# A Metal Detector for Clip Location Tracking of Stomach and Colon Cancer during Laparoscopic Surgery
## 4 Experimental Results  
### Designed Circuit Simulation Results  
The simulation results under the oscillation condition of the designed oscillator are shown in Figure 8. As shown in the figure, the oscillation condition can be divided into two types: start-up condition and steady-state condition. The start-up voltage is 2.5 V between 0 ns and 40 ns, and the steady-state oscillation voltage range is maintained as 0.0-5.7 V (output current and power of 2.3 mA and 5.75 mW) between 40 ns and 200 ns in the oscillation condition.  
Figure 9 shows the simulation result for the sine waveform of an oscillation condition using the Colpitts oscillator. As shown in the figure, the sine waveform has an input voltage (V\({}_{\text{in}}\): \(\omega_{\text{eddy}}\)) and output voltage (V\({}_{\text{out}}\): \(\omega_{\text{Hext}}\)).  
For the input voltage (V\({}_{\text{in}}\): \(\omega_{\text{eddy}}\)) of 1 V, the output voltage (V\({}_{\text{out}}\): \(\omega_{\text{Hext}}\)) is maintained as 2.6 V. If the oscillator starts operating, the steady-state oscillation voltage range is maintained from 0.0 V to 5.7 V between 40 ns and 200 ns under a sine waveform input voltage (V\({}_{\text{in}}\): \(\omega_{\text{eddy}}\)) of 1 V. However, if coupling occurs between the coil and the metal (clip) of the oscillator, the output voltage (V\({}_{\text{out}}\): \(\omega_{\text{Hext}}\)) is maintained at 2.6 V (\(\omega_{\text{metal}^{\text{-}}\)detection), as shown in Figure 10.  
Figure 8: Simulation result under the oscillation condition for Colpitts oscillator.  
Figure 9: Simulation result of the sine waveform for the Colpitts oscillator and metal (clip).  
Therefore, the phase difference between the input voltage (\(V_{\text{in}}\): \(\omega_{\text{eddy}}\)) of the oscillator and the coupling voltage (the coupling voltage between the oscillator and metal (clip)) is 90\({}^{\circ}\), as shown in Figure 11. Therefore, the \(\omega_{\text{metal-detection}}\) signal is detected at a phase difference of 90\({}^{\circ}\) between the frequency of the magnetic field (\(\omega_{\text{Hext}}\)), generated by the oscillator coil and the induced magnetic field (\(\omega_{\text{Heddy}}\)) which is caused by the induced current generated in the metal (clip), and accordingly, metal (clip) detection occurs.  
At this time, to perform the metal (clip) detection, the frequency of \(\omega_{\text{metal-detection}}\) is matched between the peak point of \(\omega_{\text{Hext}}\) and the negative peak point of \(\omega_{\text{Heddy}}\), as shown in Equation (3).  
\[\omega_{\text{metal-detection}}=\sqrt{\big{(}\omega_{\text{Heddy}}\big{)}( \omega_{\text{Hext}})}=1 \tag{3}\]  
For this reason, when \(\omega_{\text{Hext}}\) is equal to \(\omega_{\text{Heddy}}\), \(\omega_{\text{metal-detection}}=1\), the function of metal (clip) detection is realized. If \(\omega_{\text{metal-detection}}>1\) or \(\omega_{\text{metal-detection}}<1\), the metal (clip-detector does not function because \(\omega_{\text{metal-detection}}\
eq 1\). Therefore, when \(\omega_{\text{metal-detection}}=1\), the metal (clip) is detected as shown in Figure 12, and \(\omega_{\text{Hext}}\) and \(\omega_{\text{Heddy}}\) are 90\({}^{\circ}\) in phase with respect to each other. At this time, \(\omega_{\text{metal-detection}}\) is able to identify the location of tumors in the stomach or colon during laparoscopic surgery with a voltage of 2.77 V and a frequency of 11.335 kHz, with a duty cycle of 50%.  
Figure 11: Simulation result of the phase difference between Colpitts oscillator and metal (clip).  
Figure 10: Simulation result of the sine waveform with metal (clip) detection for Colpitts oscillator and metal clip.