3-Lesson_Notes_Lecture_21

# 3-Lesson_Notes_Lecture_21 - Series and Parallel Connections...

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EE 204 Lecture 21 Series and Parallel Connections and Phase Relations in Sinusoidal Circuits Series and Parallel Impedance: For the series impedances 1 Z , 2 Z , … n Z 12 .... eq n Z ZZ Z = +++ eq Z n Z 2 Z 1 Z Figure 1 For the parallel impedances 1 Z , 2 Z , … n Z 11 1 1 .... eq n Z Z =++ + eq Z n Z 1 Z 2 Z Figure 2 Series and Parallel Admittance: For the series admittances 1 Y , 2 Y , … n Y 1 1 .... eq n YY Y Y = eq Y 1 Y 2 Y n Y Figure 3

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For the parallel admittances 1 Y , 2 Y , … n Y 12 .... eq n YY Y Y = +++ eq Y n Y 2 Y 1 Y Figure 4 Example 1: Calculate the impedance to the right of “a-b” at the angular frequency 1000[ / ] rad s ω = 0.5mF 4 3mH 3 0.25mF a b Figure 5 Solution: Calculate the impedance of each element: 4 4 3 3 0.25 mF 3 1 4 1000 (0.25 10 ) jj j jC C ωω −− == = ×× 0.5 mF 3 2 1000 (0.5 10 ) j C 3 mH 33 10 (3 10 ) 3 jL j j × = Ω
eq Z 3 10 [ / ] ω = rad s Figure 6 4 j −Ω & 3 j (in series) 1 43 Z jj j = −+ = 32 j Ω− Ω 2 3 ( 2) 6 6 90 1.664 90 33.690 1.664 56.310 3 ( 2) 3 2 3.606 33.690 o oo o o Z ×− == = = + = +− eq Z 1 j Z = 2 1.66 56.31 o Z = ∠− Figure 7 1 Z j =− Ω & 2 1.664 56.310 o Z =− (in series) 312 ( ) (1.664 56.310 ) o ZZ Z j =+= −+ 3 ( ) (0.923 1.385) 0.923 2.385 Zj j j =− + = eq Z 3 0.923 2.385 = Figure 8 3 4 Z 3 3 4 4 (0.923 2.385) 4 (2.557 68.843 ) 10.228 68.843 4 4 (0.923 2.385) 4.923 2.385 5.470 25.848 eq o Z j Z j × = = ++− 1.870 68.843 25.848 1.870 42.995 1.368 1.275 o eq +

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eq Z 1.368 1.275 j Figure 9 Resistance, Reactance, Conductance, Susceptance: In general, the impedance Z is complex, it can be written as: Z Rj X =+ Where: R = resistance (the real pat of Z ) X = reactance (imaginary part of Z ) ZR jX Figure 10 Also, the admittance Y is complex in general: YGj B Where: G = conductance (the real pat of Y ) B
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## This note was uploaded on 01/16/2010 for the course EE ee204 taught by Professor Profosama during the Spring '09 term at King Fahd University of Petroleum & Minerals.

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3-Lesson_Notes_Lecture_21 - Series and Parallel Connections...

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