Technology / Technical guide
Dielectric Loss Tangent: Phase, Frequency and Equivalent Models
A real capacitor current need not lead its voltage by exactly a quarter cycle. A dissipative component changes the phase relationship. Loss tangent describes a ratio under a stated sinusoidal model; it is not itself a resistance, a leakage-current limit or proof of an insulation failure.
A dimensionless ratio needs a frequency and an equivalent-model convention.
Use the same capacitance representation and electrical boundary throughout the loss calculation.
01 / Phase definition
Measure the departure from the ideal capacitive direction.
For an ideal constant capacitor under sinusoidal voltage, current leads voltage by 90°.
For an ideal constant capacitor under sinusoidal voltage, current leads voltage by 90°. In a capacitive lossy model, define loss angle δ as the departure from that ideal lead. The current phase lead is then 90° − δ within this reference.
The dissipation factor tanδ is dimensionless. It describes the relation between dissipative and reactive components at the specified frequency. A value reported without a frequency, temperature and equivalent-model context cannot be treated as one unchanged material constant for every excitation.
02 / Parallel model
A conductance separates the in-phase current.
At one angular frequency ω, represent the device by a parallel conductance Gp and capacitance Cp, with sinusoidal phasor convention e to the jωt.
At one angular frequency ω, represent the device by a parallel conductance Gp and capacitance Cp, with sinusoidal phasor convention e to the jωt. The admittance is Y = Gp + jωCp. Its in-phase current is GpVrms, and the leading reactive-current magnitude is ωCpVrms.
Within this equivalent model tanδ = Gp/(ωCp). Gp has units of siemens, ω is in rad/s and Cp in farads. This representation can model a selected loss contribution; identifying Gp specifically with dielectric loss requires separating other dissipative mechanisms at the chosen boundary.
03 / Average power
The ratio relates loss to reactive magnitude.
For the same parallel sinusoidal model, average dissipated power is P = Vrms²Gp = ωCpVrms²tanδ.
For the same parallel sinusoidal model, average dissipated power is P = Vrms²Gp = ωCpVrms²tanδ. The reactive-power magnitude is ωCpVrms². The voltage is RMS, rather than peak, and this expression belongs to a single stated branch.
Hypothetically let ωCp = 0.001 S, Vrms = 10 V and tanδ = 0.02. Then Gp = 0.00002 S and P = 0.002 W. These invented quantities illustrate the ratio and units; they identify no MARSTON capacitor, test condition or acceptable loss limit.
04 / Series model
Do not swap series and parallel capacitance silently.
An alternative series model uses resistance Rs with capacitive-reactance magnitude 1/(ωCs).
An alternative series model uses resistance Rs with capacitive-reactance magnitude 1/(ωCs). Within that model tanδ = ωCsRs. TDK’s technical reference presents this series ratio and its frequency and temperature dependence; no component-specific limits from that reference are adopted here.
Cp and Cs describe different equivalent representations of the same measured response at one frequency and need not be identical for substantial loss. Mixing Gp with Cs, or Rs with Cp, in otherwise exact formulas changes the model. Small-loss approximations should remain explicitly identified as approximations.
05 / Mechanism scope
Whole-device loss is not purely dielectric loss.
An equivalent resistive term may include electrode, connection and other conductive contributions as well as dielectric dissipation.
An equivalent resistive term may include electrode, connection and other conductive contributions as well as dielectric dissipation. Therefore a whole-component dissipation factor does not automatically isolate the material’s polarisation loss. The physical attribution requires more than naming an equivalent circuit.
The ESR guide focuses on ripple heating in a series representation. DC leakage concerns a sustained conduction condition, while partial discharge is another phenomenon. None is defined simply by the same dimensionless tanδ label.
06 / Reading limits
A changing loss ratio does not identify one cause.
Frequency can change capacitance, conductive contribution and dielectric response together.
Frequency can change capacitance, conductive contribution and dielectric response together. A rising or falling reported ratio alone does not uniquely locate which physical contribution changed. Comparing ratios therefore requires compatible representations and reference conditions, rather than a universal assumption that higher frequency always means the same loss trend.
This explanation claims no dielectric-loss rating, capacitor material or insulation result for MARSTON equipment. It supplies no measurement or component-replacement procedure. Its purpose is to distinguish phase-related quantities and correctly bounded power expressions from actual product performance.
Related technical guides: Capacitor Dielectrics: Polarisation, Construction and Energy · Filter-Capacitor Reactive Power and Cyclic Stored Energy · Snubber Concepts: Transient Energy, Peak Voltage and Damping.
General background: TDK Electronics: Dissipation Factor and Equivalent Capacitor Models. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| Loss angle | δ = 90° − current lead | Sinusoidal capacitive reference. |
| Parallel factor | tanδ = Gp/(ωCp) | Admittance Gp + jωCp at one frequency. |
| Series factor | tanδ = ωCsRs | Series resistance and capacitance representation. |
| Average loss | P = Vrms²Gp | Single-branch parallel-model power. |
| Attribution | Device ratio versus dielectric contribution | Separate conductive and material mechanisms. |
Engineering questions.
Is tanδ measured in ohms?
No. It is a dimensionless ratio within a stated model.
Are Cp and Cs always equal?
No. Series and parallel equivalent capacitances need not match when loss is substantial.
Can peak voltage replace RMS voltage in the power formula?
Not without the corresponding conversion; the displayed expression uses RMS voltage.
Does every dissipation-factor contribution come from the dielectric?
No. Whole-device equivalent loss can include conductive structures.
Is DC leakage the same quantity as tanδ?
No. They describe different excitation conditions and quantities.
Does the example establish an acceptable product limit?
No. Its hypothetical values demonstrate arithmetic rather than a rating.
Technical enquiry
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A real capacitor current need not lead its voltage by exactly a quarter cycle. Share the model and applicable operating or design information for an engineering discussion.