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Design Note Using Copper PCB Etch for Low Value Resistance by Larry Spaziani INTRODUCTION Current sensing in power supplies and

DN-71 DN-71 Design Note Using Copper PCB Etch for Low Value Resistance by Larry Spaziani INTRODUCTION Current sensing in power supplies and motor controls demand the use of a very low value resistor. Each application varies in need for resistance value, power rating, size, form factor, inductance, temperature coefficient and accuracy. To meet some of these applications, the copper of a printed circuit board (PCB) can be utilized, but has some distinct limitations. This design note provides design equations and recommendations for designing resistors with PCB copper. DESIGN OF A COPPER PCB RESISTOR The resistance, as a function of temperature, for a piece of metal, is given by the equation: R(T) = S(T) · l a with the units R = Resistance, S(T) = Resistivity, cm l a = Length, cm = Area, cm2 The characteristics of copper which are pertinent to the design of a copper PCB resistor are [1] Electrical Resistivity: 1.7241 · 10-6 cm @ 20°C Temperature Coefficient of Resistivity: +0.0039 per °C Composition: 99.5% Pure Copper, typically 1/97 These constants apply to the standard commercially annealed copper used in PCB technology. The resistivity of copper, as a function of temperature, is therefore defined as: S(T) = 1.7241 · 10-6 · [1 + 0.0039 · (T - 20)] - cm where T is the copper temperature in °C. One PCB Definition which is also pertinent to resistor design is: 1oz copper is defined as 1 ounce of copper deposited over 1 square foot of surface area. This results in a copper clad PCB with a typical copper thickness of 0.0014 inches ±0.0002 inches. 2oz copper is simply twice as thick. Using these parameters to calculate the resistance of a given length, width, and thickness of copper PCB etch results in the formula: S(T)[ - cm] · Length[cm] Width[cm] · Thickness[cm] 1000mils · Length(mils) S(T)[ - cm] · 2.54cm = Width mils) · Thicknessmils ( ) ( R(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 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 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 DN-71 DN-71 Set Width = 150mils Allowed Current [A] Current Density Curve for Outer Layer PCB Copper Etch 20 18 16 60 14 12 10 20 Step 2: 45 Find the length of the resistor, insuring that it is designed for 10m maximum at 60°C ambient +30°C rise (copper temperature is 90°C). 30 10 8 6 From the equations 4 2 S(90) = 1.7241 · 10-6 · 0 25 50 75 [1 + 0.0039 · (90 - 20)] - cm 100 125 150 175 200 225 250 275 300 and Cross Sectional Area (Width [mils] * Thickness [mils] ) - cm 1000mils · · Length[mils] S(90) °C 2.54cm R(90) = · Width[mils] Thickness[mils] Solving for R(90°C) = 10m, using150 mils for Width and 1.4 mils for Thickness results in Length = 2.43 inches. 45 30 20 10 Final Dimensions (inches): 2.43 (L) x 0.150 (W) x 0.0014 (T) 10 25 50 75 Resistance [m] Allowed Current [A] Current Density Curve for Inner Layer PCB Copper Etch 10 9 8 7 6 5 4 3 2 1 0 100 125 150 175 200 225 250 275 300 Cross Sectional Area (Width [mils] * Thickness [mils] ) Figure 1. MIL-STD-275E MIL-STD-275E Current Density vs Temperature Rise Curve for Outer and Inner Copper Layers 9 8 7 0 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. 20 40 60 Copper Temperature [C] 80 100 Figure 2. Resistance vs Copper Temperature for Example Design The final resistance, as a function of the copper temperature, is shown in Figure 2. Step 1: 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. 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. 2 Design Note AMPS 1 2 3 4 5 6 7 8 9 10 11 12 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 DN-71 DN-71 · · 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. Some PCB physical and layout characteristics should be considered when designing a PCB resistor. 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. The thickness tolerance of PCB copper may vary from supplier to supplier and relative to location on a PCB. A typical tolerance is ±0.2mils/oz. · Etchback will reduce the copper area, thus increasing the resistance per unit length. Etchback has a larger impact with narrow runs, where the width/thickness ratio is lower. It is recommended that widths of 0.025 inches be used. · A copper resistor connected to two larger copper planes will have a lower temperature rise than predicted by the MIL-STD-275E MIL-STD-275E curves due to the heatsinking of those copper planes. CONCLUSIONS Table1. Dimension Solver for Given Current and Desired Voltage Drop for 90°C Maximum Copper Temperaturre · Curved or serpentine resistor patterns may be utilized as long as the overall width and length, including curves, is understood. · 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. REFERENCES [1] Reference Data for Radio Engineers, Howard W. Sams & Co. Inc., Sixth Edition 1977. The copper resistor, if it is on an outer PCB layer, should be solder masked over the entire resistive area. Solder on the copper will reduce the resistance. [2] MIL-STD-275E MIL-STD-275E, NOTICE 1, 8 July 1986, Military Standard Printed Wiring for Electronic Equipment. UNITRODE CORPORATION 7 CONTINENTAL BLVD. · MERRIMACK, NH 03054 TEL. (603) 424-2410 · FAX (603) 424-3460 3 IMPORTANT NOTICE Texas Instruments and its subsidiaries (TI) reserve the right to make changes to their products or to discontinue any product or service without notice, and advise customers to obtain the latest version of relevant information to verify, before placing orders, that information being relied on is current and complete. All products are sold subject to the terms and conditions of sale supplied at the time of order acknowledgment, including those pertaining to warranty, patent infringement, and limitation of liability. TI warrants performance of its products to the specifications applicable at the time of sale in accordance with TI's standard warranty. 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