TAILIEUCHUNG - Lecture Electric circuits analysis - Lecture 21: Delta-to-wye (∆-TO-Y) and wye-to-delta (Y-TO-∆) conversions

In this chapter, the following content will be discussed: Deriving the initial equations, ∆-to-y conversion, application of ∆-to-y conversion to a bridge circuit, source conversions, the superposition theorem, Thevenin's theorem, Norton's theorem, maximum power transfer theorem. | Previous Lectures 16-20 Source Conversions The Superposition Theorem Thevenin's Theorem Norton's Theorem Maximum Power Transfer Theorem DELTA-TO-WYE (∆-TO-Y) AND WYE-TO-DELTA (Y-TO-∆) CONVERSIONS Conversions between delta-type and wye-type circuit arrangements are useful in certain specialized three-terminal applications. Lecture 21 Deriving the Initial Equations Solving For R1, R2, and R3 (4) (5) Solving for RA, RB, and RC (6) (7) You don't really need to know these derivations, although understanding them will help you with your understanding of electronics in general. However, you should know the conversion formulas themselves, and be able to apply them when designing or analyzing electronic circuits. From Equation (6) ∆-to-Y Conversion Each resistor in the wye is equal to the product of the resistors in two adjacent delta branches, divided by the sum of all three delta resistors. Y-to-∆ Conversion Each resistor in the delta is equal to the sum of all possible products of wye resistors taken two at a time, divided by the opposite wye resistor. Application of ∆-to-Y Conversion to a Bridge Circuit Convert each delta network to a wye network. R1=183 kΩ, R2=490 kΩ, R3=275 kΩ Convert each delta network to a wye network R1=373 mΩ R2= Ω, R3= mΩ Convert each wye network to a delta network. RA= Ω, RB= 73 Ω, RC= Ω Convert each wye network to a delta network. RA= kΩ, RB= kΩ, RC= kΩ Find all currents in the circuit of following Figure. RT= kΩ, IT= mA, IR1 = IRY1= mA, IR2 = IRY2 = mA, VB = VA − = V, VC= V, IR4 = mA, IR5 = mA, IR3= mA RT= kΩ, IT= mA, IR1 = IRY1= mA, IR2 = IRY2 = mA, VB= V, VC= V IR4 = mA, IR5 = mA, IR3= mA RT= kΩ, IT= mA, IR1 = IRY1= mA, IR2 = IRY2 = mA, VB= V, VC= V IR4 = mA, IR5 = mA, IR3= mA BRANCH, LOOP, AND NODE ANALYSES So for (In the previous lectures 16-20), you have learned about

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• Electric circuits analysis
• Lecture Electric circuits analysis
• Electrical engineering
• Parallel Circuits
• Series Circuits
• Circuit theorems
• Series parallel circuits