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ECE 3144 Lecture 8 Dr. Rose Q. Hu Electrical and Computer Engineering Department Mississippi State University 1 Reminder for Lecture 7 • Wye-Delta or Delta-Wye transformation a a Ra R1 R2 R3 c Rc b c Rb b R R Rb Rc Ra Rc R1 a b Rb Ra R1 R2 R1 R2 R3 R R Rb Rc Ra Rc R2 a b Rc Rb R2 R3 R1 R2 R3 R R Rb Rc Ra Rc R3 a b Ra Rc R1 R3 R1 R2 R3 • Circuits with dependent sources – treat the dependent source as though it were an independent source. – write the equations that specifies the relationship of the dependent2 source to the controlling Problem solving strategy: Delta-Wye transform (HW 2.73) 2 Io 3 9 9 2 6 12 36 V 4 Io 36 V 12 18 5 12 18 I 9 2 Io 3 2 I 36 V 9 3 2 2 6 4A 9 3 Io I 3A 9 3 2 2 36 V 6 3 Problem solving strategy: Delta-Wye transform • if possible, simplify the circuits first by using seriesparallel combination techniques • Repeat step 1 until no series or parallel combination existing in the network. • Re-draw the shape of the circuit to the one you are more familiar with if necessary • Identify the Delta shape components or Wye shape components in the simplified circuit. • Determine where and how to do Wye-Delta or Deltato-Wye transforms. • Perform Wye-to-Delta (or Delta-to-Wye) transformations so that the circuit seen is represented as a series-parallel interconnection of resistors. 4 It’s your turn: how to solve the problem? 6 k 6 k I HW 2.72: Given the network, find I 21 V 12 k 2 k 18 k •First if there are resistors in series or in parallel in the circuit network given? •If there are, how to do the simplification; •If there are not, do you feel comfortable or familiar with the shape of the circuit given? •If not, redraw the circuit network. •Identify the Delta-shape or the Wye-shape which you can do the transformations. 5 Problem solving strategy: Circuit with dependent sources (HW Problem 2.85 in the textbook: for the network shown, choose the values of and such that is maximized. What is the resulting ratio , Vo /Vs ? RS Ro + VS Rin Vin RS Rin VS Rin Vin _ + Vin RL Vo _ (voltage divider for resistors in series) R R R Vo L Vin in L VS Ro RL RS Rin Ro RL (voltage divider for resistors in series) Rin RL Vo VS R R R R in o L S 6 Problem solving strategy: HW 2.69 Io 1 k 4 k IS 10 k 2 k 12 V + + I2 I3 V2 - 1 k + I1 Io 4 k IS V3 _ 10 k 2 k V1 _ 12 V 7 Summary for Chapter 2 • • • • • • • • • • Resistor, Resistance, Resistivity Ohms’law V = I*R: only linear resistors satisfy Ohm’s law. Power P = V*I= V2/R = I2R Kirchoff’s current law (KCL): The algebraic sum of the currents leaving (entering) a node is zero. Kirchoff’s voltage law: The algebraic sum of the voltages around any loop path is zero. Single loop circuit: resistors in series and voltage divider Single node circuit: resistors in parallel and current divider Circuits containing a single source and a series-parallel interconnection of resistors Wye-delta or Delta-to-Wye transformations Circuits containing dependent sources 8 Exam 1: Feb 6 • Exam 1 covers Chapter 1 and Chapter 2. • Chapter 1: Basic concepts – Charge (q), current (i), and their relationship – Voltage (v), work/energy (w), power (p), and their relationships. – Passive sign convention • The positive reference of voltage v(t) is at the same terminal the the current variable i(t) is entering. • How to determine absorbing or supplying energy? – Active elements and passive elements – Active elements • Independent sources • Dependent sources. • Chapter 2: See slide 7 9 Homework for Lecture 8 • Problems 2.79,2.80, 2.81, 2.83, 2.87 10