Source transformation with example

Source transformation

Source transformation replaces a voltage source in series with a resistance by an equivalent current source in parallel with the same resistance, or the reverse. Both give the same voltage and current at the load terminals, so it is used to simplify circuits.

Rules

• Voltage source (E, Rs) to current source: Is = E/Rs, with Rp = Rs in parallel.
• Current source (Is, Rp) to voltage source: E = Is × Rp, with Rs = Rp in series.
• The arrow of the current source points toward the + terminal of the voltage source.

  o--[Rs]--+--o  a            o--+----+--o  a
    (E)    |                    (Is)  [Rp]
  o--------+--o  b            o--+----+--o  b

Example

A 12 V source with 4 Ω in series becomes a 3 A source (12/4) with 4 Ω in parallel.

Check with an 8 Ω load:

• Voltage form: I = 12/(4 + 8) = 1 A, V = 8 V.
• Current form: I = 3 × 4/(4 + 8) = 1 A, V = 8 V.

The load results are the same, so the sources are equivalent as seen by the load. (The power lost inside the source differs, because the internal circuits are not identical.)

Note: an ideal voltage source (Rs = 0) or an ideal current source (Rp = ∞) cannot be transformed. A resistor in parallel with a voltage source, or in series with a current source, does not affect the load and can be ignored.