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# What Is a Source Transformation?

Geisha A. Legazpi
Geisha A. Legazpi

A source transformation is a process of representing a circuit from the point of view of the load, or of the next circuit. The concept of source transformation suggests that any power source can be represented as a voltage source or a current source. If the electrical impedance presented to the load or next circuit can be calculated, analysis of the circuit is simplified. Source transformation is applied to the design and testing of various types of circuits – from relatively simple direct current (DC) circuits, for steady-state power computations, to more complex circuits. For high frequencies of alternating current (AC), such as radio frequencies, source transformation aids in designing impedance matching circuits for maximum power transfer.

Any power source will present impedance under AC conditions. The mathematics involved in representing impedance under steady-state DC can be described easily. An ordinary and brand new 1.5-volt (V) cell or battery will have an open-circuit voltage of about 1.5 V. When this battery is connected to an equipment and drained of power, the voltage drops below 1.5 V. It is certain that there will be a non-zero current from the battery.

For instance, if a 1.5 V battery measures 1.4 V when a current of 0.01 ampere (A) is flowing through it, the battery can be represented as an ideal 1.5 V voltage source in series with an internal resistance. The internal resistance has a drop of 0.1 V, which is the difference of the internal ideal voltage source and the terminals output. A current of 0.01 A indicates that the resistance of the battery has to be 0.1 V/0.01 A equals 10 ohms. The 10 ohms is the computed internal resistance of the battery and is distributed inside the makeup of the electrolyte and electrodes inside the battery.

Thevenin’s theorem states that any power source is an ideal voltage source in series with an internal resistance. For transient and AC analysis, Thevenin’s theorem still applies, but complexity manifests when the resistive, capacitive, and inductive components of the internal resistance have to be computed. In the simplest impedance at steady-state DC conditions, the battery inside may be represented by a network of resistances with resistance values that are dependent on temperature and current. To describe Thevenin’s theorem in simple terms, the voltage source is treated as a short circuit, then the resistance seen at the output terminals will be computed using Ohm’s law that suggests resistances in series are added.

Under Norton’s theorem, source transformation suggests that the internal resistance is computed the same way. Instead of a zero-resistance voltage source, an infinite resistance current source is used, but the results are the same. The calculated voltage and current, and therefore the power delivered to an external load, will be the same using Thevenin or Norton’s theorem.

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