Pre-lab: Motor Control Circuits

The questions below are due on Friday March 13, 2026; 05:00:00 PM.
 
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This week will use two motors to create a fun light following cart. We will represent the motor with the following symbol:

The speed of the motor can be controlled by changing the voltage accross the two terminals of the motor. Importantly:

  • The higher the magnitude of the voltage across the motor, the faster the motor will spin.
  • If we change polarity of the voltage across the motor, it will spin in the opposite direction.
    What is the voltage drop across the motor in the circuit above? Enter a symbolic expression in terms of v_in and v_offset. Note that those variables are case-sensitive!

    Drop across motor = 
    To change the direction of the motor, we could use a bipolar supply (a supply capable of generating positive and negative voltage). Alternatively, we can supply our input voltage with a varying positive voltage, but change our offset voltage (v_{offset}), such that we the voltage drop across the motor can be positive or negative.

In other words:

  • if v_{in} < v_{offset} the voltage across the motor is negative.
  • if v_{in} > v_{offset} the voltage across the motor is positive.

In this week's lab, we're going to be building a little mobile robot, so we won't be able to use the benchtop power supplies to provide power; instead, we'll be using a 9V battery. This small supply voltage means that if we only used the 9 V battery and resistor divider, we would be able to get a swing of only (at most!) \pm4.5 Volts across the motor, which wouldn't be enough to make the robot go. As such, we'll be using a different circuit this week:

What is the voltage drop across the motor in the circuit above? In your analysis, make the ideal op-amp assumption, and ignore any limitations imposed on the op-amp's output by the power supply. Enter a symbolic expression in terms of v_in, v_offset, and/or R. Note that those variables are case-sensitive!

Drop across motor = 

Make sure you're prepared to discuss your work for solving this circuit during lab on Thursday/Friday. If you're having trouble with it, feel free to ask for help at the start of the lab; but definitely try your best.