4_basic laws, theorems, and methods of network analysis(1)
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01JULY 5, 2011
TOPIC TITLE SY / TERM OF EFFECTIVITY PREPARED BY1Basic Laws, Theorems, and Methods of Network Analysis 3rd / 2013-2014 L. Valcos
Basic Laws, Theorems,and Methods of Network Analysis:Mesh Analysis andSuperposition Theorem
01JULY 5, 2011
Different Laws and Theorems in Network Analysis
1. Mesh Analysis2. Nodal Analysis3. Thevenin’s Theorem4. Norton’s Theorem5. Superposition Theorem6. Compensation Theorem7. Millman’s Theorem
Mesh Analysis
• Mesh analysis (sometimes referred to as loop analysis or meshcurrent method) is a method that is used to solve planar circuits forthe voltages and currents at any place in the circuit.
• Planar circuits are circuits that can be drawn on a plane withno wires overlapping each other.
• Mesh analysis uses Kirchhoff’s Voltage Law to solve these planarcircuits.
• The advantage of using mesh analysis is that it creates a systematicapproach to solving planar circuits and reduces the number ofequations needed to solve the circuit for all ofthe voltages and currents.
TOPIC TITLE SY / TERM OF EFFECTIVITY PREPARED BY2Basic Laws, Theorems, and Methods of Network Analysis 3rd / 2013-2014 L. Valcos
01JULY 5, 2011
For an N-mesh network,
V1 = R11I1 - R12I2 - ... - R1nInV2 = - R21I1 + R22I2 - ... - R2nIn
...
Vn = - Rn1I1 - Rn2I2 - ... _ RnnIn
where,
V1, V2, ... Vn = algebraic sum of all the voltagesources within a mesh
R11, R22, R33, ... Rnn = sum of all resistances within the meshR12, R2n, R3n, ... Rnn = mutual or common resistance between two
currentsNotes:
• In summing for the voltages, find the “voltage rise” (added terms) and “voltage drop” (subtracted term) inreference to the direction of the current.
Voltage rise, sign is (+)
Voltage drop, sign is (-)
• Assign current in only one direction.
• Normally, mutual terms have negative sign.
TOPIC TITLE SY / TERM OF EFFECTIVITY PREPARED BY3Basic Laws, Theorems, and Methods of Network Analysis 3rd / 2013-2014 L. Valcos
01JULY 5, 2011
Superposition Theorem
States that the total linear response of a linearsystem is given by the algebraic sum of allindividual responses created by each sourceacting “alone” in the network.
LINEARSYSTEM
+v0
-
Is
+-
v1
v2
+ -
1. Set Vo be the only source by removing Is, V1, and V2
determine the first term = _____
LINEARSYSTEM
+v0
-
Is
+-
v1
v2
+ -
2. Set V1 be the only source by removing Is, V0, and V2
determine the second term = _____
LINEARSYSTEM
+v0
-
Is
+-
v1
v2
+ -
3. Set V2 be the only source by removing Is, V0, and V1
determine the third term = _____
LINEARSYSTEM
+v0
-
Is
+-
v1
v2
+ -
4. Set Is be the only source by removing V2, V0, and V1
determine the fourth term, and so on = _____
LINEARSYSTEM
+v0
-
Is
+-
v1
v2
+ -
5. Get the sum of all the individual terms reading
TOPIC TITLE SY / TERM OF EFFECTIVITY PREPARED BY4Basic Laws, Theorems, and Methods of Network Analysis 3rd / 2013-2014 L. Valcos
01JULY 5, 2011
Thank You forlistening!
Let’s some more related sample Problem Solving and Preliminary Exam to follow...
TOPIC TITLE SY / TERM OF EFFECTIVITY PREPARED BY5Basic Laws, Theorems, and Methods of Network Analysis 3rd / 2013-2014 L. Valcos