deletions | additions       diff --git a/section_Analysis_1_Direct_Fit__.tex b/section_Analysis_1_Direct_Fit__.tex  new file mode 100644  index 0000000..d5b2159  --- /dev/null  +++ b/section_Analysis_1_Direct_Fit__.tex 
...
\section{Analysis}  1. Direct Fit  $$V_{c}=\frac{1}{L}\times \frac{\Delta\theta}{\Delta B}$$  %$$\frac{\Delta\theta}{\Delta B}=\frac{\Delta V}{\Delta B} \times \frac{\Delta \theta}{\Delta V}$$  $$\theta_{B}=104 degrees; \theta_{0}=108 degrees$$  $$\Delta\theta=\theta_{B}-\theta_{0}=-0.069 radians$$  $$\Delta B=-3A\times 11.1\frac{mT}{A}=-33.3mT$$  $$\frac{\Delta\theta}{\Delta B}=\frac{-0.069radians}{-33.3mT}=0.00207\frac{radians}{mT}=2.07\frac{radians}{T}$$  $$V_{c}=\frac{1}{L}\times \frac{\Delta\theta}{\Delta B}=\frac{1}{0.1m}\times 2.07\frac{radians}{T}=20.7\frac{radians}{T*m}$$  2. Slope Fit\newline  As shown in Figure 2:  $$V=0.000443B+0.127$$  Therefore:  $$\frac{\Delta V}{\Delta B}=0.000443\frac{V}{mT}=0.443\frac{V}{T}$$  As shown in Figure 1:   $$V=\frac{0.021\times (1+cos(\frac{2\pi\times(\theta-162)}{180}))}{2}$$  Taking the derivative at $\theta=117$ degrees:  $$\frac{\Delta V}{\Delta \theta}=\frac{0.21}{2}\times(-sin(2\frac{\pi}{180}(-45)))=0.21V$$  $$\frac{\Delta\theta}{\Delta B}=\frac{\Delta V}{\Delta B} \times \frac{\Delta \theta}{\Delta V}=0.443\frac{V}{T}\times\frac{1 radian}{0.21V}=2.1095\frac{radians}{T}$$  $$V_{c}=\frac{1}{L}\times \frac{\Delta\theta}{\Delta B}=\frac{1}{0.1}\times2.1095\frac{radians}{T}=21.095\frac{radians}{T*m}$$  3. Lock-in Method  $$I_{rms}=0.6137\times V_{rms}$$  $$B=11.1\times\frac{mT}{A}\times I$$  $$Gain=G_{preamplifier}\times G_{filter}\times G_{lock-in-amplifier}\times G_{lowpass filter}=500\times2\times10\times1=10000$$  $$V_{Photodiode}=\frac{V_{output}\times1.11}{10000}$$  The main method is to change the magnetic field and then to observe the corresponding voltage output from photodiode.30mV, 40mV, 50mV and 60mV have been used to supply the magnetic field, and these are all rms values. Calculation method is shown above, and detailed numeric calculation is shown in the appendix.