Sheet resistance is the electrical resistance of a uniform thin film of material measured across any square area of that film, expressed in ohms per square (Ω/□). When you are routing power on a printed circuit board (PCB), you aren't dealing with discrete resistors; you are dealing with thin sheets of copper. Understanding how this foil behaves electrically is the difference between a board that runs cool and one that triggers thermal shutdowns or logic brownouts.
The Math Behind Ohms Per Square
The core concept of sheet resistance relies on a geometric quirk: the resistance between two opposite edges of a square piece of uniform thin film is constant, regardless of the physical size of the square. A 1 mm × 1 mm square of 1 oz copper foil has the exact same resistance as a 1 meter × 1 meter square of that same foil. The longer path length of the larger square is perfectly offset by its proportionally wider cross-sectional area.
Sheet resistance (Rs) is calculated by dividing the bulk resistivity of the material (ρ) by its thickness (t). For copper at 20°C, the bulk resistivity is approximately 1.68 × 10-8 Ω·m. Because PCB manufacturers specify copper thickness in ounces per square foot (oz/ft²), we translate that weight into micrometers to find our sheet resistance.
| Copper Weight (oz/ft²) | Thickness (μm) | Thickness (mils) | Sheet Resistance (mΩ/□) | Resistance per Inch (at 10 mil width) |
|---|---|---|---|---|
| 0.5 oz | 17.5 μm | 0.69 mils | 0.96 mΩ/□ | 96.0 mΩ |
| 1.0 oz | 35.0 μm | 1.38 mils | 0.48 mΩ/□ | 48.0 mΩ |
| 2.0 oz | 70.0 μm | 2.76 mils | 0.24 mΩ/□ | 24.0 mΩ |
| 3.0 oz | 105.0 μm | 4.13 mils | 0.16 mΩ/□ | 16.0 mΩ |
According to Eurocircuits PCB design guidelines, 1 oz and 2 oz are the industry workhorses. The final column in the table above is a practical shortcut: if you route a 10-mil wide trace, every inch of length adds exactly that many milliohms to your path.
Worked Example: Calculating Trace Resistance and Voltage Drop
Let’s apply this to a real bench scenario. You are designing a 12V LED driver board. The microcontroller needs to switch a 2A load through a low-side MOSFET. The ground return path from the LED connector to the MOSFET source pin is routed on the top layer using standard 1 oz copper. The trace is 20 mils (0.020 inches) wide and 4 inches long.
Step 1: Calculate the number of squares.
Number of squares = Length / Width
Number of squares = 4 inches / 0.020 inches = 200 squares.
Step 2: Find the total DC resistance.
From our table, 1 oz copper has a sheet resistance of 0.48 mΩ/□.
Total Resistance = 200 squares × 0.48 mΩ/□ = 96 mΩ (or 0.096 Ω).
Step 3: Calculate voltage drop and power dissipation.
Voltage Drop (V = I × R) = 2A × 0.096 Ω = 0.192V.
Power Dissipated (P = I² × R) = (2A)² × 0.096 Ω = 0.384W.
Where You Meet Sheet Resistance in Practice
Sheet resistance isn't just an academic exercise; it dictates physical layout decisions across several domains of electrical design.
- PCB Power Distribution Networks (PDN): In low-voltage, high-current digital designs (like a 1.1V core rail for an FPGA drawing 15A), a 20 mΩ trace will drop 0.3V. That drops your core voltage to 0.8V, instantly causing logic failures. Designers use sheet resistance math to pour massive copper polygons and stitch vias to parallel layers, effectively halving the sheet resistance with each added layer.
- Flexible Printed Circuits (Flex PCBs): Flex circuits often use much thinner copper (e.g., 0.5 oz or even 1/3 oz) laminated to polyimide. The sheet resistance is significantly higher, meaning flex traces must be kept exceptionally short or widened dramatically to avoid acting as unintentional fuses.
- Current Sensing Shunts: When you don't want to pay for a dedicated milliohm surface-mount shunt resistor, you can use a precisely calculated zig-zag pattern of copper trace as a cheap, integrated shunt. By knowing the exact sheet resistance of your fab house's copper, you can design a trace that yields exactly 10 mΩ for an op-amp to amplify.
- Busbars and Thin-Film Solar: While not strictly PCB copper, the exact same Ω/□ math applies to the thin silver paste fingers printed on silicon solar cells, or the stamped copper busbars inside a lithium-ion battery pack.
Common Confusions: Sheet Resistance vs. Bulk Resistivity
The most frequent mistake hobbyists and junior engineers make is conflating bulk resistivity with sheet resistance, or assuming sheet resistance is a fixed property of the material rather than the geometry.
Bulk Resistivity (ρ) is an intrinsic material property. Copper’s bulk resistivity is ~1.68 × 10-8 Ω·m whether it is a 1 mm wire or a 100 mm busbar. It is measured in ohm-meters. You can reference fundamental physics tables, such as those provided by Georgia State University's HyperPhysics, to find these baseline constants.
Sheet Resistance (Rs) is a geometric property. It changes the moment your fab house alters the copper thickness. If you specify 2 oz copper instead of 1 oz copper on your Gerber files, the bulk resistivity of the copper remains identical, but the sheet resistance is cut exactly in half.
The Temperature Trap: Both bulk resistivity and sheet resistance are highly temperature-dependent. Copper has a temperature coefficient of resistance (TCR) of roughly +0.00393 per °C. If your PCB operates in an enclosure at 70°C (a 50°C rise over the 20°C baseline), your copper sheet resistance increases by nearly 20%. A trace you calculated as 50 mΩ at room temperature will measure 60 mΩ under load. Always calculate voltage drop and thermal limits using the hot sheet resistance, not the datasheet room-temperature value.
By treating your copper pours not as perfect conductors, but as continuous sheets of resistive material, you eliminate the guesswork from PCB layout. Grab your calipers, check your fab house's stackup sheet for the exact finished copper thickness, and do the math before you route.
