Circuits Lecture 3: Mesh Analysis 李宏毅 Hung-yi Lee
Introduction Node analysis: Mesh analysis: Current + Voltage Voltage Potential Current + Voltage CurrentMesh Current Mesh: closed current path that contains no closed paths within it (Textbook, P149) Meshes are “holes” in the circuits. Mesh 1 Mesh 2 Mesh 3
Mesh analysis Target of Mesh analysis is to find the mesh currents.
Mesh analysis Consider KCL: Represent i b, i c and i d by mesh current KCL is already fulfilled
Mesh analysis Consider KVL: Represent v a, v b and v c by mesh current
For mesh 1: R a (i 1 -i s ) + R b i 1 + R c (i 1 -i 2 ) =v s Mesh analysis For mesh 3: R e (i 3 -i 2 ) + R f i 3 + v s = 0 For mesh 2: R c (i 2 -i 1 ) + R d i 2 + R e (i 2 -i 3 ) = 0 Can we always represent voltage by mesh currents?
Mesh analysis – 3 cases Represent the voltage of (1) voltage sources, (2) resistor, and (3) current sources by mesh current
Mesh analysis - current sources 1. Current sources on the perimeter of the circuit
Mesh analysis - current sources 2. Interior current sources Method 1: Consider v s as unknown variables …… Represent the voltages v d, v b, v c and v e …. (except v s ) by mesh current Solve mesh currents and v s One more equation:
Mesh analysis - current sources 2. Interior current sources Method 2: Textbook: Chapter 2.5 when the current source is parallel with a resistor
Mesh analysis - current sources 2. Interior current sources Method 2: Another point of view: when the current source is parallel with a resistor The voltage of is i s equal to R s.
2. Interior current sources Mesh analysis - current sources Method 3: supermesh
What is the final target? Node analysis is not suitable for current Mesh analysis is not suitable for voltage i If node analysis is used, it is tedious to find i If mesh analysis is used, it is tedious to find v v + -
Node v.s. Mesh Number of Equation: Number of Nodes v.s. Number of Meshes Number of Voltage sources v.s. Number of Current sources Use both to check your results