DELTA – WYE TRANSFORMATION OF RESISTANCE NETWORK INTRODUCTORY INFORMATION: Situations open arise in circuit analysis when the resistors are neither in parallel nor in series. Many circuits of the type can be simplified by using three terminal equivalent networks. These networks are the Wye (Y) or Tee (T) (see figure 4.1 a) and the Delta (â) or Pi (π) (figure 4.1 b). These networks occur by themselves or as part of larger network. They are used in three-phase networks, electrical filters and matching networks. Figure 4.1 (a) Wye or Tee Network Figure 4.1 (b) Delta or Pi Network NETWORK CONVERSION DELTA TO WYE CONVERSION Figure 4.2 Suppose it is more convenient to work with a Wye network in a place were the circuit contains a delta configuration. To obtain the equivalent resistances in the Wye network, we compare the two networks and make sure that the resistance between each pair of nodes in the delta network is the same as the resistance between the same pair of nodes in the Wye network. To transform a Delta Network to Wye Network, consider figure 4.2, we create an extra node n and follow this: R1 = Rb Rc Ra + Rb + Rc R2 = Ra Rc Ra + Rb + Rc R3 = Ra Rb Ra + Rb + Rc Each resistor in the Wye Network or Tee Network is that product of the resistors in the two adjacent Delta branches, divided by the sum of the three Delta resistors. WYE TO DELTA CONVERSION Suppose it is more convenient to work with a Delta Network in a place where the circuit contains a Wye configuration. To obtain the equivalent resistances in the Delta Network, we compare the two networks and make sure that the resistance between each pair of nodes in the Wye network is the same pair of nodes in the Delta network. The conversion formulas for transforming a Wye network to an equivalent Delta network: Ra = R1 R2 + R2 R3 + R1 R3 R1 Rb = R1 R2 + R2 R3 + R1 R3 R2 Rc = R1 R2 + R2 R3 + R1 R3 R3 The conversion rule for wye to delta is each resistor in the Delta Network is the sum of all possible products of Wye resistors taken two at a time, divided by the opposite Wye resistor. The Wye and Delta Networks are said balanced when: R1 = R2 = R3 = RY or Ra = Rb = Rc = Rī . Under this condition, conversion formula become: Ry = Rī 3 Rī = Ry 3 MATERIALS REQUIRED: • • Multimeter Resistors: 3 pcs. 1000 Ω Delta Network 3 pcs. 3000 Ω Wye Network PROCEDURE: 1. Connect the circuit as shown in Fig. 4-a. (use 3 – 1000 ohms for that circuit. 2. Turn – ON the power supply 3. Measure the voltage drop across Va ,Vb ,Vc and the current I a , I b , I c . 4. Record the measured quantity on table 4.1. 5. Connect the circuit as shown in fig. 4-b. (use 3 -3000 ohms for that circuit) 6. Turn – ON the power supply 7. Measure the voltage drop across V1 ,V2 ,V3 and the current I1 , I 2 , I 3 . 8. Record the measured quantity on table 4.2 9. Compare the data recorded form table 4.1 and 4.2. 10. Formulate relationship between wye and delta network. SCHEMATIC DIAGRAM: Figure 4-a Figure 4-b TABLE 5.1 Delta Network Va Vb Vc Ia Ib Ic V1 V2 V3 I1 I2 I3 Measured Value Computed Value Percent Difference TABLE 5.2 Wye Network Measured Value Computed Value Percent Difference Note: Include the unit. 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_____________________________________________________________________________________________________ _____________________________________________________________________________________________________ QUESTIONS: 1. Transform the given circuit to its equivalent Wye circuit. 2. Transform the given circuit t its equivalent Delta circuit. 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