A Brief Discussion on the Power Coefficient of Resistance of Coaxial Shunts

1. What Is the Power Coefficient of Resistance?

The Power Coefficient of Resistance (PCR) refers to the relative change in resistance per 1 W change in dissipated power, expressed in ppm/W.

Both the power coefficient (PCR) and the temperature coefficient of resistance (TCR) describe the influence of temperature on resistance. The difference lies in the source of the temperature change:

• PCR characterizes the resistance change caused by self-heating due to Joule loss when power is applied to the resistor.

• TCR describes the resistance drift resulting from ambient temperature variations transferred through thermal conduction.

2. How Does the Power Coefficient Affect the Coaxial Shunts?

For coaxial shunts with the same nominal specifications, a lower power coefficient results in smaller additional measurement uncertainty and therefore higher measurement accuracy.

During current measurement, the power dissipated in the shunt causes self-heating, which changes the resistance value and introduces an additional measurement uncertainty, denoted as δP. This uncertainty can be calculated using Equation (1).

……(1)

Note: Im is the measured current, and In is the nominal current.

Taking a coaxial shunt with a nominal current In of 100 A as an example, and assuming power coefficients of 100 ppm/W and 10 ppm/W, the additional measurement uncertainty δP introduced at measured currents Im of 90 A and 70 A is calculated. The results are shown in Table 1.

Table 1. Additional measurement uncertainty introduced at different power coefficients and operating currents.

From the table, it can be concluded that:

1). The lower the power coefficient, the smaller the additional measurement uncertainty δP, and the less it affects the measurement result. Therefore, coaxial shunts with a low power coefficient should be preferred.

2). The higher the operating current Im, the greater the self-heating, resulting in a larger δP.

For coaxial shunts of the same specification, a lower power coefficient results in a shorter settling time and higher measurement efficiency.

Taking coaxial shunts with a nominal current of 100 A and power coefficients of 100 ppm/W and 10 ppm/W as examples: when △R/R stabilizes to 90%, the former requires at least 7 minutes, while the latter needs only 3 minutes; when △R/R stabilizes to above 95%, the former requires at least 13 minutes, whereas the latter takes only 5 minutes—a difference of 8 minutes. The test curves are shown in Figure 1.

Figure 1. Settling-time test curves of coaxial shunts with different PCR values

3. How Does Tunkia Achieve an Ultra-Low Power Coefficient?

• Optimizing the heat-dissipation structure to improve cooling efficiency;

• Using resistors with a low temperature coefficient to reduce temperature-induced resistance variation;

• Increasing the number of resistors to reduce the power dissipation of each individual resistor.

4. Tunkia TH0420 Ultra-Low Power Coefficient Coaxial Shunt

• Applications: Precision and fast measurement of AC and DC currents over a wide range;

• Primary nominal inputs: 100 mA / 200 mA / … / 100 A / 200 A / 500 A, 12 ranges in total;

• Secondary nominal output: 1 V or 0.5 V;

• Typical annual drift: 5 ppm; maximum annual drift: 16 ppm;

• Operating frequency: DC to 100 kHz;

• Initial deviation: 30 ppm;

• Best annual stability: 12 ppm;

• Best AC/DC difference: 5 ppm @ 53 Hz, 10 ppm @ 1 kHz, 25 ppm @ 100 kHz;

• Best phase displacement: 5 μrad @ 53 Hz, 10 μrad @ 1 kHz, 300 μrad @ 100 kHz.