Source Conversion

Definition

Source conversion is the process of replacing a practical voltage source with an equivalent practical current source, or replacing a practical current source with an equivalent practical voltage source, without changing the external behavior of the circuit at the terminals.

A practical voltage source consists of an ideal voltage source in series with an internal resistance, while a practical current source consists of an ideal current source in parallel with an internal resistance. The equivalence is based on the fact that both forms produce the same terminal voltage-current relationship for the external load.

Main Content

1. Voltage Source to Current Source Conversion

• A practical voltage source $V_s$ in series with resistance $R_s$ can be converted into an equivalent current source $I_s$ in parallel with the same resistance $R_s$.
• The equivalent current source value is given by: $$I_s = \frac{V_s}{R_s}$$ The direction of the current source is from the positive terminal of the voltage source toward the negative terminal, matching the assumed current flow through the resistor.

Example:
If a 12 V source is in series with a 6 $\Omega$ resistor, it can be converted into a current source of: $$I_s = \frac{12}{6} = 2 \text{ A}$$ in parallel with a 6 $\Omega$ resistor.

This conversion is very useful when a current source form makes it easier to combine elements in parallel or apply nodal analysis.

2. Current Source to Voltage Source Conversion

• A practical current source $I_s$ in parallel with resistance $R_s$ can be converted into an equivalent voltage source $V_s$ in series with the same resistance $R_s$.
• The equivalent voltage source value is: $$V_s = I_s \times R_s$$ The polarity of the voltage source is determined by the direction of the current source and the voltage drop across the parallel resistor.

Example:
If a current source of 3 A is in parallel with an 8 $\Omega$ resistor, the equivalent voltage source is: $$V_s = 3 \times 8 = 24 \text{ V}$$ in series with an 8 $\Omega$ resistor.

This form is useful when the source needs to be expressed as a voltage source for mesh analysis or for simplifying series-connected components.

3. Conditions and Limitations of Source Conversion

• Source conversion is valid only for linear circuits containing independent sources and resistances; it is not directly applicable to non-linear components such as diodes or transistors without special consideration.
• The internal resistance must remain the same during conversion, and the source must be practical, meaning the source is accompanied by a resistance. Ideal sources alone cannot be source-converted directly because an ideal voltage source has zero internal resistance and an ideal current source has infinite internal resistance.

Important note:
Source conversion preserves the terminal behavior only for the external circuit. Internally, the source arrangement changes, but the output seen by the load remains equivalent.

Working / Process

1. Identify whether the source is a practical voltage source or practical current source.
2. Apply the conversion formula:
3. Voltage source to current source: $I_s = \frac{V_s}{R_s}$
4. Current source to voltage source: $V_s = I_s \times R_s$
5. Redraw the circuit with the equivalent source and keep the resistance in the corresponding parallel or series form, then simplify the circuit further if possible.

Advantages / Applications

• Simplifies complex circuits by changing sources into a more convenient form for analysis.
• Helps in applying nodal analysis and mesh analysis more efficiently.
• Useful in finding Thevenin and Norton equivalents and in solving networks with mixed source configurations.

Summary

• Source conversion is the replacement of a practical voltage source with an equivalent current source, or a practical current source with an equivalent voltage source.
• It is based on maintaining the same terminal behavior of the circuit.
• The formulas used are $I_s = \frac{V_s}{R_s}$ and $V_s = I_s \times R_s$.
• Important terms to remember