A differential bioamplifier is shown below.

$1$

i$.$ Find the differential gain of the bioamplifier $A_d=\frac{V_{\text{o}\text{u}\text{t}}}{V_{in}}.$ You can assume common mode voltage at the input as zero. You can assume differential inputs as $V_A=+\frac{1}{2}$ and $V_B=-\frac{1}{2}.$

ii$.$ By assuming the differential input of the amplifier as zero, find the common mode gain $A_{CM}=\frac{V_{\text{O}\text{U}\text{T}}}{V_{CM}}$ of the bioamplifier.

iii. Calculate the Common Mode Rejection Ratio $($CMRR$)$ of the bioamplifier in dB $.$

iv$.$ If you record an ECG signal with this amplifier, you observe there is a small powerline interference on the $V_{\text{O}\text{U}\text{T}}$ due to displacement current. The ECG amplitude at the output is $2$ V and the amplitude of the powerline at the output is $9$ mV $.$ Then what are the actual common voltage and the EKG signal amplitudes recorded on the electrodes?