All insulating materials fail at some level of applied voltage, and ‘dielectric strength’ is the voltage a material can withstand before breakdown occurs. Dielectric strength is measured through the thickness of the material (taking care to avoid surface effects) and is normally expressed as a voltage gradient (volts per unit length). Note that the voltage gradient at breakdown is much higher for very thin test pieces (<100µm thick) than for thicker sections.

The value of dielectric strength for a specimen is also influenced by its temperature and ambient humidity, by any voids or foreign materials in the specimen, and by the conditions of test, so that it is often difficult to compare data from different sources.

Test variables include electrode configuration and specimen geometry, and the frequency and rate of application of the test voltage. Standard strategies include:

- The ‘short-time’ test, increasing the voltage from zero at a predetermined rate (usually between 100 and 3,000V/sec) until breakdown occurs
- The ‘step-by-step’ test, initially applying half the short-time breakdown voltage, and then increasing this in equal increments, holding each level for a set period of time.

Another test term sometimes used is ‘intrinsic dielectric strength’, which is the maximum voltage gradient a homogeneous substance will withstand in a uniform electric field. This shows the ability of an insulating material to resist breakdown, but practical tests produce lower values for a number of reasons:

- Defects, voids, and foreign particles introduced during manufacture which lower the dielectric strength locally, having the effect of reducing the test values as the area tested is increased
- The presence of a stress concentration at the electrode edges or points where the electric field is higher than average
- Due to the damaging effect of an electric discharge during testing
- Because of dielectric heating, which raises the temperature and lowers the breakdown strength.

Another failure mode related to voltage stress failure is ‘**corona**’,
which is ionisation under voltage stress of air inside or at the interfaces
of insulating materials. Breakdown occurs at edges, points, interfaces, voids
or gaps at voltages which depend on the materials and part geometries.

Corona erodes the insulator surface by electron bombardment, associated heat, and sometimes secondary effects from the formation of chemical oxidising agents such as ozone and oxides of nitrogen. This effect begins immediately, and even fractions of a second of exposure at AC voltages near to breakdown will significantly reduce the breakdown strength. Corona-induced breakdown will also occur at lower voltages, but the time required will be longer.

You are designing a high-voltage circuit which contains an optoelectronic isolator. What issues relating to material breakdown should you be aware of both in your layout and in specifying materials and quality standards?

The simplest capacitor structure is a pair of parallel conducting plates separated by a medium called the ‘dielectric’. The value of the capacitance between the plates is given by the equation:

where:

*A* = the area of the plates

*t* = the separation between the plates

and ε (Greek letter epsilon) is the absolute permittivity of the dielectric, which is a measure of the electrostatic energy stored within it and therefore dependent on the material.

A more usual way of writing the equation is to replace the absolute permittivity
of the dielectric by the product term ε_{0}ε_{r}, where e_{0}
is the permittivity of free space (that is, of a vacuum), which has a value
of 8.85×10^{-12} Fm^{-1}, and e_{r} is the relative
permittivity, more usually called the ‘**dielectric constant**’.
In some literature, you will also find this dimensionless quantity (it is
a ratio) referred to as κ (Greek letter kappa).

The dielectric constant of an insulating material is therefore numerically the ratio of the capacitance of a capacitor containing that material to the capacitance of the same electrode system with vacuum replacing the insulation as the dielectric medium.

Nothing is going to have a relative permittivity less than that of a vacuum! All materials will therefore have a dielectric constant greater than 1. Dielectric constants of polymers at room temperature are normally in the range 2 to 10, the lower values generally being associated with the lowest electrical loss characteristics.

The dielectric constant of any given material varies with temperature, and for polymers a rapid increase begins near their glass transition temperature. Dielectric constants also vary as a function of frequency, and this aspect will be important when you look at high frequency designs.

Most materials used for capacitors have substantially higher dielectric constants than polymers, sometimes many tens of thousands. However, this is often achieved at the expense of stability. Most of these high-permittivity dielectrics are ceramics, such as barium titanate and these can be used as fillers in polymers to increase the dielectric constant if this is required.

As well as dielectrics breaking down, as described above, most capacitors lose a fraction of the energy when an alternating current is applied. In other words, the dielectric is less than perfect. The simplest model for a capacitor with a lossy dielectric is as a capacitor with a perfect dielectric in parallel with a resistor giving the power dissipation. The current now leads the voltage by a very little less than 90°, where the difference δ (Greek letter delta) is termed the dielectric loss angle, as seen in Figure 1.

Without bothering about the equations, the fraction of the maximum energy lost each cycle, divided by 2π is termed the ‘loss factor’ and its value is given by tan δ (‘tan delta’): typically it is values of tan δ that you will find quoted in reference material.

Make sure that you understand the difference between losses in the dielectric which happen when alternating current is applied, and for which tan δ is the measure, and insulation resistance, which is a function of the direct current that flows when a voltage is applied.

Table 1 shows some typical values of dielectric constant, loss factor, and
dielectric strength. The AC values are measured at 1MHz.

material | e_{r} |
tan δ | MVm^{-1} |
---|---|---|---|

air | 1.0006 | 0 | 3 |

polycarbonate | 2.3 | 0.0012 | 275 |

FR-4 | 4.4 | 0.035 | 70 |

alumina | 8.8 | 0.00033 | 12 |

barium titanate | 1200+ | 0.01 | 2 |

For your microwave application, why might the electronic designer with whom you are working be interested in using a special laminate (Rogers 3003) instead of FR-4 (see http://www.rogerscorporation.com/)?

Author: Martin Tarr

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