Compensation Theorem formulas
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| \( \Delta I \;=\; \dfrac{ I \cdot \Delta Z }{ Z + \Delta Z + Z_{eq} } \) | ||
| Symbol | English | Metric |
| \( \Delta I \) = Impedance from Port 1 | \(\Omega\) | \(\Omega\) |
| \( I \) = Origional Current Through the Element | \(A\) | \(A\) |
| \( \Delta Z \) = Impedance Change | \(\Omega\) | \(\Omega\) |
| \( Z \) = Origional Impedance of the Element | \(\Omega\) | \(\Omega\) |
| \( Z_{eq} \) = Equivalent Impedance of the Rest of the Network Seen from the Terminals of the Replaced Element | \(\Omega\) | \(\Omega\) |
Compensation theorem, a concept in electrical circuit analysis, states that in a linear network, any element (such as a resistor, inductor, or capacitor) can be replaced by a voltage source equal to the voltage drop across that element caused by the current flowing through it, without affecting the rest of the circuit's behavior.
This theorem is particularly useful in analyzing the effects of changes in a circuit, such as variations in impedance or component values. By substituting the element with a voltage source that matches the original voltage drop, the theorem allows engineers to simplify complex circuits and study the impact of a single component change on the overall network. It assumes linearity in the circuit, meaning the components follow Ohm’s law and superposition applies. The compensation theorem is widely applied in network analysis to determine the contribution of individual elements to the total circuit response, facilitating easier calculations in systems like amplifiers, filters, or power distribution networks.
This formula helps calculate the incremental change in current caused by the impedance variation, but the theorem's application often involves setting up equivalent circuits rather than directly using a single formula. The focus is on maintaining the same voltage across the element’s terminals to ensure the rest of the circuit remains unaffected.
The compensation theorem itself does not have a single, standalone formula but is applied through a principle that involves replacing a circuit element with an equivalent voltage source to analyze changes in the circuit.
