Michael is designing a motor driver for a wheeled mobile robot. The motor driver is designed as an inverting amplifier (using the circuit shown in Figure 1) to drive the motor in the opposite direction of the input voltage. Michael would like to select the components of the amplifier based on specific design requirements. Michael has installed a switch (Sw1) to disconnect the motor driver input signal (vin) to the system and a motor protection switch (Sw2) to disconnect the motor from the amplifier when the motor isn't used. A simplified model of a DC motor has been used, made up of a resistor and inductor in series. The DC motor generates a torque proportional to the current (iout) through the inductor. Figure 1 – Amplifier for motor driver. (a) Design an inverting amplifier by choosing suitable resistor values for R1 and R2 to produce a gain of 5 when both switches Sw1 and Sw2 are open. (5 marks) (b) Design the bias input circuit by choosing suitable resistors R3, and R4 such that the voltage vb, will be 2.5V if the positive power supply of the op-amp is connected to a 5V car battery. Again both switches are open. (6 marks) (c) Given Sw1 is open, the amplifier is turned on for enough time, such that the voltages stabilise, Michael connects the motor by closing Sw2 and the motor starts to move. Find the step response of the motor current, iout. Assume that the amplifier output resistance is negligible, it does not current limit and the motor inductor has been de-energised. (10 marks) (d) What is the steady state voltage across the motor? (2 marks)2 (e) Perform frequency response analysis from vin, to the voltage across the motor inductor, when both Switches are closed and Michael applies three different input signals of 10 Hz, 100 Hz and 1000 Hz through the system? (15 marks) (f) Plot the response calculated in part (e) in a Bode plot. (7 marks) (g) Michael has found that the motor input signal has a positive DC offset when it is applied to the motor driver. This DC offset throws off Michael's original bias circuit that he designed earlier. What single component could be used to remove the effects of this DC offset? Where would this component be placed and why?