PF and DF may be performed on shielded cable systems to determine insulation degradation to reduce in-service cable failures. These tests are applied as diagnostic testing techniques for field testing of service aged cable systems. For lossless insulation, the cable capacitance (C) per unit length can be defined by the following equation: 
where k is the dielectric constant of the insulation e0 is the permittivity (capacitance) of free space (air) di is the diameter over the insulation dc is the diameter of the conductor For cable with conventional insulating materials, the cable conductance (G) per unit length can be defined by the following equation: 
The quantity tan d gives the losses in the insulation when subjected to an electric field and is known as DF or the loss angle of insulating material. The table below provides typical values of dielectric constant k and tan ?. 
When a voltage V is applied to the loss-free insulation system (dielectric), the total current IT drawn by the dielectric is the sum of the capacitive charging current IC and loss current (resistive) IR. The angle formed by the current IT and IC is ?, and the angle formed by the IT and voltage E is ? where cos ? is the PF of the dielectric. The DF (tan ?) test allows an evaluation of an insulation system at operating voltage level and frequency. The tan ? test can also be performed at frequency other than 60 Hz, such as at VLF of 0.1 Hz during proof test conducted at such frequency. According to IEEE std 400-2001, tests conducted on 1500 miles of XLPE insulated cable have established a figure of merit for XLPE at tan d = 2.2