# Dissipation factor

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In physics, the dissipation factor (DF) is a measure of loss-rate of energy of a mode of oscillation (mechanical, electrical, or electromechanical) in a dissipative system. It is the reciprocal of quality factor, which represents the "quality" or durability of oscillation.

Physics is the natural science that studies matter, its motion and behavior through space and time, and that studies the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves.

In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object. Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The SI unit of energy is the joule, which is the energy transferred to an object by the work of moving it a distance of 1 metre against a force of 1 newton.

Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. The term vibration is precisely used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current.

## Explanation

Electrical potential energy is dissipated in all dielectric materials, usually in the form of heat. In a capacitor made of a dielectric placed between conductors, the typical lumped element model includes a lossless ideal capacitor in series with a resistor termed the equivalent series resistance (ESR) as shown below. [1] The ESR represents losses in the capacitor. In a good capacitor the ESR is very small, and in a poor capacitor the ESR is large. However, ESR is sometimes a minimum value to be required. Note that the ESR is not simply the resistance that would be measured across a capacitor by an ohmmeter. The ESR is a derived quantity with physical origins in both the dielectric's conduction electrons and dipole relaxation phenomena. In dielectric only one of either the conduction electrons or the dipole relaxation typically dominates loss. [2] For the case of the conduction electrons being the dominant loss, then

A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor but only slightly shift from their average equilibrium positions causing dielectric polarization. Because of dielectric polarization, positive charges are displaced in the direction of the field and negative charges shift in the opposite direction. This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarized, but also reorient so that their symmetry axes align to the field.

In thermodynamics, heat is energy in transfer to or from a thermodynamic system, by mechanisms other than thermodynamic work or transfer of matter. The mechanisms include conduction, through direct contact of immobile bodies, or through a wall or barrier that is impermeable to matter; or radiation between separated bodies; or isochoric mechanical work done by the surroundings on the system of interest; or Joule heating by an electric current driven through the system of interest by an external system; or a combination of these. When there is a suitable path between two systems with different temperatures, heat transfer occurs necessarily, immediately, and spontaneously from the hotter to the colder system. Thermal conduction occurs by the stochastic (random) motion of microscopic particles. In contrast, thermodynamic work is defined by mechanisms that act macroscopically and directly on the system's whole-body state variables; for example, change of the system's volume through a piston's motion with externally measurable force; or change of the system's internal electric polarization through an externally measurable change in electric field. The definition of heat transfer does not require that the process be in any sense smooth. For example, a bolt of lightning may transfer heat to a body.

A capacitor is a device that stores electrical energy in an electric field. It is a passive electronic component with two terminals.

${\displaystyle {\text{ESR}}={\frac {\sigma }{\varepsilon \omega ^{2}C}}}$

where

${\displaystyle \sigma }$ is the dielectric's bulk conductivity,
${\displaystyle \omega }$ is the angular frequency of the AC current i,
${\displaystyle \varepsilon }$ is the lossless permittivity of the dielectric, and
${\displaystyle C}$ is the lossless capacitance.

If the capacitor is used in an AC circuit, the dissipation factor due to the non-ideal capacitor is expressed as the ratio of the resistive power loss in the ESR to the reactive power oscillating in the capacitor, or

Alternating current (AC) is an electric current which periodically reverses direction, in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in which electric power is delivered to businesses and residences, and it is the form of electrical energy that consumers typically use when they plug kitchen appliances, televisions, fans and electric lamps into a wall socket. A common source of DC power is a battery cell in a flashlight. The abbreviations AC and DC are often used to mean simply alternating and direct, as when they modify current or voltage.

${\displaystyle {\text{DF}}={\frac {i^{2}{\text{ESR}}}{i^{2}|X_{c}|}}=\omega C\cdot {\text{ESR}}={\frac {\sigma }{\varepsilon \omega }}={\frac {1}{Q}}}$

When representing the electrical circuit parameters as vectors in a complex plane, known as phasors, a capacitor's dissipation factor is equal to the tangent of the angle between the capacitor's impedance vector and the negative reactive axis, as shown in the adjacent diagram. This gives rise to the parameter known as the loss tangent tan δ where

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. Because no real number satisfies this equation, i is called an imaginary number. For the complex number a + bi, a is called the real part, and b is called the imaginary part. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers, and are fundamental in many aspects of the scientific description of the natural world.

${\displaystyle {\frac {1}{Q}}=\tan \delta ={\frac {\text{ESR}}{\left|X_{c}\right|}}={\text{DF}}}$

Alternatively, ESR can be derived from frequency at which loss tangent was determined and capacitance

${\displaystyle {\text{ESR}}=\tan \delta \cdot {\frac {1}{2\pi fC}}}$

Since the DF in a good capacitor is usually small, δ ~ DF, and DF is often expressed as a percentage.

DF approximates to the power factor when ${\displaystyle {\text{ESR}}}$ is far less than ${\displaystyle X_{c}}$, which is usually the case.

In electrical engineering, the power factor of an AC electrical power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit, and is a dimensionless number in the closed interval of −1 to 1. A power factor of less than one indicates the voltage and current are not in phase, reducing the time-averaged product of the two. Real power is the instantaneous product of voltage and current and represents the capacity of the electricity for performing work. Apparent power is the average product of current and voltage. Due to energy stored in the load and returned to the source, or due to a non-linear load that distorts the wave shape of the current drawn from the source, the apparent power may be greater than the real power. A negative power factor occurs when the device generates power, which then flows back towards the source.

DF will vary depending on the dielectric material and the frequency of the electrical signals. In low dielectric constant (low-κ), temperature compensating ceramics, DF of 0.1% to 0.2% is typical. In high dielectric constant ceramics, DF can be 1% to 2%. However, lower DF is usually an indication of quality capacitors when comparing similar dielectric material.

In semiconductor manufacturing, a low-κ is a material with a small relative dielectric constant relative to silicon dioxide. Although the proper symbol for the relative dielectric constant is the Greek letter κ (kappa), in conversation such materials are referred to as being "low-k" (low-kay) rather than "low-κ" (low-kappa). Low-κ dielectric material implementation is one of several strategies used to allow continued scaling of microelectronic devices, colloquially referred to as extending Moore's law. In digital circuits, insulating dielectrics separate the conducting parts from one another. As components have scaled and transistors have gotten closer together, the insulating dielectrics have thinned to the point where charge build up and crosstalk adversely affect the performance of the device. Replacing the silicon dioxide with a low-κ dielectric of the same thickness reduces parasitic capacitance, enabling faster switching speeds and lower heat dissipation.

## Related Research Articles

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Hooke's law is a law of physics that states that the force needed to extend or compress a spring by some distance x scales linearly with respect to that distance. That is: , where k is a constant factor characteristic of the spring: its stiffness, and x is small compared to the total possible deformation of the spring. The law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1676 as a Latin anagram. He published the solution of his anagram in 1678 as: ut tensio, sic vis. Hooke states in the 1678 work that he was aware of the law already in 1660.

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In condensed matter physics, the Lyddane–Sachs–Teller relation determines the ratio of the natural frequency of longitudinal optic lattice vibrations (phonons) of an ionic crystal to the natural frequency of the transverse optical lattice vibration for long wavelengths. The ratio is that of the static permittivity to the permittivity for frequencies in the visible range .

A loop-gap resonator (LGR) is an electromagnetic resonator that operates in the radio and microwave frequency ranges. The simplest LGRs are made from a conducting tube with a narrow slit cut along its length. The LGR dimensions are typically much smaller than the free-space wavelength of the electromagnetic fields at the resonant frequency. Therefore, relatively compact LGRs can be designed to operate at frequencies that are too low to be accessed using, for example, cavity resonators. These structures can have very sharp resonances making them useful for electron spin resonance (ESR) experiments and precision measurements of electromagnetic material properties.

## References

1. "Archived copy". Archived from the original on 2009-08-22. Retrieved 2008-11-29.CS1 maint: archived copy as title (link)
2. S. Ramo, J.R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics, 3rd ed., (John Wiley and Sons, New York, 1994). ISBN   0-471-58551-3