## 3 Results and Discussion
### Phase-Amplitude Resonant Measurement Method  
Indirect temperature measurement by the proposed method is carried out due to the joint analysis of the phase and amplitude characteristics of the inductor current during the HF induction heating of the nozzle. This ensures the measurement of temperature in the layers of the nozzle material involved in the flow of HF current, i.e., the measurement is made close to the polymer. In order to implement the method, an LCL topology circuit was developed (Figure 8), the component values of which were selected using simulation modeling in the Multisim package so that the selected operating frequency (\(f\) = 115 kHz) was close to the L\({}_{2}\)C\({}_{1}\) voltage resonance frequency \(f_{0}\) = 116.2 kHz, at which the active nature of the load (inductor L\({}_{1}\) with the nozzle) is provided. The topology ensures that the voltage at the output of the HF generator and on the inductor L\({}_{1}\) is independent of the load characteristics due to its inclusion in a parallel resonant circuit L\({}_{1}\)C\({}_{1}\). The topology almost completely eliminates the influence of the circuit stray parameters on the characteristics of the current \(I\) of the inductor L\({}_{1}\) by connecting the L\({}_{1}\)C\({}_{1}\) circuit to the HF generator through the series elements L\({}_{2}\) and C\({}_{2}\). During the process of the nozzle temperature changing, a change in the electrical resistivity and relative magnetic permeability of the nozzle material occurs, which leads to a change in the ohmic resistivity and inductance of the inductor L\({}_{1}\) circuit, which causes a change in the resonant frequency \(f_{0}\) and its deviation from the frequency \(f\), which leads to a change in the amplitude and phase characteristics of the inductor L\({}_{1}\) current \(I\). Figure 7: Numerically simulated heating curves of the nozzle at a set source power level of 5% in an open-loop system for various \(V_{ext}\). Figure 8 demonstrates V\({}_{1}\) and V\({}_{2}\) that are switching power supplies operating with a phase shift of 180\({}^{\circ}\) relative to each other, the voltage of which varies from zero to 24 V (voltage V\({}_{0}\) of the HF generator). Resistors \(R^{\prime}\)2, \(R^{\prime}\)3, \(R^{\prime}\)4, \(R^{\prime}\)5 are parasitic resistances. \(R^{\prime}\)1 is the nozzle resistance. The results of the topology study in the frequency domain demonstrate the current resonance frequency \(f_{\rm T}\) = 113.5 kHz as well as the voltage resonance frequency \(f_{v}\) = 116.2 kHz. The following values of the resonant circuit, which provide the voltage resonance at a frequency of 116.2 kHz: L\({}_{1}\) = 7.8 \(\mu\)H, L\({}_{2}\) = 9.62 \(\mu\)H, C\({}_{1}\) = 450 nF were obtained. In this case, C\({}_{2}\)\(>\)C\({}_{1}\). A study in the phase-frequency domain showed that when operating at a frequency \(f_{v}\) in the L\({}_{2}\)C\({}_{1}\) circuit, the voltage at the output of the HF generator is in-phase with the current \(I\) of the inductor L\({}_{1}\), which is also confirmed in [62]. Phase frequency response (PFR) has a form close to linear in the range of about \(-\)30 to +30\({}^{\circ}\) (in the frequency range \(f_{\rm r1}\)..\(f_{\rm r2}\) about -7 kHz). In this range, it is possible to measure temperature based on phase shift changes without significant loss of accuracy. Figure 9 shows the phase response of the inductor L\({}_{1}\) current \(I\), demonstrating an approximate change in the phase shift \(\varphi\) when the frequency \(f_{v}\) deviates from the operating frequency \(f\) as a result of heating or cooling the nozzle relative to the reference temperature \(T_{r}\) = 250 \({}^{\circ}\)C. Under the condition \(T\) = \(T_{r}\), voltage resonance \(f_{v}\) = \(f\) occurs.