# 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 equivalent series resistor acts like any other resistor giving rise to voltage drops and dissipating heat. It means that the capacitor is not the perfect capacitor many of us might expect it to be.

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.

The equivalent series resistance is caused by a number of factors including the Ohmic losses in the leads and plates themselves as well as losses in the dielectric material used between the capacitor plates.

Although there can be a focus on the equivalent series resistance or tanδ of a capacitor, it is also worth remembering that the equivalent circuit of a capacitor also includes other equivalent electronic component values as well. It can include an equivalent series inductance as well as a parallel resistance.

In many instances these other components may not be applicable and may complicate the considerations and ESR may be adressed on its own, although it is worth remembering that the other electronic circuit elements also exist.

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 permanently damaged or even destroyed.

For electrolytic capacitors which tend to be the types used in higher current applications, significant temperature rises increases the ageing effects and hence reduce the expected lifetime even if they do not result in actual damage or destruction. This demonstrates the need to be aware of the ESR when selecting the right electronic component for a given electronic circuit design

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.

Obviously the ESR of a capacitor needs to be as low as possible for all electronic circuit designs so that the operation of the capacitor is as near the ideal as possible. However, in electronic circuits such as smoothing capacitors within power supplies where current levels may be high and source resistances need to be low, the ESR can be a significant factor in the selection of the right electronic component.

## 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

In order to better understand both the dissipation factor and the loss tangent it is necessary to provide concise definitions for these terms.

First, let's look at the definition of the dissipation factor:

### Dissipation factor definition:

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.

From this it can be seen that the dissipation factor of the capacitor looks more at the way in which the dielectric, especially, of the capacitor absorbs energy.

The loss tangent takes a look at the same issue, but from the viewpoint of the phase angle issues related to the absorption of energy. This figure tends to be used more widely in RF circuit design scenarios.

### Loss tangent definition:

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.

From the diagram and definition of the capacitor loss tangent it can be seen that the following equation can be derived.

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

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

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

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:

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

Where
Q = the quality factor of te capacitor
Xc = the capacitive reactance of the capacitor in Ohms
ESR = equivalent series resistance in Ohms

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.

## Effects of ESR

Equivalent series resistance is generally associated with electrolytic capacitors, and often with tantalum capacitors, because these electronic components generally have higher values of capacitance and the construction of these capacitors leads to relatively high values of series resistance.

Electrolytic capacitors are often used as energy reserves in power supplies, etc to store energy that will be supplied when the rectified voltage waveform falls in value over parts of the cycle, etc.

They can also be used in switching regulators to remove switching spikes, etc.

In both cases, losses due to ESR will reduce the ability of the capacitor to quickly source or sink charge.

For electronic circuits where the capacitor is used at the input, the ESR increases high frequency noise across the capacitor, and this decreases the effectiveness of the capacitor filtering. If the capacitor is used for output smoothing, etc, a higher ESR causes more ripple to be present as the capacitor will be unable to sink and source the required amount of current.

The ESR of a capacitor is particularly important in electronic circuit designs that have a low duty-cycle with high frequency current pulses. In these cases, the ripple voltage resulting from the higher level of ESR will be greater than expected based on capacitance alone.

It may also be found that the ESR will decrease with increasing temperature and this could mean that the ripple decreases as the assembly warms up.

Another issue in some instances is that the resistive element into what may be assumed as a purely reactive circuit can lead to unexpected shifts in phase response, and this might affect the stability of some electronic circuit designs.

## ESR specifications

The equivalent series resistance is important in many electronic circuit designs, and accordingly some capacitors are specifically manufactured to provide a low ESR. Even though ESR is important, there does not always seem to be a consistent way of specifying the ESR and this can make it difficult to compare one capacitor with another.

As ESR is dependent upon the operating temperature and the frequency, there are several variables in the specification. It is here that the way in which different manufacturers present their specifications is different.

The most common specification is for the ESR at 25°C and a frequency of 100Hz which is double the line power frequency in Europe, etc, or sometimes it is given at 120Hz as this is double the line power frequency in the USA. Sometimes a formula is presented to enable the ESR to be calculated it other frequencies.

Other capacitor manufacturers may provide the data in other ways, whilst sometimes giving methods to calculate the ESR at the required operating points. In all it can become a little confusing.

It is also interesting to note that for capacitors of comparable size and capacitance-voltage, CV rating, it is found that the electronic component with the higher capacitance and lower voltage rating will have lower ESR . Also the ESR tends to be lower for aluminium electrolytic capacitors with long, thin cases because the resistance of the foil is reduced.

A further point to note is that capacitors with larger overall case sizes can sometimes have a lower ESR as the foil thickness could be greater.

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..

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