﻿ Electrical impedance

# Electrical impedance

The impedance (Latin impedire " inhibit ", " stop "), even AC resistance, is the ratio of electric power to a consumer to ( device, line, etc. ) to the current drawn. This physical size is generally given as a complex-valued function of the advantageous frequency.

The impedance describes the property

• Of a component, more precisely a linear passive two-terminal network, the flow of an alternating electric current (see also complex AC circuit analysis ),
• A line or a medium in the electromagnetic wave propagation (see characteristic impedance ). When wave propagation is no specific component involved in the resistance, neither active nor a reactance.

## General

The impedance is the AC technology the summary of two expressions.

These two properties are mathematically summarized by showing the impedance as a complex quantity

The magnitude of the complex impedance is the impedance. The temporal shift is given by the phase shift angle can assume values ​​between -90 ° and 90 °. In other notation

Is the real part of the component of the impedance at which no phase shift occurs; this is always positive. The imaginary part is the portion to which a phase shift of 90 ° occurs; it could be positive or negative - positive when the current lags the voltage, - negative, when the voltage lagging the current. The phase-shifting portion is frequency dependent, the non- phase- share, depending on the circumstances of the frequency -dependent or be independent; see below keywords Electrical resistance.

The reciprocal of the impedance is the admittance ( complex conductivity).

The choice of terminology in this article follows the standards that specifies:

In the literature, the term impedance is used consistently and not always used interchangeably for both the complex quantity as well as the amount.

## Calculation

The impedance is the complex ratio of AC voltage and AC complex ( to represent a change of size as a complex change of size, see Complex AC circuit analysis ).

The impedance is calculated as the quotient of the real amplitudes or rms values ​​of AC voltage and the AC current

Wherein the electromagnetic wave impedance of voltage and current are replaced with other corresponding quantities: the voltage across the field strength and the current through the magnetic flux density as well as in the acoustic sound pressure and voltage across the current through the sound velocity.

## Application

Impedance is important in the adaptation of high-frequency lines, but also for the wave propagation in free space. For example, when does not match the input impedance of a device having the impedance of the line, reflections occur, which reduces the power transfer and can lead to resonance phenomena, and thus to a non- linear frequency response.

Electrodynamic loudspeakers are driven with alternating current, therefore the inductive resistance of the built voice coil causes a phase shift between current and voltage, which is frequency dependent. For this reason, it does not mention the resistance, but the impedance of the speaker.

If pulses transmitted by cable, has an ohmic resistance of the line low regard for impedance of the cable. Here it is almost always important to avoid reflections of the pulses at the opposite end of the cable. The terminating resistor is necessary to virtually real in lossless lines, ie, a ohmic resistance. This value is referred to as the characteristic impedance of the cable or line impedance. This can be frequency-dependent function of the conduction losses at low frequencies, complex-valued and strong. It can be determined by time domain reflectometry.

In biology can be used by Electric Cell - substrate Impedance Sensing the impedance to detect form changes in animal cells.

## Representation

The impedance is the ohm unit with the unit symbol Ω. In the two representations as a complex quantity Z can be their constituents and their meaning read:

• In the formulation in polar coordinates is the sum Z of the complex variable Z is the impedance; it results in the vector diagram the length of the pointer. The specified angle φ is the phase shift between voltage and current; it results in the vector diagram the rotation of the pointer relative to the real axis:
• In the formulation is in Cartesian coordinates of the real part of the effective resistance ( Resistance ) or the ohmic resistance R, which converts the transmitted active power. The imaginary part is the reactance ( reactance ) X, which converts no real power, but stores energy and after a quarter period of the generator feeds back (see reactive power):

In a consumer with an inductance L this has a positive (inductive) reactance; the voltage lags the current front. In this case, ω is the angular frequency of the oscillation. In a consumer with a capacity C, this has a negative ( capacitive ) reactance; the voltage lags the current. (For the sign convention used see Note below reactance for the derivation see complex AC circuit analysis ).

In the vector diagram for Z can be seen as an element behave,

• Inductively: pointer in the first ( upper right ) quadrant of the coordinate system, imaginary positive or
• Capacitive: pointer in the fourth ( lower right ) quadrant, negative imaginary part.

The impedance is accordingly the value of the geometric (complex) the addition of the active and the reactive impedances:

In case of technical devices are often only this amount of impedance, ie the impedance indicated. In a general network of ohmic resistors, inductors and capacitors, however, this is dependent on frequency.

Speakers have strongly frequency dependent impedances - but it will be a nominal value (eg, 4 Ω or 8 Ω ) given. According to international standard (IEC 60268 ) may be less than this nominal value by more than 20% occurring in the frequency range lowest impedance. Higher impedances at other frequencies are freely permitted.

In high-frequency cables, the ( design-related ) characteristic impedance is called the characteristic impedance. He is in coaxial cables 50 Ω to 100 Ω and for symmetrical ( two-wire ) wires 110 Ω to 300 Ω.

When antennas are called the input impedance and base resistance, it should be real at the frequency for which the antenna is provided and match the impedance of the cable (eg, 60 Ω or 240 Ω ).

## Impedance matching

In the transmission of alternating current, there is reflection of waves, when changing the impedance of a cable or of the transmission means. This is in principle not bound to the number of wavelengths on a line, with short in relation to the wavelength transmission lines, however, the change in the impedance of the transmission means has hardly any effect. At the location of a change in impedance of the incoming wave is reflected. The magnitude of the reflection coefficient r is between 0 and 1 if its magnitude is 1, the entire wave is reflected at r = 0 ( that means) occurs no reflection, we speak in this case of impedance matching. Impedance matching is often desirable in high-frequency cables and with the electromagnetic wave propagation.

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