Converting a Current Source to a Voltage Source: Understanding Source Transformation

The process of converting a current source into a voltage source is an important concept in electrical engineering. Under certain conditions, it is possible to transform a current source into a voltage source if a resistor is in series with the current source. This transformation is known as source transformation and is a fundamental concept in circuit analysis.

Understanding Current and Voltage Sources

A current source is a device that provides a constant current I regardless of the voltage across it. Conversely, a voltage source is a device that provides a constant voltage V regardless of the current flowing through it. In simple terms, a current source has a zero internal resistance, while a voltage source has infinite internal resistance.

Source Transformation: From Current Source to Voltage Source

When there is a resistor R in series with the current source, the voltage across the resistor can be calculated using Ohm's Law:

V I × R

Using this principle, the current source can be transformed into a voltage source with the same resistance in series. The transformed voltage source has a voltage equal to the product of the current of the original source and the resistance, and it is placed in series with the same resistor. This transformation maintains the same electrical behavior in the circuit.

Steps for Source Transformation

Identify the current source I and the resistor R in series with the current source. Calculate the voltage using Ohm's Law: V I × R. Replace the current source with a voltage source equal to V. Keep the resistor R in series with the new voltage source.

Example

Consider the following example with a 2 A current source in series with a 4 ohm resistor:

Calculate the voltage: V 2 A × 4 Ω 8 V. Create a 8 V voltage source in series with the 4 ohm resistor.

The new configuration will have an 8 V voltage source in series with a 4 ohm resistor, maintaining the same electrical behavior as the original circuit.

No Path for Current to Flow

It is important to note that if there is no path for current to flow, the voltage from a true current source will be infinite, regardless of the resistance. Conversely, if a resistor R is connected in parallel with a current source I, the voltage will be V I × R.

Converting a Voltage Source to a Current Source

The process of converting a voltage source to a current source is the inverse of the above steps. The technique, known as source transformation, can be used to convert current sources to voltage sources and vice versa. Before performing the conversion, it is important to understand that devices in series in a circuit will have the same current, and devices in parallel will have the same voltage. This knowledge is crucial for properly arranging the components in the circuit.

Source Transformation Formula

The conversion from a current source to a voltage source follows a specific formula:

Vs Is × R

Refer to the diagram below for a visual representation of the circuit transformation:

Circuit A represents the original current source configuration, while Circuit B represents the transformed voltage source configuration. Note how the resistor is re-arranged in series.

Courtesy of: Dummies

Conclusion

Source transformation is a powerful tool in electrical engineering that enables engineers to simplify and analyze circuits more effectively. By understanding and applying the principles of source transformation, engineers can convert current sources to voltage sources and vice versa, depending on the specific requirements of their designs. This knowledge is essential for anyone working in the field of electrical engineering or electronics.