Biomedical. Measurement and Design ELEC4623. Lectures 9 and 10 Practical biopotential amplifier design and multilead ECG systems

Transcription

1 Biomedical Instrumentation, Measurement and Design ELEC4623 Lectures 9 and 10 Practical biopotential amplifier design and multilead ECG systems

2 Feedback and stability A negative feedback system with closed loop gain G 1 G 2 > 1 and no phase shift in the loop will always be stable since we are just subtracting in-phase components from the input and amplifying. Q: What if we change the feedback to positive? A: Now we are taking a signal from the output, ADDING it to the input and amplifying it UNSTABLE!!

3 Feedback and stability Q: What if we have NEGATIVE feedback high closed loop gain Q: What if we have NEGATIVE feedback, high closed loop gain G 1 G 2, but a phase shift of 180 o in the amplifier? A: The negative feedback becomes POSITIVE feedback and we get INSTABILITY! Most modern opamps are stable when used as designed but if we are creating our own feedback loops we must be careful. Methods of preventing negative feedback instability: Reduce phase shift in the loop Reduce the loop gain at the frequency where the phase is 180 o

4 Op-amps +V BB The basic building block of amplifiers used to measure biopotentials is the operational amplifier (op-amp or opamp) A simplified circuit of a BJT (bipolar junction transistor) op-amp front end is shown right, together with the opamp s circuit symbol Ideal opamp A= (infinite gain) v+ = v- (no offset voltage) Rd = (infinite input impedance) Ro = 0 (zero output impedance) BW = (infinite bandwidth) Ф = 0 (zero phase shift) No opamp is ideal we must design the circuit to account for the characteristics of the opamp used V OUT R L I B1 v 1 v 2 Q 1 Q 2 V R C s1 R L I B2 V s2 -V (a) BB - + (b) V OUT

5 GAIN Non-ideal opamps p Typically ~ 100,000 at dc. Several stages, each of which h has stray or junction capacitance the gain falls off as the frequency increases. An inbuilt compensating capacitor causes the fall-off to start at a lower frequency, but to be of lesser slope, so that the phase shift at unity gain frequency is less than 180, making the amplifier more stable. As an amplifier, the op-amp p is never used in open-loop p mode. It always has negative feedback around it. Consequently, the poor frequency response of the op-amp itself is greatly improved, but at the expense of amplifier gain. As the gain is reduced, the frequency response is increased, the gain-bandwidth product remaining essentially constant. Op-amps such as the 741 have a unity-gain bandwidth of about 1 MHz, but for high frequency applications op-amps with bandwidths of >100 MHz are available.

6 Non-ideal opamps SLEW RATE The frequency response referred to above, is for small signal inputs. For large signals, there is an additional limitation. When rapid changes in outputs are demanded, the compensation capacitor must be charged up from an internal source that has limited current capacity. The rate of change in voltage across the capacitor is then limited, and as a consequence the rate of change of the output voltage is limited to a maximum slew rate often of the order of 1 volt per microsecond. Slew rate is not normally an issue for biological signals which have fairly long rise times, even when using micropower opamps (low slew rate)

7 Non-ideal opamps p INPUT RESISTANCE For the typical BJT op-amp, this is about 0.5 M ohms. However, the amplifier itself, because of feedback, will exhibit a much higher input resistance. For a voltage follower, it is A times as great. For an inverting amplifier, it is equal to the external input resistor value. In some applications, where extremely high input resistances are required, FET-input op-amps are useful. OUTPUT RESISTANCE Typically, this is about 100 ohms, but because of feedback in the overall amplifier, its value is reduced by a factor A and so becomes negligible for most applications.

8 Non-ideal opamps OFFSET VOLTAGE The two input voltages v+ and v- may differ by a few mv. When amplifying small signals the offset voltage may need to be nulled out. Alternatively you can use multiple gain stages with AC coupling to remove the offset. Or find a precision op-amp BIAS CURRENT Base current must flow all the time to keep the input transistors turned on Although small (e.g. 0.2μA for BJT) they cause some error because they flow through the feedback network. Also a small error because of the slight difference between the bias currents of the two input transistors (called the input offset current in the specifications).

9 NOISE Non-ideal opamps Low frequency (drift) noise is generated when temperature variations cause the offset voltage to vary At more cost, op-amps with tighter drift specification (e.g. 0.1μV/ C) are available than ordinary low-cost types Temperature drift is usually not a big issue for biomedical instrumentation which is usually used in office conditions (constant temp) Random noise is also generated Flicker noise has a 1/f power spectrum and can be high at low frequencies. It is usually the dominant electronic noise below 200 Hz Johnson or thermal noise is uniform over a wide frequency range Some op-amps exhibit bursts of noise called popcorn noise

10 Opamp flavours Bipolar junction transistor (BJT) traditionally the most common low-noise amplifiers very low input-voltage-noise density (~2nVHz -1/2 ) relatively high input-current-noise density (~1.2pAHz -1/2 ) Recall: equivalent circuit model for noisy amplifier (lecture 7&8) high bias currents (80nA) BJT amplifier's voltage noise usually dominates when its equivalent source resistance is less than 200 Ω Best suited for low input impedance applications

11 Opamp flavours JFET input opamps p Ultra-low input-current-noise density (0.5fAHz -1/2 ) Higher input-voltage-noise density (greater than 10nVHz -1/2 ) JFET designs allow single-supply supply operation Low input bias current of 1pA makes JFET amps useful for applications with high impedance sources (e.g. piezo) Not first choice for low source impedance applications, due to their larger voltage noise

12 Opamp flavours CMOS-Input Amplifiers Newer low-noise amplifier designs with a CMOS input stage offer voltage-noise performance that is comparable to bipolar designs (4.5nVHz -1/2 ),. CMOS-input amplifiers also meet or exceed the current-noise performance of the best JFET-input designs (0.5fAHz -1/2 ). Single supply operation Rail-to-rail performance Very low bias current (~1 pa): good for high input impedance The newest technology and probably best overall choice.

13 Opamp noise model R 1 v v v n i n v d - Av d - + v o R 2 v 2 i n + Amplifier gain makes the input stage is most susceptible to noise The transistor junctions produce noise-voltage (V n ) sources and noisecurrent sources (I n), modeled as shown. The noise-voltage source V n (offset voltage) is in series with the input and cannot be reduced. The noise added by the noise-current sources I n (bias currents) in can be minimised by using small external resistances (R 1 and R 2 ).

14 Basic amplifier circuits Inverting amplifier Input impedance = R 1 R1 R 2 o ( / ) V = R R V 2 1 a Non-inverting amplifier Input impedance of open loop opamp is increased v a - R 1 + v b + V = R + v o R R 2 o R v o V b

15 Basic amplifier circuits Unity gain buffer (voltage follower) Purpose is for impedance transformation All open loop gain is used to increase input impedance v b + - v o Differential amplifier R 1 + R 2 R4 R2 Vo = Vb Va R R + R R + R If R 2 R 4 = R1 + R 2 R 3 + R 4 Then 2 R R Vo = R ( Vb Va) v R a 1 Differential gain A d is R 2 /R 1 while common mode gain A - c is zero, so CMRR (A d /A c ) is R 3 infinite theoretically v b + In reality: Resistor tolerances limit CMRR to about - 20log(%tolerance) eg. 0.1% resistors CMRR~60dB R 1 R 2 R 4 v o

16 Differential Amplifier with Buffered Inputs - v 1 + R 1 R 2 v 3 - v 4 R 3 + v o - v 5 R 4 v 2 + With buffered inputs: eliminates the influences of electrode impedances on input impedance R1 and R3 have no influence on input impedance Still requires matched resistors for good CMRR

17 Instrumentation amplifier A D 2R1 R = (1 + ) R R R 3 gain 2 Advantages varying R gain does not change the common mode signal hence CMRR increases in direct proportion to differential gain (a useful property); If V + = V -, 0 V across R gain, and A CM = 1 (in first stage, see later). Large CM voltages can be handled d if the two input amps are similar, their common-mode errors tend to be cancelled by the 3rd amp due to symmetry. Disadvantages High parts count but can be bought as a single IC

18 Typical instrumentation amp V 1 V = V + D CM 2 + V ' 1 - R 4 v R 2 R 2 R 1 R 3 R 1 R V o = V V D 2 V CM V 2 ' R 4 Tune to optimise CMRR

19 Instrumentation amplifier f V cm V =, VD = V1 V2 then 2 V VD V V1 = Vcm +, V2 = Vcm 2 2 D and V = V cm Equivalent circuit of front end stage V 1 ' R 1 R 2 R 2 R 1 V 2 ' Note: midpoint V must be V CM from symmetry VD V V CM + VCM VCM 2 2 Current flowing I D V = + D R + 1 V 1' Vcm 1 2 R 2 and V D V D 2 Vcm + Vcm VD = = V = D R 2R 2R + 1 V2 ' Vcm R 2

20 Instrumentation amplifier CMRR Since V CM is not amplified, best strategy is to maximise CMRR by maximising gain of first stage R R 2 HOWEVER, AAMI says we need to cope with offsets of ± 300mV on any lead. So this limits the gain, depending on our power supplies and capacities of amp, e.g. ± 5V rails we should not use a gain much higher than 10 (may cause saturation) Note the following stage is just a common differential amplifier (with gain of R 4 /R 3 ) Output V O V + R 1 R VO / V CMRR = R R V O / V 2 3 = 4 D D 1 CM We can either use the potentiometer to get high CMRR or use precision resistors. A gain of 10 would add 20dB to CMRR attainable just from a differential amplifier.

21 Patient Protection Dangerous currents are not allowed to flow into the patient, by putting current limiting resistors in the patient leads The high impedance input (>10MΩ) guarantees that in normal operation this doesn t lead to a reduced input In the case of the amplifier breaking down (single fault condition) and shorting the input to the power supply, the current is limited by the resistors 10KΩ is usually sufficient As well as protecting the patient, it is often desirable to protect the equipment from defibrillator or other high voltage inputs. This is normally done using diodes or breakdown devices (e.g. neon tubes) See next slide The patient current limiting resistors above also protect the device

22 Defibrillation protection The first resistor must be able to withstand very high voltages for short periods of time (~10msec) Example: carbon composition type resistor (NOT film type) The second resistor limits current into the amplifier (which has its own internal protection diodes) The gas discharge tube in middle can be replaced by zener diodes It clamps the midpoint voltage to a few hundred volts The resistors also protect the patient against fault conditions and the amp against RF interference

23 Isolation amplifiers An isolation amplifier is an instrumentation amp that has its signal input circuit isolated from the power input and signal output t circuits (2-port isolator). A 3-port isolator also has isolation between power input and signal output. They provide extra CMRR and patient protection. Transfer of signal and power across the isolation barriers is via optical coupling or magnetic coupling. As they tend to be expensive, isolation in commercial devices is often put in digitally later in the circuit, especially for multi- channel devices. Input Input Power Supply 2-port Power Supply 3-port Output Output

24 Movement artefact This can induce quite large voltages on the patient, as common mode voltages, and transiently as differential voltages. It is therefore desirable not to have DC amps unless the biopotential requires it (e.g. EOG). However, putting coupling capacitors in the differential pathway is likely to degrade the CMRR because (i) of the difficulty in matching C s Cs (leads to potential divider effect) (ii) the need to provide input bias current for the op-amps i.e. dc path to common on both + and inputs (not a problem for high input impedances >10MΩ) Usually, differential input stages are DC coupled, while coupling capacitors only used when single-ended. If the gain is high before this, the capacitor might block (i.e. only discharge slowly) if an amplifier saturates, thus ceasing output for some time. The early differential stages are thus invariably designed with low gain until the signal is single-ended (after the instrumentation amp)

25 Sample design

26 Driven right leg details R a R a i d R RL

27 Right leg driven (RLD) circuit 2v cm R a v o R f Example: with reference to the figure determine the common mode voltage V cm on the patient when a displacement dspace e tcurrent tof i d = 0.2 μa flows to the patient from the power lines. Choose resistance values so that the common mode voltage is minimal and there is only a high resistance path to ground when the drive op-amps saturates. KCL at opamp -ve input 2 V / R + V / R = 0 cm a 0 f V = 2 R V / R, but 0 cm f cm a V = R i + V RL d R RLi d Vcm = (1 + 2 R / R ) RRLid V cm = (1 + G) f 0, thus where G = 2 R / R = gain of RLD cct f The effective resistance between the right leg and ground is thus R e f f = R RL/(1 + G ) a a

28 Designing RLD When the differential amplifier saturates t the saturation ti voltage appears at the input to the drive circuit and could result in a high voltage at the right leg electrode. Note due to high gain of RLD cct that it will saturate before the differential amplifier does When the RLD amp is saturated the normal laws of feedback no longer apply. Under such conditions V CM increases and there is increased current flow to the subject. R o is thus usually included to limit any current to safe levels (from 10KΩ to 5MΩ depending on other isolation). To minimise common mode voltage V cm requires the ratio R f /R a to be large. R f may be as large as 5MΩ and typically R a is around 25 KΩ giving i a loop gain of 400. The effective resistance between right leg and ground R eff is then (if R RL = 20KΩ): R = R /(1 + G) V = 50Ω 0.2 μ A e ff RL CM = 20000/ 401 = 10 μ V = 50Ω

29 RLD (continued) If the loop gain G is high and sufficient phase shift occurs, instability and oscillations can result. Note other phase shifts in circuit affect this, such as input lead shield capacitance. This can be partly compensated for by replacing R f by a capacitor (next slide), and ensuring that the amp is well isolated and has a low leakage capacitance to ground. So far we have only considered 50 Hz of mains CM voltage. But fluorescent lights can cause a CM voltage as a short burst of 1kHz of radiation at 10ms intervals which depending on the patients position and other factors, could be as large as 10-50% of the 50Hz CM voltage. This high frequency interference can be transformed into 100 Hz interference by non-linearities in the electronics or recorder. The driven right leg circuit, providing it has sufficient gain at 1 khz will also reduce this noise signal to an acceptable level.

30 Overall front end for ECG amp To avoid instability, loop - gain of driven shield Input a + circuit is made < 1 (see Lecture 7&8) 10kΩ 100Ω - + Loop gain of the driven RL circuit is 300 at 50 Hz, giving a 50 db improvement in CMRR The gain is lower at higher frequencies to avoid oscillations Input b Driven Right Leg 1nF 1MΩ kΩ

31 Electrocardiogram (ECG) A beating heart generates an electrical signal This appears throughout the body and on the surface Can be used as a diagnostic tool to assess cardiac function or simply to monitor that the heart is beating adequately. For diagnostic purposes, twelve ECG traces are usually recorded. d These are: Three limb leads leads I, II and III. Three augmented limb leads avr, avl, and avf. Six chest leads V1 to V6. Why so many? When a cardiac ischemia (lack of oxygen) occurs it can scar the tissue and perhaps p lead to an infarction (dead tissue) These conditions can change the way the ECG appears but it may only show up in one or two leads, depending where it occurs.

32 Einthoven s triangle The voltages of leads I, II and III can be considered to be projections of the equivalent cardiac dipole on an approximately equilateral triangle in the frontal plane Einthoven s triangle The bipolar limb leads add vectorially: II = I + III I = V LA V RA, II = V LL V RA, III = V LL V LA

33 ECG Limb leads Note additive effects

34 Dipoles Fixed origin dipoles in 3 dimensions require 3 variables to describe (e.g. magnitudes in x, y and z directions) We can consider the ECG to arise from the cardiac vector, which is a 3 dimensional vector changing in amplitude and direction during the cardiac ac cycle. The bipolar limb leads are measuring the projections of this dipole (during time) in the 3 lead directions 0 o, 60 o and 120 o (see previous slide) in the frontal plane

35 Generation of the ECG signal in the Einthoven limb leads At the start of the cardiac cycle the dipole begins at the sinoatrial (SA) node and is small in magnitude Voltages measured between two body surface electrodes (lead voltage) depend on: lead location heart location heart vector (position, direction and magnitude) torso volume inhomogeneities

36 Generation of the ECG signal in the Einthoven limb leads

37 Generation of the ECG signal in the Einthoven limb leads

38 Lead vector The Heart Vector may be described by H = h a + h a + h a % % % % x x y y z z h x, h y and h z are projections in directions x, y and z. The lead voltage, by superposition is then Vl = h l + h l + h l x x y y Z z = H l ~ ~ l dot product of H and vector, i.e. projection of H onto the ~ direction of l multiplied by its magnitude. ~

39 Lead vector Can be shown that: V I = H cos α V II = H cos (α-60 ) V III =Hcos(α (α-120 ) Where H is magnitude of Heart Vector, α is angle of Heart vector RA V II α V I LL H ~ V III LA Note that V I + V III = V II (show!)

40 Wilson central terminal (WCT) Frank Norman Wilson ( ) investigated how ECG unipolar potentials could be defined Wilson central terminal (WCT) was formed by connecting equal-valued resistors from each limb lead to a common node Voltage at WCT is the average of the voltages at the 3 limb electrodes provides reference potential for unipolar measurement Modern equipment does not determine this by an electrical circuit but mathematically.

41 Augmented limb leads The limb electrode voltages can form so-called unipolar rather than bipolar leads. For example, WCT could be used as a reference for each. In 1942 Goldberger noted that if the average of the other two limb leads were used instead of WCT as the reference, the signal became 50% larger Hence the term augmented avr, avl and avf But they contain the same information as the bipolar leads and can be considered redundant

42 Augmented limb leads As exercise, show that: avr = -V I V III /2 avl = V I V II /2 avf = V II V I /2 Note difference in directions of avr, avl and avf with I, II and III in the frontal plane

43 Precordial (chest) Leads Pre-cordial (in front of, the heart) In addition to the six limb leads (I, II, III, avr, avl, avf), a 12-lead ECG includes six chest leads. The chest leads look at the heart s electrical activity in a slightly offhorizontal plane around the front of the chest (traverse plane). This detects problems that might not be obvious from the standard limb leads, which measure electricity in a vertical (frontal) plane. The chest leads are often called V-leads.

44 European vs. American 12 lead ECG AHA North America IEC Europe Inscription Colour Location Inscription Colour RA White Right arm R Red LA Black Left arm L Yellow RL Green Right leg N Black LL Red Left leg F Green V1-6 Brown Chest C1-6 White

45 Information content of 12 lead ECG Much redundant information 12 leads (traces) ECG require 10 wires but only 8 A/D channels (why?) We really only need 3 leads (x, y and z) to measure in 3 planes

46 Vectorcardiography (VCG) The basic principle of vectorcardiography is illustrated based on ideal uniform lead fields which are mutually orthogonal being set up by parallel electrodes on opposite sides of the torso (bipolar configuration) Projection of Heart Vector into 3 planes frontal (coronal), traverse and sagittal Track change in 3D vector coordinates over time course of cardiac cycle

47 Frank lead system The lead matrix of the Frank VCG-system. The electrodes are marked I, E, C, A, M, F, and H, and their anatomical positions are shown. The resistor matrix results in the establishment of normalized x-, y-, and z- component lead vectors

48 References Cardiovascular Physiology Concepts