Impedance matching

In electrical engineering, impedance matching is the practice of designing or adjusting the input impedance or output impedance of an electrical device for a desired value. Often, the desired value is selected to maximize power transfer or minimize signal reflection. For example, impedance matching typically is used to improve power transfer from a radio transmitter via the interconnecting transmission line to the antenna. Signals on a transmission line will be transmitted without reflections if the transmission line is terminated with a matching impedance. Techniques of impedance matching include transformers, adjustable networks of lumped resistance, capacitance and inductance, or properly proportioned transmission lines. Practical impedance-matching devices will generally provide best results over a specified frequency band. The concept of impedance matching is widespread 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, such as in acoustics or optics.

Theory Impedance characterizes the ratio of energy components in a given domain. For constant signals, this impedance can also be constant. For varying signals, it usually changes with frequency. The energy involved can be electrical, mechanical, acoustic, magnetic, electromagnetic, or thermal. The concept of electrical impedance is perhaps the most commonly known. Electrical impedance, like electrical resistance, is measured in ohms. In general, impedance (symbol: Z) has a complex value; this means that loads generally have a resistance component (symbol: R) which forms the real part and a reactance component (symbol: X) which forms the imaginary part. This impedance characterizes the ratio between the voltage and current components in the medium. In simple cases (such as low-frequency or direct current power transmission) the reactance may be negligible or zero; the impedance can be considered a pure resistance, expressed as a real number. In the following summary we will consider the general case when resistance and reactance are both significant, and the special case in which the reactance is negligible.

Maximum power transfer matching Complex conjugate matching is used when maximum power transfer is required, namely

Z load = Z source ∗ , {\displaystyle Z_{\text{load}}=Z_{\text{source}}^{*},}

where a superscript * indicates the complex conjugate. A conjugate match is different from a reflection-less match when either the source or load has a reactive component. If the source has a reactive component, but the load is purely resistive, then matching can be achieved by adding a reactance of the same magnitude but opposite sign to the load. This simple matching network, consisting of a single element, will usually achieve a perfect match at only a single frequency. This is because the added element will either be a capacitor or an inductor, whose impedance in both cases is frequency dependent, and will not, in general, follow the frequency dependence of the source impedance. For wide bandwidth applications, a more complex network must be designed.

Phase-shifting matching network If a lossless reciprocal two-port network matches a load impedance Z L = R L + j X L {\displaystyle Z_{L}=R_{L}+jX_{L}} to a source impedance Z S = R S + j X S {\displaystyle Z_{S}=R_{S}+jX_{S}} with transmission phase shift φ {\displaystyle \varphi } (i.e., { Z S → φ Z L } {\displaystyle \{Z_{S}\xrightarrow {\varphi } Z_{L}\}} ), then the transmission matrix of the matching network can be expressed as

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