Impedance

Impedance is the complex-valued generalization of resistance. It may refer to:

  • Acoustic impedance: a constant related to the propagation of sound waves in an acoustic medium.
  • Electrical impedance: the ratio of the voltage phasor to the electric current phasor, a measure of the opposition to time-varying electric current in an electric circuit.
    • High impedance, when only a small amount of current is allowed through.
    • The characteristic impedance of a transmission line.
    • Impedance (accelerator physics), a characterization of the self-interaction of a charged particle beam.
    • Nominal impedance, approximately designed impedance.
    • Impedance matching, the adjustment of input impedance, and output impedance.
  • Mechanical impedance: a measure of opposition to the motion of a structure subjected to a force.
  • Wave impedance: a constant related to electromagnetic wave propagation in a medium.

Acoustic impedance

Acoustic impedance and specific acoustic impedance are measures of the opposition that a system presents to the acoustic flow resulting from an acoustic pressure applied to the system.

The SI unit of acoustic impedance is the pascal second per cubic metre (Pa·s/m3). There is a close analogy with electrical impedance, which measures the opposition that a system presents to the electrical flow resulting from an electrical voltage applied to the system.

Electrical impedance

Electrical impedance is a physical quantity that represents the opposition force of a circuit to the passage of alternating electric current, or, more generally, of a variable current. In other words, is the amount of opposition that an electrical element offers to current flow in a circuit when a voltage is applied at a specific frequency. It can be expressed as a complex number and is given by the relationship between voltage and current.

Commonly the impedance is indicated by \(Z\), and its unit of measurement is the ohm \((\Omega)\).

The concept of impedance generalizes Ohm’s law extending it to circuits operating in a sinusoidal regime (commonly called alternating current): in fact, in a continuous current regime, it represents the electrical resistance. It takes into account the phenomena of electric current consumption and the phenomena of electromagnetic energy accumulation.

The electrical impedance is described mathematically by a complex number, whose real part in the schematization with elements in series represents the dissipative phenomenon and corresponds to the electrical resistance, \(R\). While the imaginary part, called reactance, \(X\), is associated with the energy phenomena of accumulation.

\[\dfrac{V}{I}=Z=R+jX\]

The reciprocal of impedance is called admittance \(Y\).

How to calculate electrical impedance

To calculate the impedance of a capacitor, the formula to do so is:

\[Z_C=\dfrac{1}{2\pi fC}\]

where \(Z_C\) is the impedance in unit ohms, \(f\) is the frequency of the signal passing through the capacitor, and \(C\) is the capacitance of the capacitor. To calculate the impedance of an inductor, the formula to do so is:

\[Z_L=2\pi fL\]

where \(Z_L\) is the impedance in unit ohms, \(f\) is the frequency of the signal passing through the inductor, and \(L\) is the inductance of the inductor. If there are both capacitors and inductors present in a circuit, the total amount of impedance can be calculated by adding all of the individual impedances:

\[Z_{tot}=Z_C+Z_L\]

Mechanical impedance

Mechanical impedance is a measure of how much a structure resists motion when subjected to a harmonic force. It relates forces with velocities acting on a mechanical system. The mechanical impedance of a point on a structure is the ratio of the force applied at a point to the resulting velocity at that point.

Wave impedance

The wave impedance of an electromagnetic wave is the ratio of the transverse components of the electric and magnetic fields (the transverse components being those at right angles to the direction of propagation). If the electric field strength is expressed in volts per meter and the magnetic field strength is expressed in ampere-turns per meter, the wave impedance will have the units of ohms. The wave impedance, \(Z\), of an electromagnetic wave is given by:

\[Z=\sqrt{\dfrac{\mu}{\varepsilon}}\]

where \(\mu\) is the magnetic permeability and \(\varepsilon\) is the electric permittivity. For a transverse-electric-magnetic (TEM) plane wave traveling through a homogeneous medium, the wave impedance is everywhere equal to the intrinsic impedance of the medium. In particular, for a plane wave traveling through empty space, the wave impedance is equal to the impedance of free space. The symbol Z is used to represent it and it is expressed in units of ohms. The symbol η (eta) may be used instead of Z for wave impedance to avoid confusion with electrical impedance.

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