To confirm whether the flexible microspiral inductor made of copper wire meets the variation law and design requirements of general inductors, it is necessary to discuss the changes in the inductance value L, quality factor Q (Q factor), and selfresonant frequency (fSRF) under static and deformation states. The inductance value reflects the ability of the inductor to convert electric energy into magnetic energy; the Q factor represents the efficiency with which the inductor converts electric energy into magnetic energy and reflects the loss of the inductor. The selfresonant frequency directly determines the upper frequency limit of the normal operation of the inductor. In this work, the simulation method and physical experiment method were employed, and the measured results were compared and analyzed.
The electrical performance of the flexible microspiral inductor was simulated using Ansys HFSS (highfrequency structure simulator) to analyze the variation in its electrical performance with the frequency. By establishing the simulation model in HFSS and setting the corresponding parameters, such as the frequency, excitation source, radiation boundary, and accuracy, the simulation results, such as the admittance, inductance value, and Q factor, could be obtained. The solution process mainly comprises the following steps:
Step 1: Use SolidWorks software to model the microspiral inductors with 2.5, 4.5, and 6.5 turns. Taking the copper wire with 4.5 turns as an example, the specific modeling parameters are shown in Table 3. The model is then saved in the “x_t” format in the HFSS, and the material properties are defined.
Step 2: Set boundary conditions. In this work, the boundary condition is set as radiation boundary.
Table 3
Specific parameters of microspiral inductor modeling
Turns

Wire diameter
(mm)

Coil diameter
(mm)

Pitch
(mm)

Coil length
(mm)

Inductor dimensions
(mm)

2.5

0.2

5

3

10.5

40×20×7.5

4.5

0.2

5

3

16.5

6.5

0.2

5

3

22.5

Step 3: Set the excitation port. In this work, the lumped port is used as the excitation mode, and the integral line with the same direction is defined.
Step 4: Set solution value and mesh. The frequency scanning range set in this work is 0–1 GHz, the step size is 0.05 GHz, and the frequency scanning type is “Discrete.” The adaptive meshing function in the HFSS is used for meshing.
Step 5: Simulation solution. Based on the settings of the above parameters, the “Analyze ALL” mode is used to complete the simulation solution. The complexity of the spiral inductor geometric model, the setting of the solution value, the division of the network, and the configuration of the computer influence the simulation time.
When using the HFSS for electrical simulations, the calculation formulae for the inductance (Equation (1)) and Q factor (Equation (2)) are as follow:
Here, Y11 is the admittance, Freq is the operating frequency, Im refers to the imaginary part of 1/Y11, and Re refers to the real part of 1/Y11.
For the microspiral inductors with 2.5, 4.5, and 6.5 turns, this work simulates the inductance value and Q factor in its initial state (unstressed). Figures 3 (a) and (b) show the simulation results. As shown, with the increase ofin the number of inductor turns, the inductance increases; however, it will also lead to an increase in the parasitic capacitance and a decrease in the Q factor. The stray capacitance increases with the increase in the number of turns, thereby decreasing fSRF.
For the 4.5turn microspiral inductor, the inductance and Q factor in the initial state, deformation state 1 (the length after stretching is 50 mm), and deformation state 2 (the length after stretching is 70 mm) were simulated. Figures 3 (c) and (d) show the simulation results. With the deformation of the flexible inductor, the pitch of the copper wire increases, which reduces the mutual inductance between the coils, thereby reducing the total inductance; however, increasing the pitch reduces the parasitic capacitance and eddy current loss of the coil, thus increasing the Q factor.
Table 4
Numerical simulation results of various parameters of the microspiral inductor under different turns and deformation states
Turns

2.5

4.5

6.5

4.5
(Deformation state 1)

4.5
(Deformation state 2)

Maximum inductance value
(nH)

993.11

1509.84

1762.69

1406.89

1197.72

Maximum Q factor

82.43

69.13

61.66

71.34

77.14

fSRF (GHz)

0.39

0.45

0.48

0.38

0.44

Table 4 presents the specific data of the simulation results. From the simulation results, the changes in the inductance and Q factor with the increase in the number of turns and tensile properties of the flexible microspiral inductor are in agreement with the change law of the general flexible inductor. The results are suitable to determine the electrical performance in the subsequent experiment.