Operational amplifiers are the most commonly-used devices for analog circuit designers. They use operational amplifiers to extract, adjust, convert, buffer, combine, filter, and regulate signals in the real world. For applications that require high accuracy and stability, designers will carefully consider the input offset voltage, noise, bandwidth and other performance specifications, and choose the operational amplifier that can realize necessary performance. Sometimes errors tend to be overlapped, so choosing other components, such as data converters or voltage reference, should also be careful. Designers should also not to ignore the effects of the accuracy of the components around the amplifier, especially resistors.
Matching Degree of Resistors Affects System Accuracy
In the circuit shown below, there are four resistors and an operational amplifier, forming a differential amplifier.
The output voltage is determined by the ratio of the resistors:
From the above formula we can see that, in this example, in terms of determining the performance of the amplifier circuit, the matching of the resistor is more important than the absolute accuracy of the resistor. If R1 and R2 change in proportion, the gain will remain the same. If one resistor changes relative to another resistors, the ratio of R1 to R2 will certainly change and the gain will also change. This is also true for the commonly-used proportional circuits such as circuits of precision voltage dividers and precision gain stages, and bridge circuits. , the effects of mismatch of resistors on the performance will be explored in the following, which will be focused on three types of resistors: precision discrete resistors, traditional matching resistor arrays, and the new precision-matched thin-film resistor of series LT5400.
Let's consider a discrete resistor with an accuracy of 10 times(ie 0.1%). At room temperature, the resistance of each resistor can vary from -0.1% to +0.1% of its nominal value, so the worst matching degree of the two resistors is ±0.2% [ie (1+0.001) / (1-0.001) = 1.002] or 2000ppm, or 9-bit accuracy. As temperature changes, matching will become a bigger problem. Most resistor manufacturers specify a temperature coefficient that is independent of the specification of tolerance property. While the resistor with an accuracy of 0.1% used in this example may have a temperature coefficient of 25ppm/°C. The error result is higher than 3000ppm in the range of 0°C to 70°C. This error will converted into the gain error of the amplifier circuit, and it does not include the non-ideality of the operational amplifier itself or the error caused by other sources of error in the signal links.
If higher accuracy is required, a resistor with more accurate tolerance of 0.01% may be applied, Usually, an accurately matched resistor array can realize optimum performance of the amplifiers. The resistor array consists of multiple resistors contained in a single package, where the resistors tend to track each other as the temperature changes. For example, a resistor array of 0.01% tolerance may have a temperature coefficient of ±2ppm/°C, causing an error of 190ppm from 0°C to 70°C, which is a significant improvement compared with the case of discrete 0.1% resistors.
If more precision is needed, Linear Technology's new precision-matched thin-film resistor of series LT5400 can be used. This series of devices uses a precise layout method so that all the four thin-film resistors are balanced and share the same center point.
LT5400 is packaged in small, surface mounting with an operating voltage of ±75V. Each package includes 4 resistors with different nominal resistance values. The ratio between R1 and R2 is 1, 5, and 10 respectively, and more options are available in the future (Table 1). A large boding pad on the bottom of the package provides consistent thermal conditions for the four resistors, which minimizes the the rise of internal temperature when the power consumption is too high. This kind of design ensures that all four resistors have the same working environment.
Table 1
The LT5400 provides a better resistors matching with a matching degree of 0.01%, a matching temperature drift of 1ppm/°C , and a long-term stability error less than 2ppm after 2000 hours. As a result, the device achieves a matching error of 100ppm from 0°C to 70°C (Table 2). Its performance maintains excellent over a wide temperature range from -50°C to 150°C. The LT5400 is also very stable with the change of time, which shows a change of less than 2 ppm after 2000 hours.
Table 2
Effects of Common-Mode Voltage
In many applications, signal regulated by a amplifier is superimposed on a large (and sometimes varying) common-mode signal. Ideally, the amplifier will ignore the common-mode signal and amplify, buffer, or regulate the differential signal. If the amplifier does not effectively eliminate the common-mode signal, offset voltage and distortion would occur at the output. The Common Mode Rejection Ratio (CMRR) can measure the amplifier's isolating power to the common-mode component of the input signal. In this kind of applications, mismatch of resistors is still a very largest factor causing common-mode error. The CMRR due to resistor mismatch is usually measured in dB and can be calculated with the following formula:
In this formula, G is the nominal value of R1/R2 and ΔR/R is the matching error ratio of the resistor.
From the above examples, we can see that resistors can still play a leading role in setting the overall performance of the system. Using the equation above, we can also calculate the common mode rejection capability of the resistors. A pair of resistors with a matching degree of 0.1% will exhibit a CMRR of 54dB, and an array with a matching degree of 0.01% will exhibit a CMRR of 74dB. In terms of CMRR performance, the resistor array of series LT5400 is different from the other resistors, because the device is specially designed and tested for the strict CMRR tolerance and its CMRR tolerance is guaranteed. More specifically, It offers a guaranteed CMRR of 0.005% matching performance specification and, in the most advanced version, it has realized a CMRR of 86dB with temperature changes. This is 2 times better than the performance achieved by using only the above formulas.
Conclusion
Combining operational amplifiers with discrete components can form a wide variety of useful circuits. And when selecting external components, we should be as careful as selecting the amplifier itself. Both resistor matching (especially the matching with temperature variation) and the range of common-mode voltage are important performance specifications, which will determine the system accuracy and how much calibration work is required to achieve the required accuracy. Resistor arrays are most suitable for this type of applications, and new products such as the LT5400 four-resistor array has achieved superior accuracy.
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