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1 Source transformation An electrical source transformation is a method for simplifying circuits by replacing a voltage source with its equivilent current source , or a current source with its equivilent voltage source. Let’s take a simple voltage source along with a resistance connected in series with it. let us short circuit the output terminals of the voltage source circuit as shown below, Now 𝑽 = 𝑰 × 𝒓 ……………………….... Now, let’s take a current source of the same current I which produces same open-circuit voltage at its open terminals as shown below Northern Technical University Technical College / Mosul Computer Engineering Dep. Fundamentals of Electrical Eng. 1 st^ class Dr.Maysaloon Abed Qasim
. then 𝐈 = 𝐕 𝐫−^ ………………… 2 Now from eq1 and eq2 we get 𝒓 = 𝒓 − The open circuit voltage of both the sources is V and short circuit current of both sources is I. The same resistance connected in series in voltage source is connected in parallel in its equivalent current source. So, these voltage source and current source are equivalent to each other so a voltage source can be converted into an equivalent current source and a current source can also be converted into an equivalent voltage source. Voltage Source to Current Source Conversion
𝑣 = 2 𝐴 × 2 𝛺 = 4 𝑣𝑜𝑙𝑡
𝐼 = 4 ×
3 Ω 2 A 2 Ω 1 Ω 2 Ω 3 A 4v 4 Ω^1 Ω 3 Ω 2 Ω 1 Ω 3 Ω 2 Ω 4v 3 A 3 A 3 Ω 1 Ω 3 A 4 Ω 4A 3 Ω 1 Ω 4A 4 Ω I
Example Find equivalent resistance for the circuit shown in figure Solution Thus the circuit is reduced to that in the following figure
and subtracting Eq. (4) from Eq. (2) yields ……………………………………………………. Subtracting Eq. (4) from Eq. ( 1 ), we obtain ………………………………………………….. We do not need to memorize Eqs. (1) to (7). To transform a network to Y, we create an extra node n as shown in Fig. 3 and follow this conversion rule: Figure 3 Wye to Delta Conversion To obtain the conversion formulas for transforming a wye network to an equivalent delta network, we note from Eqs. ( 5 ) to ( 7 ) that
Dividing Eq. ( 8 ) by each of Eqs. ( 5 ) to ( 7 ) leads to the following equations: ……………………………………………………………………… ……………………………………………………………………… ……………………………………………………………………… From Eqs. (9) to (11) and Fig. 3, the conversion rule for (Y) to (Δ) is as follows: The Y and networks are said to be balanced when Under these conditions, conversion formulas become
then we can convert the connection to (Δ) Combining the three pairs of resistors in parallel, we obtain So that the equivalent circuit is shown in figure above. Hence, we find Rab we can also solve the problem starting with a delta-wye transformation. Let us transform the delta connection into a wye connection. let Rc =10Ω , Ra = 5 Ω , Rn = 12.5 Ω
This now leads to the circuit shown in the following figure
