# Conductor / Ampacity

In the following the factors influencing the **current carrying capacity of circuit boards** are named in context with **heat development** on the conductors, to provide **practical guidance** for implementation. In this complex topic, we can give you only a** basic dimensioning feeling**. If you need quite exact data, please use appropriate **special software** which takes into account: conductive pattern, layer structure and time (see TRM www.adam-research.de).

## History

The design guideline** IPC-2221** (predecessor document: MILSTD 275) is the default data source for the DC temperature resistance of conductors. The measurements thereto come from the National Bureau of Standards (**NBS**) from the 1950s and refer to a 1.6mm thick PCB with a straight current-carrying conductor (thickness 35µm) and a 35µm Cu solid area on the back. They do not consider the surrounding medium (air pressure, motion), or the layout density.

In the 1960s the American magazine **Design News** published amended recommendations. In the mid-80s, in Germany the** DIN IEC 326** comes out, which attends to this topic - the values obtained are quite similar to those from the Design News (with all advantages and disadvantages).

The tables specified here can therefore only be used to **roughly estimate** the temperature development.

## Conductor / ampacity

The following diagrams serve to** estimate heat production** for individual outer layers, depending on power load, conductor trace -width and -thickness. This applies to printed circuit boards with **conductive pattern on one side**, 1.6 to 3.2mm nominal thickness, and copper as conducting material. Additional metal coatings such as nickel, gold, or tin are not considered (diagram according to DIN IEC 326).

#### Cond. thickn. 18µm

#### Cond. thickn. 35µm

#### Cond. thickn. 70µm

#### Cond. thickn. 105µm

## Maximum current at a desired heating rate of 20 K/ 20°C

Conductor-width | max current | ||
---|---|---|---|

Conductor-width | 100µm | max current | 0,6 A |

Conductor-width | 200µm | max current | 1,0 A |

Conductor-width | 300µm | max current | 1,3 A |

Conductor-width | 400µm | max current | 1,5 A |

Conductor-width | 500µm | max current | 1,8 A |

Conductor-width | 600µm | max current | 2,0 A |

Die Berechnung der Werte ist eine Näherung aus den abgeleiteten Formeln der IPC 2221 (s. unten). Leichte Abweichung zu den Grafiken weiter oben (laut DIN IEC 326) sind der Komplexität des Themas geschuldet. Eine grobe Abschätzung sollte damit aber möglich sein.

## Formulas for calculating the maximum current

The formulas we use are based on the results of Oliver Betz (www.oliverbetz.de) and are an approximation from the formulas of the IPC, Design News and Dr. Johannes Adam.**I[A] = K x h[mm]^0,5 x w[mm]^0,64 x ΔT[K]^0,5**

I = current

K = fixed factor (2 layers: K = 3,3; 4 layers: K = 3,6)

w = conductor width

h = conductor height

ΔT = temperature increase in Kelvin (=temperature increase in degree °Celsius)

Please note: Despite careful checking of the formulas, we cannot grant any warranty for their accuracy!

The original* formula of IPC:

I[A] = 9,6 x A[mm²]^0,68 x ΔT[K]^0,43

A = w x h of the conductor**The original formula of Design News:**

I[A] = 6,4 x A[mm²]^0,69 x ΔT[K]^0,45

*In the original IPC documentation no formulas are given, these were derived by e.g. Donald Brooks.

## Additional information

Because of the unavoidable underetching in the printed circuit board production, the **maximum current carrying capacity** of the conductor **does not change in proportion to the (calculated) conductor cross section**, because it deviates from the ideal rectangular cross section (through underetching).

If we double the conductor cross-section area through a **higher copper thickness** without changing the conductor width, the **maximum current carrying capacity** of the conductor increases only **by 30% - 40%**.

To achieve a **higher current capacity**, we recommend not only to consider the thickness of the copper base lamination, but better to** increase the conductor line width**. This allows better heat dissipation and thus increase of the effective current carrying capacity is reached. The boards are also **cheaper **to produce.

When concentrating on the **temperature increase** (ΔT) of the conductor, the** length of the conductor can usually (!) be ignored**. According to the Stefan-Boltzmann law, the amount of heat produced (J) and the heat dissipation is directly proportional to the surface area, i.e. the more heat is produced through the length of a conductor, the more heat can dissipate.

In special cases (very short conductor, close to heat spreaders such as plugs, etc.) this rule does not apply and the conductor stays cooler.

The orientation of the conductor seems to have a negligible influence on the heating: standing conductors allow about 5% more power than lying.

Internal conductors are practically resilient the same as external (here is the IPC-2221 wrong).

For critical applications or transient currents, a computer-aided optimization using simulation is recommended in advance of prototyping.

## Tools and Software

Dr. Johannes Adam (formerly Flomerics) provides an easy to use 3D simulation software for printed circuit boards (TRM), further calculations and services in electronics cooling and thermal management: www.adam-research.de

Further tools, like for example the calculation of the resistance of vias can be found here (in German): http://preis-ing.de/extras/alle-berechnungen-im-schnellzugriff/widerstand-von-vias/

## Fundamental works

Dr. Johannes Adam: "Neues von der Strombelastbarkeit von Leiterbahnen" (in German)

Friar, Michael E. and McClurg, Roger H., "Printed Circuits and High Currents", Design News, vol. 23 no. 25, 1968-12-06

Hoynes d.s., NBS Report 4283 "Characterization of Metal-Insulator Laminates", von 1956.

IPC-2221A (predecessor document: IPC-D-275 bzw. MIL-STD 275) >> new edition in IPC-2152

DIN IEC 326, "gedruckte Schaltungen, Leiterplatten, Gestaltung und Anwendung von Leiterplatten", issue 3/85