## 3 A Short Overview of Selected Examples of Measuring and Monitoring Systems on Sea Ships
### Temperature Measurements in the Ship's Hazardous Areas
#### 3.3.3 Real Measurement Line with Transmitter as Second-Order Inertial Oscillation Element  
For transmitters of second-order oscillation inertial type, the transconductance y\({}_{\text{m}}\) is given by the following formula  
\[\text{y}_{\text{m}}=\text{g}_{\text{m}}\frac{\omega_{\text{o}}^{2}}{\text{s}^{ 2}+2\zeta\omega_{\text{o}}+\omega_{\text{o}}^{2}} \tag{4}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter [unit]** & **Value/Range** & **Parameter [unit]** & **Value/Range** \\ \hline C\({}_{\text{a}}\) [nF] & 4.5 & G\({}_{\text{o}}\) [mS] & 2 \\ C\({}_{\text{BS}}\) [nF] & 8 & g\({}_{\text{m}}\) [S] & 0.043–0.83 \\ C\({}_{\text{c}}\) [nF] & 1.7 & \(\Delta\)T\({}^{2}\) [\({}^{\circ}\)C] & 50–1050 \\ G\({}_{\text{T}}\) [mS] & 8.34 & \(\omega_{2}\) [rd/s] & 14,700 \\ T\({}_{\text{o}}\)\({}^{1}\) [\({}^{\circ}\)C] & 50 & - & - \\ \hline \hline \end{tabular} \({}^{1}\) T\({}_{\text{o}}\) measured temperature. \({}^{2}\)\(\Delta\)T temperature measured span.  
\end{table} 
Table 1: Parameters of real temperature measurement line for first-order inertial transmitter. Figure 11: Small signal model of the temperature measurement line, where: G\({}_{\text{T}}\)—conductivity of Pt-100 sensor, U/I—transmitter 4–20 mA, G\({}_{\text{o}}\)—equivalent conductance of all resistances in the 4–20 mA current loop I\({}_{\text{o}}\), C\({}_{\text{a},\text{b},\text{c}}\)—equivalent capacities of Pt-100 sensor and connecting cables, y\({}_{\text{m}}\)—transadmittance of transmitter R/I. where \(g_{m}\)--transconductance depends on measured range of temperature, \(\omega_{o}\)--natural frequency, \(\zeta\)--damping ratio. The analysis of stability of the circuit presented in Figure 11 was done for the set of real parameters given in Table 2[1]. Computer simulations performed for parameters given in Table 2 have shown that temperature measured line with the oscillating second-order inertial transmitter can be very unstable. As a result, the theoretically direct current \(I_{o}\) is disturbed by alternating part. Further detailed research has shown that the frequency and shape of the additional alternating current depends not only on measured range but also strongly on value of measured temperature (\(T_{o}\)) and equivalent load conductance (\(G_{o}\)). The laboratory experiments of temperature measurement line with the oscillating second-order inertial transmitter R/I presented in Figure 12 were also performed and completely confirmed theoretical considerations. The experiments were performed for different simulated temperatures from measurement range of transmitter R/I (from -30 \({}^{\circ}\)C to 60 \({}^{\circ}\)C) and for different value of \(R_{o}\) for two cases. The first one where a capacitive feedback was broken (switch K-off position) and the second case where the own capacities of sensor by switch K in position on were taken into consideration. In the second case, the capacitive feedback was rebuilt. In both cases for the same simulated temperature, the current was measured by DC ammeter. While the capacitive feedback was done, sometimes the alternating current was observed by oscilloscope. An example of one such screenshot was presented in Figure 13 for a \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter [unit]** & **Value/Range** & **Parameter [unit]** & **Value/Range** \\ \hline \(C_{a}\) [nF] & 4.5 & \(G_{o}\) [mS] & 2 \\ \(C_{b}\) [nF] & 8 & \(g_{m}\) [S] & 0.043–0.83 \\ \(C_{c}\) [nF] & 1.7 & \(\Delta T\) [\({}^{\circ}\)C] & 50–1050 \\ \(G_{T}\) [mS] & 10 & \(\omega_{o}\) [rd/s] & 20,400 \\ \(T_{o}\) [\({}^{\circ}\)C] & 0 & \(\zeta\) & 0.212 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of real temperature measurement line for oscillating second-order inertial transmitter.