BE 3600 BioInstrumentation
Midterm Exam 1: 22 February 2001, Thursday
S O L U T I O N S
This exam:
YOUR NAME: ______________________
TEST FORM CODE:
GOOD LUCK!
QUESTION 1
[ 2 POINTS ]
A neuromuscular electrical stimulation system will be used to restore hand grasp function of a quadriplegic patient. In order to provide slip information, a capacitive shear sensor is going to be used, where
H, the distance between the parallel plates is assumed to be constant.
If the shear force
Fx applied in x direction moves the plates according to the simple spring rule ( Fx = k x , k being the spring constant), calculate the capacitance as a function of shear force, i.e. C(Fx) = ?
b) 
CORRECT ANSWER
c) 
d) 
QUESTION 2
[ 2 POINTS ]
Interventional cardiologists attempt to remove atherosclerotic plaque using various mechanical tools. On of them is a catheter with a hard revolving tip. An electrical motor at the tip must be able to produce sufficient torque to break the build up. If the magnet of the motor is providing a uniform and steady magnetic field of B, what is the maximum torque produced by the motor having N turns and carrying a current of I amps (Radius of the armature is R, and width of the coil is W).
b) 
c) t
= 2 R I W Bd) t
= R I N W Be) t
= 2 R I N W B CORRECT ANSWER
QUESTION 3
[ 3 POINTS ]
An impedance plethysmography device has an AC current source producing
I1(t)=I0sin(w 0t). Device is connected to the patient using a transformer with a turn ratio of N:1.
If the transthoracic impedance of the patient is given as
R(t), determine the voltage V1(t) seen by the current source.a) 
b) 
c) 
CORRECT ANSWER
d) 
e) 
QUESTION 4
[ 3 POINTS ]
You are trying to find out how the ECG signal from a patient is displayed on the screen of a monitor. After many trials, you concluded that the displayed signal is not identical to the input, that is the ECG. You want to determine the impulse response of the display system, so you asked your technician to apply an impulse, d [k], to the system, and record its output, h[k]. Later you found out that the technician did not know what an impulse is, so he applied the x[k] as shown in the table below, and faithfully recorded to response to x[k] as y[k]. What is the h[k], i.e. the impulse response? [Hint: Try all the answers]
|
k |
… |
-2 |
-1 |
0 |
1 |
2 |
3 |
4 |
… |
|
d [k] |
… |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
… |
|
x[k] |
… |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
… |
|
y[k] |
… |
0 |
0 |
1 |
2 |
1 |
0 |
0 |
… |
|
h[k] |
… |
… |
CORRECT ANSWER IS (b)
|
k |
… |
-2 |
-1 |
0 |
1 |
2 |
3 |
4 |
… |
|
a) |
… |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
… |
|
b) |
… |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
… |
|
c) |
… |
0 |
0 |
1 |
1 |
1 |
0 |
0 |
… |
|
d) |
… |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
… |
|
e) |
0 |
1 |
1 |
1 |
0 |
0 |
0 |
QUESTION 5
[ 3 POINTS ]
A simple discrete system as shown below is used as a filter, where the u[k] is the input, and the y[k] is the output.
You want to simulate it using a computer program, so you decided to derive its state space representation. Which one of the answers below has the correct A, B, C and D values?
CORRECT ANSWER IS (c)
|
A |
B |
C |
D |
|
|
a) |
1/2 |
1/2 |
1 |
1/2 |
|
b) |
1/2 |
1/2 |
1/2 |
1 |
|
c) |
-1/2 |
1/2 |
1 |
0 |
|
d) |
-1/2 |
-1/2 |
1 |
1/2 |
|
e) |
-1/2 |
-1/2 |
1/2 |
1 |
QUESTION 6
[ 3 POINTS ]
Step response of a pressure sensor is given as
g(t) = 2 t e-2t. What is its frequency response, H(w j)?a) 
b) 
c) 
d) 
e) 
CORRECT ANSWER
QUESTION 7
[ 4 POINTS ]
Equivalent circuit model a cable is as shown below:
where
R1 is the cable resistance, R2 is the tissue resistance, and C is the capacitance between the tissue and the electrode at the end of the lead.The input signal to the cable at one end is given as follows:
Find the time domain expression for the output,
y(t).a) 
CORRECT ANSWER 
d) 
