BE 306 BioInstrumentation
Solutions to the Exam #1 Make Up:
27 April 2000, Thursday
This exam:
TEST FORM CODE:
GOOD LUCK!
PROBLEM 1
3 POINTS
X-RAYs used in radiology are produced by bombarding a metal target with high energy electrons. Electrons are accelerated in an electric field, and travel in vacuum until they hit their target. If the energy of the electron is high enough, the target releases a photon at X-RAY wavelength. These X-RAYs pass through the human body and produce an image on the X-RAY film.
If the energy of a photon is given by E=hn , where h is the Plank’s constant, and n =3x1018 Hz is the frequency of the photon, then calculate the voltage need to be applied between the acceleration plates separated by a distance of 10 cm.
PROBLEM 2
3 POINTS
An implantable device designed to treat incontinence delivers electrical stimuli to sphincter muscle in rapid succession keeping the muscle continuously contracted. When the patient is ready to defecate, stimulation must be inhibited to relax the muscle allowing the opening of the anus. Patients accomplish this by bringing a hand held magnet in close vicinity to the implanted stimulator, which detects the magnetic field using a Hall effect sensor.
In most metals, electrons are the charge carriers. Drift velocity, vd, of electrons in metals can be found by
where e-=1.602x10-19 Coulomb is the charge of an electron, me=9.11x10-31 kg is the mass of an electron, and E is the applied electric field.
A Hall effect sensor is constructed using a flat conductor with length of L=1.0 cm, and width of W=0.5 cm. If the voltage along the length of the conductor is 1 Volt, what is the voltage across the width of the conductor when a magnetic field of B=0.01 Tesla is present?
PROBLEM 3
2 POINTS
A drug pump has a motor to push drug into the blood stream through a catheter. Catheter has a cross sectional area of 1 mm2, and the max pressure in the blood vessel is 120 mmHg = 16 Kilo Pascals. Force to drive this pump will be obtained from an actuator consisting of permanent magnet producing magnetic field of B=0.1 Tesla, and a coil carrying 100 mA. If the section of the coil which is in the magnetic field is only 1 cm long, how many turns the coil must have to produce enough pressure to pump the drug into the blood stream?
PROBLEM 4
2 POINTS
An implantable device needs to be triggered by a hand held magnet. Detector consists of coil with 20 turns and area of 1 cm2. Magnetic field generated by the magnet is given by B(d)=B0/d, where d is the distance from the magnet, and B0=0.3 Teslas. What is the voltage induced on the coil when the patient is holding the magnet 6 cm away from the coil?
PROBLEM 5
2 POINTS
A wound RTD (Resistive Thermic Device) has a resistance of R and an inductance of L due to its wound geometry. If the switch S is closed at t=0, which one of the functions below represent the current flowing through the circuit?
PROBLEM 6
3 POINTS
A sensor is connected an amplifier with a long cable, where the cable can be modeled as shown below using an inductor L and a resistor R. If we are observing the signal y(t) at the input of the amplifier, what is the signal produced by the sensor, i.e. x(t)=?
PROBLEM 7
2 POINTS
Step response, g(t), of a pressure sensor is given below. If the input x(t) to the same sensor is a ramp function, find its output, y(t)=?
PROBLEM 8
4 POINTS
Find the state space representation of the following system
(assume C=1 Farad, R1=1 W , L=1 Henry, R2=1 W )
PROBLEM 9
4 POINTS
Assume that the state space representation of the system above was determined to be as shown below:
and
VC(t)=0 and
IL(t)=0 at t=0 and the input function is given as
If D T=0.1 sec for numerical calculations, use the Euler’s method to the values of Vout(t) at t=0, t=0.1, t=0.2, and t=0.3 second.
PROBLEM 10
3 POINTS
PROBLEM 11
2 POINTS
A signal is given as
What is the energy in this signal?
Charge of an electron is given as e-=1.602x10-19 Coulomb
Mass of the electron, me=9.11x10-31 kg
Plank’s Constant, h = 6.63x10-34 Joules-sec
m 0=4p 10-7 ,e 0=8.85x10-12
