2-D Array of a Liquid Crystal Display 1. WAVES & PHASORS Applied EM by Ulaby, Michielssen and Ravaioli

Chapter 1 Overview Examples of EM Applications Dimensions and Units

Fundamental Forces of Nature Gravitational Force

Force exerted on mass 2 by mass 1 Gravitational field induced by mass 1 Charge: Electrical property of particles

Units: coulomb One coulomb: amount of charge accumulated in one second by a current of one ampere. 1 coulomb represents the charge on ~ 6.241 x 1018 electrons The coulomb is named for a French physicist, Charles-Augustin de

Coulomb (1736-1806), who was the first to measure accurately the forces exerted between electric charges. Charge of an electron e = 1.602 x 10-19 C

Charge conservation Cannot create or destroy charge, only transfer

Electrical Force Force exerted on charge 2 by charge 1 Electric Field In Free Space

Permittivity of free space Electric Field Inside Dielectric Medium Polarization of atoms changes electric field

New field can be accounted for by changing the permittivity Permittivity of the material

Another quantity used in EM is the electric flux density D: Magnetic Field Electric charges can be isolated, but magnetic poles

always exist in pairs. Magnetic field induced by a current in a long wire Magnetic permeability of free space Electric and magnetic fields

are connected through the speed of light: Static vs. Dynamic Static conditions: charges are stationary or moving, but if moving, they

do so at a constant velocity. Under static conditions, electric and magnetic fields are independent, but under dynamic conditions, they become coupled.

Material Properties Traveling Waves

Waves carry energy

Waves have velocity Many waves are linear: they do not affect the passage of other waves; they can pass right through them Transient waves: caused by sudden disturbance

Continuous periodic waves: repetitive source Types of Waves Sinusoidal Waves in Lossless Media

y = height of water surface x = distance Phase velocity If we select a fixed height y0 and

follow its progress, then = Wave Frequency and Period Direction of Wave Travel

Wave travelling in +x direction Wave travelling in x direction +x direction: if coefficients of t and x have opposite signs

x direction: if coefficients of t and x have same sign (both positive or both negative) Phase Lead & Lag Wave Travel in Lossy Media

Attenuation factor xample 1-1: Sound Wave in Water Given: sinusoidal sound wave traveling in

the positive x-direction in water Wave amplitude is 10 N/m2, and p(x, t) was observed to be at its maximum value at t = 0 and x = 0.25 m. Also f=1 kHz, up=1.5 km/s.

Determine: p(x,t) Solution: The EM Spectrum Tech Brief 1: LED Lighting

Incandescen ce is the emission of light from a

hot object due to its temperature Fluoresce means to emit radiation

in consequence to incident radiation of a shorter wavelength

When a voltage is applied in a forward-biased direction across an LED diode, current flows through the junction and some of the streaming electrons are captured by positive charges

(holes). Associated with each electron-hole recombining act is Tech Brief 1: LED Basics Tech Brief 1: Light Spectra

Tech Brief 1: LED Spectra Two ways to generate a broad spectrum, but the phosphorbased approach is less expensive to fabricate because it requires only one LED instead of three

Tech Brief 1: LED Lighting Cost Comparison Complex Numbers We will find it is useful to represent sinusoids as complex

numbers z x jy z z z e j Rectangular

coordinates Polar coordinates j 1 Re z x

Im( z ) y Relations based on Eulers e j cos j sin

Identity Relations for Complex Numbers Learn how to

perform these with your calculator/com puter Phasor Domain

1. The phasor-analysis technique transforms equations from the time domain to the phasor domain. 2. Integro-differential equations get converted into linear equations with no sinusoidal functions. 3. After solving for the desired variable--such as a

particular voltage or current-- in the phasor domain, conversion back to the time domain provides the same solution that would have been obtained had Phasor Domain

Phasor counterpart of Time and Phasor Domain It is much easier to deal with

exponentials in the phasor domain than sinusoidal relations in the time domain Just need to track

magnitude/phase, knowing that Phasor Relation for Resistors Current through resistor

Time Domain Frequency Domain Time domain i I m cos t

iR RI m cos t Phasor Domain V RI m Phasor Relation for Inductors

Time domain Phasor Domain Time Domain Phasor Relation for Capacitors

Time domain Time Domain Phasor Domain

ac Phasor Analysis: General Procedure Example 1-4: RL Circuit Cont.

Example 1-4: RL Circuit cont. Tech Brief 2: Photovoltaics Tech Brief 2: Structure of

PV Cell Tech Brief 2: PV Cell Layers Tech Brief 2: PV System

Summary