Basic Electrical Engineering

1
Basic Electrical Engineering

• Lecture 10
• Course Instructor
• Engr. Sana Ziafat

2
Agenda

• Planner vs Non planner circuits
• Node analysis

3
Branches and Nodes
Branch elements connected end-to-end, nothing
coming off in between (in series) Node plac
e where elements are joinedincludes entire wire
4
Nodal Analysis

• Kirchhoffs current law is used to develop the
  method referred to as nodal analysis
• A node is defined as a junction of two or more
  branches
• Application of nodal analysis
• Determine the number of nodes within the network.
• Pick a reference node, and label each remaining
  node with a subscript value of voltage V1, V2,
  and so on.

5
Nodal Analysis

1. Apply Kirchhoffs current law at each node except
   the reference. Assume that all unknown currents
   leave the node for each application of
   Kirchhoffs current law. In other words, for
   each node, dont be influenced by the direction
   that an unknown current for another node may have
   had. Each node is to be treated as a separate
   entity, independent of the application of
   Kirchhoffs current law to the other nodes.
2. Solve the resulting equation for the nodal
   voltages.

6
Nodal Analysis

• On occasion there will be independent voltage
  sources in the network to which nodal analysis is
  to be applied. If so, convert the voltage source
  to a current source (if a series resistor is
  present) and proceed as before or use the
  supernode approach
• Assign a nodal voltage to each independent node
  of the network.
• Mentally replace independent voltage sources with
  short-circuits.
• Apply KCL to the defined nodes of the network.
• Relate the defined nodes to the independent
  voltage source of the network, and solve for the
  nodal voltages.

7
Nodal Analysis

1. Choose a reference node and assign a subscripted
   voltage label to the (N 1) remaining nodes of
   the network.
2. The number of equations required for a complete
   solution is equal to the number of subscripted
   voltages (N 1). Column 1 of each equation is
   formed by summing the conductances tied to the
   node of interest and multiplying the result by
   that subscripted nodal voltage.

8
Nodal Analysis(Format Approach)

1. We must now consider the mutual terms that are
   always subtracted form the first column. It is
   possible to have more than one mutual term if the
   nodal voltage of current interest has an element
   in common with more than one nodal voltage. Each
   mutual term is the product of the mutual
   conductance and the other nodal voltage tied to
   that conductance.

9
Nodal Analysis(Format Approach)

1. The column to the right of the equality sign is
   the algebraic sum of the current sources tied to
   the node of interest. A current source is
   assigned a positive sign if it supplies current
   to a node and a negative sign if it draws current
   from the node.
2. Solve the resulting simultaneous equations for
   the desired voltages.

10
Node Voltages

• The voltage drop from node X to a reference node
  (ground) is called the node voltage Vx.
• Example

11
Nodal Analysis Method

• 1. Choose a reference node ( ground, node 0)
• (look for the one with the most connections,
• or at the bottom of the circuit diagram)
• 2. Define unknown node voltages (those not
  connected to ground by voltage sources).
• 3. Write KCL equation at each unknown node.
• How? Each current involved in the KCL equation
  will either come from a current source (giving
  you the current value) or through a device like a
  resistor.
• If the current comes through a device, relate the
  current to the node voltages using I-V
  relationship (like Ohms law).
• 4. Solve the set of equations (N linear KCL
  equations for N unknown node voltages).

12
Example
What if we used different ref node?
node voltage set ?
Va
R1

IS
V1
R
-
2
? reference node

• Choose a reference node.
• Define the node voltages (except reference node
  and the one set by the voltage source).
• Apply KCL at the nodes with unknown voltage.
• Solve for Va and Vb in terms of circuit
  parameters.

13
Example
R
1
Va
R
5
R
I
3
1
V
V
R
R
2
1
2
4
14
Q A