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Current measurement is frequently used in the operation of electronic instrumentation. This tutorial examines resistive current sensing, I-V converters, magnetic current sensing, closed-loop current sensors, and current transformers. Ed Ramsden, Cherry Electrical Products With an impressive array of
techniques, the engineering and scientific communities measure electrical current in
applications ranging from radiation sensing to battery charging. Current is commonly
measured over a range from pico-amperes (10–12) to thousands of amperes. Electric current is the movement of charge carriers. Although positive charge carriers (e.g., ions and semiconductor holes) can transport current, the most commonly encountered currents, such as those flowing in metal conductors, consist of negatively charged electrons. The unit of current, the ampere, is equivalent to 6 x 10 18 unit charge carriers (e.g., electrons) moving past a given point each second. Current is measured principally through two effects: voltage drop and the generation of magnetic fields (see Figure 1). In the first, the passage of current through a material produces a voltage. For many conductive substances, the voltage is proportional to the current over a wide range of conditions. By measuring the induced voltage drop, you can infer the current. This is the basis for resistive current sensing. Alternatively, current can be measured by the magnetic field it generates. Moving charge carriers generate magnetic fields oriented at right angles to their motion. In empty space, the field is dependent only on the geometry of the current path and a fundamental physical quantity called permeability (µ 0 ). Permeability is a measure of how well a material, or the lack of a material in the case of a vacuum, can conduct magnetic fields. The major advantage of magnetic current sensing is isolation--no direct contact with the circuit being monitored is required. Resistive Current Sensing Highly linear and stable resistors have been available as standard circuit components for decades, and resistive current sensing is well known and understood. You put the sense resistor in series with the circuit in which you want to measure current and then measure the voltage drop across the resistor. You determine the current using Ohm's law: I = V/R (1) where: Although this basic scenario captures the essence of resistive current sensing, it ignores many details necessary for a successful implementation. Various application and system interface requirements, combined with nonideal component behaviors, can complicate the design of a good resistive current sensor. The first step of a practical system is to make the voltage measurement. Here you'll encounter two common situations: high-side current measurements and low-side (or ground-returned) current measurements. In a high-side measurement (see Figure 2A), you have to use a differential amplifier to measure the voltage difference across the resistor and report the measurement as a ground-referenced signal. In many cases, general-purpose instrument amplifiers can perform the task, but some devices are better suited to this type of application. For example, the Burr-Brown INA-117 will function with a common-mode signal as high as ±200 V, simplifying current measurement in moderately high-voltage systems. Maxim's MAX4173 operates from a single supply and will function with a common-mode signal of up to 28 V, making it especially useful in low-voltage/single-supply systems.
In a low-side measurement scheme (see Figure 2B), you measure current flowing back to ground, and one of the terminals of the sense resistor is tied to ground. In this case, you can use the voltage at the ungrounded terminal of the sense resistor to determine current. Because of the fuzzy nature of ground in a system that handles any significant amount of current, using a differential amplifier to measure the voltage across the sense resistor may also be warranted in a low-side current sensor (see Figure 2C). This is especially true when the sense resistor is mounted on a circuit board, because the voltage measured on a circuit-board ground can vary considerably, depending on where the measurement is made.
With both high-side and low-side sensing schemes, you encounter a number of problems. Voltage Drop. The voltage drop created by the sense resistor can interfere with the operation of the circuit into which it is inserted. This requires you to balance the voltage needed to make an accurate measurement against the amount of voltage drop that can be tolerated by the application. Power Dissipation. In addition to generating a voltage across a resistor, current generates heat in the device, where the power dissipated is P = I 2 R. Although small resistors don't require much consideration from a thermal-design perspective (other than not exceeding their maximum power ratings), manufacturers often make larger devices to be mounted on heat sinks. These devices will fail rapidly when operated near rated power without proper heat sinking. Ignoring the maximum power and temperature ratings of sense resistors can shorten their useful life--often in spectacular ways. Parasitic Series Resistance. Low-value resistors (<1 Parasitic Parallel Resistance. With high-value sense resistors (>1 M
While some parasitic effects are unavoidable, one major trap for the unwary results from subtleties in resistor construction. Wire-wound and film resistors can have substantial parasitic inductance if not properly designed. In the case of a wire-wound resistor--which is a coil of resistance wire wound on an insulating form--it's easy to see where the inductance comes from. In some instances, particularly with high-power resistors, you can actually see the outline of the coil under the outer insulator. In the case of film resistors, the resistance element is a layer of resistive film deposited on a cylindrical substrate. To get higher resistance, the film is often cut in a spiral pattern. If this is the case for a particular resistor you happen to be using, you also get an inductor thrown in at no additional charge. You can avoid this problem by using resistors designed to minimize parasitic inductance. I-V Converters While the techniques described here work well when measuring moderate currents (milliamperes to tens of amperes), they run into difficulties when used to measure small currents, such as those with magnitudes of less than a microampere. Currents of this order of magnitude are commonly produced by photodiodes (optical) and piezoelectric sensors to measure vibration and pressure. To effectively interface with these types of devices, a technique called I-V conversion is commonly used.
To illustrate the need for specialized current-sensing techniques for
low current levels, consider the case of a typical photodiode. The hypothetical device has
a current output of 10 µA when illuminated and 10 nA in total darkness (dark current). At
first, it seems trivial to connect a 1 M
But if you implement this solution, you'll quickly encounter several problems. First,
the photodiode is a nonideal current source in two respects (see Figure 5B): it has a
finite output impedance that varies over voltage, and it has a limited compliance range
(<1 V) into which it can deliver any current at all. Although you would expect 10 µA
through 1 M This leads to the second problem. When properly used, a good photodiode is a highly
linear device, but a simple resistive load can ruin its linearity unless the resistance is
very small. A 10 K
An op-amp circuit commonly called an I-V converter (see Figure 6) solves many of
these problems. The circuit works not by trying to accurately measure a large voltage drop
but by balancing the incoming current with a separately generated current and then
detecting the difference. To understand how the I-V converter operates, assume that the op
amp is in negative feedback mode and will swing its output to whatever value it can to
make the input voltage at its summing node (the negative terminal) 0. To take a 1 µA
input current to the summing node, the op amp will have to draw 1 µA out through R F
. Assuming that the voltage at the summing node is 0, this implies the output
voltage will be 1 V (1 V/1 M V OUT = – R F * I IN (2) For a modest amount of complexity, the I-V converter provides substantial benefits over simple resistive current sensors when dealing with low-level signals. First, because the op amp is actively trying to maintain its summing node at 0 V, the input appears to be a short circuit to the transducer. For a high-impedance current-output transducer, a short circuit is the ideal electrical load to drive, allowing for the most dynamic range and the least nonlinearity. Another benefit is that the voltage across the transducer is held constant. Finally, because a short circuit represents a low-impedance load, the I-V converter maximizes the transducer's frequency response. Magnetic Current Sensing You can also detect electric current by the magnetic field it induces. The principal advantage of using magnetic current sensing is that the sensing circuit need not have direct electrical connection with the current being sensed. The isolation is advantageous in circumstances where safety is critical, such as when measuring currents in high-voltage circuits. In free space, the magnetic field existing around an infinitely long straight conductor is given by:
where: I = current in amperes r = distance from the center of the µ 0 = the permeability of free space B = magnetic field in tesla
In theory, by placing a magnetic sensor a known distance from a conductor, you can infer the current flowing through it. In practice, however, simply holding a magnetic sensor near a conductor is not an especially good way of sensing current. The accuracy of the measurement is highly dependent on the sensor-to-conductor separation. And the fields generated by moderate currents at reasonable distances are feeble--1 A generates a field of only 0.4 gauss at a distance of 1 cm, approximately equivalent to the earth's magnetic field. Finally, other nearby conductors or geometric changes (i.e., flexing) in the conductor will introduce further inaccuracies. However, this technique can work well when used to measure currents on a PCB. Figure 7 shows how this can be done using a giant magnetoresistive (GMR) magnetic field sensor. A current flowing through a PCB trace will generate a field parallel to the PCB directly over the trace. GMR devices are sensitive to fields in this orientation. This technique works because the conductor-to-sensor separation is small (<1 mm) and tightly controlled and because the conductors are rigidly fixed in space (i.e., in the PCB traces). Finally, GMR devices are highly sensitive and can readily discriminate small magnetic fields. To make a good general-purpose magnetic current sensor, you have to provide a means of directing the magnetic flux to the magnetic transducer. You can accomplish this by using a toroidally shaped ring of highly permeable material (>>µ ) as a flux concentrator (see Figure 8). In this device, the magnetic sensor resides in a slot, or gap, cut in the toroid. Hall effect sensors are popular magnetic sensors for this application, and slotted toroids are readily available to accommodate common types of Hall effect sensors. For reasons that will become apparent later, this type of current sensor is known as an open-loop device. A current sensor with a flux concentrator has several advantages over a device that relies on fields in free space. The first and most significant advantage is that such a sensor becomes insensitive to the position of the current-carrying conductor. For a properly designed current sensor, placement of the conductor through the concentrator has a nearly insignificant effect on overall sensitivity. The concentrator also increases the field available to the magnetic sensor. Sensitivity is dependent on gap width being inversely proportional. For a typical slotted ferrite toroid with a 0.06 in. gap, you can expect about 6–8 gauss per ampere, depending on the toroid geometry and materials. With a toroidal current sensor, you can boost the effective sensitivity of the device by increasing the number of times the conductor passes through the toroid. Sensitivity is increased by the number of turns--two turns provides twice the sensitivity of one turn. The turn count is determined by the number of times the conductor passes through the hole. The way in which you wind the turns will have minimal effect on sensitivity as long as the turns are evenly spaced around the toroid. Try to avoid crowding the turns to one side of the device. But the use of a flux concentrator is not without its problems. The major drawbacks stem from the nonideal behaviors of the high-permeability material used in the concentrator (see Figure 9). The first problem is that of magnetic saturation. As the current through the toroid increases, there is a point at which the increase in the magnetic field is no longer proportional. For most materials, this point is not a sharp transition but occurs gradually, so the maximum useful range of a current sensor may be limited by what is considered acceptable accuracy, as opposed to hard saturation. Another nonideal behavior associated with flux concentrators is that of hysteresis, or memory. When a toroid is magnetically driven in one direction and then the magnetic drive is removed, the toroid retains a small amount of field (called remanant flux) in the direction of the original drive. For some magnetic materials, such as hardened steel, the remanant flux can be a few hundred gauss, but for others, such as soft ferrite materials, it may be only a fraction of a gauss. The overall effect of hysteresis on the operation of a current sensor is to cause a shift in the zero-current output. Choosing the right toroid material is the best way to deal with this problem. Ferrite materials are commonly used in current-sensing applications because low-hysteresis varieties are readily available at low cost. By running a conductor through a toroid, you add inductance to the circuit. Even though the inductance developed by a single turn may be small (<1 µH), the total inductance will increase as the square of the number of turns. When using many turns to increase sensitivity, the series inductance can interfere with the operation of the circuit being measured and limit the current sensor's frequency response.
Closed-Loop Current Sensors One way to avoid some of the nonlinear behaviors of the flux concentrator and the magnetic sensor is by balancing the current being measured with a known current, as is done in the I-V converter (see Figure 10). An op amp maintains a feedback loop that matches the measured current with a balance current developed through a resistor. The op amp's voltage output is proportional to the balance current, which in turn tracks the measured current. Because magnetic flux is being canceled out, or balanced, it's possible to cancel out a large measured current with a much smaller balance current by using more turns of wire on the balance winding than on the measurement winding. Because turn ratios of 1000:1 and more are readily achievable, you can build a current sensor capable of measuring currents of hundreds of amperes while only needing a few tens of milliamperes of balance current. And because the magnetic flux through the toroid is close to zero, saturation is no longer dependent on the toroid and is limited by how much current the feedback circuit can deliver. Because of the use of feedback, this type of current sensor is commonly referred to as a closed-loop device.
Current Transformers When the current is strictly AC and contains no DC or offset components, current transformers offer simple, isolated current measurement. Like the magnetic current sensor, a current transformer is often constructed with a toroid that is made of some magnetic material (see Figure 11A). A current transformer operates much like any other transformer, with the current in the primary and secondary windings related by: i S N S = i P N P (4) where: i P = primary current i S = secondary current N P = the number of turns in the primary N S = the number of turns in the secondary windings (see Figure 11B) The primary current induces a secondary current,
which is converted into a voltage by a load resistor (R L ) (see Figure 11C). In a typical current transformer application, the secondary will have more turns than the primary, which will often have just one turn. This will result n the secondary current being substantially lower and more manageable than the primary current. Surprisingly, an ideal current transformer doesn't appear as an inductive load, as the Hall effect current sensor did. Instead, it looks as if a resistor was added in series with the primary winding. The value of this resistor is given by: This parasitic resistance results in what is known as insertion loss and will cause voltage drops in the primary circuit exactly as a real resistor of the same value would if in series. In the case of an ideal transformer, the above description would be the end of the story. Nonideal transformers, however, require a few additional design considerations. For current measurement at low to moderate frequencies (<10 kHz), the most important considerations are mutual coupling and secondary reactance. Mutual coupling is the degree to which the flux generated by the primary winding passes through the secondary, and vice versa. For an effective transformer, try to get as high a degree of mutual coupling as possible. Fortunately, common architectures (e.g., toroids and E-cores) readily provide high degrees of coupling. Appropriate amounts of reactance are also required for the transformer to behave in a close-to-ideal manner; the reactance of the secondary circuit at the frequencies of interest must be significantly higher (>10 *) than its total resistance. Otherwise the transformer's secondary current will not accurately reflect the primary current. Although it's possible to calculate the inductance of the secondary circuit from the first principals and the material properties, toroid manufacturers usually provide this information in their catalog for each model, expressed in mH/1000 turns. To compute the reactance of a winding at a given frequency, you use:
where: f = the operating frequency in Hz A l = the characteristic inductance in N = the number of turns Although magnetic saturation is a concern in a current transformer, the amount of AC needed to cause saturation is significantly greater than you would expect. This is because in a well-designed transformer, operating within its intended frequency range, the induced secondary current generates flux in opposition to that which is developed by the primary current. This greatly reduces the overall flux in the toroid. A DC, however, will easily saturate the toroid because no opposing DC with be induced in the secondary circuit. For this reason, current transformers are often a bad choice for use with circuits carrying any significant amounts of DC. Saturation, however, can be detected by observing the output waveform and looking for distortion. Conclusion To implement an effective current sensor, you must understand the available technology
and the application in which it is to be used. This article has outlined the requirements,
implementations, and pitfalls of a few current sensing methods, based on the use of both
resistive and magnetic techniques.
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) often
have lead resistances that are a substantial fraction (1% or more) of their rated
resistance. This makes the resistor's value a function of the lead length. The solution is
to use separate wiring paths for the current-carrying circuits and the measurement
circuits (see Figure 3). This arrangement is referred to as the four-wire, or kelvin,
measurement technique. Because of the arrangement's popularity, many low-value precision
resistors are designed with four terminals--two for carrying current and two for measuring
the voltage across the resistance element. 
resistor across the photodiode and measure the voltage
drop (see Figure 5A). 
