# Resistance Values of PCBs

#1

Copper is a common conductive metallic layer on the surface of Copper Clad Boards/ Bare Printed Circuit Boards (PCBs). Before looking for the resistance value of your PCBs, please note that the resistance values of copper will vary when the temperature changes. To calculate these values, the following equations can help.

For example, refer to the below figure about resistance values per unit area of copper in different temperatures. Note the physical dimensions given for the copper; thickness (t) 35μm, width (w) 1mm, and length (ʅ) 1mm.

When calculating the general resistance, R , you can use the following formula .
R = (ρ x ʅ) / (t x w) X 10 [mΩ], where

• ʅ : Conductor length [mm]
• w : Conductor width [mm]
• t : Copper thickness [μm]
• ρ : Resistivity of copper [μΩcm ], where
** ρ (@ 25°C)= 1.72 μΩcm
** ρ (T) = p (@ 25°C) x { 1 + 0.00385 ( T - 25) } [μΩcm]
** T : Temperature

When calculating from the resistance value Rp per unit area, you can use following formula .
R = Rp x ( ʅ / w ) / ( 35 / t ) [mΩ], where

• Rp : Resistance value referred from graph [mΩ]
• ʅ : Conductor length [mm]
• w : Conductor width [mm]
• t : Copper thickness [μm]

Then resistance value ( R ) at 25°C, PCB copper size at the width 3mm and length 50mm is

• R = 0.49 x ( 50 / 3 ) x (35 / 35 ) = 8.17mΩ

Therefore your voltage drop becomes 24.5mV when 3A current is flowing at 25°C.
However at 100°C, the resistance value increases by 29% and voltage drop becomes 31.6mV.

#2

Ascertaining the obstruction of printed circuit board tracks

It is once in a while important to know the DC obstruction of a track, and its opposition can be determined from the equation

R = ρ*L/A

where

R is the conclusion to-end track obstruction in Ohms

ρ is the resistivity of the track material in Ohm Meters

L is the track length in meters

An is the track cross sectional territory in square meters

as indicated by the universal MKS standard of units.

Track Opposition ®

A material with a higher resistivity ρ (the characteristic quality to oppose the stream of power) will show higher track opposition. Along these lines

R α ρ

A more extended track length L will expand track obstruction (power needs to push its way through a more drawn out way.) Along these lines

R α L

A bigger track cross-area A will diminish the track opposition (bigger cross segment implies that it is less demanding for the power to go through.) Consequently

R α 1/A

Opposition is in this way

R = K* ρ* L/A

where K is a steady. In the event that we picked helpful units, K = 1, and the recipe decreases to

R = ρ*L/A

Resistivity, ρ (Rho)

What is ρ? The resistivity ρ of the metal is a proportion of its characteristic capacity to oppose the stream of power, and in MKS units is the opposition in Ohms between the two end appearances of a bit of the material which is one square meter in cross area and one meter long, and is given in “Ohm Meters”

Sources will cite an assortment of qualities for ρ. This is on the grounds that the resistivity fluctuates with material temperature, atomic structure (as indicated by whether the material was electro-saved, hardened from liquid, rolled, strengthened, and so forth.), polluting influence substance, and that’s only the tip of the iceberg.

With the end goal of this discourse, we accept that your material providers can give the resistivity particular to their copper, or other metal, at room or working temperature. A conceivable MKS figure for ρ for copper will be in the area of 1.65E-8 Ohm Meters, or 0.0000000165 Ohm Meters.

Altering Rho to suit the estimation units you utilize

Perplexity, fear and mistake regularly emerge on the grounds that some transformation of the MKS esteem for ρ is required to adapt to the assortment of units which are ordinarily utilized in industry. No one gauges track measurements and territories in meters.

In Metric units, microns (some of the time called micrometers with the image μm or mm) are more typical for cross segment measurements. Track length is all the more ordinarily in centimeters or millimeters (cm or mm)

In American units, considerably more disarray rules when changing over to thousandths of an inch (old name “mil”, now the IPC standard is “thou” or “thousandth”) for the cross area, and creeps for the length. Realizing that one meter is roughly 39.37 inches, you can infer an estimation of ρ which considers your preferred units. See straightaway.

Ordinary balanced qualities for Rho ρ

You may locate the accompanying estimations of ρ to be valuable in ascertaining opposition of tracks and associations.

For copper:

= 1.65E-8 ohm meters around in MKS units where cross areas (for instance W, W1, T see later) and L are altogether estimated in meters

= 6.50E-1 ohm meters around in American units where cross segments are estimated in mils (thousandths of an inch) and L is in inches

= 1.65E1 ohm meters around in metric units where cross segments are estimated in microns (micrometers) and L is in millimeters.

For gold:

= 2.35E-8 ohm meters roughly in MKS units where cross segments and L are altogether estimated in meters

= 9.35E-1 ohm meters roughly in American units where cross areas are estimated in mils (thousandths of an inch) and L is in inches

= 2.35E1 ohm meters roughly in metric units where cross areas are estimated in microns (micrometers) and L is in millimeters

Cross Segment Zone (A)

The average cross sectional profile of a scratched track is trapezoidal, shown by the figure. The cross sectional zone, An, of a trapezoid is found from the condition

A = 0.5*(W1 + W2)*T1

Figure 1

Be that as it may, the equation R =ρL/A holds whatever the cross sectional shape. You essentially need to figure A for that shape.

Making the count simple

Polar’s Track Opposition Mini-computer is accessible as a possibility for the Si8000 and Si9000. It incorporates a discourse confine that can peruse the current structure esteems from the field solver or permit you enter material sort, track shape and length; the Track Obstruction Adding machine will give you an answer in Ohms for the follow you depict.

You’ll discover the Track Obstruction Mini-computer valuable for power supply applications or on the off chance that you are chipping away at fine geometries and need to think about arrangement misfortune.