1. *** Answers ECE473 Problems ***
  2. ********* Spring 2003 **********
  3. Prob. 9.1: 0.4738sin(377t) V
  4. Prob. 9.2: (wBl**2)/2 Note: I've used B for the magnitude of the magnetic field to avoid confusion.
  5. Prob. 9.3: 0.2sin(10000t) A, counterclockwise
  6. Prob. 9.21: 3e-04(z**2)cos(1e04t) C/m**3
  7. Prob. 9.22: a. Jd=20sin(1e09t-4y)ax A/m**2, D=-2e-08cos(1e09t-4y)ax C/m**2, b. 1.44
  8. Prob. 9.32: a. Es=4exp(-j(3x+10deg))ay + exp(j(3x+110deg))az, b. Hs=(1/r)sin(theta)exp(-j5r)atheta, c. Js=6exp(-3x)exp(-j(2x+90deg))ay + 10exp(-x)exp(-j5x)az
  9. Prob. 9.33: a. A=5cos(wt-betax-36.87deg)ay, b. B=(20/rho)cos(wt-2z)az, c. C=(10/r**2)(2.236)sin(theta)cos(wt-phi+63.43deg)aphi
  10. Prob. 9.34: As = -j4 ax + 3 ay, B = 10zcos(wt-z+90deg) ax
  11. Prob. 10.1: a. +x direction, b. u=1.047e06 m/s, lambda=1.047 m, T=1e-06 s, c. Be careful with sketch as it is inverted, i.e. carefully solve for function at t=0.
  12. Prob. 10.3: a. 5.41 + j6.13 1/m, b. 1.025 m, c. 5.125e+07 m/s, d. 101.41ang(41.43deg) ohms, -0.05917exp(-(5.41+j6.13)x)exp(-j41.43deg) ay A/m
  13. Prob. 10.4: a. 1820, b. 1.0125 S/m, c. 1.771e-11 - j3.223e-08 F/m, d. 9.999 Np/m, e. 13.96ang(44.98deg) ohms
  14. Prob. 10.8: a. 20 ns, b. 2.9945 m, c. sigma=1.059e-03 S/m and eta=187.94ang(2.718deg) Ohms so E=2.255exp(-0.1y)sin(3.1416e08t-2.098y+2.72deg) az kV/m
  15. Prob. 10.11: a. -x direction, b. 7.162e-10 F/m, c. E = 1.047sin(2e08t +6x) az V/m
  16. Prob. 10.20: sigma = 1.8765e-04 S/m so delta = 56.72 m and u = 1.495e08 m/s
  17. Prob. 10.22: a. 2.29 ohms, b. 207.9 ohms, c. 12131 Hz
  18. Prob. 10.32: a. E1=-1512sin(wt-5x)az + 506.2sin(wt+5x)az V/m, b. 2685ax W/m**2, c. 2.01 or 6.05 dB
  19. Prob. 10.33: 2.607e-05 H/m
  20. Prob. 11.1: G=0, R=0.0354 ohm/m, L=50.265 nH/m, C=221.4 pF/m
  21. Prob. 11.2: C=0.2346 pF, delta=2.09e-05 m, R=0.014 ohms
  22. Prob. 11.5: a. Zo=29.586-j21.428=36.531ang(-35.91deg) ohms, u=6.823e+07 m/s, b. z=5.04 m
  23. Prob. 11.6: a. gamma=0.2898+j3.2779 1/m, u=2.30e08 m/s, Zo=69.0 ohms, b. 5.554 m, c. 0.2396 m
  24. Prob. 11.12: Zo=71.71ang(39.76deg) ohms and td=178.3 ns
  25. Prob. 11.14: gammaL=0.25294ang(29.57deg), s=1.677
  26. Prob. 11.20: a. Zin=j29.374 ohms and Vo=5.75ang(102deg) V, b. Zin=j40ohms, VL=7.249ang(102deg) V, c. V=13.067ang(102deg) V, d. V=3.796ang(-78deg) V
  27. Prob. 11.21: a. 46.875 ohms, b. 77.419ang(-90deg) Vrms
  28. Prob. 11.24: Zin=29.64ang(-43.15deg) ohms and GammaL=0.469ang(51.33deg)
  29. Prob. 11.27: a. j300 ohms, b. 14.2ang(11.68deg) ohms
  30. Prob. 11.40: la=0.085Lambda, da=0.128Lambda and lb=0.265Lambda, db=0.372Lambda
  31. Prob. 11.44: f=750 MHz and ZL=130-j60 ohms
  32. Prob. 13.1: H=(50*Beta/Mu*r)sin(wt-Beta*r)(sin(Phi)atheta+cos(Theta)cos(Phi)aphi) A/m and E= (-(50*Beta*Nu/Mu*r)sin(wt-Beta*r)(cos(Theta)cos(Phi)atheta-sin(Phi)aphi) V/m
  33. Prob. 13.2: 0.1257 V/m
  34. Prob. 13.3: Hs=j2.5e-04aphi A/m and Es=j9.425e-02atheta V/m
  35. Prob. 13.5: Rrad=1.974 ohms
  36. Prob. 13.6: Gamma=0.3713ang(42.52deg) and s=2.181
  37. Prob. 13.11: a. 9.07 mA, b. 0.25 mW
  38. Prob. 13.14: 0.2222 W
  39. Prob. 13.16: Pave = ((1.5(sin(theta)**2)/(4(pi)r**2))Prad, i.e. given formula is correct
  40. Prob. 13.17: Gd = 8sin(theta)cos(phi), b. D = 8
  41. Prob. 13.18: f(theta)=(cos(pi*cos(theta))+1)/sin(theta), i.e. given formula is correct; sketch looks like a bow tie!
  42. Prob. 13.25: Es=(j*eta*beta*Io*dl/(2pi*r))sin(theta)cos((beta*d/2)*cos(theta))exp(-j*beta*r)atheta
  43. Prob. 13.30: a. AF=ABS(cos(pi*cos(theta)))*SQRT(1+cos(pi*cos(theta)))/SQRT(2), b. AF=ABS(cos(pi*(cos(theta)+1)/2))*SQRT(1+cos(pi*(cos(theta)+1)/2))/SQRT(2)
  44. Prob. 13.34: 38.95 nW
  45. Prob. 13.35: 21.29 pW
  46. Prob. 13.37: 79.5 or 19 dB
  47. Prob. 13.38: 7.12 mW
  48. Prob. 13.41: 77.52 W