Investigating DC Characteristics in Testing Precision Current Shunts for Steady State

Abstract

This paper provides information on the performance study of precision current shunts in the context of their output voltage stability. Besides, it briefly focuses on the phenomena affecting the steady state of these measuring instruments. The authors present a methodology for testing current shunts to ensure a high-quality result of current measurement. The investigation highlights three characteristics of shunts (the dependence of resistance on temperature, the response of the output voltage to a fast increase of current, and the transition from a cold state to a warm one). The test equipment with precision shunts were considered during the experimental examination. The results of an investigation confirmed satisfactory operational properties and compliance with the needs of laboratories. Additionally, the authors emphasize using a precision shunt as a measuring standard when calibrating other instruments like high-precision digital ammeters. From this point of view, the simplified mathematical modeling of the change in the AC-DC transfer difference, depending on the resistance change caused by the warming current, was carried out.

Appendix: Modeling AC-DC Transfer Difference Change Due to Resistance Change

Consideration of the internationally agreed definition is necessary to understand the essence of the assumption about the invariance of the relative AC-DC transfer difference. This quantity appears between the alternating current and equivalent direct current flowing through the current shunt in turn, provided that the output voltage of this shunt is the same in both cases [10]. An expression of this characteristic is

$$\delta_{I} = I_{AC} /I_{DC} {-}1,\quad \left( {{\text{if}}\quad U_{AC} = U_{DC} } \right),$$

(A-1)

where I_AC and I_DC are the alternating and direct currents, respectively; U_AC and U_DC are the alternating and direct output voltages of the precision shunt.

The difference between the alternating current and direct current arises due to the presence of the reactive component of the shunt resistance. Generally, precision shunts have several design elements: input connector, input disks, crossbars, output circle, and disk, a wire between the circle and output connector, output connector. The electric model can be composed of the resistances of different parts of the shunt, capacitances, and inductances.

For ease of modeling, the current shunt impedance can be represented as the complex sum of the active and inductive components Z = R + jX_L (if the inductive component is predominant in the reactance) for the series connection model of resistance and inductance. In this case, the expression (A-1) can be transformed into the form

$$\delta_{I} = U_{AC} /Z/U_{DC} /R{-}1 = R/Z{-}1.$$

(A-2)

One should adapt expression (A-2) for the changed shunt impedance to estimate the change in the AC-DC transfer difference:

$$\delta_{I} + \Delta \delta_{I} = \frac{R + \Delta R}{{\sqrt {\left( {R + \Delta R} \right)^{2} + X_{L}^{2} } }} - 1$$

(A-3)

Evaluating the minuend change is enough to estimate the effect of the current on the AC-DC transfer difference. For this purpose, the first partial derivative (sensitivity coefficient) should be determined:

$${{\partial \left( {\Delta \delta_{I} } \right)} \mathord{\left/ {\vphantom {{\partial \left( {\Delta \delta_{I} } \right)} {\partial \left( {\Delta R} \right)}}} \right. \kern-0pt} {\partial \left( {\Delta R} \right)}} = \frac{{X_{L}^{2} }}{{\sqrt {\left[ {\left( {R + \Delta R} \right)^{2} + X_{L}^{2} } \right]^{3} } }}.$$

(A-4)

Knowing the specific value of resistance change, one can estimate a magnitude of AC-DC transfer difference change by multiplying the sensitivity coefficient by resistance change. One can estimate the probable reactive component, knowing the concrete value of the resistance R and the desired value of AC-DC transfer difference. Thus, for the investigated shunt with a resistance of 0.1 Ω for the AC-DC transfer difference of -10 μA/A, the equivalent reactive component will be 0.45 mΩ, assuming for simplification the serial connection of the impedance components. For the same shunt, for the expected AC-DC transfer difference of -100 μA/A, the value of the equivalent reactance will be about 1.42 mΩ. The data of Table 1 of Sect. 3 were used to evaluate the AC-DC transfer difference change due to resistance increase assuming no change of the reactive component. The results are given in Table

Table 3 Results of modeling AC-DC difference change for series connection in impedance

3.

The obtained data of Table 3 show that the magnitude of AC-DC transfer difference decreases with a current flow (with corresponding warm-up) of the shunt for the model considered. Obviously, for a resistor and an inductor connected in series, as the resistance increases, the contribution of reactivity to the creation of the AC-DC transfer difference decreases following the expression (A-3).

The second version of the simple current shunt model can be represented as a parallel connection of resistance and capacitance. In this case, the value of the impedance will be determined by the well-known formula as

$$\left| Z \right| = \frac{{R \cdot X_{C} }}{{\sqrt {R^{2} + X_{C}^{2} } }}.$$

(A-5)

Farther, expression (A-1) is transformed as follows

$$\delta_{I} = \sqrt {{{R^{2} } \mathord{\left/ {\vphantom {{R^{2} } {X_{C}^{2} }}} \right. \kern-0pt} {X_{C}^{2} }} + 1} - 1.$$

(A-6)

One can determine the sensitivity coefficient as the first partial derivative using the expression:

$${{\partial \left( {\Delta \delta_{I} } \right)} \mathord{\left/ {\vphantom {{\partial \left( {\Delta \delta_{I} } \right)} {\partial \left( {\Delta R} \right)}}} \right. \kern-0pt} {\partial \left( {\Delta R} \right)}} = \frac{{\left( {R + \Delta R} \right)^{2} /X_{C}^{2} }}{{\sqrt {\left( {R + \Delta R} \right)^{2} /X_{C}^{2} + 1} }}.$$

(A-7)

For the shunt under study with a resistance of 0.1 Ω, for the desired AC-DC transfer difference of 10 μA/A, the equivalent reactive component will be 22.36062 Ω, assuming a parallel connection of the impedance components. For the same shunt with AC-DC transfer difference of 100 μA/A, the equivalent reactive component will be about 7.070891 Ω.

The results of the second modeling of the AC-DC transfer difference change due to resistance increase assuming no change of the reactive component are given in Table

Table 4 Results of modeling AC-DC difference change for parallel connection in impedance

4.

The obtained data of Table 4 show that AC-DC transfer difference increases with the current increase (with warm-up) of the shunt under study for the second considered model. Obviously, the current through the capacitor will increase when the resistance will increase if resistor and capacitor are connected in parallel. As a result, the contribution of reactance to the creation of the AC-DC transfer difference increases following the expression (A-6).

According to the results of Tables 3 and 4, the AC-DC transfer difference change due to warm-up during current flow is negligibly small, and it can be ignored.

Models close to a real precision current shunt are more sophisticated. Additionally, the physical properties of the materials of the construction elements and the shunt geometry change slightly due to thermal expansion. Therefore, a minor change in the overall shunt reactance also occurs. However, this study neglects mentioned physical processes, assuming a much stronger relationship between changes in temperature and changes in resistance.