Source Transformation in AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE) PDF Download

Source transformation in the frequency domain involves transforming a voltage source in series with an impedance to a current source in parallel with an impedance, or vice versa.

This method helps us to analyze the ac circuit with more than one independent sources.

Source TransformationSource TransformationAs we go from one source type to another, we must keep the following relationship below:

Source Transformation in AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)

  • The main idea of this method’s principle is to substitute voltage source in series with a resistor to a current source in parallel with a resistor or vice versa for dc circuit.
  • Make sure to use impedance instead of the resistor when you analyze the ac circuit with this method.
  • This theorem is developed by Jacob Millman. This method simplifies multiple parallel sources to an equivalent single resistor.
  • This method is also used for a circuit with an unbalanced bridge circuit.
  • This method is also known as Millman Theorem. This theorem is useful to simplify a circuit with multi-voltage sources or multi current sources to a single source.
  • Even it has a unique name, this method also has its basic principle from Ohm’s Law and Kirchhoff’s Law.
  • But you need to remember, this method only works on a circuit that can be redrawn accordingly.
  • The polarity of all voltage sources in the circuit is referenced to the same point.

Question for Source Transformation in AC Circuits
Try yourself:By using source transformation voltage source in series resistor is replaced by __________
View Solution

Note:

Can we apply source transformation on Dependent Source?

  • Yes, you can apply source transformation techniques to circuits containing dependent sources, just as you would with independent sources. Source transformation is a common method used to simplify circuits by converting voltage sources to current sources or vice versa, and changing their associated resistors accordingly.

  • Source transformations work for both dependent and independent sources, but the process can be a bit more complex when dealing with dependent sources, especially if their values depend on circuit variables. The general idea is to replace the original source with an equivalent source that simplifies the circuit while maintaining the same voltage and current relationships.

Let us cover the technique from the example below:

Example:

Calculate Vx in the circuit of Figure . using the method of source transformation
Source Transformation in AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)

Solution:

We transform the voltage source to a current source and obtain the circuit in Figure. where
Source Transformation in AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)

The parallel combination of 5 Ω resistance and (3 + j4) impedance gives
Source Transformation in AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)

Converting the current source to a voltage source yields the circuit in Figure.
Source Transformation in AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)
where,
Source Transformation in AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)

Using voltage division,
Source Transformation in AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE)

The document Source Transformation in AC Circuits | Network Theory (Electric Circuits) - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Network Theory (Electric Circuits).
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FAQs on Source Transformation in AC Circuits - Network Theory (Electric Circuits) - Electrical Engineering (EE)

1. What is source transformation in AC circuits?
Ans. Source transformation is a technique used in AC circuits to simplify complex circuits by converting voltage sources to current sources or vice versa. This helps in analyzing and solving circuits more easily using Ohm's Law and Kirchhoff's Laws.
2. How does source transformation work in AC circuits?
Ans. Source transformation involves converting a voltage source and its series impedance to an equivalent current source and its parallel impedance, or vice versa. This is done by using Ohm's Law to calculate the equivalent current or voltage values based on the source and impedance values. The transformed circuit will have the same behavior and voltage/current values as the original circuit.
3. What are the benefits of using source transformation in AC circuits?
Ans. Source transformation offers several benefits in AC circuit analysis. It simplifies complex circuits by converting voltage sources to current sources or vice versa, making it easier to apply Ohm's Law and Kirchhoff's Laws. It reduces the number of elements in the circuit, making it more manageable for calculations. It also helps in determining the Thevenin or Norton equivalent circuits, which are useful in circuit analysis and design.
4. Can source transformation be applied to both series and parallel AC circuits?
Ans. Yes, source transformation can be applied to both series and parallel AC circuits. In series circuits, voltage sources can be transformed into current sources with parallel impedance, while in parallel circuits, current sources can be transformed into voltage sources with series impedance. The transformed circuits will have the same voltage and current values as the original circuits.
5. Are there any limitations or considerations when applying source transformation in AC circuits?
Ans. While source transformation is a powerful technique, there are a few limitations and considerations to keep in mind. It is important to ensure that the transformation is valid and does not violate any circuit laws or assumptions. Additionally, the transformed circuit may have different impedance values, which can affect the overall behavior of the circuit. It is crucial to carefully analyze the circuit and consider the impact of the transformation before applying it.
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