Question

UESTION 1 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 (Swi) 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 is not 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. Motor 4? 5V in 10 mH iout 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 S_w1 and S_w2 are open.

(b) Design the bias input circuit by choosing suitable resistors R3 and R4 such that the voltage v_b will be 0.5V if the positive power supply of the op-amp is connected to a 5V battery. Again both switches are open.

(c) Given S_w1 is open, the amplifier is turned on for enough time, such that the voltages stabilise, Michael connects the motor by closing S_w2 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.

(d) What is the steady state voltage across the motor?

(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?

(f) Plot the response calculated in part (e) in a Bode plot.

(g) Michael realises that his motor can only have a positive voltage and so his robot can only go forwards. If Michael has a second 5V battery, redraw the circuit to allow the motor voltage to vary from +5V to -5V as vin varies from 0V to 3V, respectively. Note that Michael will need to change both the gain and the bias voltage at the non-inverting input.

Please help me do this practice question

Answer 1

(a) The switch Swl and Sw2 are open. The modified circuit diagram is shown below R. Design an inverting amplifier choosing the required values of R and R Write the expression for the gain of an inverting amplifier 4, The gain of the inverting amplifier is negative means it has a phase shift of 180° compared to input. The magnitude of the gain is, | 4,- _ Substitute 5 for A, R2 5 = Take the value of the resistor R is 1 k2

Find the value of R, 5 1 k2 R 5 k Hence, the value of the resistances are R is 1 k2 and R, is 5 k2 (b) The circuit diagram is shown below R3 5 V R Switches Swl and Sw2 are open circuited. The op-amp is in inverting amplifier configuration. The magnitude of the voltage gain of the amplifier is www

14,2 a Substitute 5 for A and 0.5 V for v 0.5 5 G 0.1 V 1 The voltage at point a is va equals to 0.1 V It is obtained from the power supply of 5V using the resistors R and R Write the expression for the voltage va in terms of the voltages R and R -x(5 V) R R + -x (5 V) 0.1 R3+R =0.02 RR R 0.02(RR,) 0.98R, 0.02R 0.02R3 0.98 R 0.0204R R 49R If R is 1 k, then R, will be 49 k2

(c) The switch Swl is open and the switch Sw2 is just closed. The only input to the op-amp is the 5V source voltage that is used to provide a 0.5 V input at the inverting terminal. Since the switch Sw2 is just closed and thus, the current through the motor prior to the switch being closed is zero. The motor has a conductor and the current through the inductor cannot change instantaneously thus, the current through the inductor at the time instants 0 and 0 are zero. 0A -(.0)71-(o)7 Determine the steady state current through the motor. In steady state the inductor acts as a short circuit, thus, the current through the inductor at steady state is, i () 40 0.5 4 0.125 A Determine the time constant of the circuit. R 10 mH 4 0.01 4 -0.0025 s Determine the expression for the inductor current ()7-(0)()- () 0.125+(0-0.125)e 0.0025s 0.125(1-e10) 400f Hence, the step response of the motor current is 0.125(1-e

(d) Determine the steady state voltage composed of an inductor; in the steady state the inductor acts as a short circuit In steady state the inductor acts as a short circuit, thus, the current through the inductor at steady state is, across the motor. The motor is ()7! 40 2.5 4 0.125 A Determine the steady-state voltage across the motor vi (0)x R =0.125x 4 -0.5 V Hence, the steady-state voltage is 0.5 V According to the HOMEWORKLIB POLICY, first four subparts are answered.