B B 1 1 Prof CK Tse Graph Theory Systematic Analysis 18 Relationship between Q

B b 1 1 prof ck tse graph theory systematic analysis

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B = [ B 1 | 1 ]
Prof. C.K. Tse: Graph Theory & Systematic Analysis 18 Relationship between Q and B It is always true that Q 1 = – B 1 T or B 1 = – Q 1 T B = [ B 1 | 1 ] Q = [ 1 | Q 1 ] Thus, once we have Q , we know B , and vice versa.
Prof. C.K. Tse: Graph Theory & Systematic Analysis 19 Applications The basic cutset and loop matrices will be used to formulate independent Kirchhoff’s law equations. This will give much more efficient solution to circuit analysis problems. Mesh —enhanced— General loop analysis Nodal —enhanced— General cutset analysis
Prof. C.K. Tse: Graph Theory & Systematic Analysis 20 Recall: mesh analysis Mesh analysis — good for circuits without current sources Problem occurs when circuits have a current source: WASTE OF EFFORT! WHY? The unknowns are actually partially known!
Prof. C.K. Tse: Graph Theory & Systematic Analysis 21 Redundancy in mesh analysis USUAL MESH ANALYSIS: Obviously if we define the unknowns according to the usual mesh-analysis. We have 2 equations with 2 unknowns. This is UNNECESSARY because the current source actually gives the current values indirectly! I 1 I 2 = 1 A. CLEVER METHOD: We define unknowns such that the 1A source is exactly one of the unknowns. Then, we save an equation! So, we have 1 equation with 1 unknown.
Prof. C.K. Tse: Graph Theory & Systematic Analysis 22 Another example CLEVER METHOD: We define unknowns such that the 1A source and 2A source are exactly the unknowns. Then, we save two equations! So, we have 0 equation with 0 unknown. Usual mesh assignment:
Prof. C.K. Tse: Graph Theory & Systematic Analysis 23 Question How to make the clever method a general method suitable for all cases?
Prof. C.K. Tse: Graph Theory & Systematic Analysis 24 Redundancy in nodal analysis USUAL NODAL ANALYSIS: Obviously if we define the unknowns according to the usual nodal analysis, V 1 , V 2 and V 3 we have 3 equations with 3 unknowns. This is UNNECESSARY because the voltage source actually gives the voltage values indirectly! V 1 V 2 = 2 V. CLEVER METHOD: We define unknowns such that the 2V source is exactly one of the unknowns. Then, we save an equation! Here, we use branch voltages. So, we have 2 (cutset) equations with 2 unknowns. + V 1 + V 2 + V 1 + V 2 + V 3 + V 3
Prof. C.K. Tse: Graph Theory & Systematic Analysis 25 Another example USUAL NODAL ANALYSIS: CLEVER METHOD: We define unknowns such that the sources overlap with unknown branches. Then, we save three equations! Here, we use branch voltages. So, we have 0 equation with 0 unknown. + V 1 + V 2 + V 1 + V 2 + V 3 + V 3
Prof. C.K. Tse: Graph Theory & Systematic Analysis 26 Same question How to make the clever method a general method suitable for all cases?
Prof. C.K. Tse: Graph Theory & Systematic Analysis 27 Key to systematic methods Graph theory •Tree / basic cutset KCL equations •Co-tree / basic loop KVL equations The first step is define an appropriate tree! Hint: where should we put all the voltage sources?
Prof. C.K. Tse: Graph Theory & Systematic Analysis 28 Standard tree Take branches into the tree according to the following priority: All voltage-source branches All resistor branches that do not close a path The remaining all go to the co-tree.

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• Summer '16
• Martin Chow
• Graph Theory, Mesh Analysis, branch, Voltage source, Voltage drop, Systematic Analysis

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