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Basic Experiment and Design of Electronics EQUIVALENT CIRCUITS Ho Kyung Kim, Ph.D. hokyung@pusan.ac.kr School of Mechanical Engineering Pusan National University Outline • Superposition theorem • Thévenin’s and Norton’s theorem • Maximum power transfer theorem • Wheatstone bridge 2 Superposition theorem • In any linear circuit containing multiple independent sources, the current or voltage at any point in the network may be calculated as the algebraic sum of the individual contributions of each source acting alone. v B1 v B 2 Ri 0 i v B1 v B 2 v B1 v B 2 i B1 i B 2 R R R – in order to set a voltage source equal to zero, replace it with a short circuit – in order to set a current source equal to zero, replace it with an open circuit Thévenin's theorem • When viewed from the load, any network composed of ideal voltage and current sources, and of linear resistors, may be represented by an equivalent circuit consisting of an ideal voltage source vT in series with an equivalent resistance RT. ① find the equivalent resistance presented by the circuit at its terminal ② compute the Thévenin voltage Norton's theorem • When viewed from the load, any network composed of ideal voltage and current sources, and of linear resistors, may be represented by an equivalent circuit consisting of an ideal current source iN in parallel with an equivalent resistance RN. ① find the equivalent resistance presented by the circuit at its terminal ② compute the Norton current Determination of equivalent resistance ① remove the load ② zero all independent voltage and current sources ③ compute the total resistance between load terminals Note that the computed resistance is equivalent to that which would be encountered by a current source connected to the circuit in place of the load. RT R1 || R2 R3 Computing the Thévenin voltage • The equivalent (Thévenin) source voltage is equal to the open-circuit voltage at the load terminals (with the load removed). ① ② ③ ④ remove the load, leaving the load terminals open-circuited define the open-circuit voltage vOC across the open load terminals solve for vOC Thévenin voltage, vT = vOC R1 vS R3 R2 +0V- + + vOC vOC - iL RL vOC v R 2 v S R2 R1 R2 R2 vT R1 R2 iL RT R L ( R1 || R2 ) R3 R L vS Computing the Norton current • The Norton equivalent current is equal to the short-circuit current that would flow if the load were replaced by a short circuit. ① ② ③ ④ replace the load with a short circuit define the short-circuit current iSC to be the Norton equivalent current solve for iSC Norton current, iN = iSC vS v v v R1 R2 R3 v vS R2 R3 R1 R3 R2 R3 R1 R2 i N i SC R2 v vS R3 R1 R3 R2 R3 R1 R2 Maximum power transfer theorem • The Thévenin and Norton models imply that some of the power generated by the source will necessarily be dissipated by the internal circuits within the source. Thévenin equivalent • Then, how much power can be transferred to the load from the source under the most ideal conditions? Power absorbed by the load, RL; PL i L2 RL Load current, iL; iL Then, we have; PL vT2 ( RT R L ) 2 RL Maximum PL can be obtained when PL 0 R L PL vT2 ( RT R L ) 2 2vT2 R L ( RT R L ) 0 R L ( RT R L ) 4 RL = RT vT RT R L Wheatstone bridge • • a resistive circuit widely used as measurement circuit The source voltage divides between each resistor pair according to the voltage divider rule; v ad v S R2 R1 R2 and vbd v S Rx R3 R x R2 Rx v ab v ad vbd v S R1 R2 R3 R x Self-assigned HW • Rizzoni (5th ed.), Ch. 3 – 51, 52, 53, 54, 56, 58, 59, 60, 73, 75 14

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