Impedance is a very useful concept in the subject of power delivery. In general it provides information about the load being driven by the power source. For the output torque of an automobile transmission, the impedance is the output torque divided by the angular velocity that such torque will sustain. For a jet engine, the impedance is the thrust (force) divided by the air-speed that such thrust will sustain, and for a fluid pump, the impedance is the pressure it delivers divided by the volume flow rate that such pressure sustains. In general, an impedance is the ratio of a force or other physical imposition capable of power delivery, to the reaction that such imposition can sustain, where the reaction is defined such that the product of the imposition and sustained reaction has the units of energy per unit time, or power.

For most mechanical systems, a device's impedance varies with the conditions of the situation (such as what slope the automobile is climbing, or the viscosity of the fluid being pumped by the pump), but an electrical impedance will either be a constant value or it will depend on the frequency component of the driving signal. As illustrated in Figure 1, below, an electrical impedance Z is a two-terminal device which transports electrical charge between its terminals at a time-rate I, measured in Coulombs per second (Amperes), such that I is proportional to the voltage V (electrical pressure) applied across the two terminals. Each circle represents a two-terminal charge pump known as a voltage source, which can sustain the electrical pressure difference given by its indicated voltage V, E1 or E2 as indicated.
The value of the impedance is Z, and as shown above it represents the constant of proportionality in the relationship between the voltage V and the current I. This relationship is known as Ohm's Law, which states:

where V is the difference in the electrical pressures applied across the two terminals, and Z is measured in Ohms (Volts per Ampere). In Fig 1(a), the pressure difference V is applied directly across the terminals of the impedance device Z, but at (b), each pressure E1 and E2 is generated with respect to an ambient (ground) pressure. Thus, E1 and E2 are referred to as the electric "potentials" of the terminals connected to the impedance. This is the more typical means of signal measurement used in electronic circuits. Thus, the electrical pressure difference V applied across the two terminals is usually measured as the potential difference E1 - E2. For any given potential difference (voltage) across the two terminals, as the impedance Z increases, the current I decreases proportionately. Likewise, for any given impedance Z, if the voltage is increased, the current must increase proportionately.

In general, the values of E, V and I are expressed as complex, phasor values, having a common sinusoidal frequency throughout the equation. As such, any real-valued voltage applied across the impedance can be accurately represented as a superposition of sinusoidal components, as implied by the Fourier Integral Theorem.

The use of impedance theory (aka classical network theory) has concentrated its interests in three natural and theoretically fundamental types of impedance. The simplest of these forms is the resistance, R, whose current at any given time is proportional to the applied voltage at that time. The other two impedances are known as the capacitance, C, and the inductance, L. For these, the time-dependent functions v(t) and i(t) obey the respective relationships,

where the conventional dx/dt notation denotes the time rate of change in the arbitrary variable x. Because the inductor cannot change its current rapidly in the absence of a large voltage, and because the capacitor cannot change its voltage rapidly in the absence of a large current, these devices have some very useful capabilities in frequency discrimination circuits. Fundamental theory of Laplace Transforms readily shows that the capacitor's impedance has the magnitude of 1/wC, where w is the angular frequency component under consideration; and the inductor's impedance has the magnitude wL. It also follows that for any given signal frequency component, the inductor's current lags its voltage by 90 degrees in phase, whereas in contrast the capacitor's current leads it's own voltage by 90 degrees in phase. As such, for a series wiring of a capacitor and an inductor, where the current i(t) is the same in both, their voltage components for any given frequency are of opposite sign, so they tend to cancel each other out as seen by the external circuitry. So their series impedance is consequently smaller than either of their individual impedances. Because their voltages subtract in accordance with Kirchhoff's Loop Law, the impedance of the series combination is wL - 1/wC. Likewise, when the two are wired in parallel, so that they have the same voltage, their currents are of opposite sign and thereby partially cancel each other out. As such, the impedance of their parallel combination as seen externally is larger than the impedance of either one component. These neutralization characteristics are, for both these wirings, most profound at the angular frequency given by the reciprocal of the square root of the product LC, for this is the frequency at which their impedances are equal and opposite.

We have long been able to manufacture capacitors that approximate the equation (2), for the most part with suitable precision; but the manufacture of inductors that closely approximate the description in equation (1) has been plagued by numerous barriers, especially at low frequencies. As such it has been found advantageous for many applications to simulate inductors electronically. Simulation of impedances is also helpful for such purposes as realizing capacitors and/or inductors whose values are continuously variable.

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