In the realm of simplified RTD ratiometer system designs, the lurking errors attributed to the self-heating of resistors in the signal pathway are critical. These errors, often underestimated, can lead to significant deviations in desired performance levels.
Essentially, the design pivots around ratiometer measurements. Here, the crux lies in the analog-to-digital converter (ADC) and its dependency on the absolute value of the reference resistor, RREF. Intriguingly, the journey of the excitation current through RREF is not without consequence. As it traverses, it dissipates power, giving rise to heat. This heating, seemingly innocuous, is a catalyst for resistance fluctuations, thereby impacting the system’s precision. Beyond this, in a broader spectrum, the phenomenon of resistor self-heating plays a pivotal role in varied domains like current sensing and power measurement. Its influence is directly proportional to the resistor's absolute value, as this determines the resistance alteration in response to power consumption.
Delving into the specifics, the temperature coefficient (TC) of a resistor is its resistance’s response to temperature variations. Expressed in parts per million per degree Celsius (ppm/°C), this coefficient offers insight into the resistor's stability. For instance, a 1% resistor exhibits a TC of roughly +/-100ppm/°C, in stark contrast to high-precision metal foil resistors, which boast a TC below 0.1ppm/°C. Interestingly, the efficiency of smaller surface mount components (0201, 0402, 0603, etc.) in power dissipation is notably lower, resulting in astoundingly high self-heating coefficients θSH, at times surpassing 1000°C/W. Despite their modest rated power of less than 0.1W, these diminutive resistors undergo rapid temperature shifts with power dissipation. Yet, resistor data sheets often omit these self-heating coefficients.
Analysis and Calculation of Resistor Self-Heating Effects
Nevertheless, a reverse-engineering approach is viable using the power rating derating curve. This curve demarcates the resistor's maximum power dissipation at a given ambient temperature, ensuring the temperature does not breach its specified maximum. Furthermore, it's critical to note that resistors cannot function at 100% rated dissipation (TMAX_PWR100%) at temperatures as high as 85°C. From these data points—operating temperature, maximum temperature, and power rating—one can deduce the self-heating coefficient, SH. This coefficient is then instrumental in quantifying heat gain, paving the way for calculating resistance changes due to power dissipation. Consequently, this enables an assessment of its impact on overall system accuracy. Hence, in your next high-precision resistor-based system design, remember to factor in the nuances of resistor self-heating!