Loss Tangent - Discrete Circuit Perspective

Discrete Circuit Perspective

For discrete electrical circuit components, a capacitor is typically made of a dielectric placed between conductors. The lumped element model of a capacitor includes a lossless ideal capacitor in series with a resistor termed the equivalent series resistance (ESR), as shown in the figure below. The ESR represents losses in the capacitor. In a low-loss capacitor the ESR is very small, and in a lossy capacitor the ESR can be large. 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 representing the loss due to both the dielectric's conduction electrons and the bound dipole relaxation phenomena mentioned above. 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 lossless capacitance.

When representing the electrical circuit parameters as vectors in a complex plane, known as phasors, a capacitor's loss tangent 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. The loss tangent is then

.

Since the same AC current flows through both ESR and X_c, the loss tangent is also the ratio of the resistive power loss in the ESR to the reactive power oscillating in the capacitor. For this reason, a capacitor's loss tangent is sometimes stated as its dissipation factor, or the reciprocal of its quality factor Q, as follows

.