04-Circuit Analysis Nodal 2 Supernodes

04-Circuit Analysis Nodal 2 Supernodes - Nodal Analysis II...

Info iconThis preview shows pages 1–15. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Nodal Analysis II: Voltage Sources and Super-Nodes © Fred Terry Fall, 2008
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 Two Cases • Voltage Source Between Reference/Ground and 2 nd Node • Voltage Source Between 2 Non-Reference Nodes – Supernode
Background image of page 2
3 Nodal Analysis Example: Voltage Source to Ground • Find all the node voltages in the circuit at left • Label the Non-trivial nodes • Write KCL equations at each labeled node • Solve the resulting system of linear equations 4 Ω 8 Ω 2 Ω 4 Ω 3V 2i x i x + -
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 Label Nodes &Write KCL Equations •V 1 =3V – NO KCL EQUATION FOR THIS NODE – WHY???? 4 Ω 8 Ω 2 Ω 4 Ω 3V 2i x i x V 1 V 2 V 3 + -
Background image of page 4
5 KCL Equations for Other 2 Nodes 4 Ω 8 Ω 2 Ω 4 Ω 3V 2i x i x V 1 =3V V 2 V 3 + -
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
6 KCL Equations for Other 2 Nodes 4 Ω 8 Ω 2 Ω 4 Ω 3V 2i x i x V 1 =3V V 2 V 3 + -
Background image of page 6
7 KCL Equations for Other 2 Nodes 4 Ω 8 Ω 2 Ω 4 Ω 3V 2i x i x V 1 =3V V 2 V 3 + - 23 1 111 1 1 1.5 248 8 2 VV V A ⎡⎤ ++ + = = ⎢⎥ ΩΩΩ Ω Ω ⎣⎦ KCL: Node 2 KCL: Node 3 1 12 2 11 1 1 20 . 7 5 88 4 4 1.5 22 2.25 81 8 4 x x i V A V iA combining A + = = ΩΩ Ω Ω == −− + = Ω Ω
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
8 Collect Equations and Solve • 2 Nodal Equations with the 2 NODE VOLTAGES AS THE ONLY UNKNOWNS •A n s w e r s : –V 2 = +1.5V 3 = -1.5V ( ) ( ) ( ) ( ) 11 23 0.875 0.125 1.5 1.125 0.0.375 2.25 VV A A −− Ω+ −Ω= −Ω+ + Ω=
Background image of page 8
9 Check 4 Ω 8 Ω 2 Ω 4 Ω 3V 2i x =1.5A i x=0.75A V 1 =3V V 2= 1.5V 3 =-1.5V + - 1.125A 0.375A 0.375A
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
10 Extension: Equivalent Circuit Modeling • Model the Circuit “seen” at nodes a&b • V-I Characteristics 4 Ω 8 Ω 2 Ω 4 Ω 2i x i x V 2 V 3 a b
Background image of page 10
11 4 Ω 8 Ω 2 Ω 4 Ω 2i x i x V 2 V 3 a b
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
12 4 Ω 8 Ω 2 Ω 4 Ω 2i x i x V 2 V 3 a b V 1 = V T +- V T I T 23 1 111 1 1 1 248 8 2 2 T VV V V ⎡⎤ ++ + = = ⎢⎥ ΩΩΩ Ω Ω Ω ⎣⎦ KCL: Node 2 KCL: Node 3 1 12 2 11 1 1 1 2 88 4 4 4 22 3 81 8 4 4 xT T x T i V V i combining V ⎤⎡ + = = ⎥⎢ Ω ΩΩ Ω Ω ⎦⎣ −− == + = Ω Ω Ω
Background image of page 12
13 4 Ω 8 Ω 2 Ω 4 Ω 2i x i x V 2 V 3 a b V 1 = V T +- V T I T () 11 2 3 2 3 3 2 e 7/8 1/8 1/2 9/8 3/8 3/4 0.5 0.5 0.5 0.5 24 2 4 2.5 5 48 8 R1 . 6 5 T T TT T T T TTT T q T V V V V V V VV V V I IV V V I −− ΩΩ ⎡⎤ = ⎢⎥ ⎣⎦ = ⎛⎞ =+= + ⎜⎟ Ω Ω ⎝⎠ == Ω = Ω ±²²³ ² ² ´± ²³²´ Looks Like A Linear Resistor!
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
14 Variation: Change One Resistor 4 Ω 8 Ω 2 Ω 6 Ω 3V 2i x i x V 1 =3V V 2 V 3 + - 23 1 111 1 1 1.5 28 8 2 6 VV V A ⎡⎤ ++ + = = ⎢⎥ ΩΩ Ω Ω ⎣⎦ Ω KCL: Node 2 KCL: Node 3 1 12 2 11 1 1 20 . 7 5 88 4 4 1.5 22 2.25 81 8 4 x x i
Background image of page 14
Image of page 15
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/31/2011 for the course EECS 215 taught by Professor Phillips during the Spring '08 term at University of Michigan.

Page1 / 32

04-Circuit Analysis Nodal 2 Supernodes - Nodal Analysis II...

This preview shows document pages 1 - 15. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online