Standardization of PCB Connectors

Abstract: The specification parameters of wires can be easily obtained from various materials, but how to use these parameters to calculate the resistance of PCB connectors? This article will introduce the relationship between wire specifications and PCB connector size, as well as the functional relationship between resistance and size and temperature to calculate the resistance of connectors in PCB design.

A large amount of information on size-related wire electrical parameters (commonly called wire specifications) can be obtained from various publications and manuals. However, there is little information on how to use this information to analyze the parameters of PCB connectors. The following article will introduce the relationship between wire specifications and connector area, as well as how to use the functional relationship between connector resistance and size and temperature.

Background Information

The American wire gauge (AWG) system was established by J.R. Brown in 1857 and is called the Brown & Sharp (B&S) gauge. From the production process of wires, it can be known that wires are drawn through a series of holes with gradually decreasing diameters, and the wire gauge roughly reflects the number of steps required for drawing. For example, a wire with a gauge of 24 is drawn 4 more times than a wire with a gauge of 20. The table lists the current wire specifications and their corresponding diameters and cross-sectional areas.

These steps are not specifically defined in all the materials, but one thing is consistent: the diameter of specification 0000 (4/0) is defined as 0.4600 inches; the diameter of specification 36 is 0.0050 inches. The geometric dimensions of other specifications are between two points. If these dimensions are evenly distributed, the ratio between any two adjacent diameters can be obtained by the following formula (Note: there are 39 levels between specification 0000 and specification 36).

In fact, the diameters of various specifications are not evenly distributed. The ratio between any two adjacent diameters in the table is very close to the calculation result of this formula, but after multiple levels, there will be a large deviation due to the accumulation of errors. Therefore, the calculated value using the above formula is an approximation rather than an actual value.

Calculation equation

In the curve diagram of diameter, common logarithm of diameter and wire specification, it can be seen that the growth of diameter has a certain rule, and the logarithm of wire diameter and wire specification curve is almost a straight line. The equation of this curve is: Gauge = -9.6954 – 19.8578×Log10(d), where d is the wire diameter in inches.

The cross-section of a printed circuit board connection wire is rectangular rather than circular. Therefore, the following equation can be defined with the cross-sectional area as a variable: Gauge = 1.08 0.10×Log10(l/a), where a is the cross-sectional area in square inches.

When the cross-sectional area of the wire is known, the equivalent wire gauge can be calculated by the above equation. Conversely, when the wire gauge is known, the cross-sectional area of the connecting wire can be calculated by the following equation: Area = l/(10(10×Gauge – 10.8))

Wire resistance

Some parameter values of the relevant specifications are often provided in the wire gauge table. These parameter values can be used to estimate the resistance of a certain length of wire. The calculation of the connecting wire resistance is slightly more complicated than the calculation of the wire resistance. Each metal has a resistivity (sometimes called characteristic resistance), and the relationship between resistivity, wire length, cross-sectional area and resistance is: R=ρ×l/a

Where R is the resistance in ohms, l is the wire length, and a is the cross-sectional area. The units of resistivity are expressed in ohms and length units. The resistivity of pure copper is usually: ρ=1.724 (microohm-cm) or ρ=0.6788 (microohm-cm)

This parameter can be used to calculate the resistance of any copper connection wire, that is, the resistivity is divided by the cross-sectional area of the connection wire and multiplied by the length of the connection wire. However, it must be noted that the resistivity changes with temperature, and the resistivity usually given is the resistivity at 20°C. Therefore, the resistance value calculated using this resistivity is the resistance at an ambient temperature of 20°C.

The resistance of the connecting wire increases with temperature. The parameter called “temperature coefficient of resistance” can indicate the magnitude of this change. The following formula can be used to calculate the effect of this parameter on the resistance size: R2/R1 = 1 0.00393×(T2-T1)

Where R1 and T1 are the reference resistance and reference temperature (in °C), respectively. T2 is the new temperature, and R2 is the resistance at the new temperature.

Solder layer

Finally, let’s analyze the change in the resistance of the connecting wire caused by the solder layer. The resistance of any conductor is a function of its resistivity. The connecting wire and the solder layer can be considered as parallel conductors during analysis. Assuming that the solder layer and the connecting wire have the same width and length, only the thickness of the connecting wire and the solder layer needs to be considered.

The resistivity of copper is 1.724 micro-ohm-cm, while the resistivity of tin is 11.5 micro-ohm-cm, which is 6.7 times higher than that of copper. The resistivity of lead is 22 micro-ohm-cm, which is about 13 times higher than that of copper. Therefore, based on the ratio of tin and lead in the solder, the resistivity of the solder layer is about 10 times higher than that of a copper connection wire of the same thickness.

Since the size of the shunt between conductors is inversely proportional to the resistance, with the same thickness of copper wire and solder layer, about 90% of the current flows through the copper wire (the remaining current flows through the solder layer). Therefore, the effect of the solder layer on the connection line resistance and voltage drop can usually be ignored in non-precise measurements.

Standardization of PCB Connectors