Download 2012 Problems

Name (Last, First):
_____________________________________________________
BENG 186B Winter 2012
Final
• This exam is closed book, closed note, calculators are OK.
• Circle and put your final answers in the space provided;
show your work only on the pages provided. Include units.
• Do not attach separate sheets. If you need more space, use
the back of the pages.
• Points for each problem are given in [brackets], 100 points
total.
1
2
3
4
5
6
7
8
9
10
Total
/10
/16
/10
/10
/10
/10
/10
/10
/10
/4
/100
Useful schematics and equations:
The Goldman-Hodgkin-Katz (GHK)
equation:
E = ( 60mV ) ! log10
Common mode gain and
differential gain:
PK "#K + $% + PNa "# Na + $% + PCl "#Cl & $% i
vo = Ad vd + Ac vcm
PK "#K + $% + PNa "# Na + $% + PCl "#Cl & $% o
vd = va – vb
o
i
o
i
vcm = (va + vb) / 2
1. Circle the letter of the best (one and only one) answer for each. [10 pts; 1 pt
each]
A) Which one of these statements is correct:
a)
b)
c)
d)
e)
Macroshocks need less current than microshocks to be fatal.
DC is not the most susceptible frequency to cause injury.
The let-go current depends on the proximity of the heart.
Atrial fibrillation is the major cause of electrocution death.
The stimulation current threshold is independent of time.
B) Ground Faults:
a)
b)
c)
d)
e)
Occur when the chassis comes in contact with ground.
Are evidence of persistent seismic activity.
Can be alleviated by using grounded plugs.
Are a major concern in wireless devices.
Both a) and d)
C) When measuring the saturation of oxygen in hemoglobin with optical
absorbance transducers:
a)
b)
c)
d)
e)
The isosbestic point will have maximum relative absorptivity.
The received signal is not affected by ambient light.
Absorptivity is independent of the path of the light.
Absorbance is independent of substance concentration.
May interfere with ECG instrumentation.
D) To resolve the spectrum of blood pressure wave measurements up to the
tenth harmonic for a heart rate of 120 bpm, the sampling frequency must be at
least:
a)
b)
c)
d)
e)
10 Hz
20 Hz
40 Hz
120 Hz
240 Hz
E) Air bubbles in a direct intravenous catheter pressure transducer:
a) Increase the capacitance.
b) Increase the inertance.
c) Increase the resistance.
d) Increase the bandwidth.
e) Both a) and d)
F) Which of the following biopotentials has the highest frequency range?
a) EOG
b) EEG
c) ECG
d) EMG
e) ECoG
G) What does the Severinghaus electrode measure?
a) SO2
b) PCO2
c) PO2
d) pH
e) None of the above
H) What is the advantage of comparator hysteresis?
a) Improved power efficiency
b) Improved accuracy
c) Better noise immunity
d) Higher speed
e) Larger gain
I) Which degrades the CMRR of a bioinstrumentation amplifier?
a) Lower common mode gain
b) Higher input impedance
c) Higher output impedance
d) Narrower bandwidth
e) Larger input impedance mismatch
J) Which of the following initiates action potentials in neurons?
a) Influx of Na+
b) Outflux of Na+
c) Influx of K+
d) Outflux of K+
e) Both b) and c)
2. Short answer, write your answer only in the space provided. [16 pts; 2 pts
each]
(a) What are the impedances of a capacitor C and an inductor L in steady state
at frequency f ?
C:
L:
What do they become at DC?
C:
L:
(b) Given a step input, sketch and label the transient response of an
underdamped, a critically damped, and an overdamped second order low pass
filter at a particular natural frequency. Indicate which one settles the fastest.
Underdamped:
Critically damped:
Overdamped:
(c) The following diagram shows a simple transformer consisting of two coils
with number of windings nin = 100 at the input and nout = 10 at the output. For
an AC input voltage of magnitude Vin = 120V, calculate the magnitude Vout of
the output voltage. What would the output voltage be for a 120V DC voltage
input?
Vin
Vout
AC:
DC:
(d) A strain gauge is stretched by 1% and its resistance increases from 50 kΩ to
52 kΩ. Calculate the gauge factor for this strain gauge.
(e) Use digital logic to determine output bit values for the given input bit values
on the chart for the circuit shown below.
B1
B3
B2
B0
Input Bits
B0
B1
0
0
1
0
0
1
1
1
Output Bits
B2
B3
(f) A membrane separates a container into two compartments. The “inside”
compartment contains a solution of 100 mmol NaCl and 10 mmol KCl in 10
mL of water. The “outside” compartment contains a solution of 1 mmol of
NaCl and 10 mmol of KCl in 1 L of water. The membrane has equal
permeability to all ions. Calculate the membrane potential.
The Goldman-Hodgkin-Katz (GHK) equation:
E = ( 60mV ) ! log10
PK "#K + $% + PNa "# Na + $% + PCl "#Cl & $% i
o
o
PK "#K + $% + PNa "# Na + $% + PCl "#Cl & $% o
i
i
(g) What is the difference between a polarizable and non-polarizable electrode?
(h) State one advantage of grounding the chassis of an instrument.
3. [10 pts]. Consider the following circuit generating an output current Iout.
You may assume that the op-amp is not saturated.
R
R
Vin
R
R
Iout
ZL
(a)
[6 pts] Find the output current Iout as a function of input voltage Vin.
Answer: Iout = ____________________
(b)
[4 pts] For Vin = 1V and R = 10 kΩ, sketch Iout as a function of ZL
from 0 to 1 MΩ. Label the axes and indicate units on the graph.
4. [10 pts] A syringe made of a slightly compliant material like plastic and
attached to a thin metal needle can be modeled by the following electrical
analogue. The arrows indicate the direction of fluid “current” flow.
Iin
=
Rsyr
Iout
Csyr
a) [1 pt] How does the resistance Rsyr depend on the syringe length L and
syringe diameter D?
b) [3 pts] Find the input impedance Zin(jω) of the system. (Hint: remember the
impedance characteristics of an ideal current source and load.)
Answer: Zin(jω) = ____________________
c) [3 pts] Find the output impedance Zout(jω) of the system.
Answer: Zout(jω) = ____________________
d) [3 pts] Find the transfer function H(jω) = Iout /Iin.
Answer: H(jω) = ____________________
5. [10 pts] Sketch the voltage waveforms V1, V2, and V3 over time for the
heartbeat detector circuit shown below, for V0 given by the input pulse
oxymetry waveform shown. Indicate the time and voltage scale on the
waveforms. The equation for the 555 timer circuit is T = 1.1RC, where R =
90.9 kΩ and C = 1 µF.
+5V
+5V
V0
V1
OP27
LM311
-5V
1kΩ
999kΩ
-5V
10kΩ
R
+5V
V2
7
6
2
C
4
8
TLC
555
1
3
5
10nF
90kΩ
-5V
V3
V0 [V]
1m
0.5m
0
-0.5m
1
2
t [s]
-1m
V1 [V]
0
t [s]
V2 [V]
5
0
t [s]
-5
V3 [V]
5
0
t [s]
-5
6. [10 pts] Two identical immunologically sensitive field-effect transistors
(IMFETs) are connected in a Wheatstone bridge to measure binding affinity of
an antigen in a sample solution relative to a reference solution. The
conductance of each IMFET is given by gds = (W/L)µQox, where Qox = 2qS
and S is the antigen surface binding density.
R
Vo
1V
R
S sample
S ref
a) [5 pts] Find the output voltage Vo in terms of the surface binding densities
Ssample and Sref.
Answer: Vo = ____________________________
b) [5 pts] Sketch Vo as a function of Ssample/Sref. On the graph indicate values
at Ssample/Sref = 0 and 1, and where the sensitivity is maximum.
Vo
[ V]
1
0
-­‐ 1
1
2
3
4
5 S
sample/ S ref
7. [10pts] A Clark electrode blood PO2 reader is shown below, with an
Ag/AgCl electrode and a Pt electrode immersed in the blood sample at room
temperature. For the Ag/AgCl electrode, the half-cell potential is Ehc1 = 0.223
V, and the impedance parameters are Rd1 = 320 kΩ, Cd1 = 1 pF, and Rs1 = 0.1
kΩ. For the Pt electrode, the half-cell potential is Ehc2 = 1.2 V, and the
impedance parameters are Rd2 = 180 kΩ, Cd2 = 0 pF, and Rs2 = 0.1 kΩ.
VC
VA
E ach electrode:
Rd
Rs
Pt
Ag/AgC l
EL.
E hc
S OL .
Cd
a) [1 pts] Find the open-circuit voltage between the electrodes VA – VC at rest.
Answer: Voc = ____________________________
b) [4 pts] Find the impedance between the electrode VC and VA.
Answer: Z(jω) = ____________________________
c) [3 pts] Now we apply a voltage VA – VC = 0.7 V between the electrodes, and
measure the current I. Find the value of I when the rate of oxygen consumption
is 10-9 mol/s. The equation for the Clark electrode is:
O2 + 2H2O + 4KCl + 4e- à 4KOH + 4ClThe Faraday constant is F = 96,500 C/mol.
Answer: I = ____________________________
d) [2 pts] What happens if VA – VC = -1.2 V? Explain briefly.
8. [10 pts] An ECG measurement circuit is wired to RA, LA, and LL electrodes
on the body as shown below. The node voltages Va through Vf are connected
through switches to a differential amplifier with inputs Vin+ and Vin- in order to
measure each ECG lead in the frontal plane as the voltage Vin+ - Vin-.
R
Va
R
Vc
Vb
R
R
Vd
Vf
R
R
Ve
a) [6 pts] Complete the following chart. For each of the leads I through aVR,
indicate which of the voltages Va through Vf should be connected to the
amplifier inputs Vin+ and Vin-. An example is shown.
Lead
example
I
II
III
aVF
aVL
aVR
+
Vin
Va
Vin
Vb
-
b) [4 pts] Draw the 2-pole, 6-throw (2P6T) switch diagram connecting the
voltages Va through Vf to the inputs Vin+ and Vin- of the amplifier. The throw
positions should be in the order I, II, III, aVF, aVL, aVR.
9. [10 pts] Consider the differential bioamplifier shown below.
VA
+
VIN
10kΩ
101kΩ
101kΩ
1kΩ
+
VOUT
-
-
99kΩ
VB
10kΩ
99kΩ
a) [4 pts] Find the differential gain of the bioamplifier Ad = VOUT / VIN for
a differential input VIN and output VOUT as shown. Here you may
assume that the common mode potential at the input is zero.
b) [4 pts] Find the common-mode gain Ac = VOUT / VCM of the
bioamplifier. Here you may assume that the differential input is zero.
c) [2 pts] Calculate the common-mode rejection ratio (CMRR) of the
bioamplifier in units dB.
10. [4 pts]
Wireless Non-contact ECG and EEG
a) [1 pt] Does non-contact capacitive sensing work better at lower or higher
frequencies? Why?
b) [1 pt] What are some of the effects of cotton clothing on the noise
performance of through-shirt non-contact ECG?
Wireless and Global Health
a) [1 pt] What is cardiotocography and what does it measure?
b) [1 pt] What does Dr. Saldivar mean by the “Double Burden of Disease”?