Transcript Document

EE188L EE I Laboratory
Lab #4
KVL, KCL and Nodal
Analysis
Lab #3 Overview


First Week
•
•
•
Simulation using MultiSim (see Multisim.ppt)
Wye-Delta calculations
Activity #2 – Build circuit
• Measure voltages, calculate currents
• Verify KVL (through step 10 of Activity #2)
Second Week
•
Activity #2 – Build same circuit
•
•
Activity #3 – Modify circuit using Delta-Wye
Nodal Analysis Calculations
• Verify KCL
• Change source voltage
Multisim Window
Wye-Delta Transformation
c
R1
c
a
a
Ra
Rc
R3
R2
Delta or D
Rb
Wye or Y
b
b
Y to Δ
Equations
Ra Rb  Rb Rc  Ra Rc
R1 
Rb
R R  Rb Rc  Ra Rc
R2  a b
Rc
R R  Rb Rc  Ra Rc
R3  a b
Ra
Δ
Ra 
to Y
R1 R2
R1  R2  R3
R2 R3
Rb 
R1  R2  R3
R1 R3
Rc 
R1  R2  R3
Kirchhoff’s Voltage Law, KVL
1
R1
2.2 k
+ VR1
3V
R2
3.7 k
2
-
-
R3
1.0 k
VR3
+
- VR2
3
+
-
VR4
R4
5.4 k
+
0
Loop (0, 1, 2, 0)
V0,1 + V1,2 + V2,0 = 0 V
-3 V + VR1 - VR3 = 0 V
Loop (0, 3, 2, 0)
V0,3 + V3,2 + V2,0 = 0 V
VR4 + VR2 - VR3 = 0 V
For example:
V1,2 = - V2,1 = VR1
Nodal Analysis 1
entering
leaving
A current is entering the node if the current is leaving the device.
A current is leaving the node if the current is entering the device.
Nodal Analysis 2
1
R1
1.5 k
2
Apply Ohm’s Law (I = V/R) for R1:
current entering node 2 = (V1 - V2) / R1
current leaving node 2 = (V2 - V1) / R1
Kirchhoff’s Current Law, KCL
1
R1
2.2 k
R2
3.7 k
2
IR1
3V
IR2
R3
1.0 k
3
IR2
IR3
Shade indicates a node
IR4
R4
5.4 k
0
KCL at node 2:
Ientering  Ileaving
I R1  I R3  I R2
V1  V2 V0  V2 V2  V3


2.2 k
1.0 k
3.7 k
At node 1, V1=3 v. due to source
At node 0, V0=0 v. due to ground
KCL at node 3:
V2  V3 V3  V0

3.7 k
5.4 k
Nodal Analysis
1
R1
2.2 k
R2
3.7 k
2
IR1
3V
IR2
R3
1.0 k
IR3
3
IR2
Shade indicates a node
IR4
R4
5.4 k
0
Substitute the known voltages into the equations that were obtained at nodes 2 & 3
Solve the two equations for V2 and V3
You can put the two equations in matrix form and solve using Matlab or any
mathematics program (or your calculator).