PCB News - Calculation of resistance in printed circuit board

This article will introduce the use of the relationship between the wire size and the size of the printed board connection line in the PCB design, as well as the functional relationship between the resistance and the size and temperature to calculate the resistance of the connection line.

A large amount of information about the electrical parameters of the wire (usually called wire gauge) related to the size can be obtained from various publications and manuals. But how to use this information to analyze the parameters of the printed circuit board connection line is scarce. The following will introduce the relationship between the wire size and the area of the connecting wire, and how to use the function of the resistance of the connecting wire and the size and temperature.

Background information

American Wire Gauge (AWG) system was established by J.R. Brown in 1857, called Brown & Sharp (B&S) specification. It can be known from the production process of the wire that the wire is drawn through a series of holes with gradually decreasing diameters, and the specifications of the wire roughly reflect the number of steps required for drawing. For example, a wire with a gauge of 24 is pulled 4 times more than a wire with a gauge of 20. Listed in the table are the current wire specifications and their corresponding diameter and cross-sectional area.

There is no specific definition of these steps in all the materials, but one thing is consistent: specification 0000 (4/0), its diameter is defined as 0.4600 inches; specification 36, its diameter is 0.0050 inches. The geometric dimensions of other specifications are between two points. If these sizes are evenly distributed, the ratio between any two adjacent diameters can be obtained by the following formula (note: there are 39 levels between size 0000 and size 36).

Actually, the diameter of each specification is not evenly distributed. The ratio between any two adjacent diameters in the table is very similar to the calculation result of this formula, but after multiple levels, there will be a large deviation due to the accumulation of errors, so the calculated value using the above formula is an approximate value rather than an actual value .

Calculation equation

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

The cross section of the printed circuit board connection line is rectangular instead of circular. Therefore, the equation that can define the cross-sectional area as a variable is as follows: Specification = 1.08 0.10*Log10 (l/a), where a is the cross-sectional area and the unit is square inches.

When the cross-sectional area of the wire is known, the equivalent wire size can be calculated by the above formula. On the contrary, when the wire size is known, the cross-sectional area of the connecting wire can be calculated by the following formula: Area = l/(10(10*specification-10.8))

Wire resistance

Some parameter values of related specifications are often provided in the wire specification table. Through these parameter values, the resistance of a certain length of wire can be estimated. The calculation of the resistance of the connecting wire is slightly more complicated than the calculation of the resistance of the wire. Every metal has a resistivity (sometimes called characteristic resistance). 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 length of the wire, and a is the cross-sectional area. The units of resistivity are represented by ohms and length units. The resistivity of pure copper is usually: ρ=1.724 (microohm-cm) or ρ=0.6788 (microohm-cm)

Use this parameter to calculate the resistance of any copper connection wire, that is, divide the resistivity by the cross-sectional area of the connection wire and multiply it by the length of the connection wire. But 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 the resistivity is the resistance at an ambient temperature of 20°C.

The resistance of the connecting wire increases with temperature. A parameter called "temperature coefficient of resistance" can indicate the magnitude of this change. The influence of this parameter on the resistance can be calculated with the following formula: R2/R1 = 1 0.00393*(T2 -T1)

where R1 and T1 are the reference resistance and reference temperature (unit: °C). T2 is the new temperature and R2 is the resistance at the new temperature.

Solder layer

Finally, let's analyze the change of the solder layer to the resistance of the connecting wire. The resistance of any conductor is a function of its resistivity, and the connecting wire and solder layer can be regarded as parallel conductors in the 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 need to be considered.

The electrical resistivity of copper is 1.724 microohm-cm, while the electrical resistivity of tin is 11.5 microohm-cm, which is 6.7 times higher than copper. The electrical resistivity of lead is 22 microohm-cm, which is about 13 times higher than copper. Therefore, according to the content ratio of tin and lead in the solder, the resistivity of the solder layer is about 10 times higher than that of the copper connection wire of the same thickness.

Since the size of the shunt between the conductors is inversely proportional to the resistance, about 90% of the current flows through the copper wire under the same thickness of the copper wire and the solder layer (the remaining current passes through the solder layer). Therefore, the influence of the solder layer on the resistance and voltage drop of the connecting wire can usually be ignored during inaccurate measurement.

The above is the introduction to the calculation of the circuit resistance of the printed board.Ipcb is also provided to PCB manufacturers and PCB manufacturing technology