Dissipation Factor (DF)
DF and "loss tangent" are largely equivalent terms describing capacitor dielectric losses. DF refers specifically to losses encountered at low frequencies, typically 120 Hz to 1 KHz. At high frequencies, capacitor dielectric losses are described in terms of loss tangent (tan ð). The higher the loss tangent, the greater the capacitor's equivalent series resistance (ESR) to signal power. In addition, the poorer its Quality Factor (low Q), the greater its loss (heating) and the worse its noise characteristics.
When a capacitor is used as a series element in a signal path, its forward transfer coefficient is measured as a function of the dielectric phase angle, (theta). This angle is the difference in phase between the applied sinusoidal voltage and its current component. In an ideal capacitor, (theta) equals 90°. In low-loss capacitors, it is very close to 90o. (See Figure 3)
For small and moderate capacitor values, losses within the capacitor occur primarily in the dielectric, the medium for the energy transfer and storage. The dielectric loss angle, ð, is the difference between (theta) and 90o and is generally noted as tan o. The name "loss tangent" simply indicates that tan ð goes to zero as the losses go to zero. Note that the dielectric's DF is also the tangent of the dielectric loss angle. These terms are used interchangeably in the literature.
Figure 2A: A film capacitor model showing Dielectric Absorption (Rda + Cda). The total instantaneous charge on a capacitor may be expressed as Q = V C(Tt) + Qa (VTt), where C is the measured capacitance, V the applied electrode potential, Qa the absorbed charge not directly contributing to electrode potential, T the temperature, and t the time.
Quality Factor (Q)
Quality Factor (Q) is the ratio of the
energy stored to that dissipated per cycle. For a reactive component, this
is defined:
Q = Xc/ Resr = tan (theta)
In one aspect, Q is a figure of merit in that it defines a circuit
component's ability to store energy compared to the energy it wastes. The
rate of heat conversion is generally in proportion to the power and
frequency of the applied energy. Energy entering the dielectric, however,
is attenuated at a rate proportional to the frequency of the electric
field and the loss tangent of the material. Thus, if a capacitor stores
1000 joules of energy and dissipates only 2 joules in the process, it has
a Q of 500. The energy stored in a capacitor (joules. watt-sec) = 1/2 C(V).
Equivalent Series Resistance (ESR)
Equivalent series resistance (ESR) is
responsible for the energy dissipated as heat and is directly proportional
to the DF. A capacitor should be depicted as an ESR in series with an
ideal capacitance (C). ESR is determined by:
ESR = (Xc/Q = Xc (tan ð), with Q = 1/DF.
From this, we can see that "lossy" capacitors and those that
present large amounts of Xc will be highly resistive to the signal power.
Circuit designs employing low Q capacitors usually produce large quantities of unwanted heat because tan ð and DF (or 1/Q) typically increase in a non-linear fashion with rising frequency and temperature. With some capacitors, this effect is enhanced by the naturally occurring decreased capacitance at high frequencies. High currents also produce increase heat, which in turn again increases the ESR and DF.
Even with substantial changes in current flow, high Q (low DF) capacitors will not exhibit the value shifts common to equivalent components exhibiting high DF, ESR, and other parasitics. Low ESR reduces the unwanted heating effects that degrade capacitors. This is an important goal in designing these components for high -current, high-performance applications, such as power supplies and high-current filter networks.
As Figure 4 shows, the significance of loss-contributing factors depends to some degree on the value of the capacitor.
Figure 3: This shows capacitive vector represented in the impedance plane. In an ideal capacitor, (theta) = 90° and tan ð = 0 (for R = 0).
As capacitance increases, different factors have more influence on the capacitor's total ESR.
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