A half bridge configuration is implemented with same strain gauges of gauge factor $G_F=2\mathrm{.}0.$ The minimum strain needs to be measured is $10$ microstrain, the maximum strain is around $3000$ microstrain. $(10$ points total$)$

a$.$ Show the steps to find the range of voltage output if the source supply is $5$ V and an amplifier $($shown on the right$)$ is applied with

$R_f=9\mathrm{.}99k,R_1=10*(4$ points$)$

$\frac{V_G}{E_t}=\frac{G_F}{2}\frac{10}{2}{V}_G=\frac{E_e{G}_F}{2}=\frac{5v210{10}^{-6}}{2}$

$V_0=50{10}^{-6}V1000=50{10}^{-6}V$

$V_0=05v$

$3000$ me

$V_G=\frac{5v23000{10}^{-6}}{2}=15{10}^{-3}v$

$V_0=15{10}^{-3}v1000=15v$

range is

$0\mathrm{.}05$ v

$15$ V

b$.$ Show the steps to find the minimum number of bits and full scale voltage required for the $\frac{A}{D}$ converter of the DAQ system. $($Consider choses from $4,8,12,16,24$ bits, and $5,10,15,24$ Volts$)(6$ points$)$

Full scale voltage $E_{FS}=15-0\mathrm{.}05=14\mathrm{.}9v$