Sensing elements for current measurements – Part 1
Introduction
The fundamentals to translating the analog world into the digital domain reduces to a handful of basic parameters. Voltage, current, and frequency are electrical parameters that describe most of the analog world. Current measurements are used to monitor many different parameters, with one of them being power to a load.
There are many choices of sensing elements to measure current to a load. The choices of current sensing elements can be sorted by applications as well as the magnitude of the current measured. This write up is part one of a three part series that discusses different types of current sensing elements. The focus of this article is evaluating current measurements using a shunt (sense) resistor.
Element 1: Shunt Resistor
Figure 1: Picture of a Shunt (Sense) Resistor
Shunt resistors are the most versatile and cost effective means to measure current. A shunt resistor cost ranges from a few pennies to several dollars. A shunt resistor’s price is differentiated by value, temperature coefficient, power rating and size. Shunt resistors commonly increase in cost for lower temperature coefficient (TC) and for higher power rating while offering precision features in a small package size.
With the knowledge of Ohm’s Law and the magnitude of the current to be measured, a shunt resistor is able to be designed into many applications. The simplicity of the design in process makes a resistor a versatile current sensing element.
In choosing a sense resistor value, the full scale voltage drop across the sense resistor and the maximum expected current measured for the application has to be known.
When possible, the voltage across the sense resistor should be kept to a minimum to lower the power dissipated by the sensing element. Low power dissipated by the sense resistor limits the heating of the resistor. A small temperature change to the sensor resistor results in a smaller resistance change versus all current sensing values. The stability and accuracy of the sense resistor versus all currents improves with a constant value shunt resistor.
For most current sensing applications, the minimum and maximum measurable currents are known. The designer chooses the allowable voltage drop across the shunt resistor. For this discussion, assume the current measured is bidirectional. The max shunt voltage is chosen as ±80mV. Assume the max measured current is ±100A. The shunt (sense) resistor value is calculated using Equation 1.
Equation 1: Using Ohm’s Law to calculate the Shunt Resistor Value.
For this example, the shunt resistor, Rsense, is calculated to equal 0.8mΩ. Table 1 is a list of other calculated shunt resistor values for a series of full scale current values.
Table 1: Shunt resistor values and minimum Power rating for several full scale currents.
The minimum power rating for the sense resistor is calculated in Equation 2.
Equation 2: The minimum Power Rating calculation of the Sense Resistor.
The minimum power rating of sense resistor is calculated as 8W for the example. A general rule of thumb is to multiply the power rating calculated using Equation 2 by 2. This allows the sense resistor to survive an event when the current passing through the shunt resistor is greater than the measurable maximum current. The higher the ratio between the power rating of the chosen sense resistor and the calculated power rating of the system, the less the resistor heats up in high current applications.
The temperature coefficient (TC) of the sense resistor directly degrades the current measurement accuracy. The surrounding temperature of the sense resistor and the power dissipated by the resistor results in a sense resistor value change. The change in resistor temperature with respect to the amount of current that flows through the resistor is directly proportional to the ratio of the power rating of the resistor versus the power being dissipated. A change in sense resistor temperature results in a change in sense resistor value resulting in a change in measurement accuracy for the system. The change in a resistor value due to a temperature rise is calculated using Equation 3.
Equation 3: The equation to calculate the resistance change when temperature changes.
ΔTemperature is the change in temperature in Celsius. RsenseTC is the temperature coefficient rating for a sense resistor. Rsense is the resistance value of the sense resistor at the initial temperature.
The change in the sensing element resistance is directly proportional to the current passing through resistor. The package size of the sense resistor determines the sensing element ability to counter temperature rise due to the power being dissipated by the resistor. The thermal resistance of the sensing elements package, Θja, should be considered when choosing a sensing resistor. Θja is the primary thermal resistive parameter to consider in determining the temperature rise in a resistor. Θja is the thermal resistance between the resistor and the temperature outside the resistor. Table 2 lists the thermal resistances of common surface mount packages.
Table 2: The thermal resistance of surface mount resistors referenced from Vishay application notes 28844 and 60122.
Table 2 validates the intuitive conclusion that there is a greater temperature rise in smaller packages resulting in a larger resistance changes.
A 0.8mΩ sense resistor with 50A through it dissipates 2W. The resistance change is calculated using Equation 4.
Equation 4: An equation that relates the current flow through a sense resistor to the temperature change of a resistor.
In Equation 4, I2 * Rsense is the power dissipated by the shunt resistor. Θja is the thermal resistance of the sense resistor chosen. Assuming a 2512 is the sense resistor’s package, the change in temperature of the resistor is calculated as 50C. Assume the RsenseTC is 100ppm/C. The change in resistance, using equation 3, is calculated as 4uΩ. 4uΩ does not seem like a sizable change in resistance. To interpret the number a different way, compare the resistance change to the overall resistance value. 50A of current changes the resistor by 0.5% from nominal. This results in a 0.5% current measurement error due to the change in shunt resistance.
Figure 2 plots current measurement error due to resistor self-heating. Smaller packages have less material to prevent the resistor from self-heating. Therefore, smaller packages have lower power dissipation limits. A method of increasing the power rating of a resistor while preserving a small footprint is to choose a wide package. The thermal resistance of a 0406 package roughly equals the thermal resistance of a 1206 package.
Figure 2: A plot of current measurement error caused by resistor self-heating.
It is often hard to readily purchase shunt resistor values for a desired current. Either the value of the shunt resistor does not exist or the power rating of the shunt resistor is too low. A means of circumventing the problem is to use two or more shunt resistors in parallel to set the desired current measurement range.
Assume that a 0.8mΩ shunt resistor with an 8W power rating is not readily available. Assume the power ratings and the shunt resistor values available for design are 1mΩ/4W, 2mΩ/4W and 4mΩ/4W.
Let’s use a 1mΩ and a 4mΩ resistor in parallel to create the shunt resistor value of 0.8mΩ. Figure 2 shows an illustration of the shunt resistors in parallel.
Figure 3: A simplified schematic illustrating the use of two shunt resistors to create a desired shunt value.
The power to each shunt resistor should be calculated before calling a solution complete. The power to each shunt resistor is calculated using Equation 5.
Equation 5: Power Equation through a resistor
The power dissipated by the 1mΩ resistor is 6.4W. 1.6W is dissipated by the 4mΩ resistor. 1.6W exceeds the rating limit of 1W for the 1mΩ sense resistor. Another approach would is use three shunt resistors in parallel as illustrated in Figure 4.
Figure 4: Increasing the number of shunt resistors in parallel to create a shunt resistor value reduces the power dissipated by each shunt resistor.
Using Equation 5, the power dissipated to each shunt resistor yields 3.2W for the each 2mΩ shunt resistor and 1.6W for the 4mΩ shunt resistor. All shunt resistors are within the specified power ratings.
Layout
The layout of a current measuring system is equally important as choosing the correct sense resistor and the correct analog converter. Poor layout techniques could result in severed traces, signal path oscillations, magnetic contamination which all contribute to poor system performance.
Trace Width
Matching the current carrying density of a copper trace with the maximum current that passes through is critical in the performance of the system. Neglecting the current carrying capability of a trace results in a large temperature rise in the trace, and a loss in system efficiency due to the increase in resistance of the copper trace. In extreme cases, the copper trace could be severed because the trace could not pass the current. The current carrying capability of a trace is calculated using Equation 6.
Equation 6: The minimum PCB trace width for currents that pass through the trace.
Imax is the largest current expected to pass through the trace. ΔT is the allowable temperature rise in Celsius when the maximum current passes through the trace. TraceThickness is the thickness of the trace specified to the PCB fabricator in mils. A typical thickness for general current carrying applications (<100mA) is 0.5oz copper or 0.7mils. For larger currents, the trace thickness should be greater than 1.0oz or 1.4mils. A balance between thickness, width and cost needs to be achieved for each design. The coefficient k in Equation 6 changes depending on the trace location. For external traces, the value of k equals 0.048 while for internal traces the value of k reduces to 0.024. The k values and Equation 6 are stated per the ANSI IPC-2221(A) standards.
Trace Routing
It is always advised to make the distance between voltage source, sense resistor and load as close as possible. The longer the trace length between components will result in voltage drops between components. The additional resistance reduces the efficiency of a system.
The bulk resistance, ρ, of copper is 0.67µΩ/in or 1.7µΩ/cm at +25°C. The resistance of trace can be calculated from Equation 7.
Equation 7: Trace resistance calculation
Figure 5 illustrates each dimension of a trace.
Figure 5: Illustration of the trace dimensions for a strip line trace
For example, assume a trace has 2 oz of copper or 2.8mil thickness, a width of 100mil and a length of 0.5in. Using Equation 7, the resistance of the trace is approximately 2mΩ. Assume 1A of current is passing through the trace. A 2mV voltage drop results from trace routing.
Current flowing through a conductor takes the path of least resistance. When routing a trace, avoid orthogonal connections for current bearing traces
Figure 6: Avoid routing orthogonal connections for traces that have high magnitude through currents.
Orthogonal routing for high current flow traces could result in current crowding, localized heating of the trace and a change in trace resistance
Figure 7: Use arcs and 45 degree traces to safely route traces with large current flows.
The utilization of either arcs or 45 degree traces in routing large current flow traces will maintain uniform current flow throughout the trace. Figure 7 illustrates the routing technique.
Connecting Sense Traces to the Current Sense Resistor
Ideally, a 4 terminal current sense resistor would be used as the sensing element. Four terminal sensor resistors can be hard to find for specific values and sizes. Often a two terminal sense resistor is designed into the application.
Sense lines are high impedance by definition. The connection point of a high impedance line reflects the voltage at the intersection of a current bearing trace and a high impedance trace.
The high impedance trace should connect at the intersection where the sense resistor meets the landing pad on the PCB. The best place to make a current sense line connection is on the inner side of the sense resistor footprint. The illustration of the connection is shown in Figure 7. Most of the current flow is at the outer edge of the footprint. The current ceases at the point the sense resistor connects to the landing pad. Assume the sense resistor connects at the middle of the each landing pad, this leaves the inner half of the each landing pad with little current flow. With little current flow, the inner half of each landing pad is classified as high impedance and perfect for a sense connection.
Figure 8: Connecting the sense lines to a current sense resistor.
Current sense resistors are often smaller than the width of the traces that connect to the footprint. The trace connecting to the footprint is tapered at a 45 degree angle to control the uniformity of the current flow.
Magnetic Interference
The magnetic field generated from a trace is directly proportional to the current passing through the trace and the distance from the trace the field is being measured at. Figure 8 illustrates the direction the magnetic field flows versus current flow.
Figure 9: The conductor on the left shows the magnetic field flowing in a clockwise direction for currents flowing into the page. Current flowing out of the page has a counter clockwise magnetic flow.
The equation in Figure 8 determines the magnetic field, B, the trace generates in relation to the current passing through the trace, I, and the distance the magnetic field is being measured from the conductor, r. The permeability of air, μo, is 4π *10-7 H/m.
When routing high current traces, avoid routing high impedance traces in parallel with high current bearing traces. A means of limiting the magnetic interference from high current traces is to closely route the paths connected to and from the sense resistor. The magnetic field cancels outside the two traces and adds between the two traces. Figure 9 illustrates a magnetic field insensitive layout.
If possible, do not cross traces with high current. If a trace crossing cannot be avoided, cross the trace in an orthogonal manor and the furthest layer from the current bearing trace. The inference from the current bearing trace will be limited.
Figure 10: Closely Routed Traces That Connect to the sense resistor reduces the magnetic interference sourced from the current flowing through the traces.
Summary:
Using a sense resistor to measure current is straight forward as long as proper care is taken with respect to layout and in choosing a sense resistor. The power rating and temperature coefficient parameters of a sense resistor are critical for designing a high accuracy current measurement system. With the knowledge of Ohms law, sense resistors are easy to design with. A drawback of the technology is that a sense resistor consumes power which eats into voltage headroom and lowers the efficiency of some applications.
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