- Source Transformation Definition: Source transformation is defined as a technique to simplify circuit analysis by converting between equivalent voltage and current sources using Thévenin’s and Norton’s theorems.
- Voltage to Current Conversion: This conversion involves calculating the current supplied by a shorted voltage source and connecting the same resistance across the current source.
- Current to Voltage Conversion: Converts a current source into a voltage source by applying Ohm’s law to determine the voltage across an open circuit.
- Circuit Simplification: Source transformation allows easier analysis and understanding of complex circuits by changing the type of sources without altering electrical behavior.
- Educational Resources: Additional learning materials, like video explanations, are available for those who prefer visual or auditory learning methods.
What is a Source Transformation?
Source transformation can simplify linear circuit analysis without changing the behaviour seen at the selected pair of terminals.
The following example derives both equivalent forms.
Start with an ideal voltage source V and a finite, nonzero resistance connected in series R.
The pair is a Thévenin source model. R may represent an equivalent network resistance, not only the physical internal resistance of one source.
For the ideal model, calculate the current that would flow if the output terminals were shorted. Do not physically short a real source unless an approved test method and correctly rated equipment require it.
Applying Kirchhoff Voltage Law to the above circuit yields:
Here, I is the calculated short-circuit current delivered by the ideal voltage source and series resistance: I = V/R.
The Norton equivalent uses an ideal current source I = V/R in parallel with the same resistance R. Its open-circuit voltage is IR = V, as shown below.
Applying Kirchhoff Current Law at node 1 gives:
Equations (i) and (ii) give the source relation:
Both models have open-circuit voltage V, short-circuit current I and resistance R seen from the terminals. The resistance connected in series with the voltage source becomes a parallel resistance in the equivalent current source model.
The models are therefore equivalent for every load connected to those terminals, within the linear model’s range.
The two forms are circuit duals, but their internal branch currents, voltages and power are not identical. Only their external terminal relation is preserved.
Use I = V/R for voltage-to-current conversion and V = IR for current-to-voltage conversion. Keep the same resistance value and change its series or parallel connection.
The video below gives another explanation of current-to-voltage source conversion:
Voltage Source to Current Source Conversion
Consider a voltage source V with resistance r in series. The equivalent Norton current is:
This is the calculated short-circuit current of the Thévenin model.
The Norton model uses that current and connects the same resistance r in parallel with the ideal current source. The figure shows the transformation.
Current Source to Voltage Source Conversion
For the reverse transformation, take an ideal current source I in parallel with resistance r. By Ohm’s law, the open-circuit voltage is:
The Thévenin equivalent is a voltage source V = Ir in series with the same r. This conversion requires a finite resistance; ideal zero- or infinite-resistance edge cases cannot be transformed by dividing or multiplying in the usual way.
