# Capacitor ESR, Dissipation Factor, Loss Tangent & Q

### Important parameters associated with capacitors include: ESR– equivalent series resistance, dissipation factor, loss tangent, & Q.

ESR or the equivalent series resistance of the capacitor, its DF or dissipation factor, loss tangent and Q or quality factor are all important factors in the specification of any capacitor.

Factors like the ESR, dissipation factor, loss tangent and Q are important in many aspects of the operation of a capacitor and they can determine the types of application for which the capacitor may be used.

ESR, DF and Q are all aspects of the performance of a capacitor that will affect its performance in areas such as RF operation. However ESR, and DF are also particularly important for capacitors operating in power supplies where a high ESR and dissipation factor, DF will result in large amount of power being dissipated in the capacitor.

## Capacitor ESR, equivalent series resistance

The equivalent series resistance or ESR of a capacitor has an impact on many areas where capacitors may be used. The resistor acts like any other resistor giving rise to voltage drops and dissipating heat.

The ESR of the capacitor is responsible for the energy dissipated as heat and it is directly proportional to the DF. When analysing a circuit fully, a capacitor should be depicted as its equivalent circuit including the ideal capacitor, but also with its series ESR.

Capacitors with high values of ESR will dissipate power as heat. For some circuits with only low values of current, this may not be a problem, however in many circuits such as power supply smoothing circuits where current levels are high, the power levels dissipated by the ESR may result in a significant temperature rise. This needs to be within the operational bounds for the capacitor otherwise damage may result, and this needs to be incorporated within the design of the circuit. If the temperature rise is too high, then the capacitor may be damaged or even destroyed. For electrolytic capacitors, significant temperature rises reduce the expected lifetime even if they do not result in actual damage or destruction.

It is found that when the temperature of a capacitor rises, then generally the ESR increases, although in a non-linear fashion. Increasing frequency also has a similar effect.

## Dissipation factor and loss tangent

Although the ESR figure of a capacitor is mentioned more often, dissipation factor and loss tangent are also widely used and closely associated with the capacitor ESR.

Although dissipation factor and loss tangent are effectively the same, they take slightly different views which are useful when designing different types of circuit. Normally the dissipation factor is used at lower frequencies, whereas the loss tangent is more applicable for high frequency applications.

## Dissipation factor and loss tangent definitions

The definitions of dissipation factor and loss tangent can be defined:

• Dissipation factor:   The dissipation factor is defined as the value of the tendency of dielectric materials to absorb some of the energy when an AC signal is applied.
• Loss tangent:   The loss tangent is defined as the tangent of the difference of the phase angle between capacitor voltage and capacitor current with respect to the theoretical 90 degree value anticipated, this difference being caused by the dielectric losses within the capacitor. The value δ (Greek letter delta) is also known as the loss angle.

Thus:

$\mathrm{tan}\delta =\mathrm{DF}$

$\mathrm{tan}\delta =\frac{1}{Q}$

$\mathrm{tan}\delta =\frac{\mathrm{ESR}}{{X}_{c}}$

Where:
δ = loss angle (Greek letter delta)
DF = dissipation factor
Q = quality factor
ESR = equivalent series resistance
Xc = reactance of the capacitor in ohms.

## Capacitor Q

It is convenient to define the Q or Quality Factor of a capacitor. It is a fundamental expression of the energy losses in a resonant system. Essentially for a capacitor it is the ratio of the energy stored to that dissipated per cycle.

It can further be deduced that the Q can be expressed as the ratio of the capacitive reactance to the ESR at the frequency of interest:

$Q=\frac{{X}_{c}}{\mathrm{ESR}}$

As Q can be measured quite easily, and it provides repeatable measurements, it is an ideal method for quantifying the loss in low loss components.

The capacitor Q is an important parameter for circuits like filters and oscillators. In these circuits any losses will result in reduced Q for the capacitor itself and for the whole filter or oscillator resonant circuit. This can result in reduced performance.

Capacitor ESR, dissipation factor, loss tangent and Q are all important aspects of the loss within a capacitor. They are all linked and essentially different methods of looking at the same issue. However they are used in different areas of circuit design as such capacitor ESR, dissipation factor, loss tangent and Q are all seen in the specification sheets, but for different capacitors used in different areas..

More Basic Concepts:
Voltage     Current     Resistance     Capacitance     Power     Transformers     RF noise     Decibel, dB     Q, quality factor