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There are several approaches to understanding reflections, but the relationship of reflections to the conservation laws is particularly enlightening. A simple example is a step voltage, () (where is the height of the step and () is the unit step function with time ), applied to one end of a lossless line, and consider what happens when the line is terminated in various ways.
In telecommunications and transmission line theory, the reflection coefficient is the ratio of the complex amplitude of the reflected wave to that of the incident wave. The voltage and current at any point along a transmission line can always be resolved into forward and reflected traveling waves given a specified reference impedance Z 0.
The input impedance of an infinite line is equal to the characteristic impedance since the transmitted wave is never reflected back from the end. Equivalently: The characteristic impedance of a line is that impedance which, when terminating an arbitrary length of line at its output, produces an input impedance of equal value. This is so because ...
In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit. [1]Quantitatively, the impedance of a two-terminal circuit element is the ratio of the complex representation of the sinusoidal voltage between its terminals, to the complex representation of the current flowing through it. [2]
The bones in the middle ear function as a series of levers, which matches mechanical impedance between the eardrum (which is acted upon by vibrations in air) and the fluid-filled inner ear. Horns in loudspeaker systems are used like transformers in electrical circuits to match the impedance of the transducer to the impedance of the air.
The telegrapher's equations then describe the relationship between the voltage V and the current I along the transmission line, each of which is a function of position x and time t: = (,) = (,) The equations themselves consist of a pair of coupled, first-order, partial differential equations. The first equation shows that the induced voltage is ...
In optics, the Hagen–Rubens relation (or Hagen–Rubens formula) is a relation between the coefficient of reflection and the conductivity for materials that are good conductors. [1] The relation states that for solids where the contribution of the dielectric constant to the index of refraction is negligible, the reflection coefficient can be ...
Dual Miller theorem actually expresses the fact that connecting a second current source producing proportional current = in parallel with the main input source and the impedance element changes the current flowing through it, the voltage and accordingly, the circuit impedance seen from the side of the input source.