## 3 Results
Rectangular pulses with the same duration as those used in the calibration processes were used as input power functions. The amplitude \(k\) of the pulse \(i_{m}\), which corresponds to the excitation power of the heating resistor, was the only parameter estimated in each measurement during  
Figure 5: Measured temperature curves (solid lines) vs. curves fitted using calorimeter model (dashed lines) in function of time: (**a1**,**b1**,**c1**) novel calorimeter model R5C, (**a2**,**b2**,**c2**) model R1C1 corresponding to corrected-slope method. Excitation configurations: (**a1**,**a2**) \(i_{1}(t)=0\) mW, \(u_{1}(t)=59.4\) W, \(i_{2}(t)=14.1\) mW, \(u_{2}(t)=59.4\) W (**b1**,**b2**), \(i_{3}(t)=56.4\) mW, \(u_{3}(t)=59.4\) W (**c1**,**c2**). the validation phase. Single-parameter fitting was a less complicated problem than the least-square fitting of seven RC parameters conducted in the calibration process. Because of that simplification, a global optimization algorithm was replaced with the least-square linear algorithm, which converged much faster. All the values of the thermal power and the measurement errors are listed in Table 2. The relative measurement error was calculated using the following formula:  
\[e=\left|\frac{P_{true}-P_{estimated}}{P_{true}}\right|100\% \tag{3}\]  
Identifying the equivalent electrical models allowed the calorimeter to be calibrated and used to measure the actual value of the input heating power, even when disturbed by an external heat flow. The estimated power values were plotted as a function of the true power values, as shown in Figure 6.  
One can observe that both models' responses remain approximately linear within the analyzed range. Compared to the commonly used R1C1 model, the C2R5 model applied to our non-adiabatic calorimeter resulted in an improvement across the entire range of calibrated power values. The most significant improvement in the estimated power accuracy is observed at low heating power levels, where the influence of heat from the transmitting coil represents a relatively large portion of the measured power. In this region, a noticeable increase in estimation accuracy is achieved, with the error decreasing from 16% for the R1C1 model to just 2.5% for the C2R5 model (Figure 7). Although the \begin{table}
\begin{tabular}{c c c c c c} \hline
**Power at Excitation** & **True Input Power** & \multirow{2}{*}{**Estimated Input Power Value [mW]**} & \multirow{2}{*}{**Relative Error [\%]**} \\
**Coil [W]** & & & & & \\ \hline  & & **C2R5** & **C1R1** & **C2R5** & **C1R1** \\ \hline
38.05 & 25.08 & 25.67 & 29.11 & 2.36 & 16.09 \\
38.05 & 39.19 & 39.92 & 41.59 & 1.88 & 6.14 \\
38.05 & 76.80 & 76.81 & 77.72 & 0.02 & 1.19 \\
38.05 & 100.31 & 100.05 & 99.60 & 0.26 & 0.71 \\
38.05 & 156.74 & 154.49 & 153.54 & 1.43 & 2.04 \\
38.05 & 189.66 & 186.65 & 185.60 & 1.58 & 2.14 \\ \hline \end{tabular}
\end{table} 
Table 2: Relative errors of input heating power according to identified lumped-element models. Figure 6: Estimated heating power as a function of the heat power set on the controlled heat source, based on the novel calorimeter model (**a**) and the model corresponding to the corrected-slope method (**b**). The estimated curve (red solid line with circle markers) and the linear model (blue solid line). improvement in accuracy is less pronounced at higher power values, a reduction in error is still noticeable. For the upper calibration range, the error is reduced to approximately 1.5%.