## 2 Description of the Calculable Resistors
### Wire Heat Treatment Process  
The next step to be considered in the development of CRs is the heat treatment of the wire to decrease their TC. In this research, Evanohm-S [31] and Isaohm [32] wire spools with previous heat treatment by the manufacturer were tested; the properties of these kinds of alloys make it possible to realize a heat treatment to modify their TC. As was reported by [PERSON] [5], regardless of the heat-treating temperature used in the wire, its TC decreases from the positive value of 50 \(\upmu\Omega\)/\(\Omega\)/\({}^{\circ}\)C, passes through zero, and eventually reaches a minimum value of around \(-\)35 \(\upmu\)m of diameter and a resistivity of 154.8 \(\upmu\Omega\)/\(\Omega\)/\({}^{\circ}\)C; if heat treatment continues, the TC starts becoming less negative, passing through zero again, and continue increasing slowly. At higher temperatures, less time is needed to achieve a change in the TC; however, these parameters depend on the NiCr alloy wire and on their gauge. This behavior is represented by Figure 3. Hence, to decrease the TC of NiCr alloy wires, there are two  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Impedance** & **Bifilar** & **Quadrifilar** & **Octofilar** \\ \hline \(M_{1}\) & 0.057 \(\upmu\)H & 0.345 \(\upmu\)H & 0.117 \(\upmu\)H \\ \hline \(M_{2}\) & \(\cdots\cdots\cdots\) & 0.315 \(\upmu\)H & 0.086 \(\upmu\)H \\ \hline \(M_{3}\) & \(\cdots\cdots\cdots\) & \(\cdots\cdots\) & 0.074 \(\upmu\)H \\ \hline \(M_{4}\) & \(\cdots\cdots\cdots\) & \(\cdots\cdots\cdots\) & 0.070 \(\upmu\)H \\ \hline \(L\) & 0.880 \(\upmu\)H & 4.156 \(\upmu\)H & 2.360 \(\upmu\)H \\ \hline \(C_{0}\) & 1.304 pF & 4.410 pF & 10.284 pF \\ \hline \(C_{1}\) & 0.164 pF & 0.862 pF & 0.278 pF \\ \hline \(C_{2}\) & \(\cdots\cdots\cdots\) & 0.537 pF & 0.084 pF \\ \hline \(C_{3}\) & \(\cdots\cdots\cdots\) & \(\cdots\cdots\) & 0.049 pF \\ \hline \(C_{4}\) & \(\cdots\cdots\cdots\) & \(\cdots\cdots\) & 0.042 pF \\ \hline \(G_{0}\) & 9.981 aS & 52.823 aS & 78.692 aS \\ \hline \(G_{1}\) & 1.257 aS & 6.600 aS & 1.666 aS \\ \hline \(G_{2}\) & \(\cdots\cdots\cdots\) & 4.110 aS & 0.640 aS \\ \hline \(G_{3}\) & \(\cdots\cdots\cdots\) & \(\cdots\cdots\) & 0.378 aS \\ \hline \(G_{4}\) & \(\cdots\cdots\cdots\) & \(\cdots\cdots\) & 0.320 aS \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parasitic impedances values of bifilar, quadrifilar and octofilar CRs.  
independent variables, temperature and time of the heat treatment. An explanation of the relationships between the heat treatment time and the temperature is described by [PERSON] in [5].  
The process to achieve a TC below 1 \(\upmu\Omega/\Omega/^{\circ}\)C consists of the following steps: (A) Measuring the TC of a wire segment of the spool without heat treatment. (B) Determine where the TC is plotted in Figure 3 graph (C) Perform heat treatment to a non-heat-treated wire segment. (D) Take a section of the heat-treated wire and measure their TC. (E) Depending on the change of the TC, analyze if more or less treatment time or temperature is needed to achieve the required TC. (E) Repeat steps B to D until the desired TC is obtained. A suitable time and temperature to carry out the first heat treatment might be 1 hour at 400 \({}^{\circ}\)C.  
To measure the wire TC, copper terminals were placed at the end of the tested wire segments using the spot-welding technique; placing the wire segment inside an aluminum shielding submerged in an oil bath with programmable temperature control, a set of 1 \({}^{\circ}\)C steps, every four hours, from 20 \({}^{\circ}\)C to 26 \({}^{\circ}\)C, were performed. In parallel, the resistance of the wire was measured as a four-terminal terminal resistor through an Agilent 3458A meter.  
The heat treatment was carried out by winding three meters of wire on a glass support. Then the support was placed in a quartz case inside a homemade temperature oven able to reach temperatures up to 450 \({}^{\circ}\)C.