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Transcript
Circuits Lecture 3: Mesh Analysis 李宏毅 Hung-yi Lee Mesh 1 Introduction Mesh 2 Mesh 3 • Node analysis: Current + Voltage Voltage Potential Current Mesh Current • Mesh analysis: Current + Voltage Mesh: closed current path that contains no closed paths within it (Textbook, P149) Meshes are “holes” in the circuits. Mesh analysis i1 i2 i2 i3 i1 i3 Target of Mesh analysis is to find the mesh currents. Mesh analysis Consider KCL: ib ic id 0 Represent ib, ic and id by mesh current ib i1 ic i2 i1 id i2 KCL is already fulfilled Mesh analysis Consider KVL: va vb vc vs Represent va, vb and vc by mesh current va Ra i1 is vb Rbi1 vc Rc i1 i2 Mesh analysis For mesh 1: Ra(i1-is) + Rbi1 + Rc(i1-i2) =vs For mesh 2: Rc(i2-i1) + Rdi2 + Re(i2-i3) = 0 For mesh 3: Re(i3-i2) + Rfi3 + vs = 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 vs as unknown variables vs vd vb vs 0 vc ve vs …… is Represent the voltages vd, vb, vc and ve …. (except vs) by mesh current Solve mesh currents and vs One more equation: is i2 i1 Mesh analysis - current sources • 2. Interior current sources Method 2: when the current source is parallel with a resistor Textbook: Chapter 2.5 Mesh analysis - current sources • 2. Interior current sources Method 2: when the current source is parallel with a resistor Another point of view: The voltage of is is equal to Rs. vs Rs im ix Mesh analysis - current sources • 2. Interior current sources Method 3: supermesh Rd i1 i3 Rb i1 i3 vs Rc i2 i3 Rc is i1 i3 is Rei2 Re is i1 is i2 i1 i2 is i1 Example 4.9 10i1 6i1 5 3i1 4 6(i1-5) + 10i1 + 3(i1+4) = 20 →i1=2A Exercise 4.11 Special case: current sources are parallel with resistors Exercise 4.11 i1 3mA 6k i1 2mA i1 5k i1 5k i1 3m 4k i1 2m 6k 0 Non-planar Circuit • Mesh analysis cannot be applied on non-planar circuit Cannot transform this circuit into planar circuit Non-planar Circuit • Some non-planar circuits can be transformed into planar circuit B A C A C B Non-planar Circuit • Some non-planar circuits can be transformed into planar circuit Non-planar Circuit • Why mesh analysis cannot be applied on nonplanar circuit? 6 meshes? 5 meshes Node v.s. Mesh Node v.s. Mesh • What is the final target? • Node analysis is not suitable for current • Mesh analysis is not suitable for voltage i v + If node analysis is used, it is tedious to find i - If mesh analysis is used, it is tedious to find 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 Homework • 4.38 • 4.42 Thank you! Answer • 4.38 • V1=24, v2=-16, v3=20 • 4.42 • I1=3, i2=3.5, i3=3, v1=0, v2=15 Acknowledgement • 感謝 林楷恩 (b02) • 糾正錯誤的作業答案