.

Michael Faraday (1791-1867) London. Faraday began as Davy's laboratory assistant. Faraday became the greatest experimentalist in electricity and magnetism of the 19th century. He produced an apparatus that was the first electric motor and in 1831 he succeeded in showing that a magnet could induce electricity.

The voltage induced in a coil moving through a non-uniform magnetic field was demonstrated by this apparatus. As the coil is removed from the field of the bar magnets, the coil circuit is broken and a spark is observed at the gap.

The first transformer: Two coils wound on an iron toroid.


Heinrich F.E. Lenz (1804-1865), Estonia (then in Russia). He was a professor at the University of St. Petersburg who carried out many experiments following the initiatives of Faraday. He is memorialized by the law which bears his name - the electrodynamic action of an induced current equally opposes the machanical inducing action- which was later recognized to be an expression of the conservation of energy.

Samuel F.B. Morse (1791-1872), He conceived the electric telegraph and made the first working model in 1835.

Ernst Werner von Siemens (1816-1892) Prussia. He began chemistry experiments that led to his invention of the first electroplating system. In 1837 he invented improvements in the development of early telegraphic systems.

William Thomson (Lord Kelvin) (1824-1907), at the University of Glasgow. Thomson is most famous for his work in thermodynamics, but his theoretical analysis of cable transmissionand his inventions (1854-1858) made the transatlantic cable possible.

Joseph Henry (1799-1878) Albany, New York. He worked to improve electromagnets and was the first to superimpose coils of wire wrapped on an iron core. In 1830 he observed electromagnetic induction, a year before Faraday.


25


James Prescott Joule (1818-1889), studied at Manchester under Dalton. At age twenty-one he published the "I2R" law. Two years later, he published the first determination of the mechanical equivalent of heat. He became a collaborator with Thomson and they discovered that the temperature of an expanding gas falls. The "Joule-Thomson effect" was the basis for the large refrigeration plants constructed in the 19th century.

Gustav Robert Kirchhoff (1824-1887), German, At the age of 21, he presented laws which allow calculation of the currents, voltages, and resistances of electrical networks. In further studies he demonstrated that current flows through a conductor at the speed of light. His other work established the technique of spectrum analysis which he applied to determine the composition of the Sun.

George Gabriel Stokes (1819-1903) British physicist and mathematician famous for a basic theorem of vector analysis. Stokes was the first to suggest the reason for the Fraunhoferlines.

James Clerk Maxwell (1831-1879) Edinburgh. He is ranked with Newton and Einstein for the fundamental nature of his many contributions to physics. Most importantly, he originated the concept of electromagnetic radiation and his field equations (1873) led to Einstein's special theory of relativity.

John William Strutt (Lord Rayleigh) (1842-1919), He is most famous for his discovery of Argon and his work in acoustics. He worked on the precision determination of electrical standards and his work on the scattering of light explained the blue color of the sky.



John Henry Poynting (1852-1914), one of Maxwell's students, He published papers which showed that energy flow can be expressed in a simple formula using the electric and magnetic fields.

Alexander Graham Bell (1847-1922) was a Scottish-born American audiologist. He is famous for his invention of the telephone.

Nikola Tesla (1856-1943) came to the U.S. from Austria-Hungary. Tesla held more than 700 patents. His inventions included the principle of the rotating magnetic field machine, the induction motor, polyphase alternating-current systems, the Tesla coil transformer, wireless communication, radio, and fluorescent lights.

George Westinghouse (1846-1914) was the inventor and industrialist who fought for the adoption of ac electric power in the U. S. Westinghouse purchased transformers and an ac generator in Europe and set up an ac power system in Pittsburgh. He bought Tesla's ac motor patents and hired Tesla to adapt the motor for use in his power system.

Charles Proteus Steinmetz (1865-1923) His work at GE on hysteresis loss, ac circuit theory, and high power discharges provided the basis for the progress in ac circuits at the turn of the century.

Heinrich Rudolf Hertz (1847-1894) was the first to broadcast and receive radio waves. He produced electromagnetic waves in the laboratory and measured their wavelength and velocity. He showed that the nature of their reflection and refraction was the same as those of light, confirming that light waves are electromagnetic radiation obeying the Maxwell equations.


26


Guglielmo Marconi (1874-1937) Italian physicist who obtained a patent for a successful system of radio telegraphy (1896) and remained a leader in radio technology for four decades. In 1909 he received the Nobel Prize for Physics. Marconi succeeded in receiving signals transmitted across the Atlantic Ocean despite the curvature of the Earth. This was the start of the vast development of radio communication and broadcasting.

Aleksandr Stepanovich Popov (1859-1906) is acclaimed in Russia as the inventor of radio. Learning of Hertz's work, in 1895 Popov constructed an apparatus that could register electrical disturbances due to lightning, and then suggested that it could be used for receiving man-made signals. In 1896, he demonstrated the transmission of radio wave signals between different parts of the University of St. Petersburg.

Albert Abraham Michelson (1852-1931) German-born U.S. physicist who established the speed of light as a fundamental constant. He received the 1907 Nobel Prize for Physics.

Oliver Heaviside (1850-1925), He introduced the operational calculus (Laplace transforms) to study transient currents in networks and theoretical aspects of problems in electrical transmission. In 1902, Heaviside theorized that a conducting layer of the atmosphere existed that allows radio waves to follow the Earth's curvature.

Hendrik Antoon Lorentz (1853-1928), University of Leiden, sought to explain the origin of light by the oscillations of charged particles inside atoms. Under this assumption, a strong magnetic field would affect the wavelength. Lorentz arrived at the formulas known as the Lorentz transformations to describe the relation of mass, length and time for a moving body. These equations form the basis for Einstein's special theory of relativity.



Jagadish Chandra Bose was one of the pioneers of modern science in India. His research was on the properties of electro-magnetic waves. His major achievement was to demonstrate the similarity of responses to stimulation among the living and the nonliving as well as thefundamental similarity of responses in plant and animal tissues.

Bose believed that by focusing on the boundaries between different physical and biological sciences, he would be able to demonstrate the underlying unity of all things. Bose's biological researches were founded initially by the discovery that an electric receiver seems to show science of fatigue after continued use. He can rightly be called the inventor of wireless telegraphy. Bose was the first in the world to fabricate and demonstrate in public (1895) the device that generated microwaves-radio waves of very short wave length. But his invention was not patented before Guglielmo Marconi (1896) who became internationally recognised as the inventor.

http://www.webindia123.com/personal/scientist/bose.htm

An appreciation of J.C. Bose's pioneering work in millimeter wavesSarkar, T.K.; Sengupta, D.L.; IEEE Antennas and Propagation Magazine, IEEEVol 39, Oct. 1997 pp 55 - 62

27


Electrostatic Fields• Produced by static charge distribution

• Common example: Cathode Ray Tube (CRT)

• Other examples

– Electric power transmission, X-ray machines, lightning protection

– Components and active devices in solid state electronics

– Touchpads, LCDs, printers…

– Electrodeposition, electrochemical machining,

– Vacuum tubes

– ECG, EEG, ..


Electrostatic Fields• Produced by static charge distribution

• Common example: Cathode Ray Tube (CRT)

• Other examples

– Electric power transmission, X-ray machines, lightning protection

– Components and active devices in solid state electronics

– Touchpads, LCDs, printers…

– Electrodeposition, electrochemical machining,

– Vacuum tubes

– ECG, EEG, ..

28


Coulomb’s Law• Based experimental studies

• Formulated by Charles Augustin de Coulomb in 1785

• Deals with the force a point charge exerts on another point charge

– Point charge means the dimensions of the body are infinitesimal

– Units for measuring charge is Coulomb

– 1 Coulomb is equivalent to approximately 6x1018 electrons (i.e., electron charge e=-1.6019x10-19C)

• Coulomb’s law states that the force between two point charges Q1 and Q2is

– Along the line joining them

– Directly proportional to the product Q1Q2 of the charges

– Inversely proportional to the square of the distance between them

221

rQQkF=


Coulomb’s Law• Mathematical representation of Coulomb’s Law

where

As the radius increases, the force is ‘spread’ over the surface of the sphere

ε0 is permittivity of free space =8.854x10-12F/m

• To include directions:

• When more than one charge is present, we use the principle of superposition to find the net force

– Can be used to calculate the electric field at a point

– In special (symmetrical) situations Gauss’ law may be easier to apply

221

rQQkF =

041πε

=k

1220

21

4 RRQQ aF12 πε

=

Q1 Q2

Q1 Q2

Q1

Q0

Q3

Q2

29


Electric Field Intensity• aka Electric field Strength, E

• This is the force per unit charge when placed in the electric field

• Direction of E is along F• Units Newtons/Coulomb or Volts/meter

• When multiple point charges are present, the net electric field is the vector sum of individual contributions

• In many practical problems, charges may be considered distributed continuously along a line, surface, or volume. The total charge is obtained by integration.

QFE =

Q1

Q0

Q3

Q2

330

303

03

20

202

03

10

101

00

)(4

1)(4

1)(4

1rr

rrrr

rrrr

rrE−

−+

−

−+

−

−=

QQQπεπεπε


Distributed charge--Line• Line charge distribution

– Recall earlier discussion was about point charges

– When distributed over a line, we should talk of its density

– Typically, ρ is used in charge distribution

• Being a linear distribution; ρL is used [Coulomb/meter]• ρL =constant for uniform distribution• In general, ρL can be a mathematical function

• Examples of Line charge distribution

Uniform charge distribution

Let the linear density be ρL.

Elemental charge is

Net charge

dldQ Lρ=

y

x

z z=a

z=b

dz

dlQb

az L

L L

∫∫

==

=

ρ

ρ

Similarly one can think of charge distributions over a surface or a volume. surface charge density ρs [C/m2]volume charge density ρv [C/m3]

The net charge in these cases may be obtained by integrating over the surface area or the volume, as the case may be.

As an example, for a surface distribution in the xy plane, we use dS=dxdyIn the Cartesian coordinate system

BTW, in the cylindrical coordinate system, the equivalent isdS = ρdφ dρ

30


Review of Coordinate Systems• The convention used to define a location in some space.

– Defined by an origin and a number of unit vectors.

– These unit vectors are usually orthogonal and span the entire space.

• This is a system for assigning an n-tuple of numbers or scalars to each point in an n-dimensional space.

– "Scalars", depending on context, can mean real numbers, complex numbers or elements of some other commutative ring.

• Examples of coordinate systems

– The Cartesian coordinate system (also called the "rectangular coordinate system"), which, for three-dimensional flat space, uses three numbers representing distances.

– The polar coordinate systems: • Circular coordinate system (commonly referred to as the polar coordinate system)

represents a point in the plane by an angle and a distance from the origin. • Cylindrical coordinate system represents a point in space by an angle, a distance from the

origin and a height. • Spherical coordinate system represents a point in space with two angles and a distance

from the origin. http://en.wikipedia.org/wiki/Coordinate_systems


Example for 2-Dimensional Space

P1

P2

P3

P4

P2

P3

P4

P1

Cartesian coordinate System (Rectangular) Polar coordinate System

Coordinates:P1: (2.6,6.6)P2: (-5.6,2.3)P3: (-3.6,-3.6)P4: (4,-7)

Coordinates:P1: (7,67.5°)P2: (6,157.5°)P3: (5,225°)P4: (8,300°)

Usual notation: (x, y)Space: (-∝<x< ∝, -∝<y< ∝)

Usual notation: (ρ,φ)Space: (0≤ ρ < ∝, 0 ≤ φ <360°)

31


Coordinate Transformations• Polar to Rectangular

– x =ρ cosφ; y = ρ sinφ

• Rectangular to Polar

– ρ = sqrt(x2+y2); φ = tan-1(y/x)

– Signs of x and y may be considered toextend to all quadrants

• Without much effort now we can extend these to Cartesian and Cylindrical coordinate systems for 3D space

– z-coordinate has the same meaning in both

Rectangular:P1: (2.6,6.6)P2: (-5.6,2.3)P3: (-3.6,-3.6)P4: (4,-7)

Polar :P1: (7,67.5°)P2: (6,157.5°)P3: (5,225°)P4: (8,300°)

Rectangular:P1: (2.7,6.5)P2: (-5.5,2.3)P3: (-3.5,-3.5)P4: (4,-6.9)

Polar :P1: (7.1,68.4°)P2: (6,157.7°)P3: (5.1,225°)P4: (8,300°)

Cartesian System notation: (x, y, z)Space: (-∝<x< ∝, -∝<y< ∝, -∝<z< ∝)

Cylindrical System notation: (ρ,φ, z)Space: (0≤ ρ < ∝, 0 ≤ φ <360°, -∝<z< ∝)


Cylindrical Coordinate System

P (x,y,z)=P(ρ,φ,z)

x

y

z

φ ρy=ρ sinφ

x=ρ cosφ

z

When do you use cylindrical systems?Several problems can have a line symmetry. For example radiations from a wire (heat, EM, etc.) In such cases we orient the coordinate system such that z-axis coincides with the wire.The magnitude radiated energy is independent of φ and z. Hence the problem is easier to solve in the cylindrical system. This explains why we kept the line charge distribution along z-axis!

If you assume for a moment that the line charge is distributed along the entire z axis, the force on a charge or electric field (E) at P would be radial.

How do we resolve this (force/field) in terms of rectangular system? So, to understand the components of the E field at P due to such a charge distribution, we should know how unit vectors along coordinate directions get transformed

32


Transformation of Vectors• Since the z-axis has the same

meaning, the unit vector along z is the same for both systems

−=

z

y

x

z AAA

AAA

1000cossin0sincos

φφφφ

φ

ρ

φ x

y

aφ

aρφ

φ

aρ = ax cosφ+ ay sinφaφ = (-)ax sinφ+ ay cosφ

We can therefore use the following matrix approach for transformation of vectors

−=

zz

y

x

AAA

AAA

φ

ρφφφφ

1000cossin0sincos

Or, conversely,


Spherical coordinate System• Useful in problems having three dimensional symmetry; e.g., radiations from a

point source.

• Note that, for a point charge at the origin, the force acting on another such charge on the surface of a sphere (anywhere) is radial

• In such problems spherical coordinate system would be the most useful

araφaθ

y

z

x

θ

φ

Coordinate of a point: (r, θ, φ)Space: (0≤ r < ∝, 0 ≤ θ <180°, 0 ≤ φ <360°)

−−−=

−

−=

===

=+

=++= −−

z

y

xr

r

z

y

x

AAA

AAA

AAA

AAA

rxryrxxy

zyx

zyxr

0cossinsinsincoscoscos

cossinsincossin

0sincoscossincossinsinsincoscoscossin

cossinsincossin

tantan 122

1222

φφθφθφθθφθφθ

θθφφθφθφφθφθ

θφθφθ

φθ

φ

θ

φ

θ

33


Constant Coordinate SurfacesCartesian

• x=constant

• Y=constant

• z=constant

y

z

x

Cylindrical

• ρ=constant

• φ=constant

• z=constant


Differential elements for Vector Calculus• In Cartesian coordinate System

– Differential displacement

d l = dx ax + dy ay + dz az

– Differential normal area

d S = dydz axdxdz aydxdy az

– Differential volume

dv = dxdydz

• In Cylindrical coordinate System

– Differential displacement

d l = dρ aρ + ρdφ aφ + dz az

– Differential normal area

d S = ρdφ dz aρdρ dz aφρdρ dφ az

– Differential volume

dv = ρdρdφdz

34


Distributed charge--Line• Line charge distribution

– Recall earlier discussion was about point charges

– When distributed over a line, we should talk of its density

– Typically, ρ is used in charge distribution

• Being a linear distribution; ρL is used [Coulomb/meter]• ρL =constant for uniform distribution• In general, ρL can be a mathematical function

• Examples of Line charge distribution

Uniform charge distribution

Let the linear density be ρL.

Elemental charge is

Net charge

dldQ Lρ=

y

x

z z=a

z=b

dz

dlQb

az L

L L

∫∫

==

=

ρ

ρ

Similarly one can think of charge distributions over a surface or a volume. surface charge density ρs [C/m2]volume charge density ρv [C/m3]

The net charge in these cases may be obtained by integrating over the surface area or the volume, as the case may be.

As an example, for a surface distribution in the xy plane, we use dS=dxdyIn the Cartesian coordinate system

BTW, in the cylindrical coordinate system, the equivalent isdS = ρdφ dρ


Due to a point charge located at the origin

Electric Potential• We have already used the Coulomb’s law to determine the force on a charge and hence the

Electric field intensity

• This can also be used to determine the Work done in displacing a charge from point A to B

• To move this by a small elemental distance d l is

dW = -F.d l = -Q E.d l

• Total work done

• Potential difference between points A and B is

• Solving

VA and VB are potentials at A and B

If we start from infinity, V is the potential of a point

∫ ⋅−=B

AdQW lE

∫ ⋅−==B

AAB dQWV lE

RrQ aE 2

04πε=

rQV

VVrr

Q

drr

QV

AB

AB

rr

B

AAB

0

0

20

4

114

4

πε

πε

πε

=

−=

−=

⋅−= ∫ aa

Note that

∫∞ ⋅−=r

dV lE

35


Electric Flux Density• For practical reasons, the electric field intensity depends on the medium.

• A new quantity is defined which is independent of the medium:

D = ε0 E

• Electric flux is defined in terms of D:

Ψ = ∫D.d S

• One line of electric flux emanate from +1C and terminate at -1C

• D is called Electric Flux Density

• aka Electric DisplacementR

v

Rdv aD ∫= 24π

ρ


Gauss’ Law• Total electric flux through any closed surface is equal to the total charge

enclosed by that surface

– One of the fundamental laws of Electromagnetics

– One of Maxwell Equations

– Gauss’ Law is an alternative statement of Coulomb’s law

– Provides easy approach to finding E and D for symmetric charge distributions

• Also, recalling

for a closed path,

∫∫∫∫∫

=⋅∴

=

⋅==

=

dvd

dvQ

dd

Q

enc

enc

v

v:RHS

:LHS

ρ

ρ

ψψ

ψ

SD

SD

∫∫=⋅

⋅=∞

0lE

lE

d

dV r

Maxwell Equation for Static EM fields

Maxwell Equation

36


Magnetostatics• Magnetic field is produced by a current, which is a flow of charges.

• Fundamental law: Biot-Savart’s law

– Magnetic field intensity dH produced at a point P by a differential current element Idl is proportional to the product Idl and the sine of the angle between the element and the line joining P to the element and is inversely proportional to the square of the distance R between P and the element.

– In terms of distributed current sources,

– Using vector notation:

– For distributed current sources such as line current

surface current

volume current

2

2

4

4sin

RIdd

RIdldH

R

π

πα

alH

×=

=

∫

∫

∫

×=

×=

×=

v

R

S

R

L

R

Rdv

RdS

RId

2

2

2

4

4

4

π

π

π

aJH

aKH

alH


Analogies in Magnetic Field Quantities

• Ampere’s circuital Law

– The line integral of the tangential component of H around a closed path is equal to the net current enclosed by the path.

– Note that the statement is similar to the Gauss’ Law in Electrostatics

• Magnetic Flux Density

– B = µH

• Magnetic flux

• An isolated magnetic charge does not exist

• Therefore,

∫∫ ⋅==⋅Senc dId SJlH

SB dS

⋅= ∫ψ

0=⋅∫ SB d

Maxwell Equation for Static EM fields

Maxwell Equation

Similar to Gauss’ Law

Similar LHSfor E field

37


Maxwell EquationsFor static fields For time varying fields

Gauss’ Law

No magnetic monopole

Faraday’s Law

Ampere’s Law (modified)

• Maxwell equations summarizes all known laws of electromagnetism, including transient behaviors

– Faraday’s law to incorporate the electromotive induction

– Ampere’s law to incorporate displacement currents (e.g., during the charging of a capacitor)

• Focus on the physical principles rather than the mathematical expressions per se.

∫∫∫∫

∫∫

=

=

=

=

SL

L

s

v vs

dd

d

d

dvd

SJlH

lE

SB

SD

..

0.

0.

. ρ

∫∫

∫∫

∫∫∫

∂∂

+=

∂∂

−=

=

=

SL

SL

s

v vs

dt

d

dt

d

d

dvd

SDJlH

SBlE

SB

SD

..

..

0.

. ρ


Physical Interpretations of MEs• Gauss’ Law

– The net electric flux out of closed surface is equal to the total charge enclosed within the volume

• Magnetic analogy

– The net magnetic flux out of closed surface is zero, as there are no isolated magnetic monopoles.

• Faraday’s Law

– The electromotive force (emf) induced on a closed loop of conductor is equal to the negative of the time derivative of the magnetic flux through the area enclosed by the loop

• This equation relates the electric and magnetic fields. • This equation e.g. describes how electric motors and electric generators work.

• Ampere’s Law

– The magnetomotive force (mmf) in a closed path is equal to the total of conduction current and displacement current through the area enclosed by this.

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq.html#c1

38


• Constitutive relations for a generalized medium are given by

Where

D: Electric displacement densityE: Electric field strengthB: Magnetic flux densityH: Magnetic field strengthr: Position vector of a point in the mediumω: angular frequency=2πft: time instant

• For linear, homogeneous isotropic dielectric materials:

• Similarly, for homogeneous linear magnetic materials:

( )t,= ω, ,, rHEDD ( )t ,,, , ωrHEBB =

Constitutive Relations in EM

( )rEJJ ,=

( )HHHMHHB mm χµχµµµµ +=+=+== 10000

( )EEEPEED ee χεχεεεε +=+=+== 10000

P : Dielectric polarizationM : Magnetic polarizationχe : Electric susceptibility χm: Magnetic susceptibilityε0 : Permittivity of free space

=8.854x10-12 F/mµ0 : Permeability of free space

=4πx10-7 H/m

radio frequency integrated circuits and systems - …kjvinoy/rfics/set1.pdf · pl. report any...

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