1. 16.360 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.:

2. 16.360 Lecture 1 Electromagnetic spectrum

3. 16.360 Lecture 1 Electromagnetic bands and applications

4. 16.360 Lecture 2 Electric field Electric forces on point charges, Columb’s law

5. 16.360 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

6. 16.360 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),

7. 16.360 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:

8. 16.360 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

9. 16.360 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),

10. 16.360 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

11. 16.360 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,

12. 16.360 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)

13. 16.360 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

14. 16.360 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

15. 16.360 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

16. 16.360 Lecture 3 Waves in phasor domain Recall waves, traveling wave in time domain In phasor domain + x direction - x direction

17. 16.360 Lecture 3 A question Answer: a traveling wave in phasor domain What’s this? Complex amplitude

18. 16.360 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