For any Linear Resistive Network there exists: Thevenin Equiv. Network Norton Equivalent Network V OC- open-circuit voltage appearing across the terminals of the network, and R TH- Thevenin equivalent resistance when all independent sources are deactivated. I SC – current through load when replacing load with a short circuit Equations Solve for R TH 1. Deactivate all ind. srcs (leave dep. srcs) 2. Remove the load R L *In circuits w. dependent sources, may need to apply a voltage or current source between A & B, then apply the definition R TH = V OC / I SC Finding V TH 1. Remove load R L AB to rest of network. a. Sources remain unchanged. b. Use methods such as superposition, mesh, nodal, V-Division, etc… Finding I SC 1. Replace load R L in original circuit with a short circuit. a. Sources remain unchanged. Coefficient Approach V-I Char. Of Thev: V AB = R TH I A + V OC V-I Char. Of Nort: I A = (1/R TH )V AB- I SC 1. Obtain an equation in one of the above forms allows us to match the coefficients of the above equations to determine R TH , V OC , I A , or G TH . Measured Data 1. Substitute the given data into V-I Char. Eqs: Thev: V AB = R TH I A + V OC or Nort: I A = (1/R TH )V AB- I SC 2. Put into matrix form 3. Solve for remaining variables. General Solving Procedures 1. Have ways to find V OC , I SC , R TH directly using above techniques 2. After solving for 2 of the 3, below are listed ways to solve for 3 rd
*Extra condition for constructing Thev and Nort equivalents for active networks – all controlling voltages or currents must be within the 2-terminal network whose Thev/Nort equiv are being sought. 1. Since there are no ind. internal srcs, the Thev equiv. consists of a single resistance, R TH (V OC = I SC = 0) 2. Write an equation(s) to relate the terms in the 2-terminal network via previous solving techniques (KCL, KVL, Mesh, Nodal, etc…) 3. If one equation, match coeficients with the V-I char. equations of a Thev. Or Nort. Equiv. network. 4. If set of equations, solve using matrix operations. Maximum Power Transfer Theorems, Requirements, Conditions, Assumptions, and Definitions 1. Always put circuit in Thevenin or Norton Equivalent form 2. Fixed R TH Equations
Always True Under M.P.T. Inductors
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