Resistors play a key role in precision amplifier applications. In addition to establishing the gain of the amplifier, they are used for biasing and calibration of the offset voltage. As precision amplifier applications are designed to amplify small signals accurately with minimal distortion or error precise resistor value matching is critical.
Precision amplifiers are critical components in instrumentation, data acquisition, and sensor interfacing applications. In this article, we discuss the causes of resistor mismatch and potential solutions. These include replacing discrete resistors with resistor network components.
Resistor Matching Defined
Resistor value matching is defined as the consistency of resistance values across multiple resistors in a circuit. Any external factor that acts more on one resistor in relation to another will affect the accuracy of the amplifier circuit.
Mismatched resistor values can lead to gain and offset voltage errors in amplifiers. The gain error (a percentage) is proportional to the ratio of resistor mismatch to the nominal resistor value. Offset voltage error is directly proportional to the difference in resistance values.
The Causes Of Resistor Mismatch
Common causes of mismatch are:
- Tolerance variations
- Temperature effects
- Resistor ageing
- External stressors
Resistor tolerance: is the permissible range of deviation in the resistance value of a resistor from its specified or nominal resistance value. In matched resistor applications, it is important to select resistors with a low tolerance (%). This limits the potential variance in resistance between resistors.
Temperature Effects: In matched resistor applications, temperature effects can cause resistance variations and errors.
TCR is a measure of how much a resistor’s resistance changes with temperature. For precision applications, it is essential to use resistors with a low TCR. This minimises the variation in resistance change across resistors for a given temperature variation.
It is important to note minimising TCR values may still introduce errors in highly sensitive circuits. Self-heating of resistors and localised heating caused by other components are issues to consider.
Ageing: Temperature extremes, adverse environmental conditions, electrical pulse and mechanical stresses can combine to age a resistor. This generally leads to an increase in resistance over time. In precision amplifier applications, it is a problem if one resistor ages more (or less) compared to other resistors in the circuit.
External Stressors: Stability is a measure of the repeatability of a resistance measurement over time. Mechanical, environmental and electrical stresses can all impact resistor stability.
In precision amplifier applications, an external stressor may cause a mismatch if it affects one resistor more than others.
Why Resistor Networks?
Resistor networks can address many of the problems discussed above, as outlined below.
Tolerance: Wherever possible, resistor tolerance values should be matched. In the case of discrete resistors, this requires selection during manufacture or testing, which increases their cost significantly.
A combination of material properties, the manufacturing process, resistor design, final resistor trim and quality control measures define the tolerance of a thick film resistor.
In a network, the material properties and manufacturing process are consistent across resistors. Although tolerance matching remains a challenge, this removes some of the variables.
Temperature: Temperature effects are minimised by selecting discrete resistors with low TCR values. The materials used, the construction and the manufacturing process determine the Temperature Coefficient of Resistance (TCR) of a thick-film resistor.
Different materials exhibit varying levels of resistance change with temperature. Substrate properties also influence how resistive materials respond to temperature changes. Resistor parameters are determined by the thick film resistor materials, within a given range, and the resistor geometry.
The only way to achieve an exact ratio between resistors is to print all with the same material or materials blend, with the same dimensions. Any dimensional difference between resistors will result in differences in TCR. However, this variance is minimised by printing all resistors in a network with the same resistor blend.
Stressors: As discussed above, mechanical, environmental and electrical stresses all affect resistor stability. In precision amplifier applications, it is important to eliminate any variance across resistors.
As resistors are in close proximity in a resistor network, the impact of external factors is the same across resistors. This reduces the impact of variance in resistance values over time.
Resistor Network Application Issues
As discussed above, resistor networks offer several potential advantages over discrete devices in precision amplifier applications. However, there are potential application challenges the system designer should address.
A major advantage of resistor networks is high component packaging density. However, this can complicate circuit board track routing. Higher component density in one location on the system board can increase track lengths and signal integrity.
Several resistors in a relatively small area also increase the demand for heat dissipation in that location. It is, therefore, important to position the network component in a location with good airflow/cooling.
With resistors in close proximity on a substrate, there is the potential for cross-talk between devices. Specialist resistor manufacturers will be aware of the issue and take steps to minimise the impact, but there are limits.
Resistor value matching is a critical consideration in precision amplifier applications. As explored above, the selection and matching of resistors impact on key amplifier parameters. These include gain accuracy, common-mode rejection, and offset voltage.
When selecting components, system designers must weigh performance against cost. Using a resistor network to replace discrete devices is one potential solution.