Impedance matching

In electronics, impedance matching is the practice of designing the input impedance of an electrical load or the output impedance of its corresponding signal source to maximize the power transfer or minimize signal reflection from the load. A source of electric power such as a generator, amplifier or radio transmitter has a source impedance equivalent to an electrical resistance in series with a frequency-dependent reactance. Likewise, an electrical load such as a light bulb, transmission line or antenna has an impedance equivalent to a resistance in series with a reactance.
The maximum power theorem states that maximum power is transferred from source to load when the load resistance equals the source resistance and the load reactance equals the negative of the source reactance: the reactances cancel each other out with their opposing dependency on frequency. Another way of saying this using complex numbers is the load impedance must equal the complex conjugate of the source impedance. If this condition is met the two parts of the circuit are said to be impedance matched.
In a direct current (DC) circuit, the condition is satisfied if the load resistance equals the source resistance. In an alternating current (AC) circuit the reactance depends on frequency, so circuits which are impedance matched at one frequency may not be impedance matched if the frequency is changed. Impedance matching over a wide band will generally require complex, filter-like structures with many components except in the trivial case of constant source and load resistances when a transformer can be used.
In the case of a complex source impedance ZS and load impedance ZL, maximum power transfer is obtained when





Z


S



=

Z


L



∗





{\displaystyle Z_{\mathrm {S} }=Z_{\mathrm {L} }^{*}\,}
where the asterisk indicates the complex conjugate of the variable. Where ZS represents the characteristic impedance of a transmission line, minimum reflection is obtained when





Z


S



=

Z


L






{\displaystyle Z_{\mathrm {S} }=Z_{\mathrm {L} }\,}
The concept of impedance matching found first applications in electrical engineering, but is relevant in other applications in which a form of energy, not necessarily electrical, is transferred between a source and a load. An alternative to impedance matching is impedance bridging, in which the load impedance is chosen to be much larger than the source impedance and maximizing voltage transfer, rather than power, is the goal.

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