BIOMEDICAL INSTRUMENTATION PROBLEM SHEET 1

Transcription

1 BIOMEDICAL INSTRUMENTATION PROBLEM SHEET 1 Dr. Gari Clifford Hilary Term (Exemplar Finals Question) a) List the five vital signs which are most commonly recorded from patient monitors in high-risk hospital patients. For one of these vital signs, give an example of abnormal patient condition which can be detected by a change in that vital sign. (3 marks) b) The circuit in the Figure is an instrumentation amplifier used to record a single channel of ECG using three electrodes A, B and C. The input voltages U a, U b, V a and V b, the output voltage V o and the resistor ratios x and y are as shown on the Figure. (Nominal electrode impedance at A and B = R a = R b = 3 kω; amplifier input impedance to ground R in (for both positive and negative terminals) = 10 MΩ.) i. For a lead II recording, where would the electrodes A, B and C be placed on the human body? (2 marks) ii. Show that the differential gain of the amplifier, V o /(V a V b ), is given by y(1+ 2x) (6 marks) BIOMEDICAL INSTRUMENTATION PROBLEM SHEET 1, DR. GARI CLIFFORD, HT 2012 PAGE 1

2 iii. Show that, when the electrode impedances R a and R b become unequal such that R b > R a, the common-mode voltage U is amplified by the following factor: (2 marks) iv. If R a remains at its nominal value of 3 kω but R b rises to a value of 6 kω, what is the signal-to-noise ratio at the output of the amplifier, when the ECG input voltage measured between A and B is 0.5 mv and the common-mode input voltage is 50 mv? Assume that all the noise is caused by the common-mode input voltage. (3 marks) 2. Figure 2 shows the circuit of an instrumentation amplifier used for recording the ECG. The right arm of the patient is connected to point A, the left arm to point B and the right leg to the ground at G. The common-mode voltage arising out of the capacitive coupling of the patient to ground is 10mV peak-to-peak, and a common-mode rejection ratio of 78dB is measured at 50Hz. (a) Calculate the differential gain of the input stage (up to the diodes), taking into account the 100k protection resistors. (b) What is the mid-band frequency for this circuit? (The mid-band frequency is the halfway point, on a logarithmic scale, between the high-pass and low-pass cut-offs). Estimate the differential gain for the overall circuit at this frequency. (c) Obtain an expression for the transfer function for v/(v A - v B ) and hence calculate the differential gain for the overall circuit at 50Hz. (d) Sketch the frequency response of the circuit. (e) If it is specified that any unbalance in electrode contact impedances should not lead to more than 0.5mV peak-to-peak error in v, what is the maximum unbalance that the circuit can tolerate? Figure 2 BIOMEDICAL INSTRUMENTATION PROBLEM SHEET 1, DR. GARI CLIFFORD, HT 2012 PAGE 2

3 3. The two op-amp instrumentation amplifier of Figure 3a is to be used as an ECG amplifier. Assuming that the op-amps are ideal, (a) Show that the common-mode gain is zero when R1 R2 R4 R3 (b) Find the value of the differential gain under this condition. (c) Why will it not be possible in practice to have a common-mode gain of zero? 4. A typical trace obtained with the ECG amplifier is shown in Figure 3b. From this trace, calculate the following: (a) heart rate (b) P-R interval (c) S-T level (d) Ratio of QRS amplitude to T-wave amplitude. Which of the above is clinically significant and why? Figure 3 (a) (b) 5. Figure 4 shows part of a driven right-leg circuit for recording the ECG between the left arm (LA) and the right arm (RA). The displacement current i d (from power lines to ground) induces a common-mode voltage v cm on the surface of the body. The commonmode voltage v cm is sampled by two resistors each of value R a and used to generate a current at the output of right-hand most op-amp. This current is then driven into the right leg to cancel the displacement current i d. (a) Show that the input stage (first two op-amps) has unity common-mode gain. (b) Show that the effective resistance between the patient and the ground, R eff, is given by R eff Ro R 1 G where R e is the electrode contact impedance for the right leg and e G 2R f Ra. BIOMEDICAL INSTRUMENTATION PROBLEM SHEET 1, DR. GARI CLIFFORD, HT 2012 PAGE 3

4 (c) Explain why this circuit enhances patient safety. (d) It is sometimes necessary to defibrillate a patient to restore their heart to a normal rhythm. In this process a capacitor, which has been charged to approximately 5 kv is discharged across the patient's in a short space of time. Would it be appropriate to keep the circuit in Figure 4 attached to the patient at such a time? If not, how might the circuit be modified? Figure 4 6. Figure 5 shows the block diagram of a circuit for 4-electrode electrical impedance plethysmography. (a) Explain how the breathing-related pulsatile changes Z are extracted at the output of the demodulator. Why is it not possible to use a high-pass filter instead? (b) Assume that Z + Z = Z 2 = Z 3 = 100 and Z v = -j2000 (capacitive). How large is the error caused by a 10 change in Z 2? Is an error of this magnitude important? (c) Design the filter circuit which could be used to allow the same two electrodes (plus one ground electrode) to monitor ventilation by electrical impedance plethysmography as well as record the patient s ECG, with no cross-interference. Assume that the resistive component of the chest impedance at 100 khz (the frequency at which the circuit operates) is about 100 BIOMEDICAL INSTRUMENTATION PROBLEM SHEET 1, DR. GARI CLIFFORD, HT 2012 PAGE 4

5 Figure 5: Block diagram of four-electrode electrical impedance plethysmograph BIOMEDICAL INSTRUMENTATION PROBLEM SHEET 1, DR. GARI CLIFFORD, HT 2012 PAGE 5

6 Answers 1. (b) (iv) 30.5 db 2. (a) db (b) 1.58 Hz; db (c) 42.6 db e) 2.5 k R 3. (b) 1 1 R 2 4. (a) 96 beats/min (b) s (c) 0 mv (d) (b) 0.05% (c) Passive high-pass filter with C = μf BIOMEDICAL INSTRUMENTATION PROBLEM SHEET 1, DR. GARI CLIFFORD, HT 2012 PAGE 6