equationsforfinalexam

equationsforfinalexam - e j = cos + j sin , E (t ) = Re [...

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Unformatted text preview: e j = cos + j sin , E (t ) = Re [ Es e jt ] Es = - j H s H s = j Es + J s Ds = V , s Bs = 0 2 E s + Es = 0 2 2 = 2 Es = ax ( Ae- j z + Be j z ) Ae - j z - j z For Es = ax ( Ae ), H s = a y = u= , in free space, = o = 120 () o 1 1 = = = 3 108 m/s , in free space, u = o o u 2 = f = = 2 - 1 , 2 + 1 T= 22 2 + 1 E 1+ SWR = = max 1- E min Differential Elements Cartesian coordinates Cylindrical coordinates Spherical coordinates 41. Intrinsic impedance of free space 0 = 0 120 377 0 D. Transmission lines 42. Characteristic impedance Z0 = 43. Propagation constant = + j = 44. Phase velocity v= (R + jL) (G + jC) (general) = 0 + j LC (lossless) R + jL G + jC (general) Z0 = L C (lossless) (general) v= 1 1 = LC (lossless) 45. Voltage expression on a line for a wave propagating in the z direction V (z) = V0+ e-jz + V0- ejz 46. Current expression on a line for a wave propagating in the z direction I(z) = 47. Reflection coefficient from load ZL L = ZL - Z0 ZL + Z0 V0+ -jz V0- jz e - e Z0 Z0 48. Voltage standing wave ratio on a line with reflection coefficient L SW R = |Vmax | 1 + |L | = |Vmin | 1 - |L | 49. Input impedance of a transmission line seen at a distance l from a load ZL Z(l) = Z0 ZL + jZ0 tan(l) Z0 + jZL tan(l) ...
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