## 4 Results and Discussion
### Wire-Wound Solenoid Inductor  
Figure 5a illustrates the simulation results of inductance variation, corresponding to the full injection of the different ferrofluids. As can be seen in this figure, the minimum inductance is obtained at vacuum. When the channel is empty, the core is filled by air, where the permeability is approximately equal to vacuum. As tunable fluidic based inductors, ferrofluids will be used for injection into the core. According to the permeability of the injected liquid, the inductance is varied. In this work, four ferrofluids, referred to as EMG901, EMG905, EMG909 and EMG911, were applied to, respectively, initial magnetic permeabilities of 5.4, 3.1, 1.9 and 1.3, magnetic saturation equal to 66 mT, 44 mT, 22 mT and 11 mT, and magnetic particle concentrations 11.8%, 7.8%, 3.9% and 2%.  
The maximum inductance is achieved for EMG901. EMG901 has the highest permeability among the applied ferrofluids. The simulated inductance for vacuum is 54.4 nH at 100 MHz, and increases to 65.4, 86.1, 105.6 and 187.3 nH for EMG911, EMG909, EMG905 and EMG901, respectively. Figure 5b shows the simulated corresponding quality factor. For all fluids, the quality factor obtained is over 300 at 100 MHz. The quality factor slightly decreases when the ferrofluids are injected. However, the quality factor reduction is more severe for EMG901. Figure 5c shows the simulated tuning ratio. The maximum tuning ratio obtained is larger than 243% for EMG901 at 100 MHz. For other ferrofluids, the tuning ratio obtained is from 20.22% to 243%, for a frequency range of a few MHz to 900 MHz.  
Figure 4: The 3D view of inductor designed in High Frequency Structure Simulator (HFSS) (**a**) Wire-wound inductor [25], (**b**) wire bond inductor [26].  
Figure 6 shows the measurement result of the fabricated wire-wound inductor. As simulated, the maximum inductance is obtained for EMG901, while the vacuum presents the minimum achievable inductance. In Figure 6a, the measured inductance values are 55, 62.4, 68.8, 78.6 and 101 nH at 200 MHz, respectively, for vacuum, EMG911, EMG909, EMG905 and EMG901. The maximum quality factor is \(\sim 10^{-3}\). The maximum value of the maximum inductance is \(\sim 10^{-3}\).  
achieved during vacuum at 120 for 150 MHz. The quality factor slightly drops when the ferrofluids are injected. Figure 6c shows the tuning ratio of the fabricated wire-wound inductor. The measured tuning ratio for EMG901 at 200 MHz is 83.5%, while it increases to 90.6% at 300 MHz. As for the EMG911, EMG 909 and EMG905, the tuning ratios are 13.3%, 25% and 42.9%, respectively. Table 3 showed the comparison between the simulated and measurement result for the wire-wound inductor. As shown in the Table 3, the Q factor and tuning range for the simulated and measurement result at 100 MHz for EMG901 were 300%, 243%, 53.7% and 83.5%, respectively. The reason for the large difference between simulation and measurement data is because, in simulation, one only considers open space without close channel, thus, the effect of inner wall surface properties such as surface tensioning and meniscus force were not considered in the simulation model. Thus, the simulation was assumed to be a smooth movement of fluid in the channel. The simulation also assumes, as an ideal case, that parasitic capacitance is not included in this model. In the measurement result, the difficulties of movement fluidic and parasitic capacitance were affecting the value of inductance, and this contributed to the low tuning ratio and Q factor. The tuning ratio percentage is calculated by  
\[\left(\frac{L_{2}-L_{1}}{L_{1}}\right)\times 100 \tag{1}\]  
where \(L_{1}\) and \(L_{2}\) are the minimum and maximum achieved inductances.  
Figure 6: _Cont._