Principles of Biomedical Systems & Devices. Lecture 11 Biopotential Amplifiers

Transcription

1 PBS&D Fall 2004 Polkar Prncples of Bomedcal Systems & Devces Lecture 11 Bopotental Amplfers

2 Ths Week n PBS&D PBS&D Fall 2004 Polkar Bopotental Amplfers Op-amps and basc amplfer crcuts Invertng vs. non-nvertng amplfers Three-op-amp dfferental amplfers (nstrumentaton amplfers) Comparators Integrators / Dfferentators Actve flters Lowpass, hghpass, bandpass flters Frequency response of amplfers Other desred propertes of bopotental amplfers

3 Operatonal Amplfers PBS&D Fall 2004 Polkar v = A( v v ) A voltage at υ 1, the nvertng nput, s greatly amplfed and nverted to yeld υ o. A voltage at υ 2, the nonnvertng nput, s greatly amplfed to yeld an nphase output at υ o.

4 Ideal Operatonal Amplfers PBS&D Fall 2004 Polkar υ 1 υ A υ 0 The two nputs are υ 1 and υ 2. A dfferental voltage between them causes current flow through the dfferental resstance R d. The dfferental voltage s multpled by A, the gan of the op amp, to generate the output-voltage source. Any current flowng to the output termnal υ 0 must pass through the output resstance R o.

5 Ideal Op-amps PBS&D Fall 2004 Polkar Assumptons: A = (nfnte gan) υ 0 =0, when υ 1 = υ 2 (no offset voltage) R d = (nput mpedance s nfnte) R 0 = 0 (output mpedance s zero) Bandwdth = (no frequency-response restrctons) Two basc rules 1. When the op-amp s workng n ts lnear range, the two nput termnals are at the same voltage, that s υ 1 = υ 2 (due to nfnte gan) 2. No current flows nto ether nput termnal of the op amp, that s 1 = 2 = 0 (due to assumed nfnte nput mpedance)

6 PBS&D Fall 2004 Polkar Basc op-amp Crcuts Invertng Amplfer saturaton υ o R f 10 V υ R -10 V 10 V Vrtual ground + υ o υ Slope = -R f / R -10 V v v 0 = R R f

7 PBS&D Fall 2004 Polkar Basc op-amp Crcuts Summng Amplfer Vo = - R F ( V 1 / R 1 + V 2 / R 2 + V 3 / R 3 ) = - ( V 1. R F / R 1 + V 2. R F / R 2 + V 3. R F / R 3 )

8 PBS&D Fall 2004 Polkar Basc op-amp Crcuts Non-nvertng Amplfer R R f υ + Buffer υ o υ o υ - + Non-nvertng amplfer υ o Gan =1, What good s a buffer? 10 V Slope = (R f + R )/ R -10 V 10 V υ v R f + 0 = v R R -10 V What f R =0?

9 PBS&D Fall 2004 Polkar Sngle Op-Amp Dfferental Amplfers υ 3 v o = ( v v ) 4 R 3 3 R 4 υ 4 If υ 3 = υ 4 υ 0 =0 Common mode gan, G c =0 If υ3 υ4 υ 0 α R 4 /R 3 Common mode rejecton rato? Why s t mportant? CMRR = G G d c Dfferental mode gan, G d = R 4 /R 3 G c =?, G d =?

10 PBS&D Fall 2004 Polkar Three Op-Amp Dfferental Amplfers What s a potental problem wth the sngle op-amp dfferental amp? R υ 1 R υ R f R f The nput resstance can be too low for certan applcatons One way to ncrease the nput resstance s too add a buffer to each nput. But, whle we are at t, we mght as well get some amplfcaton out of t too, so we can add the nonnvertng amplfer to each nput. Then, not only we get hgh nput mpedance, but we can obtan gan as well. How about ths one? (In terms of CMRR?)

11 PBS&D Fall 2004 Polkar Three Op-Amp Dfferental Amplfers Better soluton: Instrumentaton Amplfer G G c d = 1 = 2R2 + R 1 R 1 Hgh nput mpedance Hgh CMRR Gan controllable

12 Comparators PBS&D Fall 2004 Polkar υ o υ R 1 10 V Wth hysteress (R 3 > 0) R 1 υ o -10 V 10 V υ ref R 3 + R 2-10 V - υ ref υ Wthout hysteress (R 3 = 0) When R 3 = 0, υ o ndcates whether (υ + υ Ref ) s greater or less than 0 V. When R 3 s larger, the comparator has hysteress Would we want to have hysteress n a comparator? Why / why not?

13 Rectfers PBS&D Fall 2004 Polkar R xr (1-x)R Control gan, 1/x D 1 D 2 I-V Characterstc? 10 V υ o υ + R -10 V 10 V D 3 D 4 υ o = υ x υ V Full-wave precson rectfer. For υ > 0, the nonnvertng amplfer at the top s actve, makng υ o > 0. For υ < 0, the nvertng amplfer at the bottom s actve, makng υ o > 0. Crcut gan may be adjusted wth a sngle pot.

14 PBS&D Fall 2004 Polkar Sngle Op-Amp Full Wave rectfer υ R = 2 kω R f = 1 kω v o + D R L = 3 kω

15 A three-mode ntegrator Wth S 1 open and S 2 closed, the dc crcut behaves as an nvertng amplfer. Thus υ o = υ c and υ o can be set to any desred ntal conducton. Wth S 1 closed and S 2 open, the crcut ntegrates. Wth both swtches open, the crcut holds υ o constant, makng possble a lesurely readout. Integrators PBS&D Fall 2004 Polkar v 0 = RC 1 1 t c vdt + v 0 V0( jω) V ( jω) = = Z Z f 1 = jωrc 1/ jωc R 1 = jωτ Crcut gan decreases as frequency ncreases

16 Dfferentators PBS&D Fall 2004 Polkar to prevent oscllaton v 0 = RC dv dt V V jω) ( jω) 0 ( = Z Z f = 1/ = jωrc R jωc = jωτ

17 PBS&D Fall 2004 Polkar Actve Flters Lowpass Flter C f Log scale V 0 (jω) V (jω) R R f 1.0 υ υ o τ Small + τ Large ω Small ω large Log scale ω V V 0 ( jω ) ( jω ) = Z Z f = ( R / jωc ) f (1 jωc f R f ) + R f = (1 + R jωr f f C f ) R ω >> 1/τ ntegrator ω << 1/τ nv. amp What s τ (tme constant)?

18 PBS&D Fall 2004 Polkar Actve Flters Hghpass Flter υ C R R f υ o + V V jω) ( jω) 0 ( = Z Z f = (1 R jωc f ) + R

19 PBS&D Fall 2004 Polkar Actve Flters Bandpass Flter C f υ C R R f υ o +

20 PBS&D Fall 2004 Polkar Characterstc Frequency Responses 100 I HP Bode plot (gan versus frequency) for varous flters. Integrator (I); dfferentator (D); low pass (LP), 1, 2, 3 secton (pole); hgh pass (HP);bandpass (BP). Corner frequences f c for hgh-pass, lowpass, and bandpass flters BP LP D k f c f c Frequency, Hz

21 PBS&D Fall 2004 Polkar Read on your own from your text and references for project

22 PBS&D Fall 2004 Polkar Frequently Observed Problems (FOP) Frequency dstorton It s mportant to know the expected bandwdths of the sgnals beng measured. Is 1~150 Hz flat frequency spectrum adequate for ECG measurements/ How about EMG? How about EEG? Flters must be desgned very carefully to avod frequency dstorton What effects would frequency dstorton have on the sgnal?

23 Bandwdth Requrements PBS&D Fall 2004 Polkar Measurement Range Frequency, Hz Method Blood flow 1 to 300 ml/s 0 to 20 Electromagnetc or ultrasonc Blood pressure 0 to 400 mmhg 0 to 50 Catheter, Cuff or stran gage Cardac output 4 to 25 L/mn 0 to 20 Fck, dye dluton Electrocardography 0.5 to 4 mv 0.05 to 150 Skn electrodes Electroencephalography 5 to 300 µ V 0.5 to 150 Scalp electrodes Electromyography 0.1 to 5 mv 0 to Needle electrodes Electroretnography 0 to 900 µ V 0 to 50 Contact lens electrodes ph 3 to 13 ph unts 0 to 1 ph electrode pco 2 40 to 100 mmhg 0 to 2 pco 2 electrode po 2 30 to 100 mmhg 0 to 2 po 2 electrode Pneumotachography 0 to 600 L/mn 0 to 40 Pneumotachometer Respratory rate 2 to 50 breaths/mn 0.1 to 10 Impedance Temperature 32 to 40 C 0 to 0.1 Thermstor

24 Saturaton / Cutoff Dstorton PBS&D Fall 2004 Polkar Due to non-deal nature of op-amps, as well as the fnte CMRR, an offset voltage s typcally observed at the output even when the two nputs are at the same potental Hgh off-set voltages, as well as electrode dsplacement or mproperly adjusted amplfers can cause saturaton / cutoff dstorton, where hgh ampltude sgnals are truncated / chopped off. Ths can be prevented by usng a nullng pot to set the v o to zero, when v 1 =v 2.

25 Ground Loops PBS&D Fall 2004 Polkar Patents who are hooked to ECGs at clncal envronments are often also connected to other devces Each devce s typcally grounded through the ground termnal of the power outlet, however, grounds at dfferent outlets may be at slghtly dfferent grounds ground loops! Ground loops cause a non-zero ground current to flow between the devces through the patent: Common mode sgnal nterference: If CMRR s not hgh enough, ths can dstort the actual sgnal beng measured Unsafe: In case of a hazard, ths current can potentally cause electrocuton

26 PBS&D Fall 2004 Polkar Interference from Power Lnes The power lnes that provde the power to the ECG as well as to a multtude of other devces run throughout the room and cause sgnfcant nterference at 60Hz. Other devces / sgnals may also cause nterference 60 Hz EMG

27 Electrc Feld Couplng PBS&D Fall 2004 Polkar Power lne 120 V C 2 C 1 C 3 C 3 does not cause nterference snce ts current flows through the ECG on to ts ground However, current C 1 and C 2 flow through the skn electrode mpedances Z 1 and Z 2 (not through the ECG) to ground Z G Z 1 I d1 A Body resstance of 500Ω s neglgble compared to others Z 2 I d2 B Soluton: Sheld the leads, lower Z 1 and Z 2 Z G Electrocardograph G v = I I d1+ ( Z Z ) d2 v A B d1 d1 Z 1 1 d 2 6nA 20kΩ = 120µ V 2 Z 2

28 But wat there s more! PBS&D Fall 2004 Polkar υ cm Z 2 C b db υ cm Power lne Dsplacement current flowng through the body Z V Z n Z n A B v cm = dbzg = ( 0.2µA)(50kΩ) = 10mV In poor electrcal envronments, db >1µA v cm >50mV Ths s a common mode sgnal. Not a problem for perfect amplfers, but n practce, no amplfer has perfect CMRR. Ths causes the voltage dfference Electrocardograph v A v B = v cm Z Z Z 2 n 1 20kΩ 10mV 5MΩ = 40µV υ cm Z G db G Notceable on an ECG, and unacceptable on EEG! Need to reduce the dfference on skn-electrode mpedance, or just the mpedances themselves, and ncreasng amplfer nput mpedance.

29 Magnetc Interference PBS&D Fall 2004 Polkar Faraday s law Voltage s nduced due to changng magnetc feld created by the power lnes, fluorescent lghts, other devces, (esp. electrosurgery, dathermy) etc. V α B, A. It can be mnmzed by. Reducng B by sheldng. Keep ECG/leads away from magnetc sources (almost mpossble). Reducng the effectve area of the loop. Magnetc-feld pckup by the elctrocardograph (a) Lead wres for lead I make a closed loop (shaded area) when patent and electrocardograph are consdered n the crcut. The change n magnetc feld passng through ths area nduces a current n the loop. (b) Ths effect can be mnmzed by twstng the lead wres together and keepng them close to the body n order to subtend a much smaller area.

30 Transent Protecton PBS&D Fall 2004 Polkar Electrc devces, even n normal and ntended use may also damage other devces. Partcularly true wth the electrosurgcal unts that apply very hgh voltages (300 ~ 9000 ~2MHz, w/100 ~750W) If the ground connecton to these unts are faulty, and/or f hgher then normal output resstance s present, they may elevate patents potental sgnfcantly over the ground. Even at very short ntervals, ths may be adequate to fry an ECG machne, or at a mnmum cause transent effects. How to make sure that hgh voltages are not appled to other devces, such as ECGs, when they are present?

31 Transent Protecton PBS&D Fall 2004 Polkar

32 PBS&D Fall 2004 Polkar Mdterm Desgn Assgnment Due Nov 8 Desgn and buld an amplfer specfcally for ECG sgnals. Ths s an open ended desgn lab assgnment. You get to choose all specfcatons, but you must make sure that the sgnals you get are amplfed wthout loss of any fdelty. You wll need to experment wth a number of dfferent (actve) flter alternatves to make sure that you maxmze the SNR. The order of the flter, the gan, CMRR, etc. are all parameters that you need to determne. You wll receve the sgnals from a smulator, therefore you need not be too concerned about solatng the source, however, you have to make sure that you buld a hgh nput mpedance amplfer. Alternatvely, use an solated amplfer and try on yourself!