(Solved): 3) Triple Op Amp instrumentation amplifier a) Derive the differential-mode transfer function of the ...

3) Triple Op Amp instrumentation amplifier a) Derive the differential-mode transfer function of the differential amplifier shown in Figure 3. Assuming an ideal Op-Amps. What does $R_G$ do? b) Design the differential amplifier for a differential gain of $100\left(A_d=\frac{v_{\text{out }}}{v_A-v_B}=\frac{v_{\text{out }}}{v_d}\right)$, making $R_2=R_2^{\prime },R_1=R_1^{\prime },R_3=R_4$. c) Assuming that $V_{CC}=V_{EE}=12\mathrm{V}$. Simulate circuit to obtain its gain and bandwidth. Plot the common-mode rejection ratio (CMRR) as a function of frequency. Assume that CMRR is defined as $CMRR=\frac{A_d}{A_{cm}}$ d) Derive the common mode gain transfer function $\left(A_{cm}=\frac{v_{\text{out }}}{v_{cm}}\right)$ assuming that the feedback resistors are not matched: $R_2=R_2^{\prime }+1\%$. Repeat the simulation for CMRR and plot it vs frequency. e) Verify by simulation that CMRR changes if the node $N_C$ is connected to ground. Fig. 3: Triple Op-Amp instrumentation amplifier