This exam:

• Consists of 10 questions,
• Score from this exam will determine 30% of your grade,
• You have 75 minutes to complete the exam,
• Closed books, closed notes, but use of calculators is allowed,
• Please mark your answers on the SCORE SHEET using pencils,
• Some problems have higher points, budget your time accordingly,
• Do not forget to mark your ID NUMBER and TEST FORM code.

Q1. (2 points) You are working at a hospital as biomedical engineer in charge of maintenance of in house equipment. ECG amplifiers used in the operating room of this hospital have two leads attached to the patient's chest travelling from the ECG amplifier to the patient, bundled in a single cord. Nurses complain that they intermittently loose the ECG signal, and get it back when they move the long cable around. You suspect that there might be a short in the cable, i.e. insulation is worn and the two cables are touching each other. You would like to cut the cable where the short is and repair it. You ask your technician to connect a 1.5 V battery at one end of the cable, between the two leads. He informs you that when the short is in place, there is a 2.6 A current going through the cable. You find out that the cable is made out of copper wire with a diameter of 0.5 mm. Your handbooks specify the conductivity of copper as 1.7x10^-8 W -meter. How far is the short from the end of the cable?

1. 1.06 meters
2. 2.12 meters
3. 3.33 meters (CORRECT ANSWER)
4. 6.66 meters
5. 13.33 meters

Q2. (2 points) Your employer, Hitachi Medical, is designing a new MRI machine, which requires a large coil where the patients are supposed lay down inside. You decide that a length of 2 meters should be sufficient to accommodate most subjects. Nuclear physicists ask that the magnetic field should measure around 1.0 Tesla within the MRI machine. If the maximum current that the superconductor could carry is 2 kilo-Amps, how many turns of the coil would you need to have on this machine?

1. 1,592 turns
2. 7,854 turns (CORRECT ANSWER)
3. 15,708 turns
4. 795,775 turns
5. 112,994 turns

Q3. (2 points) In order to allow patients to control the amount of drug being dispensed by their implantable drug pump, you would like to design a feature where a Hall effect sensor detects the magnetic field produced by a magnet placed over the implant by the patient. You built a prototype and found out that the electrodes spaced 2 mm apart and oriented perpendicular to the current flow would pick up 1 m V when a magnetic field of 0.1 Tesla was applied. What is the drift velocity of the charge carriers (electrons in the metal)?

1. 5 mm/sec (CORRECT ANSWER)
2. 5 meters/sec
3. 200 meters/sec
4. 5 km/sec
5. 3x10⁸ meters/sec

Q4. (4 points) We are attempting to power an implantable device using externally applied magnetic field. At its implant location, magnetic field is a sinusoid with a frequency of 100 KHz and amplitude of 1x10^-3 Teslas. If an output voltage of 3.6 Volts is desired, how many turns a pick-up coil with area of 1 cm² needs to have?

Q5. (5 points) A Holter monitor is an externally worn device which records the vital signs of a patient under ambulatory conditions. Using modern electronics technology, designers brought its power consumption down to 10 mW. During a battery change, we would like the device to maintain its operations, for about 10 seconds. You are proposing to use a capacitor and charge it to 5 Volts before disconnecting the old battery and use the energy stored on the capacitor to power the device until the new battery is connected. What size capacitor will you need?

1. 5 milli-Farads
2. 20 milli-Farads
3. 40 milli-Farads
4. 4 Farads
5. 125 Farads

Q6. (2 points) Impulse response of a flow sensor is given as shown below. Is this a linear system?

1. Yes, it is linear, because output is constant until the input is applied at t=0.
2. No, its response to an impulse is an exponential decay
3. No, it has a discontinuity at t=0
4. No, steady state value is 0.9 volts (CORRECT ANSWER)
5. Can not be determined without applying a second input

Q7. (2 points) What is the impulse response of the following system?

1. 

 

2. 

 

3. 
4. (CORRECT ANSWER)
5. 

Q8. (3 points) Impulse response, h(k) and the input x(k) of a sensor are shown below. Find the output.

CORRECT ANSWER FOR THE PROBLEM ABOVE IS (E).

Q9. (4 points) Equivalent circuit of the tissue-electrode interface is shown below. Find its state-space representation.

CORRECT ANSWER IS (E) BECAUSE:

Q10. (4 points) A long cable that you use for connecting your sensor and amplifier have the following characteristic, where R = 100 kW and C = 10 m F. If we excite this system with the x(t) as specified below, what is the output signal, y(t)?

CORRECT ANSWER IS (B) BECAUSE:

FOR THIS PROBLEM, YOU WOULD NEED TO USE THE FOURIER TRANSFORM TABLES.