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02_-_Kirchoff_laws

# 02_-_Kirchoff_laws - Kirchoffs Laws(Chapter 2 s s s s s s...

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Kirchoff’s laws EE 210 © Jeffrey Mayer 2003-2006, David Salvia 2006. All rights 1 Kirchoff’s Laws (Chapter 2) Kirchoff’s Voltage and Current Laws Single Loop and Single Node-pair Analysis Source and Resistor Combinations Delta-Wye Transformations Voltage and Current Division Practical Sources and Source Transformations

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Kirchoff’s laws EE 210 © Jeffrey Mayer 2003-2006, David Salvia 2006. All rights 2 Kirchoff’s Laws Kirchoff’s Laws: constraints on the currents and voltages associated with the circuit elements due to their interconnection in a particular circuit/network Along with i-v relationships of the specific circuit elements (e.g. Ohm’s law), Kirchoff’s Laws form the basis for circuit analysis Satisfying i-v relationships and Kirchoff’s laws simultaneously leads to a set of linear algebraic equations that can be solved to find all voltages and currents in a circuit Two methods for solving circuits: Ad hoc approach – applying various constraints in a non-structured wasy; often leads to an analysis that is more complicated than necessary Algorithmic approaches – organized methods of writing appropriate equations for solving a circuit
Kirchoff’s laws EE 210 © Jeffrey Mayer 2003-2006, David Salvia 2006. All rights 3 Kirchoff’s Voltage Law (KVL) The algebraic sum of voltage drops around a loop is zero. Alternate 1: the algebraic sum of the voltage rises around a loop is zero. Alternate 2: the sum of the voltage drops is equal to the sum of the voltage rises around a loop. 0 = + - b c a v v v 0 = - - - d b a v v v 0 = + c d v v + v a - C A B D + v c - - v b + + v d - Loop 1 Loop 2 Loop 3 Around Loop 1: Around Loop 2: Around Loop 3:

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Kirchoff’s laws EE 210 © Jeffrey Mayer 2003-2006, David Salvia 2006. All rights 4 Kirchoff’s Voltage Law (cont.) Three important implications: The parallel connection of voltage sources is not allowed: 0 V + - + - + - A voltage source supplying zero voltage is equivalent to a short circuit: Even if v 1 v 2 , and thus KVL is not violated, it is considered bad form to include both voltage sources in the schematic. v 1 v 2
Kirchoff’s laws EE 210 © Jeffrey Mayer 2003-2006, David Salvia 2006. All rights 5 Kirchoff’s Voltage Law (cont.) It is not possible to have a set of voltage sources be the only circuit elements in a loop. v a , v b , and v c cannot simultaneously be independent and satisfy the constraint equation arising from KVL. + - + - + - v a v b v c 0 = - - c b a v v v

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Kirchoff’s laws EE 210 © Jeffrey Mayer 2003-2006, David Salvia 2006. All rights 6 Kirchoff’s Current Law (KCL) The algebraic sum of the currents out of a node is zero. Alternate 1: the algebraic sum of the currents into a node is zero. Alternate 2: the sum of the currents out of a node is equal to the sum of the currents into the node.
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02_-_Kirchoff_laws - Kirchoffs Laws(Chapter 2 s s s s s s...

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