Source transformation simplifies circuit analysis by representing any power source as either a voltage or current source. Thevenin’s and Norton’s theorems describe the internal resistance of a power source, aiding in the design of circuits for maximum power transfer.
A source transform is a process of representing a circuit from the point of view of the load or the next circuit. The concept of source transformation suggests that any power source can be represented as either a voltage source or a current source. If it is possible to calculate the electrical impedance presented to the next load or circuit, the 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 calculations, to more complex circuits. For high frequencies of alternating current (AC), such as radio frequencies, source transformation aids in the design of impedance-matching circuits for maximum power transfer.
Any power source will exhibit impedance under AC conditions. The mathematics involved in representing steady-state DC impedance can be described easily. A normal, new 1.5 volt (V) cell or battery will have an open circuit voltage of approximately 1.5 V. When this battery is connected to equipment and becomes discharged, the voltage will drop below 1.5 V. It is certain that there will be a non-zero current from the battery.
For example, if a 1.5 V battery measures 1.4 V when flowing a current of 0.01 ampere (A), the battery can be represented as an ideal voltage source of 1.5 V in series with an internal resistance. The internal resistance has a drop of 0.1V, which is the difference between the internal ideal voltage source and the output of the terminals. A current of 0.01A indicates that the battery resistance should be 0.1V/0.01A equal to 10 ohms. The 10 ohms is the calculated internal resistance of the battery and is distributed within the composition of the electrolyte and electrodes within the battery.
Thevenin’s theorem states that any power source is an ideal voltage source in series with an internal resistance. For AC and transient analysis, Thevenin’s theorem still applies, but the complexity arises when the resistive, capacitive, and inductive components of the internal resistance have to be calculated. In the simplest impedance under steady-state DC conditions, the internal battery can be represented by a resistance network with temperature- and current-dependent resistance values. 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 calculated using Ohm’s law which suggests adding resistances in series.
According to Norton’s theorem, the source transformation suggests that the internal resistance is calculated in 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’s or Norton’s theorem.
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