Source transformation is a technique used to simplify electrical circuits by converting sources of power from one type to another. This is particularly useful when working with series and parallel circuits. The fundamental idea behind source transformation is that any voltage source in series with a resistor can be converted into an equivalent current source in parallel with the same resistor, and vice versa. Source transformation is a fundamental technique in circuit analysis used to simplify complex electrical circuits. It involves converting a voltage source in series with a resistor into an equivalent current source in parallel with a resistor, or vice versa. This method significantly reduces circuit complexity, facilitating straightforward analysis.

This article focuses on the source transformation. We will discuss its basics, need, types, and advantages in detail. The information in this article helps you extensively in your SSC JE Electrical,  RRB JE, and GATE Electrical preparation journey

Why Source Transformation is used?

• Simplifies complex circuit networks for easier analysis.
• Facilitates easy application of other circuit analysis methods, such as node voltage or mesh current methods.
• Reduces the complexity of mixed-source circuits.

Types of Source Transformation

• Voltage Source to Current Source Conversion: A voltage source with a series resistor can be converted into a current source with a parallel resistor.
• Current Source to Voltage Source Conversion: A current source in parallel with a resistor can be converted into a voltage source in series with the same resistor.

Source Transformation refers to the process of replacing one type of source with an equivalent source. Specifically, a practical voltage source can be converted into an equivalent current source, and similarly, a practical current source can be transformed into an equivalent voltage source. This technique simplifies circuit analysis by allowing engineers to use whichever source configuration is more convenient for the problem at hand. The process of converting a voltage source into a current source is a core aspect of source transformation. Here's how it's done:

Step-by-Step Conversion

1. Identify the voltage source in series with a resistor.
2. Convert the voltage source into an equivalent current source using the formula:

\(I= \frac{V}{R} \)

Where, V is the voltage of the source, and R is the series resistor.

3. The current source will have the current I, and the resistor will now be in parallel with the current source.

Fig-Source Transformation

A practical voltage source, or simply a voltage source, consists of an ideal voltage source in series with an internal resistance or impedance. In the case of an ideal voltage source, this internal impedance would be zero. The key characteristic of a voltage source is that the output voltage remains constant, regardless of the load current. Examples of voltage sources include cells, batteries, and generators. On the other hand, a practical current source, or simply a current source, consists of an ideal current source in parallel with an internal resistance or impedance. For an ideal current source, this parallel impedance is considered infinite.

Semiconductor devices, such as transistors, are often modelled as current sources. Similarly, the output produced by either a direct or alternating voltage source can be referred to as a direct current (DC) or alternating current (AC) source, respectively, depending on whether the voltage is constant or varies over time.

• Figure A shows a practical voltage source in series with the internal resistance rv, and circuit B represents a practical current source with parallel internal resistance ri

For the practical voltage source, the load current will be:

\(Il_{v}= \frac{V}{r_{V}+r_{L}} \)

Where,

• ILv is the load current for the practical voltage source
• V is the voltage
• rv is the internal resistance of the voltage source
• rL is the load resistance.

It is considered that the load resistance rL is connected at the terminal x-y. Similarly, for the practical current source, the load current is given as:

\(iL_{i}= I\frac{r_{i}}{r_{i}+ r_{L}} \)

Where,

• iLi is the load current for the practical current source
• I is the current
• ri is the internal resistance of the current source
• rL is the load resistance connected across the terminal x-y in the figure B

Two sources become identical, when above given both equations are equated. 

\(\frac{V}{r_{v}+ r_{L}}= I\frac{r_{i}}{r_{i}+ r_{L}}\)

Where, V= IR

And we will get:

r_{v}+ r_{L}= r_{i}+ r_{L}

r_{v}= r_{L}

Therefore, for any practical voltage source, if the ideal voltage is V and the internal resistance is rv, the voltage source can be replaced by an equivalent current source I with the internal resistance rv in parallel with the current source.

Voltage Source to Current Source Conversion

Therefore, for any practical voltage source, if the ideal voltage is V and the internal resistance is rv, the voltage source can be replaced by an equivalent current source I with the internal resistance rv in parallel with the current source.

Fig-Voltage Source to Current Source Conversion

Here, \(I_{s}= \frac{V}{R}\)

Current Source to Voltage Source Conversion

In the circuit diagram below, a current source connected in parallel with a resistance is transformed into a voltage source by placing the resistance in series with the voltage source.

Fig-Current Source to Voltage Source Conversion

Here,

Advantages of Source Transformation

The source transformation technique offers several benefits, particularly when dealing with complex circuits:

1. Simplifies Circuit Analysis: By reducing the number of components in a circuit, source transformation makes the overall analysis faster and more manageable, especially for circuits with multiple sources and resistors.
2. Reduces Complexity: It helps in reducing a multi-source circuit into simpler single-source circuits, often making it easier to apply methods like Ohm’s law, Kirchhoff’s Current Law (KCL), and Kirchhoff’s Voltage Law (KVL).
3. Efficient Use in Theoretical and Practical Circuits: Whether you're dealing with theoretical problems or real-world applications, the ability to transform sources helps in both DC and AC circuit analysis.
4. Improves Accuracy in Competitive Exams: In exams, quickly reducing circuits using source transformation techniques ensures faster and more accurate results, particularly in subjects like network theory.
5. Flexibility in Complex Circuit Designs: Engineers use source transformation when working with large-scale circuits to reduce their complexity without altering the performance or behaviour of the system.

Steps for Source Transformation

1. Identify the part of the circuit suitable for transformation.
2. Apply the transformation using the above equations.
3. Simplify the resulting circuit to analyze it easily.
4. Repeat, if necessary, to further simplify the circuit.

Important Points for Source Transformation

• The resistor value remains unchanged.
• Transformation doesn't alter the external behavior of the circuit; it remains electrically equivalent from the viewpoint of external terminals.
• Not applicable when the resistor is absent or is not directly connected to the source.

Limitations of Source Transformation

• Cannot be used if the resistor is not directly connected to the source.
• Practical circuits might become overly simplified, potentially overlooking nuances like internal resistances or real-world loading effects.

This article concludes all the information related to source transformation, which helps to propel your preparation for various AE/JE examinations. To boost your preparation, you should test yourself through a series of Mock Tests for Electrical Engineering Exams. You can check the syllabus for the AE/JE exam. You can visit the Testbook app to keep yourself updated with all the exam-oriented information related to the upcoming examinations, including GATE Electrical, SSC JE, ESE, RRB JE, and state AE/JE Electrical exam.