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. Useful schematics and equations: The Goldman-Hodgkin-Katz (GHK) equation: P K # K + $ % + P E = ( 60mV )! log o Na # Na + $ % + P o Cl # Cl & $ 10 P K # K + $ % + P i Na # Na + $ % + P i Cl # Cl & $ % i % o Common mode gain and differential gain: v o = A d v d + A c v cm v d = v a v b v cm = (v a + v b ) / 2 1 /10 2 /16 3 /10 4 /10 5 /10 6 /10 7 /10 8 /10 9 /10 10 /4 Total /100
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) Macroshocks need less current than microshocks to be fatal. b) DC is not the most susceptible frequency to cause injury. c) The let-go current depends on the proximity of the heart. d) Atrial fibrillation is the major cause of electrocution death. e) The stimulation current threshold is independent of time. B) Ground Faults: a) Occur when the chassis comes in contact with ground. b) Are evidence of persistent seismic activity. c) Can be alleviated by using grounded plugs. d) Are a major concern in wireless devices. e) Both a) and d) C) When measuring the saturation of oxygen in hemoglobin with optical absorbance transducers: a) The isosbestic point will have maximum relative absorptivity. b) The received signal is not affected by ambient light. c) Absorptivity is independent of the path of the light. d) Absorbance is independent of substance concentration. e) 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) 10 Hz b) 20 Hz c) 40 Hz d) 120 Hz e) 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) S O2 b) P CO2 c) P O2 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 CM 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 n in = 100 at the input and n out = 10 at the output. For an AC input voltage of magnitude V in = 120V, calculate the magnitude V out of the output voltage. What would the output voltage be for a 120V DC voltage input? V in V out 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. B 1 B 3 B 0 B 2 Input Bits Output Bits B 0 B 1 B 2 B 3 0 0 1 0 0 1 1 1 (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: P K # K + $ % + P E = ( 60mV )! log o Na # Na + $ % + P o Cl # Cl & $ 10 P K # K + $ % + P i Na # Na + $ % + P i Cl # Cl & $ % i % o
(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 I out. You may assume that the op-amp is not saturated. V in I out Z L (a) [6 pts] Find the output current I out as a function of input voltage V in. Answer: I out =
(b) [4 pts] For V in = 1V and = 10 kω, sketch I out as a function of Z L 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. I in syr I out = C syr a) [1 pt] How does the resistance syr depend on the syringe length L and syringe diameter D? b) [3 pts] Find the input impedance Z in (jω) of the system. (Hint: remember the impedance characteristics of an ideal current source and load.) Answer: Z in (jω) =
c) [3 pts] Find the output impedance Z out (jω) of the system. Answer: Z out (jω) = d) [3 pts] Find the transfer function H(jω) = I out /I in. 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 = 1.1C, where = 90.9 kω and C = 1 µf. +5V V0 1kΩ +5V OP27-5V 999kΩ V1 10kΩ +5V LM311-5V 90kΩ V2 C 7 6 2 4 8 TLC 555-5V 1 5 3 10nF V3
V0 [V] 1m 0.5m 0-0.5m -1m 1 2 t [s] 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 g ds = (W/L)µQ ox, where Q ox = 2qS and S is the antigen surface binding density. S sample 1V V o S ref a) [5 pts] Find the output voltage V o in terms of the surface binding densities S sample and S ref. Answer: V o =
b) [5 pts] Sketch V o as a function of S sample /S ref. On the graph indicate values at S sample /S ref = 0 and 1, and where the sensitivity is maximum. V o [ V] 1 0 1 2 3 4 5 S sample / S ref - 1
7. [10pts] A Clark electrode blood P O2 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 E hc1 = 0.223 V, and the impedance parameters are d1 = 320 k, C d1 = 1 pf, and s1 = 0.1 k. For the Pt electrode, the half-cell potential is E hc2 = 1.2 V, and the impedance parameters are d2 = 180 k, C d2 = 0 pf, and s2 = 0.1 k. V C V A E ach electrode: d s Pt Ag/AgC l E L. E hc S OL. C d a) [1 pts] Find the open-circuit voltage between the electrodes V A V C at rest. Answer: V oc = b) [4 pts] Find the impedance between the electrode V C and V A. Answer: Z(jω) =
c) [3 pts] Now we apply a voltage V A V C = 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: O 2 + 2H 2 O + 4KCl + 4e - à 4KOH + 4Cl - The Faraday constant is F = 96,500 C/mol. Answer: I = d) [2 pts] What happens if V A V C = -1.2 V? Explain briefly.
8. [10 pts] An ECG measurement circuit is wired to A, LA, and LL electrodes on the body as shown below. The node voltages V a through V f are connected through switches to a differential amplifier with inputs V in + and V in - in order to measure each ECG lead in the frontal plane as the voltage V in + - V in -. V a V b V c V f V d V e a) [6 pts] Complete the following chart. For each of the leads I through av, indicate which of the voltages V a through V f should be connected to the amplifier inputs V in + and V in -. An example is shown. Lead V in + V in - example V a V b I II III avf avl av
b) [4 pts] Draw the 2-pole, 6-throw (2P6T) switch diagram connecting the voltages V a through V f to the inputs V in + and V in - of the amplifier. The throw positions should be in the order I, II, III, avf, avl, av.
9. [10 pts] Consider the differential bioamplifier shown below. + V A 101kΩ 10kΩ 101kΩ V IN 1kΩ + - 99kΩ - V OUT V B 10kΩ 99kΩ a) [4 pts] Find the differential gain of the bioamplifier A d = V OUT / V IN for a differential input V IN and output V OUT as shown. Here you may assume that the common mode potential at the input is zero.
b) [4 pts] Find the common-mode gain A c = V OUT / V CM of the bioamplifier. Here you may assume that the differential input is zero. c) [2 pts] Calculate the common-mode rejection ratio (CM) 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?