# Investigation of Electromagnetic Angle Sensor Integrated in FR4-Based Scanning Micromirror
## 3 Experimental Results and Discussion  
Figure 3a shows the schematic drawing of the measurement setup of the angle sensor. The micromirror works at the resonance point (361.8 Hz). The scan angle is controlled by adjusting the driving voltage amplitude, and can be calculated according to the length of laser scan line and the distance between the optical screen and the micromirror. The length of laser scan line can be measured accurately through a position sensitive detector (PSD). Meanwhile, the corresponding output signal of the angle sensor is amplified by a simple voltage amplifier with a gain of 400, and then measured using an oscilloscope. After this amplifier, the signal amplitude can reach a level of several hundred millivolts, which is large enough to be detected by the oscilloscope. The photograph of the real experimental setup is shown in Figure 3b. In order to measure the coupling voltage coupled from the driving signal, and keep the device virtually undamaged at the same time, we take away the magnets of the assembled micromirror, so that the mirror plate cannot move due to the absence of a magnetic field, and then excite the driving coil to see the output of the sensing coil. Figure 4 illustrates the comparison of the driving signal, sensor output, and coupling signal in the sensing coil coupled from the driving signal in time domain. We can observe that the sensor output signal is nearly in phase with the driving signal. The small phase difference of 5.1\({}^{\circ}\) is caused by the superposed coupling signal in the sensing coil, and it is close to the theoretical value of 4.4\({}^{\circ}\) calculated by Equation (14). Meanwhile, the coupling signal in the sensing coil has a phase difference of 89.6\({}^{\circ}\) with the driving signal, which is also very close to the theoretical value of 90\({}^{\circ}\) calculated  
from Equation (11). Both the minor errors between the experimental and theoretical values could be attributed to electronic noise and a little measurement error. Figure 5a plots the relationship between the coupling voltage in the sensing coil and the driving voltage. We can see that the amplitude of the coupling voltage is proportional to that of the driving voltage. The test data is in good agreement with the theoretical result obtained by Equation (11), although there is a little deviation between them. The deviation is caused by the minor error between the real and simulated mutual inductances. Owing to the difference between the real and simulated material parameters, the simulated mutual inductance inevitably deviates a little from the real value. According to Figure 5b, we can see a clear linear relationship between the sensor output voltage and the optical scan angle of the micromirror. The correlation coefficient \(r\) can reach 0.9995. This is well consistent with the theoretical relation determined by Equation (13). The sensitivity of the angle sensor can be determined as 55.0 mV\({}_{\text{p}}\)/\({}^{\circ}\), which is also very close to the theoretical value of 55.2 mV\({}_{\text{p}}\)/\({}^{\circ}\), calculated by Equation (13). The difference between the experimental and theoretical values can be attributed to the process error. In addition, a little nonlinear behavior of the test result is observed in Figure 5b. It is caused by the coupling effect between the driving and sensing coils. By comparing Equation (9) with (13), we can find that the parameter of torsional stiffness \(K\) is introduced in Equation (13) when considering the coupling voltage in the sensing coil coupled from the driving signal. Owing to the nonlinear spring effect of the torsion bars [15; 24], \(K\) is not a constant, but varies with the change of the scan angle. Thus, a little nonlinear behavior of the test result is observed. The theoretical result is perfectly linear because \(K\) is assumed to be a constant in the theoretical calculation. Figure 4: Comparison of the driving signal, sensor output and coupling signal in the sensing coil coupled from the driving signal in time domain.