If an electrical energy source and an electrical consumer are directly connected to one another in an electrical circuit , then power adjustment (also resistance adjustment and load adjustment ) is understood to mean the condition under which the maximum output or available electrical power of a source is determined. It is also understood to be an action through which the maximum power is achieved on the load.

For example, in measurement , high-frequency and communications technology , adaptation means establishing a relationship between the output impedance of a source and the input impedance of the connected consumer (sink). In the case of ohmic behavior, the power is adjusted by adjusting these resistances.

This type of adaptation is required for sources that can only generate low electrical power and whose power should be passed on as comprehensively as possible. Such weak sources include antennas and certain types of sensors . The more fully the power is used, the better a measurement signal can be transmitted and evaluated without interference or a message without loss of content. In the case of linear sources and sinks, at best half of the deliverable or available power is actually delivered ; the efficiency is then 50%. The other half is lost as power loss in the internal resistance of the source.

## Demarcation

• Power adjustment is a term from the field of linear networks . In the following it is assumed that the internal resistance of the source and its external resistance , the input resistance of the sink, are linear resistances .${\ displaystyle R _ {\ text {i}}}$${\ displaystyle R _ {\ text {a}}}$
• Current electrical energy sources for the purpose of energy supply have an abundant oversupply in comparison to the power requested by the consumer. Their goal is the highest possible degree of efficiency. They are not designed for power adjustment , but for voltage adjustment (for voltage sources) or current adjustment (for current sources).
• The Lei s tung adjustment does not involve the line matching be confused when it comes to the transmission of signals via an electrical line disturbing reflections of waves or pulses to avoid.

## burden

### Ohmic resistances

The power transmitted by a linear voltage source is much smaller than the maximum power that can be output with very small and very large external resistances:

1. If so, the terminal voltage almost collapses, the power at the external resistance becomes low, the power generated is almost completely converted into heat at the internal resistance.${\ displaystyle R _ {\ text {i}} \ gg R _ {\ text {a}}}$
2. If so , there is almost no current, which also leads to a low output at the external resistance.${\ displaystyle R _ {\ text {a}} \ gg R _ {\ text {i}}}$
In red the display of the power delivered in relation to the maximum power that can be delivered.
In green the course of the efficiency of a linear voltage source.
Both values as a function of the relation to applied.${\ displaystyle R _ {\ text {a}}}$${\ displaystyle R _ {\ text {i}}}$

In between there is a maximum of the power output with the so-called resistance adjustment. In the diagram on the right, this operating point is shown in the curve shape shown in red at maximum relative power with a resistance ratio of

${\ displaystyle {\ frac {R _ {\ text {a}}} {R _ {\ text {i}}}} = 1}$

reached. This requires

${\ displaystyle R _ {\ text {i}} = R _ {\ text {a}}}$.

In this case the output voltage is half of the open circuit voltage and the power that can be used at the consumer is ${\ displaystyle U_ {0}}$${\ displaystyle P}$

${\ displaystyle P _ {\ mathrm {max}} = {\ frac {{U_ {0}} ^ {2}} {4 \ cdot R _ {\ text {i}}}}}$ .

The efficiency , shown as a green line in the diagram, results in ${\ displaystyle \ eta}$

${\ displaystyle \ eta = {\ frac {R _ {\ text {a}}} {R _ {\ text {a}} + R _ {\ text {i}}}}}$

and amounts to 50% with performance adjustment. In this case the external resistance consumes the same power as the internal resistance of the source.

### Impedances

In the case of alternating voltage and the internal impedance of the source and the external impedance of the sink, there is an impedance matching if the complex conjugate values ​​of the impedances are the same ${\ displaystyle {\ underline {Z}} _ {\ text {i}} = R _ {\ text {i}} + \ mathrm {j} X _ {\ text {i}}}$${\ displaystyle {\ underline {Z}} _ {\ text {a}} = R _ {\ text {a}} + \ mathrm {j} X _ {\ text {a}}}$

${\ displaystyle {\ underline {Z}} _ {\ text {i}} = {\ underline {Z}} _ {\ text {a}} ^ {*} \ qquad {\ text {also}} \ qquad R_ {\ text {i}} = R _ {\ text {a}} \ qquad {\ text {and}} \ qquad X _ {\ text {i}} = - X _ {\ text {a}}}$.

This adaptation only exists at a certain frequency at which the reactances stand out. The source then delivers a maximum of active power to the sink. This is in formal agreement with the direct current circuit

${\ displaystyle P _ {\ text {W, max}} = {\ frac {{U_ {0}} ^ {2}} {4 \ cdot R _ {\ text {i}}}}}$ .

In information technology (only there), impedance matching also plays a role as apparent power matching , which is both reflection and line matching. The maximum apparent power is output for this purpose:

${\ displaystyle {\ underline {Z}} _ {\ text {i}} = {\ underline {Z}} _ {\ text {a}}}$.

## application

If there are several components in the path of a high-frequency signal, each sink must be adapted to its source. Lines in the chain count as a sink at their beginning and as a source at their end. Assemblies that are to be put together are manufactured with the same impedance if possible. In professional HF technology it is 50 Ω. Otherwise, the source and sink must be matched to one another by means of a matching network. In the case of purely ohmic impedances, the matching network can be a transformer that matches the impedance of the source to the sink.

Wherever reflections on lines must be avoided, i.e. where line adaptation is required, power adaptation is also used. In the case of large high-frequency powers, such as those that occur in output stages in larger transmission systems, an efficiency of only 50% is undesirable, which is why a smaller source impedance is selected in order to enable higher efficiency. Line matching is only present between the line and the sink (transmitting antenna), which is sufficient to avoid signal reflections.

With improved technology, more and more voltage matching is being used instead of power matching. This also applies in audio engineering and in the hi-fi sector, where the output resistance of the amplifier (usually around 0.1 Ω) is significantly less than a tenth of the load resistance. In particular, audio output stages with a very low output resistance enable a high damping factor , whereby natural resonances of the loudspeaker are attenuated by short-circuiting the back induction of a loudspeaker diaphragm that oscillates (e.g. after an impulsive / percussive audio signal). Information such as "8 Ω" describes a permissible load resistance that the output can drive.

The power adjustment is also used for digital interfaces such as AES / EBU and S / PDIF . In particular, the sample rate of 384 kHz, which is already common in today's digital audio technology, requires a low-reflection provision of a bandwidth of around 250 MHz due to the adjustment of input, cable and output impedance ; otherwise, if the characteristic impedance is not observed , reflections in the cable and thus jitter will occur as well as to dropouts and crackling, in the worst case to a breakdown of the synchronization and failure of the digital data connection.

## literature

• Dieter Zastrow: Electrical engineering, a basic textbook . 17th edition. Vieweg + Teubner, 2010, ISBN 978-3-8348-0562-1 , p. 68-71 .

## Individual evidence

1. IEC 60050, see DKE German Commission for Electrical, Electronic and Information Technologies in DIN and VDE: Internationales Electrotechnical Dictionary - IEV. IEV number 702-07-14.
2. Marlene Marinescu, Nicolae Marinescu: Electrical engineering for study and practice: direct, alternating and three-phase currents, switching and non-sinusoidal processes . Springer Vieweg, 2016, p. 72
3. ^ Hans Fricke, Paul Vaske: Electrical Networks: Fundamentals of Electrical Engineering, Part 1 . Teubner / Springer, 17th ed. 1982, p. 87
4. Horst Steffen, Hansjürgen Bausch: Electrical engineering: Basics . Teubner, 6th edition 2007, p. 109
5. ^ Herbert Schneider-Obermann: Basic knowledge of electrical, digital and information technology. Vieweg, 2006, p. 55
6. ^ Marlene Marinescu, Jürgen Winter: p. 236
7. a b Steffen Paul, Reinhold Paul: Fundamentals of electrical engineering and electronics 3: Dynamic networks, time-dependent processes, transformations, systems. Springer Vieweg, 2017, p. 245
8. ^ Ekbert Hering, Klaus Bressler, Jürgen Gutekunst: Electronics for engineers and scientists . Springer Vieweg, 6th edition 2014, p. 255
9. ^ Stefan Weinzierl (ed.): Manual of audio technology . Springer, 2008, p. 962 ( limited preview in Google book search)
10. Stefan Weinzierl: p. 469 ff ( limited preview in the Google book search)
11. Andreas Friesecke: The audio encyclopedia: A reference work for sound engineers . 2nd Edition. Walter de Gruyter , Berlin 2014, ISBN 978-3-11-034013-6 , pp. 276 ff . ( limited preview in Google Book search)
12. ^ Jon D. Paul: Digital Audio Transmission Impairment and Link Failure: Test Data, and Recommendations for Improved Industry Standards and Reference Designs. (PDF; 1.8 MB) Scientific Conversion, Inc., 2014, p. 13 , accessed on September 5, 2018 (English).