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Relative Permittivity (Dielectric Constant)
Before one can understand how signal propagation occurs within a PCB, we must consider the importance of a primary electrical parameter, E ' r, identified as relative permittivity or dielectric constant.
The relative dielectric constant, E ' r, is a measure of the amount of energy stored in a dielectric insulator per unit electric field, and hence a measure of the capacitance between a pair of conductors (trace-air, trace-trace, wire-wire, trace-wire, etc.) in the vicinity of the dielectric compared to the capacitance of the same conductor pair in a vacuum. The relative dielectric constant of vacuum is approximately equal to 1.0. All materials have a dielectric constant significantly greater than one. The larger the number, the more energy stored per unit insulator volume. The higher the capacitance, the slower the electromagnetic field travels through the transmission line.
Electromagnetic waves propagate at a speed that is dependent on the electrical properties of the surrounding medium. Propagation delay is typically measured in units of picoseconds/distance (inch or cm). Propagation delay is the inverse of velocity of propagation (the speed at which data is transmitted through conductors). The dielectric constant varies with material parameters. Factors that influence the relative permittivity of a given material include the electrical frequency, temperature, extent of water absorption (also forming a dissipative loss), and electrical characterization technique. In addition, if the PCB material is a composite of two or more laminates, the value of E ' r may vary significantly, as the relative amount of resin and glass of the composite varies.
In air, or vacuum, the velocity of propagation is the speed of light. In a dielectric material, the velocity of propagation is slower (approximately 0.6 times the speed of light for common PCB laminates). Both the velocity of propagation and the effective dielectric constant are given by the equation below.
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(velocity of propagation) |
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(dielectric constant) |
where
C = 3*108 meters per second, or about 30 cm/ns (12 in/ns)
E ' r = effective dielectric constant
Vp = velocity of propagation
The effective relative permittivity, E ' r, is what is experienced by an electrical signal transmitted along a conductive path. Effective relativity permittivity can be determined by using a Time Domain Reflectometer (TDR) or by measuring the propagation delay for a known length line and calculating the value.
FR-4, currently the most common material used in the fabrication of a PCB, has a dielectric constant that varies with the frequency of the signal within the material. Most engineers generally assume that E ' r is in the range of 4.5 to 4.7. These values, referenced by designers for many years and are based on measurements taken with a 1-MHz reference signal. Measurements were not made on FR-4 material under actual operating conditions, especially with today’s high-speed designs. What worked over 20 years ago is insufficient for today's products. A more accurate value of E ' r is determined by measuring the actual propagation delay of a signal in a trace using a TDR.
The figure below shows the "real" value of E ' r for FR-4, based on research by the Institute for Interconnecting and Packaging Electronics Circuits Organization (IPC). This chart is provided in document IPC-2141, Controlled Impedance Circuit Boards and High-speed Logic Design.
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