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.

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