Exercise 2: Delta and Wye Transformations

Transcription

1 Exercise 2: Delta and Wye Transformations EXERCISE OBJECTIVE When you have completed this exercise, you will be able to convert between delta and wye circuits. You will verify your results by comparing calculated and measured values. DISCUSSION To determine the value of a resistor in a delta network, divide the sum of all cross products in the wye network with the value of the resistor that is opposite to the unknown resistor. A formula is used to calculate each resistor in the equivalent delta network. For example, the following formula yields the 1 resistance. (Y1 Y2) + (Y2 Y3) + (Y3 Y1) VALUE OF 1 = Y3 The numerator, or cross products of the Y network, does not change. Festo Didactic P0 253

2 The denominator, or opposite Y resistor, is the value of the Y network resistor that is opposite to the delta resistor you wish to determine. 2 and 3 are adjacent to Y3. To determine the unknown value in a wye network, divide the product of the two adjacent resistors in the delta network by the sum of the delta network resistors. A formula is used to calculate each resistor in the equivalent wye network. For example, the following formula yields the Y3 resistance. 2 3 VALUE OF Y3 = Festo Didactic P0

3 The denominator, or sum of the delta resistors, does not change. The numerator is the product of the delta network resistors that are adjacent to the Y resistor you wish to determine. PROCEDURE Locate the DELTA TO WYE or WYE TO DELTA circuit block. Do not insert a two-post connector into the PI NETWORK. Measure the individual resistances of the Y NETWORK. YR1 = (Recall Value 1) YR2 = (Recall Value 2) YR3 = (Recall Value 3) Festo Didactic P0 255

4 Use your measured wye resistor values to calculate the values required for an equivalent delta network. YR1 = (Step 2, Recall Value 1) YR2 = (Step 2, Recall Value 2) YR3 = (Step 2, Recall Value 3) (YR1 YR2) + (YR1 YR3) + (YR2 YR3) DRB = YR2 DRB = (Recall Value 4) DRA = (Recall Value 5) DRC = (Recall Value 6) Measure the individual resistors on the PI NETWORK, and compare your readings to the calculated delta values. 256 Festo Didactic P0

5 Do your measured values and calculated values agree within tolerance? a. yes b. no Use your ohmmeter to compare the terminal resistances between the Y NETWORK and the NETWORK. Is the delta network equivalent to the wye network? a. yes b. no Based on your Y to conversion results, can you convert a delta network into an equivalent Y network? a. yes b. no CONCLUSION You can convert a wye network into an equivalent delta network. You can convert a delta network into an equivalent wye network. Converted networks do not have the same individual resistive values as the original network, but they possess identical network terminal resistances. Festo Didactic P0 257

6 REVIEW QUESTIONS 1. In a delta network to wye network conversion, the denominator of the conversion formula is the a. sum of the products of all resistors. b. difference of the products of all resistors. c. sum of all resistors. d. None of the above 2. In a delta network to wye network conversion, the numerator of the conversion formula is the a. sum of two adjacent pairs. b. difference of two adjacent pairs. c. product of two adjacent pairs. d. sum of the products of two adjacent pairs. 258 Festo Didactic P0

7 3. Which formula can be used to convert one leg of a wye network into a delta value? a. (R1 R2) + (R2 R3) + (R3 R1) RC = R1 RA RB R1 = b. RA + RB + RC c. Either of the above d. None of the above 4. Simplifying a resistive bridge network requires a a. wye to delta conversion. b. wye to wye conversion. c. delta to delta conversion. d. delta to wye conversion. Festo Didactic P0 259

8 5. The circuits a. draw identical current from the voltage source. b. have identical component voltage drops. c. are not equivalent to each other. d. draw different current from the voltage source. 260 Festo Didactic P0