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Using Copper PCB Etch for Low Value Resistance by Larry Spaziani

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Design Note
Using Copper PCB Etch for Low Value Resistance by Larry Spaziani
S(T) ·
The use of a low value sense resistor implies that the current in that resistor can be quite high. A copper etch on a PCB will self heat due to the power dissipated by the resistor. MIL-STD-275E 2 provides design guidelines relating copper etch current to temperature rise and etch dimensions. Figure 1 recreates sections of the MILSTD-275E curves. A temperature rise, above ambient temperature, can be found by knowing the current and the area of the copper etch.
Design Note
Current Density Curve for Outer Layer PCB Copper Etch
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Allowed Current A
Cross Sectional Area (Width mils Thickness mils )
Current Density Curve for Inner Layer PCB Copper Etch
Cross Sectional Area (Width mils Thickness mils )
Allowed Current A
Resistance m
9 8 7 0 20 40 60 Copper Temperature C 80 100
Figure 1. MIL-STD-275E Current Density vs Temperature Rise Curve for Outer and Inner Copper Layers Example: Calculate the length and width of a 10m MAXIMUM PCB resistor using 1oz on an outer layer of a PCB. The resistor must carry 10A maximum while maintaining no more than a 30°C temperature rise above ambient. Ambient temperature for normal operation is 10°C to 60°C. Step 1: Find the cross sectional area to carry 10A with 30°C rise, and solve for the minimum width of the resistor. From Figure 1, 205 mils2 are required to carry 10 Amperes. 1oz copper is 1.4mils thick, resulting in a minimum width for the resistor of 146mils.
Figure 2. Resistance vs Copper Temperature for Example Design
The final resistance, as a function of the copper temperature, is shown in Figure 2. Table 1 provides the required dimensions for a 1oz PCB copper resistor given a maximum current and desired voltage drop. Table 1 assumes a maximum operating ambient temperature of 60°C, with the width specified for a 30°C temperature rise. The required resistance is equal to V / I and is calculated at a copper temperature of 90°C.
Design Note
Desired Voltage Drop 10mV 25mV 50mV PCB Etch Length in 0.162 0.405 0.810 0.243 0.608 1.215 0.405 1.013 2.025 0.648 1.620 3.240 0.891 2.228 4.456 1.053 2.633 5.266 1.377 3.443 6.886 1.701 4.253 8.506 2.025 5.063 10.126 2.430 6.076 12.152 2.754 6.886 13.772 3.078 7.696 15.392
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Width in 0.010 0.015 0.025 0.040 0.055 0.065 0.085 0.105 0.125 0.150 0.170 0.190
Vias through the resistor will effect the resistance. Curved or serpentine resistor patterns may be utilized as long as the overall width and length, including curves, is understood. A copper resistor connected to two larger copper planes will have a lower temperature rise than predicted by the MIL-STD-275E curves due to the heatsinking of those copper planes.
CONCLUSIONS The design of a PCB copper resistor is straightforward once operating parameters such as voltage drop, operating current and operating ambient temperature are known. Tolerances due to PCB technology will effect the accuracy of a PCB resistor and should be considered. The length-to-width ratio of a PCB resistor is quite large due to the low resistivity of copper, but when the area is available on a PCB, this resistor is essentially free. Applications which require current limiting are ideal for use with a PCB resistor, as current limiting can be set quite accurately at the maximum operating temperature where current limiting is most critical. Average current mode control applications require precise voltage drops independent of temperature and current levels. PCB resistors are therefore not recommended for use as an Average Current Mode control sense resistor. REFERENCES 1 Reference Data for Radio Engineers, Howard W. Sams & Co. Inc., Sixth Edition 1977. 2 MIL-STD-275E, NOTICE 1, 8 July 1986, Military Standard Printed Wiring for Electronic Equipment.
Table1. Dimension Solver for Given Current and Desired Voltage Drop for 90°C Maximum Copper Temperaturre
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