## 2 Materials and Methods
### Measurement Method  
The measurement is based on the enhanced induction methodology, where, for the excitation, the triangular-shaped magnetic field generated by the excitation coil is used. The sensing part is represented by the sensing coil used for the detection of the induced voltage peak caused by the domain wall motion. The microwire is alternately excited to the positive and negative values of the excitation magnetic field, which must be large enough to overcome the switching field of the microwire in the local field, e.g., the minimum is twice the local stationary Earth's magnetic field magnitude generally. In the moment when the local magnetic field achieves the switching field value, the domain wall is propagated, and it travels from one end of the microwire to the other through the whole volume of the microwire. This domain wall motion causes the creation of a voltage peak in the sensing coil and the process is repeated with the opposite polarity--see Figure 2.  
The main enhancement of this method is in the measurement of the time intervals \(T^{+}\) and \(T^{-}\) as the carriers of information about the measured tensile stress, when the voltage peaks occur (during the positive and negative magnetization process, respectively). Although the time can be measured with high accuracy, in this way, it is possible to obtain much more precise measurement results.  
For the value of the switching field, the following relationship can be written:  
\[H_{sw}=H_{M}\bigg{(}\frac{T^{+}+T^{-}}{T}-1\bigg{)}, \tag{3}\]  
where \(H_{M}\) is the maximum value of the intensity of the switching field and \(T\) is the half period of the excitation field.  
The intensity of the external magnetic field \(H_{0}\) can be determined according to the following relationship:  
\[H_{0}=-H_{M}\frac{(T^{+}-T^{-})}{T}. \tag{4}\]  
From these relationships and from Figure 2, it is obvious that measurement of the time intervals \(T^{+}\) and \(T^{-}\) can be used for the determination of the microwire switching field \(H_{sw}\) and also for the intensity of the external magnetic field \(H_{0}\). Therefore, the described principle can be applied  
Figure 2: Measurement principle of the tensile stress sensor based on the magnetic microwire.  
for the measurement of multiple physical quantities. Considering the mechanical tensile stress measurement, the measurement of the \(H_{\text{s}aw}\) is crucial.  
For the tensile stress measurement, the electronics based on the VEMA 040 magnetometer was used. This is a four-channel vector relaxation magnetometer with simultaneous sampling using the time interval measurement for the determination of the measured physical quantity manufactured by the EDIS vvd company, through which the applied research performed at the Department of Aviation Technical Studies has been launched in the industry. The control electronics is based on a CPLD (Complex Programmable Logical Device) with a resolution of 10 ns. For the microwire excitation and for the microwire response sensing, the coil system involving the excitation and sensing coils was used. Thanks to the special design of these coils, it is possible to place them in the proximity of the sensing element and to sense the microwire response contactlessly. There is no necessity to place the inspected component into the cylindrical coil system, as is usually the case [42; 43; 44; 45]. The measurement block diagram can be seen in Figure 3.