Dissipation factor

# Dissipation factor

Discussion

Encyclopedia
In physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, the dissipation factor (DF) is a measure of loss-rate of energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

of a mode of oscillation
Oscillation
Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...

(mechanical, electrical, or electromechanical) in a dissipative system
Dissipative system
A dissipative system is a thermodynamically open system which is operating out of, and often far from, thermodynamic equilibrium in an environment with which it exchanges energy and matter....

. It is the reciprocal of Quality factor, which represents the quality of oscillation.

For example, electrical potential energy is dissipated in all dielectric
Dielectric
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 in a conductor, but only slightly shift from their average equilibrium positions causing dielectric...

materials, usually in the form of heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...

. In a capacitor
Capacitor
A capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...

made of a dielectric placed between conductors, the typical lumped element model
Lumped element model
The lumped element model simplifies the description of the behaviour of spatially distributed physical systems into a topology consisting of discrete entities that approximate the behaviour of the distributed system under certain assumptions...

includes a lossless ideal capacitor in series with a resistor termed the equivalent series resistance
Equivalent series resistance
Practical capacitors and inductors as used in electric circuits are not ideal components with only capacitance or inductance. However, they can be treated to a very good approximation as ideal capacitors and inductors in series with a resistance; this resistance is defined to be the equivalent...

(ESR) as shown below. 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. Note that the ESR is not simply the resistance that would be measured across a capacitor by an ohmmeter
Ohmmeter
An ohmmeter is an electrical instrument that measures electrical resistance, the opposition to an electric current. Micro-ohmmeters make low resistance measurements. Megohmmeters measure large values of resistance...

. The ESR is a derived quantity with physical origins in both the dielectric's conduction electrons and dipole relaxation phenomena. In a dielectric only one of either the conduction electrons or the dipole relaxation typically dominates loss. For the case of the conduction electrons being the dominant loss, then

, where
is the dielectric's bulk conductivity,

is the angular frequency
Angular frequency
In physics, angular frequency ω is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity...

of the AC current i,

is the lossless permittivity
Permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...

of the dielectric, and

is the lossless capacitance.

If the capacitor is used in an AC
Alternating current
In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....

circuit, the dissipation factor due to the non-ideal capacitor is expressed as the ratio of the resistive
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...

power loss in the ESR to the reactive power oscillating in the capacitor, or

.

When representing the electrical circuit parameters as vectors in a complex
Complex number
A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...

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 diagram to the right. This gives rise to the parameter known as the loss tangent
Loss tangent
The loss tangent is a parameter of a dielectric material that quantifies its inherent dissipation of electromagnetic energy. The term refers to the tangent of the angle in a complex plane between the resistive component of an electromagnetic field and its reactive component.-Electromagnetic...

δ where

.

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
Power factor
The power factor of an AC electric power system is defined as the ratio of the real power flowing to the load over the apparent power in the circuit, and is a dimensionless number between 0 and 1 . Real power is the capacity of the circuit for performing work in a particular time...

when is far less than , which is usually the case.

DF will vary depending on the dielectric material and the frequency of the electrical signals. In low dielectric constant
Dielectric constant
The relative permittivity of a material under given conditions reflects the extent to which it concentrates electrostatic lines of flux. In technical terms, it is the ratio of the amount of electrical energy stored in a material by an applied voltage, relative to that stored in a vacuum...

(low-k
Low-K
In semiconductor manufacturing, a low-κ dielectric is a material with a small dielectric constant relative to silicon dioxide. Although the proper symbol for the dielectric constant is the Greek letter κ , in conversation such materials are referred to as being "low-k" rather than "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.