TCR matched Thick film resistor networks are found in Analog-to-digital and Digital-to-analog converters, Precision amplifiers, Voltage references and Temperature sensors.
In this post, we cover errors in sensitive analysis and measurement equipment caused by a mismatch in resistor Temperature Coefficient of Resistance (TCR). We discuss the merits of using a resistor network to replace discrete devices.
Thick Film Resistors
During the thick film resistor manufacturing process, a resistor material is screen printed onto a substrate, dried and cured and then fired at high temperature.
The resistor material is a mixture of metal oxide, a binder and a glass frit. The binder holds the metal oxide in place and helps it bind to the substrate. The glass frit melts at high temperatures and enhances adhesion, conductivity, and stability.
A single resistor on a single substrate delivers a discrete resistor device. Alternatively, many resistors are added to a single substrate to produce a resistor network.
Temperature Coefficient of Resistance (TCR)
Temperature coefficient of resistance (TCR) is a measure of how the electrical resistance of a material changes with temperature. It quantifies the relative change in resistance per degree Celsius (or Kelvin) change. TCR is expressed in units of parts per million per degree Celsius (ppm/°C)
Several thick film resistor design and manufacturing factors impact the TCR of a resistor device. These include the aspect ratio of the thick film resistor and the ink composition used in the resistor print process.
Controlling these factors across different manufacturing lots is a problem leading to potential wide variations in resistor TCR. It is possible to select devices from the same lot with closely matched TCR, but this is time consuming and mixed lots at the end customer can be an issue.
Why TCR Matching?
In measurement and analysis equipment, ambient temperature changes or localised heating effects can cause errors. The proximity of external heat sources can impact the resistance of one resistor relative to the other.
Differences in resistor manufacturing and materials cause variations in the temperature coefficient of resistance across two discrete devices. This, in turn, drives differential self-heating caused by uneven power dissipation.
For example, a common application is resistor divider circuits in precision amplifier applications. Here, two (or more) resistors provide a known reference or input voltage.
The amplifier gain is directly proportional to the reference voltage (Vout = R2/R1 x Vin). Hence, any shift in resistor parameters will cause a corresponding error in the gain.
A high TCR in one resistor relative to the other will mean, for a given temperature, its resistance will vary from the norm more than the other. The ratio of R1 to R2 and the gain will change, resulting in an error.
To avoid a performance mismatch of the resistors matched resistor TCRs, tight ratio tolerances and excellent load-life stability are required. A common solution is to print both resistors with the same material. This means they should track together as much as the difference in design allows. However, this solution is not practical if the resistor ratio is too high.
The ideal solution is to employ resistors with a TCR of zero (the resistor maintains a fixed value regardless of temperature). A more practical method is to ensure both resistors change by the same magnitude (as a percentage) in response to the temperature change. This is resistor matching.
Thick Film Resistor Networks
One solution to the resistor matching issue is to use a thick-film resistor network device. A shared fabrication process and a common substrate deliver improved TCR matching performance.
Resistor devices are in close proximity and subject to the same external influences. The impact of any self-heating is shared across devices. The shared substrate also helps to maintain a uniform thermal environment for the resistive elements, further improving TCR matching.
In some designs, resistors within the network are specifically paired or balanced against each other based on their TCR values. This means that if one resistor increases in resistance due to a temperature rise, another resistor with a correspondingly negative change can compensate, thereby maintaining overall circuit stability.
Resistor Network Manufacturing Issues
When matching resistors in a network, the material composition and manufacturing process are significant factors.
The first step is to identify the required TCR matching specification for the application. This can range from tight TCR matching (e.g., ±50 ppm/°C) to more relaxed requirements (e.g., ±100 ppm/°C). The tighter the TCR matching requirement, the more critical the other design considerations become.
The resistive material used in the thick film network should be selected to ensure consistent TCR characteristics. The substrate should have a low and stable thermal expansion coefficient to minimise thermally induced resistance changes.
It is best to match TCR in thick film resistors by printing both (or all) resistors in a divider with the same thick film resistor blend or decade material. That way absolute TCR will be in the same area for both resistor elements and their resistance values will move together in the same direction.
The physical layout of the resistors on the substrate can influence TCR. By designing resistors to be close to each other, they share similar temperature environments. This proximity helps in achieving more uniform thermal characteristics across the network.
TCR Matching Challenges
Matching TCR values on a thick film resistor network is a challenge. Especially if there is a very high ohmic primary resistor and low ohmic secondary as TCR is dependent on the resistor material and its length. There are ways to compensate to some degree, but there are limits.
The longer the resistor element needs to be in order to handle the applied voltage, the worse the TCR will be. It is near to impossible to match TCR over a range of voltages. Resistors are measured and trimmed at low voltages. In high voltage applications not only does the TCR change, but the VCR affects the resistance. This is an issue with all resistor technologies.
A thick film resistor network offers several advantages over discrete devices. To address the technical issues outlined above it is best to work with a thick film resistor network manufacturer. They can deliver samples for analysis to help the system designer assess what is achievable.