The resistance of printed circuit board (PCB) traces impacts current capacity, voltage drop, power dissipation, and signal quality. Accurately calculating trace resistance is important during PCB design to ensure proper performance. This guide provides designers useful formulas and an easy-to-use trace resistance calculator to determine resistance based on trace dimensions and copper properties.
Factors Affecting Trace Resistance
The key factors that influence trace resistance include:
- Trace length – longer traces have higher resistance
- Trace width – wider traces have lower resistance
- Trace thickness – thicker copper has lower resistance
- Copper resistivity – intrinsic property based on material
- Trace temperature – resistance increases with temperature
Accurately accounting for each of these parameters allows calculating the total trace resistance.
Trace Resistance Calculation Formulas
There are two common formulas for calculating trace resistance:
General Formula
Where:
- R = Trace resistance (Ω)
- ρ = Copper resistivity (Ω-m)
- L = Trace length (m)
- A = Trace cross-sectional area (m^2)
Wide Trace Formula
For traces wider than 2x their thickness:
Where:
- R = Trace resistance (Ω)
- ρ = Copper resistivity (Ω-m)
- L = Trace length (m)
- w = Trace width (m)
- t = Trace thickness (m)
These formulas relate trace dimensions to resistance.
Copper Resistivity Values
The resistivity of copper varies based on composition and temperature:
| Material | Resistivity at 20°C | Temperature Coefficient |
|---|---|---|
| Pure Copper | 1.72 x 10^-8 Ω-m | 3.9 x 10^-3 Ω-m/°C |
| Electrodeposited Copper | 1.72 x 10^-8 Ω-m | 3.9 x 10^-3 Ω-m/°C |
| Rolled Copper | 1.78 x 10^-8 Ω-m | 3.9 x 10^-3 Ω-m/°C |
Use temperature coefficient to adjust resistivity for temperature.
Converting Units
Trace dimensions and resistance must be converted to standard metric units:
- Length – convert mil to meters by dividing by 39.37
- Width/Thickness – convert mil to meters by dividing by 39.37
- Resistance – convert Ω/square to Ω by multiplying by trace length in meters
Unit conversions enable using standard formulas.
Trace Resistance Calculator
This calculator determines the resistance of a PCB trace based on its dimensions and copper properties:
python
import math def calculate_trace_resistance(length_m, width_m, thickness_m, rho=0.000000017): if width_m > 2*thickness_m: area_m = thickness_m * width_m else: area_m = (thickness_m * width_m) / 1.6 resistance = (rho * length_m) / area_m return resistance
To use:
- Enter trace length in meters
- Enter trace width in meters
- Enter trace thickness in meters
- Function will calculate resistance in ohms
This calculator simplifies determining trace resistance for any PCB design.
Trace Resistance Examples
Let’s go through some examples of using the formulas and calculator:
Example 1
- Trace length: 1500 mils
- Trace width: 8 mils
- Trace thickness: 1 ounce (35 μm)
- Copper resistivity: 1.72 x 10^-8 Ω-m at 20°C
- Convert units:
- Length = 1500 mils / 39.37 = 38.1 mm
- Width = 8 mils / 39.37 = 0.203 mm
- Thickness = 1 oz = 35 μm = 0.035 mm
- Use wide trace formula:
- R = (1.72 x 10^-8 Ω-m) * (0.0381m) / (0.035mm * 0.203mm)
- R = 0.452 Ω
Example 2
- Trace length: 2500 mils
- Trace width: 0.2 mm
- Trace thickness: 0.5 oz (18 μm)
- Temperature: 65°C
- Convert units:
- Length = 2500 mils / 39.37 = 63.5 mm
- Adjust resistivity for temperature:
- 65°C -> 1.72 x 10^-8 * (1 + (65-20)*0.0039) = 2.04 x 10^-8 Ω-m
- Use calculator:
- R = calculate_trace_resistance(0.0635, 0.2e-3, 18e-6, 2.04e-8)
- R = 0.601 Ω
The calculator simplifies trace resistance calculations for any trace geometry and conditions.
Guidelines for Maximum Trace Resistance
To avoid issues, target these maximum trace resistances by application:
- Power traces: 0.05-0.1 Ω
- Ground traces: 0.02-0.05 Ω
- Digital signals: 0.1-0.2 Ω
- High-speed signals: 0.02-0.1 Ω
- Sensitive analog signals: 10-50 Ω
Higher resistances may impact performance, voltage drop, or signal integrity.
Increasing or Decreasing Trace Resistance
To change trace resistance:
Increase Resistance
- Reduce trace width
- Use thinner copper weight
- Lengthen the trace distance
- Meander trace to lengthen within same space
Decrease Resistance
- Widen trace width
- Use thicker copper ounces
- Shorten trace length
- Make trace as straight as possible
- Use lower resistivity material like silver
Temperature Effects on Resistance
To account for temperature:
- Determine temperature rise from ambient
- Calculate adjusted resistivity
- Use new resistivity in resistance formula
For example, with a rise of 45°C above 20°C ambient:
- New resistivity = 1.72 x 10^-8 * (1 + 0.0039 * 45) = 2.0 x 10^-8 Ω-m
High Frequency Effects on Resistance
At higher frequencies:
- Resistance increases due to skin effect
- Use surface roughness modeling
- Remove skin effect depth from cross-section
- Consult resistor company model values
This accounts for current crowding at board edges.
Frequently Asked Questions
How does plating thickness contribute to trace resistance?
Traces are plated to a certain thickness over the base copper. Ensure plating is included in total thickness when calculating resistance.
When do I need to model traces as transmission lines?
At trace lengths over 1/10 of signal wavelength, transmission line models become necessary for precision resistance.
What is the difference between DC and AC resistance?
At DC or low frequency the simple resistance formulas are valid. At higher AC frequencies, additions such as skin effect become significant.
What is the best software for trace resistance analysis?
Many PCB design suites now incorporate resistance calculators and thermal modeling. ANSYS and Cadence are two common advanced modeling tools.
How can I measure trace resistance on a real board?
Use a multimeter with four-point probing to measure resistance between trace endpoints. This eliminates contact resistance.
Conclusion
The resistance of PCB traces affects current capacity, voltage drop, and signal performance. Using the presented formulas and calculator, designers can accurately determine trace resistance based on physical dimensions, copper properties, and operating temperature. Modeling trace resistance during design helps identify any issues early so traces can be optimized for maximum performance and reliability. Combining these models with thermal analysis ensures traces withstand operating currents and temperatures. Equipped with an understanding of trace resistance calculation, PCB designers can deliver robust boards engineered for electrical performance.
