Download Lecture 7: Circuit Analysis - Equivalent Circuits and Source Transformations and more Slides Microelectronic Circuits in PDF only on Docsity! 1 Lecture 7, Slide 1EECS40, Fall 2003 Prof. King Lecture #7 OUTLINE • Node-Voltage Method (cont’d) – circuits with dependent sources • Source Transformations • Mesh-Current circuit analysis – method – circuit with a current source Reading Chapter 4.3-4.9 Lecture 7, Slide 2EECS40, Fall 2003 Prof. King Equivalent Circuit Concept • A network of voltage sources, current sources, and resistors can be replaced by an equivalent circuit which has identical terminal properties (I-V characteristics) without affecting the operation of the rest of the circuit. + vA _ network A of sources and resistors iA ≡ + vB _ network B of sources and resistors iB iA(vA) = iB(vB) 2 Lecture 7, Slide 3EECS40, Fall 2003 Prof. King • Voltage sources in series can be replaced by an equivalent voltage source: • Current sources in parallel can be replaced by an equivalent current source: Source Combinations i1 i2 ≡ i1+i2 – + – + v1 v2 ≡ – + v1+v2 Lecture 7, Slide 4EECS40, Fall 2003 Prof. King Circuit Analysis Approaches • The Node-Voltage method can always be used to solve a circuit, but techniques for simplifying circuits (using “equivalent circuits”) are useful: – series and parallel combination reductions – ∆-Y and Y-∆ conversions – source transformations – Thevenin and Norton equivalent circuits (to be covered in Lecture 8) 5 Lecture 7, Slide 9EECS40, Fall 2003 Prof. King Derivation of Relationship between vs and is L s L RR vi + = RLR iL is + vL – a b – + RL iL+ vL – vs R s L L iRR Ri + = ss Riv = a b Lecture 7, Slide 10EECS40, Fall 2003 Prof. King Source Transformation Example • Find Io – + 60 V 6 Ω – + 15 V 3 Ω 3 ΩIo 6 Lecture 7, Slide 11EECS40, Fall 2003 Prof. King NODAL ANALYSIS (“Node-Voltage Method”) 0) Choose a reference node 1) Define unknown node voltages 2) Apply KCL to each unknown node, expressing current in terms of the node voltages => N equations for N unknown node voltages 3) Solve for node voltages => determine branch currents MESH* ANALYSIS (“Mesh-Current Method”) 1) Select M mesh currents such that at least one mesh current passes through each branch M = #branches - #nodes + 1 2) Apply KVL to each mesh, expressing voltages in terms of mesh currents => M equations for M unknown mesh currents 3) Solve for mesh currents => determine node voltages Formal Circuit Analysis Methods *A mesh is a loop that does not enclose any other loops. A mesh current is not necessarily identified with a branch current. Lecture 7, Slide 12EECS40, Fall 2003 Prof. King 1. Select M mesh currents. 2. Apply KVL to each mesh. 3. Solve for mesh currents. Mesh Analysis: Example #1 7 Lecture 7, Slide 13EECS40, Fall 2003 Prof. King Problem: We cannot write KVL for meshes a and b because there is no way to express the voltage drop across the current source in terms of the mesh currents. Solution: Define a “supermesh” – a mesh which avoids the branch containing the current source. Apply KVL for this supermesh. Mesh Analysis with a Current Source ia ib Lecture 7, Slide 14EECS40, Fall 2003 Prof. King Eq’n 1: KVL for supermesh Eq’n 2: Constraint due to current source: Mesh Analysis: Example #2 ia ib
