Lecture 1 Units and dimensions Six fundamental International System of Units DimensionsUnitsymbol Lengthmeterm Masskilogramkg Timeseconds Electric CurrentAmpereA TemperatureKelvinK Amount of substance molemol any other dimension can be derived from the fundamental dimensions, e.g.:

Lecture 1 Electromagnetic spectrum

Lecture 1 Electromagnetic bands and applications

Lecture 2 Electric field Electric forces on point charges, Columb’s law

Lecture 2 Magnetic field by constant current r I B = 2r2r II    =  r  0,  r: relative magnetic permeability  r =1 for most materials = 2r2r I   H =  B

Lecture 3 Traveling wave y(x,t) = Acos(2  t/T-2  x/ ),  (x,t) = 2  t/T-2  x/, y(x,t) = Acos  (x,t),

Lecture 3 Traveling wave y(x,t) = Acos(2  t/T+2  x/ ), Velocity = 0.6 /0.6T = /T Vp = dx/dt = - /T Phase velocity:

Lecture 3 Phasor V R (t) Vs(t)V C (t) i (t) Vs(t) = V 0 Sin(  t+  0 ), V R (t) = i(t)R, V C (t) = i(t)dt/C, Vs(t) = V R (t) +V C (t), V 0 Sin(  t+  0 ) = i(t)dt/C + i(t)R,Integral equation, Using phasor to solve integral and differential equations

Lecture 3 Phasor Z(t) = Re( Z e jtjt ) Z is time independent function of Z(t), i.e. phasor Vs(t) = V 0 Sin(  t+  0 ) ) j(  0 -  /2) = Re(V 0 e jtjt e jtjt e = Re(V), V = V 0 e j(  0 -  /2),

Lecture 3 Phasor i(t) = Re( I e jtjt ) ), = Re(I jtjt e i(t)dt = Re( I e jtjt )dt jj 1 V 0 Sin(  t+  0 ) = i(t)dt/C + i(t)R, time domain equation: phasor domain equation: jj jj TimePhasor V R (t) Vs(t)V C (t) i (t) V + I R, = I jCjC 1

Lecture 3 Phasor domain Back to time domain: V + I R, = I jCjC 1 I = V R + 1/(j  C) = V 0 e j(  0 -  /2), i(t) = Re( I e jtjt ) = Re ( jtjt ) R + 1/(j  C) V 0 e j(  0 -  /2) e V R (t) Vs(t)V C (t) i (t) V 0 Sin(  t+  0 ) = i(t)dt/C + i(t)R,

Lecture 3 An Example : V L (t) Vs(t) = V 0 Sin(  t+  0 ), V R (t) = i(t)R, V L (t) = Ldi(t)/dt, Vs(t) = V R (t) +V L (t), V 0 Sin(  t+  0 ) = Ldi(t)/dt + i(t)R,differential equation, Using phasor to solve the differential equation. V R (t) Vs(t) i (t)

Lecture 3 Phasor i(t) = Re( I e jtjt ) ),= Re(I jtjt e di(t)/dt = Re(d I e jtjt )/dt jj V 0 Sin(  t+  0 ) = Ldi(t)/dt + i(t)R, time domain equation: phasor domain equation: jtjt e Re(V) Re( I e jtjt ), )L + = Re(I jtjt e jj

Lecture 3 Phasor domain Back to time domain: V + I R, = I jLjL I = V R + (j  L) = R + j  L) V 0 e j(  0 -  /2), i(t) = Re( I e jtjt ) = Re ( jtjt ) R + (j  L) V 0 e j(  0 -  /2) e

Lecture 3 Steps of transferring integral or differential equations to linear equations using phasor. 1.Express time-dependent variables as phsaor. 2.Rewrite integral or differential equations in phasor domain. 3.Solve phasor domain equations 4.Change phasors variable to their time domain value

Lecture 3 Waves in phasor domain Recall waves, traveling wave in time domain In phasor domain + x direction - x direction

Lecture 3 A question Answer: a traveling wave in phasor domain What’s this? Complex amplitude

Lecture 3 Electromagnetic spectrum. Recall relation: f = v. Some important wavelength ranges: 1.Fiber optical communication: = 1.3 – 1.5  m. 2.Free space communication: ~ 700nm – 980nm. 3.TV broadcasting and cellular phone: 300MHz – 3GHz. 4.Radar and remote sensing: 30GHz – 300GHz