Maximum power transfer theorem

The theorem states that a source delivers maximum power to a load when the load impedance equals the complex conjugate of the source impedance. In resistive circuits, this condition reduces to equal source and load resistances.

Thevenin's theorem: A linear circuit viewed from two terminals can be replaced by an ideal voltage source in series with an equivalent resistance or impedance. The equivalent source impedance makes the load-matching condition straightforward to derive.
Impedance matching network: A circuit that transforms the impedance presented by a load so it meets a desired source impedance. Such networks implement conjugate matching between a source and its load.
Power efficiency: The ratio of useful output power to input power in a system. At the resistive maximum-power condition, an ideal source resistance dissipates as much power as the load.
Electrical power: The rate at which electrical energy is transferred or converted, measured in watts. The theorem maximizes the power absorbed by the load.
Norton’s theorem: A linear circuit viewed from two terminals can be replaced by an ideal current source in parallel with an equivalent resistance or impedance. Its parallel equivalent gives another route to calculate power delivered to a load.
L-network: A two-reactive-component matching circuit arranged as a series element and a shunt element. It is a simple, common network for matching unequal resistive source and load impedances.
Voltage matching: Connecting source and load to achieve a desired voltage relationship rather than maximum load power. Many circuits prioritize preserving voltage and efficiency instead of matching resistances for peak power.
Ohm's law: The relation between voltage, current, and resistance expressed as voltage equals current times resistance. Combining it with the source model gives load power as a function of load resistance.
Complex impedance: A frequency-dependent opposition to alternating current represented by a complex number combining resistance and reactance. Conjugate matching applies to both the resistive and reactive parts of impedance.
Smith chart: A graphical tool for analyzing complex impedances and reflection coefficients in transmission-line systems. It helps engineers find the reactances needed to achieve a conjugate match.

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