Dielectric losses are the part of electrical energy that an insulating material converts into heat in an alternating field, because its polarisation lags behind the field and a small conduction current flows. They are measured as the dielectric dissipation factor tan δ, the ratio of active power to reactive power. The polyester film Hostaphan RN reaches a tan δ of 0.0020 at 50 Hz, the polyimide film Kapton HN 0.0018 at 1 kHz, and PTFE sits at 0.0002. This article works out how much heat such values produce, compares the common films and papers and shows when the dissipation factor really matters in the choice of insulation materials and when it is only a diagnostic value.
Why an insulating material heats up in an alternating field
An electric field displaces charges in the insulating material. Electron clouds deform, ions in the lattice shift slightly from their position, and polar molecular groups rotate towards the field. In an alternating field this happens a hundred times per second at 50 Hz and tens of thousands of times with an inverter. Every reorientation costs energy if the charges cannot follow fast enough. That energy stays in the material as heat.
Four mechanisms contribute to the losses, with very different weight:
- Electronic polarisation follows the field practically without delay up to optical frequencies and causes hardly any loss at technical frequencies.
- Ionic polarisation concerns crystals and ceramics and only becomes lossy in the infrared.
- Orientation polarisation of polar groups (esters in PET, amides in polyamide, hydroxyl in cellulose, water) is sluggish and the main source at mains and inverter frequencies.
- Interfacial polarisation occurs in laminates and papers, where charges accumulate at the boundaries between fibre, resin and oil. It acts mainly at low frequencies.
On top of that comes a small conduction current that also flows under DC voltage and is described by the insulation resistance. In good insulating materials it is negligible compared with repolarisation, in damp or contaminated materials it is not. This gives the most important rule for material selection: non-polar plastics such as PE, PP and PTFE have no dipoles that would have to follow the field and therefore the lowest dissipation factors. How polar and non-polar plastics differ in all electrical properties is covered in the article on electrically insulating plastics.
The dissipation factor tan δ in formulas
In an ideal capacitor the current leads the voltage by exactly 90°, only reactive power flows. In a real insulating material the phase angle is smaller by the loss angle δ, i.e. 90° minus δ. The tangent of this angle is the dielectric dissipation factor:
- tan δ = active power P divided by reactive power Q
- tan δ = εr″ / εr′, the imaginary part divided by the real part of the permittivity
- tan δ = 1 / Q, the reciprocal of the quality factor of a capacitor or resonant circuit
The power loss follows from the dissipation factor. For a component with capacitance C at the RMS voltage U and angular frequency ω = 2π · f, P = U² · ω · C · tan δ. For the heat generated in each cubic centimetre of the insulating material, the calculation uses the electric field strength E: p = ω · ε₀ · εr · tan δ · E². The formula shows what drives the losses. Frequency, permittivity and dissipation factor enter linearly, the field strength squared. Twice the voltage across the same film means four times the heat.
Capacitor datasheets often give the same value as DF (dissipation factor) or as equivalent series resistance ESR, with ESR = tan δ / (ω · C). The German term Verlustfaktor has a second meaning, however. In mechanics and rheology tan δ describes the damping of a material as the ratio of loss modulus to storage modulus. That value has nothing to do with the electrical dissipation factor.
How much heat dielectric losses generate
The order of magnitude decides whether the dissipation factor matters for a component. The table works through the formula for a field strength of 10 kV/mm using manufacturer datasheet values. The calculation is our own, the input values come from the datasheets of Mitsubishi Polyester Film (Hostaphan RN), DuPont (Kapton HN), Arclin (Nomex 410) and, for PP, from the middle of the range quoted by capacitor manufacturers.
| Material and condition | εr | tan δ | Power loss at 10 kV/mm |
|---|---|---|---|
| PET film Hostaphan RN, 50 Hz, 23 °C | 3.3 | 0.0020 | 1.8 mW/cm³ |
| PET film Hostaphan RN, 50 Hz, 150 °C | 3.6 | 0.0048 | 4.8 mW/cm³ |
| Aramid paper Nomex 410, 0.25 mm, 60 Hz, 50 % RH | 2.7 | 0.006 | 5.4 mW/cm³ |
| Aramid paper Nomex 410, 0.25 mm, 60 Hz, 96 % RH | 3.2 | 0.011 | 11.7 mW/cm³ |
| PP film, 1 kHz | 2.2 | 0.0003 | 3.7 mW/cm³ |
| Polyimide film Kapton HN 25 µm, 1 kHz | 3.4 | 0.0018 | 34 mW/cm³ |
| PET film Hostaphan RN, 1 kHz, 23 °C | 3.3 | 0.0052 | 96 mW/cm³ |
At mains frequency these are milliwatts. A 0.25 mm thick PET slot liner with an area of 10 cm² has a volume of 0.25 cm³ and generates less than half a milliwatt even at 10 kV/mm. In a 400 V motor only about 1.6 kV/mm is present across the same film, and the power loss drops quadratically to roughly one fortieth. The heat in a winding is generated in the copper, as Joule's law describes. The insulation contributes practically nothing.
The picture changes as soon as frequency and field strength are both high. From 50 Hz to 1 kHz the frequency rises by a factor of 20, but the heat loss of the PET film by a factor of 53, because its tan δ rises too. The effect is clearest in a capacitor. A 10 µF film capacitor carrying 20 V of ripple voltage at 10 kHz handles 251 var of reactive power. With PET film (tan δ around 0.013 at 10 kHz) that becomes 3.3 W of heat, with PP film (around 0.0005) only 0.13 W. That is why DC link and pulse capacitors are made of polypropylene film, more on this in the article on capacitor insulation.
Dissipation factors of insulating films and papers
Datasheet values for tan δ can only be compared together with frequency, temperature and humidity. The table therefore gives the test condition and the source for each value. For semi-finished products made of engineering plastics such as PA, PVC or PEEK, a broader table is in the article on insulating plastics.
| Material | tan δ | Condition | Source |
|---|---|---|---|
| PTFE | 0.0002 | 100 Hz and 1 MHz, IEC 60250 | PTFE semi-finished product datasheet |
| Mica (muscovite) | 0.0001 to 0.0004 | 15 °C | Muscovite mica datasheet |
| PP capacitor film | 0.0001 to 0.0005 | 1 kHz | Film capacitor manufacturer data |
| Polyimide film Kapton HN | 0.0016 to 0.0026 | 1 kHz, 12.7 to 125 µm, ASTM D150 | DuPont Kapton HN Data Sheet |
| PET film Hostaphan RN | 0.0020 / 0.0052 / 0.021 | 50 Hz / 1 kHz / 1 MHz, 23 °C, VDE 0345 | Mitsubishi Polyester Film |
| PET film Mylar | 0.0025 / 0.0050 / 0.016 | 60 Hz / 1 kHz / 1 MHz, 25 °C, ASTM D150 | DuPont Teijin Films |
| Aramid paper Nomex 410, 0.25 mm | 0.006 / 0.011 | 60 Hz, 50 % / 96 % RH, ASTM D150 | Arclin Nomex 410 Technical Data Sheet |
| Pressboard, oil-impregnated | around 0.01 | 1 kHz, 20 °C, 1 to 5 % water by weight | Omicron, dielectric analysis of power transformers |
The ranking follows the chemistry. PTFE, PP and mica have no polar groups or a rigid lattice and stay below 0.0005. Polyimide and PET carry polar groups in the chain and sit one order of magnitude higher. Papers made of aramid or cellulose also absorb water. Details on the materials are in the articles on Kapton, Nomex, pressboard and micanite, the mica material for high temperatures.
What drives the dissipation factor: frequency, temperature and humidity
Frequency
The statement that the dissipation factor rises with frequency appears in many guides and only holds up to a limit. Hostaphan RN reads 0.0020 at 50 Hz, 0.0052 at 1 kHz and 0.021 at 1 MHz. At 240 MHz and at 9.3 GHz, however, Mitsubishi measures 0.0060 again. Mylar shows the same pattern with 0.016 at 1 MHz and 0.008 at 1 GHz. The reason is relaxation: the dissipation factor of a polar material peaks where the frequency matches the mobility of its dipoles and falls again above that, because the dipoles can no longer follow the field at all. PP, by contrast, stays low across the entire technical range, from 0.0001 to 0.0005 at 1 kHz to at most 0.0025 at 100 kHz.
Temperature
With rising temperature, dipoles and charge carriers become more mobile. Hostaphan RN rises at 50 Hz from 0.0020 at 23 °C to 0.0048 at 150 °C, its permittivity from 3.3 to 3.6. For transformers, tan δ is therefore referenced to 20 °C. According to IEEE C57.12.90, a value measured at 40 °C is multiplied by 0.64, one measured at 60 °C by 0.41. More heat produces more losses, which in turn produce more heat. If the component cannot dissipate the heat faster than it is generated, the insulation heats up until thermal breakdown. This mechanism mainly affects materials with a high tan δ under high field strength and is one reason why the dielectric strength of thick insulation drops per millimetre.
Humidity
With a permittivity of around 80 and a high dissipation factor, water is the strongest disturbance in any insulating material. The datasheets show how much it matters:
- Nomex 410 at 0.25 mm doubles its tan δ at 60 Hz from 0.006 at 50 % to 0.011 at 96 % relative humidity, at 1 kHz it rises from 0.014 to 0.025.
- Kapton HN rises from 0.0015 to 0.0035 between dry and saturated air, although polyimide film is considered insensitive to moisture.
- Oil-impregnated pressboard reaches a tan δ of around 0.02 at 0.01 Hz with 1 % water by weight and close to 1 with 5 %. At 1 kHz all moisture levels sit around 0.01.
The last point has a practical consequence. Moisture shows up in the dissipation factor mainly at low frequencies. Omicron measured more than 100 power transformers and found the same tan δ of 0.5 % at 50 Hz with both 1.4 % and 4 % water by weight in the cellulose. Anyone who wants to detect moisture measures across a wide frequency range down to millihertz.
Dielectric absorption is a separate effect
Dielectric absorption is often equated with dielectric losses but describes something else: the recovery voltage of a capacitor. After short-circuiting, sluggish dipoles stay aligned for seconds to minutes and build up a voltage at the electrodes again. It is measured to EN 60384-1: charge at rated voltage for 60 minutes, discharge through 5 Ω for 10 seconds, measure the recovering voltage after 15 minutes. Typical values are 0.05 to 0.1 % for PP film, 0.2 to 0.25 % for PET film, 0.6 to 1 % for X7R ceramic and around 10 % for aluminium electrolytic capacitors.
Both effects share the same root, sluggish orientation polarisation, and that is why PP films perform best in both. For safety, absorption matters more than the dissipation factor: a high-voltage capacitor that has already been discharged can recharge to a life-threatening voltage.
How the dissipation factor is measured
For solid insulating materials, IEC 62631-2-1 applies today. It describes the measurement of permittivity and dissipation factor with AC voltage between 0.1 Hz and 10 MHz on a plate specimen with a guard ring electrode that ensures a homogeneous field. Many datasheets still cite the older IEC 60250 or the American ASTM D150. In equipment diagnostics, tan δ is measured on the finished asset:
- Insulating oil to IEC 60247, in the lab for example at 90 °C, 50 Hz and 2,000 V in a test cell with 2 mm electrode spacing. A rising value indicates ageing or contamination.
- Medium-voltage cables with VLF test voltage at 0.1 Hz. According to IEEE 400.2, aged XLPE cable at 1.0 U₀ is considered good below 4 × 10⁻³, above 50 × 10⁻³ action is needed. Rising values point to water trees in the insulation.
- Transformers and bushings at mains frequency or across a wide frequency range, to separate moisture in paper and pressboard from the conductivity of the oil.
A dissipation factor measurement does not replace testing for partial discharges. A single defect channel in the insulation can destroy an installation without measurably raising the tan δ of the whole cable. Both quantities can, however, be recorded in one run at 0.1 Hz.
When the dissipation factor decides the material choice
Our assessment from working with motor, transformer and appliance manufacturers: for insulation parts at mains frequency, tan δ is not a selection criterion. Slot liners, phase separators, slot wedges and layer insulation are chosen by insulation class, dielectric strength and mechanics. The calculation above shows why. The dissipation factor becomes the first criterion in four cases:
- Capacitors, especially DC link, snubber and pulse capacitors. Here there is hardly an alternative to PP.
- High-frequency and signal engineering, where tan δ directly determines attenuation. PTFE, PE and PP are the materials here, and in older resonant circuits also polystyrene film in Styroflex capacitors.
- Humid locations with papers and pressboard, where the dissipation factor indicates ageing and moisture content.
- High-frequency welding as the reverse case. It needs a tan δ above 0.01, otherwise the seam does not heat up. PVC can therefore be HF welded, PP and PTFE film cannot.
The obvious objection concerns inverter-fed motors: several kilohertz of switching frequency should multiply the losses in the insulation. The frequency does rise, but the field strength in the slot stays low. The damage in inverter windings comes from voltage peaks and the resulting partial and corona discharges that erode the insulation. Anyone looking to improve here invests in corona-resistant materials and laminates, not in a film with a tenth of the dissipation factor.
Insulation parts made of low-loss films at GOBA
GOBA is the largest European converter of Mitsubishi Hostaphan thick films. The values in this article therefore come from the datasheet of a film we slit every day. From roll stock we produce slit rolls from 5 to 1,600 mm wide with a width tolerance of plus or minus 0.1 mm in contract slitting. In stamping and forming we process material thicknesses from 0.023 to 3.0 mm, which includes 25 µm polyimide film for high-temperature parts. We supply Kapton, Nomex, Mylar and Hostaphan as UL-listed branded material, details on the polyester grades are on the polyester films page. Send us your drawing, voltage, frequency and operating temperature, and we will propose the material whose datasheet fits your operating point.
