Delta is the angle between the impedance vector and the imaginary
axis in the complex impedance plane.

δ = 90° - φ
A mathematical capacitor (or perfect capacitor) has a tangent delta = 0

Quality factor

In the technical capacitor there is an active power P_{D}
which is due to the energy dissipation in the resistances.
The capacitor quality factor Q is given by:

where P_{R} is the capacitor reactive power, the one which is used. The loss factor is the inverse of the quality factor.
It may be written with the complementary angle of φ , which is δ .
Tangent delta may also be given by the ration of the losses and reactive
power.

P_{D} the mean losses power averaged during a cycle, in the case where r_{p} is very large,
is given by:

With U(t) = U_{o} sin ωt, the current is given by:

P_{D} is finally given by:

P_{R} the mean reactive power is given by:

Tan δ at “high”
frequency

At high frequency where the effect of the series resistance is
dominating, the electric circuit of a technical capacitor may be simplified to an equivalent
series resistance ESR ~ R_{s}. The loss factor is given by:

Tan
δ at “low frequency”

At low frequency where the effect of the parallel resistance is dominating, the electric circuit of a technical capacitor may be
simplified to an equivalent parallel resistance EPR ~ R_{p}.
The loss factor is given by:

Tan δ of the dielectric material
beweeen the electrode

The parallel part has two contributions which behavior differs as a
function of the frequency: the « ohmic » losses contribution and the polarisation losses.

Total tan δ

To determine the total losses, a series resistance is added in
series in front of the circuit C_{p},r_{p}.

Introducing the tangent delta expression found in the case of a equivalent
parallel circuit, it comes out that:

=>

Introducing the tangent delta expression found in the case of an equivalent series
circuit, and defining the equivalent series capacitance C_{s} to simplify the equation:

By comparison with the impedance expression in the case of a series
equivalent circuit (R_{s} ,C_{s}) of a technical capacitor (r_{p},r_{s}, C_{p}):

Total tan δ frequency behavior

Parallel capacitor

Series capacitors

Dielectric material

Complex permittivity

The loss factor is given by

Dielectric polarization

Interface polarization to be considered for « DC » applications.

Polarization by orientation to be considered at industrial frequency.

Ionic polarization to be considered in the microwave and infra-red frequency domain.

Electronic polarization to be considered in the optical frequency domain.