Wye-Delta Transformation
One of the most confusing factors in circuit analysis is the resistors. Instances are often introduced in circuit analysis when you find a hard time in determining if the resistors are connected in series or parallel.
- Fig. 2.1
As you can see, there's a bridge circuit in Fig 2.1. How are you going to combine
R1 through R6 when the resistors are neither in series nor parallel?
This problem can be simplified by using three-terminal equivalent networks. These are the wye(Y) or tee(T) network shown in Figure 2.2 and the delta(∆) or pi (Π) shown in Figure 2.3. These networks occur by themselves as part of a larger network.
Figure 2.2
(a) Y , (b) T
Figure 2.3
(a) ∆ , (b) Π
Our main goal here is how to identify them when they occur as part of the network and how to apply wye-delta transformation or vice-versa to analyze the given network.
DELTA to WYE TRANSFORMATION
If a circuit contains a delta (∆,Π) configuration, it is more convenient to work with wye network. In short, transform it to Wye(Y) to find its equivalent resistance.In layman’s term, so that you can easily remember Delta to Wye conversion, the word “Wye” always implies a number just like in algebra. And the resistor values are given already labeled as, Ra, Rb, Rc . Therefore, since you are to transform it to wye, the equivalent to be looked for is R1, R2, R3 .
In this case, let n be the number of resistor to be looked for as you transform delta to wye network.
The formula will be Rn= the value of the resistors on the two adjacent sides
Summation of all the resistors given
It does not follow a direction or a pattern. What you have to remember is our layman’s general formula for this conversion since we have noticed that it is only applicable for delta to wye conversion.
Example:
Use Figures 2.2 and 2.3.
Transformation looks like this.
WYE to DELTA TRANSFORMATION
If a circuit contains a Y (Y, T) configuration, it is more convenient to work with delta network. In short, transform it to Delta (∆) network to find its equivalent resistance.
In layman’s term, so that you can easily remember Wye to Delta conversion, the word “Delta” gives you clue that the resistor to be solve is letters namely Ra, Rb, Rc . And the resistor values are given already labeled as, R1, R2, R3 . This is opposite from the first conversion method(Delta to Wye).
Therefore, since you are to transform it to delta, the equivalent to be looked for is Ra, Rb, Rc .
In this case, let n be the letter of resistor to be looked for as you transform wye to delta network.
The formula will be Rn= the summation of the products of two resistors in order
the opposite given Y resistor
The numerator in the formula gives you a pattern where the products of (R1 xR2), (R2 xR3), and (R3 xR1) are summed up. What you have to remember is our layman’s general formula for this conversion since we have noticed that it is applicable for wye to delta conversion.
OR
Rn= (R1 xR2)+(R2 xR3)+(R3 xR1)
Ropposite of Rn
LEARNING/SUMMARY
- That in making the transformation, you do not take anything out of the circuit or put anything new. You are merely substituting different but mathematically equivalent three-terminal network patterns to create a circuit in which resistors are either in series or in parallel, allowing you to calculate Req if necessary.
- We, the bloggers, we also had and even having a hard time in transforming a complicated circuit since there is a lot of elements involved. So, as we advice, in redrawing circuits, observe first and choose the proper transformation as we have provided figures above as you guide.
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