## Skin Effect Calculator
*June 18, 2007*

Electrical current always flows in the path that results in the lowest expenditure of energy. At lower frequencies, current flows in a path that reduces I^2*R losses. This is the path of shortest distance and is fairly intuitive to think about.

At higher frequencies, things get a little strange. (more...)

## Four-Layer High-Speed PCB Design
*May 29, 2007*

When minimum cost and high-speed are required, a four-layer board may be the answer. High-Speed PCB design generally requires controlled impedance traces and good power and ground planes in order to meet signal integrity and power integrity requirements. Four-Layer PCBs are essentially made of 2 two-layer hardboards â€śgluedâ€ť together with a pre-preg spacer in between them. The thickness of the pre-preg is not as well controlled as that of the hardboards. So, for good controlled impedance traces, it is recommended to use the layers separated by hardboard as signal and ground. The layers separated by pre-preg can be used as power and ground.

Thus, a recommended stack up for a high-speed four-layer board is; (more…)

## Effects Of Corners In PCB Traces
*April 6, 2007*

A novel SPICE simulation technique was developed to investigate the effects of corners in PCB traces. The PCB traces were modeled by breaking them down into tiny squares or finite elements. A SPICE sub-circuit was made for the finite element and a small square symbol with one pin on each face was also created for it. Many such symbols were then placed in a schematic (like tiles) to graphically and electrically represent a PCB trace. A comparison was then done between a straight trace, one with a 90 degree square corner, and another with a 90 degree corner beveled at 45 degrees. (more…)

## Transmission Line Calculator
*March 6, 2007*

The Excel based tool (see link below) calculates the capacitance and inductance per unit length as well as the impedance of a transmission line. It may be applied to wires, PCBs, etc. (more…)

## PCB Thermal Copper Area
*February 16, 2007*

I published the following Zoho Sheet to calculate the PCB copper surface area to cool a device based on its power dissipation.

It is embedded below and can also be opened in its own window.

## Conductive Ink Traces
*June 14, 2006*

Conductive ink, for example the Dow Corning PI-2000 series of Silver Polymeric Interconnect Materials, can be used to print conductive circuit traces. Generally, the ink is applied using a screen printing technique, with typical print thicknesses of 25 um to 40 um. Sheet Resistivity is specified in milliohms/square at a 25 um print thickness and varies from 8 to 81 for the currently available inks. For comparison, copper has a Sheet Resistivity of 0.68 milliohms/square at a 25 um thickness.

The Sheet Resistivity can be used to calculate the resistance of the printed traces as follows:

Resistance = Sheet_Resistivity*(Length/Width)*(Ref_Thickness/Thickness)

where "Ref_Thickness" is the thickness at which the "Sheet_Resistivity" is specified in the ink's data sheet and "Thickness" is the actual thickness of the ink you are printing.

**The Calculator**

(more...)

## Find PCB Trace Width Based on Power
*April 20, 2006*

I had a request for a calculator to find the width of a PCB trace based on its voltage drop or power dissipation. This time I am trying something new. I made the calculator as an Excel Spreadsheet and posted it on Zoho Sheet. Let me know how the Zoho Sheet works for you.

Note that there are two tabs - one for voltage drop and one for power dissipation. The sheet is embedded below or can be opened in its own window by clicking the following link:

http://www.zohosheet.com/public.do?fid=3083## PCB Via Calculator
*March 12, 2006*

This Javascript web calculator calculates the resistance, voltage drop, and power loss of printed circuit board vias. Note that vias are made out of plated copper which typically has a resistivity of 1.7E-6 to 2.2E-6 Ohm-cm. The calculator has an input box for the resistivity which defaults to 1.9E-6 Ohm-cm.

Updates:

May 22, 2006 - Added thermal resistance calculation.

January 19, 2007 - Minor Clarifications.

March 28, 2007 - Updated resistivity. See comment 12.

June 21, 2007 - Added estimated ampacity. See comment 17.

**Inputs:
**

Finished Hole Dia | ||

Plating Thickness | ||

Via Length |

**Optional Inputs:
**

Applied Current | Amps | |

Plating Resistivity | Ohm-cm |

**Electrical Results:
**

Resistance | Ohms | |

Voltage Drop | Volts | |

Power Loss | Watts | |

Estimated Ampacity | Amps |

**Thermal Results:
**

Thermal Resistance | Deg. C/Watt |

**Notes:
**Resistance = Resistivity*Length/Area

Area = pi*(Inner_dia + Plating_thk)*Plating_thk

Resistivity = 1.9E-6 Ohm-cm (plated copper)

(plated copper is much more resistive than pure copper)

Copper Thermal_Resistivity = 0.249 cm-K/W (at 300K)

Est_Ampacity [Amps] = k*(Temp_Rise [deg C])^b*(Area [mils^2])^c

For IPC-2221 external layers: k = 0.048, b = 0.44, c = 0.725

**References:**

[1] "Constructing Your Power Supply - Layout Considerations", by Robert Kollman

http://focus.ti.com/lit/ml/slup230/slup230.pdf

[2] "Current Carrying Capacity of Vias", by Doug Brooks and Dave Graves

http://www.ultracad.com/articles/viacurrents.pdf

## PCB Trace Width Calculator
*January 31, 2006*

This Javascript web calculator calculates the trace width for printed circuit boards based on a curve fit to IPC-2221 (formerly IPC-D-275). Also see the via calculator.

**New features:**

- Results update as you type
- Several choices of units
- Units and other settings are saved between sessions
- Blog format allows user comments

**Inputs:
**

Current | Amps | |

Thickness |

**Optional Inputs:
**

Temperature Rise | Deg | |

Ambient Temperature | Deg | |

Trace Length |

**Results for Internal Layers:
**

Required Trace Width | ||

Resistance | Ohms | |

Voltage Drop | Volts | |

Power Loss | Watts |

**Results for **External Layers in Air:

Required Trace Width | ||

Resistance | Ohms | |

Voltage Drop | Volts | |

Power Loss | Watts |

**Notes:**

The trace width is calculated as follows:

First, the Area is calculated:

Area[mils^2] = (Current[Amps]/(k*(Temp_Rise[deg. C])^b))^(1/c)

Then, the Width is calculated:

Width[mils] = Area[mils^2]/(Thickness[oz]*1.378[mils/oz])

For IPC-2221 internal layers: k = 0.024, b = 0.44, c = 0.725

For IPC-2221 external layers: k = 0.048, b = 0.44, c = 0.725

where k, b, and c are constants resulting from curve fitting to the IPC-2221 curves

**For geometry diagrams, click on the pictures below.**

**For frequently asked questions, see the comments.**

## PCB Trace Resistance Calculator
*January 24, 2006*

This online web calculator finds the resistance of copper PCB traces (a.k.a. tracks) of given width, thickness, length, and temperature. It can also be used for copper bars (e.g. bus bars). Several choices of common units are available. Enter the Width and Thickness below. Optionally, enter the Temperature and Length, or just leave the default values. (To find the needed trace width based on current, see the PCB Trace Width Calculator.)

May 17, 2006 - Added (lateral) thermal resistance calculations.

January 18, 2007 - Clarified equations.

**The Calculator**

(more...)