EE201 Lecture 34 P 1 SSS cont A sinusoidal function x t Acos t can be represented as x t Re Aej t Re Aej t ej For constant and known angular frequency Phasor of x t X X Aej A Note The ej t term of Anej tej is contained in all terms of the differential equation that describes the behavior of any first or second order circuit Therefore ej t can be cancelled from all terms but it is understood the frequency remains unchanged Summation of Phasors x2 t A2cos t 2 x1 t A1cos t 1 X1 A1 1 X2 A2 2 x1 t x2 t X1 X2 EE201 Lecture 34 P 2 Example KCL to find current I3 I3 I2 10 60o I1 10 60o Im I1 10 60o Re I3 I1 I2 10 I3 10 0o I2 10 60o EE201 Lecture 34 P 3 Multiplication of complex numbers z a jb c jd ac bd j ad bc Multiplication of Phasors X X1 j x X2 j X1 1 X2 2 X X1X2 1 2 Example I Y j V 2 5 10o 3 26o I 7 5 36o A Division of complex numbers z a jb c jd a jb c jd c jd c jd ac bd j bc ad c2 d2 Division of Phasors X X1 j X2 j X1 1 X2 2 X1 X X2 1 2 EE201 Lecture 34 P 4 Conversion rectangular to polar coordinates z x jy x2 y2 ejtan 1 y x Example Find the SSS response for i1 and i2 10 0 5 H 100 cos 100 t V 10 F 1000 Step 1 find equivalent impedance Zeq Zeq j R10 j L Z C R ZL j j50 YC j j C j0 00314 S Zeq j 10 j50 0 001 j0 00314 1 Zeq j 165 53 6o EE201 Lecture 34 P 5 Step 2 calculate input current I from Zeq Vs 100 0 0 6 52 3 A I Zeq 167 52 3 Step 3 use current division to find I1 and I2 I1 YC Yeq I 0 00314 90 0 0033 73 1 I 0 95 16 9 I I1 0 95 16 9 0 6 52 3 0 57 69 2 A i1 t 0 57 cos t A I2 YR Yeq I 0 001 0 0 0033 73 1 I 0 30 73 1 I I2 0 30 73 1 0 6 52 3 0 18 20 8 A i2 t 0 18 cos t A
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