1. 8C120 - 2010 Inleiding Meten en Modellen – 8C120 Prof.dr.ir. Bart ter Haar Romeny Dr. Andrea Fuster Faculteit Biomedische Technologie Biomedische Beeld Analyse www.bmia.bmt.tue.nl

2. 8C120 - 2010 Chapter 3 - Webster Operational Amplifiers and Signal Processing

3. 8C120 - 2010 The three major operations done on biological signals using Op-Amps: 1)Amplifications and Attenuations 2)DC offsetting: add or subtract a DC 3)Filtering: Shape signal’s frequency content Applications of Operational Amplifier In Biological Signals and Systems

4. 8C120 - 2010 Ideal Op-Amp Figure 3.1 Op-amp equivalent circuit. The two inputs are  1 and  2. A differential voltage between them causes current flow through the differential resistance R d. The differential voltage is multiplied by A, the gain of the op amp, to generate the output-voltage source. Any current flowing to the output terminal v o must pass through the output resistance R o. Most bioelectric signals are small and require amplifications

5. 8C120 - 2010 20 transistors 11 resistors 1 capacitor Inside the Op-Amp (IC-chip)

6. 8C120 - 2010 Ideal Characteristics 1- A =  (gain is infinity) 2- V o = 0, when v 1 = v 2 (no offset voltage) 3- R d =  (input impedance is infinity) 4- R o = 0 (output impedance is zero) 5- Bandwidth =  (no frequency response limitations) and no phase shift

7. 8C120 - 2010 Two Basic Rules Rule 1 When the op-amp output is in its linear range, the two input terminals are at the same voltage. Rule 2 No current flows into or out of either input terminal of the op amp.

8. 8C120 - 2010 Inverting Amplifier Figure 3.3 (a) An inverting amplified. Current flowing through the input resistor R i also flows through the feedback resistor R f. (b) The input-output plot shows a slope of -R f / R i in the central portion, but the output saturates at about ±13 V. RiRi ii oo i RfRf i + - (a) 10 V (b) ii oo Slope = -R f / R i -10 V

9. 8C120 - 2010 Summing Amplifier 11 oo - + R2R2 R1R1 RfRf 22

10. 8C120 - 2010 Example 3.1 ii v b ii oo oo - + +15V +10 0 Time  i +  b /2 -10 (a)(b) 5 kW -15 V RbRb 20 kW RiRi 10 kW RfRf 100 kW Voltage, V The output of a biopotential preamplifier that measures the electro-oculogram is an undesired dc voltage of ±5 V due to electrode half-cell potentials, with a desired signal of ±1 V superimposed. Design a circuit that will balance the dc voltage to zero and provide a gain of -10 for the desired signal without saturating the op amp.

11. 8C120 - 2010 Follower (buffer) Used as a buffer, to prevent a high source resistance from being loaded down by a low-resistance load. In other words: it prevents drawing current from the source. oo ii + -

12. 8C120 - 2010 Noninverting Amplifier oo 10 V ii Slope = (R f + R i )/ R i -10 V RfRf oo ii i + - i RiRi

13. 8C120 - 2010 Differential Amplifiers R4R4 R4R4 R3R3 R3R3 v3v3 v4v4 vovo Differential Gain G d Common-mode rejection ratio CMMR Common Mode Gain G c For ideal op amp if the inputs are equal then the output = 0, and the G c =0. No differential amplifier perfectly rejects the common-mode voltage. Typical values range from 100 to 10,000 Disadvantage of one-op-amp differential amplifier is its low input resistance

14. 8C120 - 2010 Instrumentation Amplifiers Advantages: High input impedance, High CMRR, Variable gain Differential Mode Gain

15. 8C120 - 2010 Comparator – No Hysteresis uouo uiui u ref 10 V -10 V v2v2 +15 -15 uiui uouo - + R1R1 R1R1 R2R2 u ref If (v i +v ref ) > 0 then v o = -13 Velsev o = +13 V R 1 will prevent overdriving the op-amp v 1 > v 2, v o = -13 V v 1 < v 2, v o = +13 V

16. 8C120 - 2010 Comparator – With Hysteresis uiui uouo - + R1R1 R1R1 R2R2 R3R3 u ref uouo uiui - u ref 10 V -10 V With hysteresis -10 V 10 V Width of the Hysteresis = 4V R3 Reduces multiple transitions due to mV noise levels by moving the threshold value after each transition.

17. 8C120 - 2010 Rectifier 10 V (b) - 10 V oo ii 10 V - + (a) D3D3 R R o=o= ii - + D2D2 D1D1 D4D4 xR (1-x)R ii x Full-wave precision rectifier: a) For  i > 0, D 2 and D 3 conduct, whereas D 1 and D 4 are reverse-biased. Noninverting amplifier at the top is active (a) D2D2 v o ii - + xR(1-x)R

18. 8C120 - 2010 Rectifier 10 V (b) - 10 V oo ii 10 V - + (a) D3D3 R R o=o= ii - + D2D2 D1D1 D4D4 xR (1-x)R ii x Full-wave precision rectifier: b) For  i < 0, D 1 and D 4 conduct, whereas D 2 and D 3 are reverse-biased. Inverting amplifier at the bottom is active (a) D4D4 v o ii - + xR i R

19. 8C120 - 2010 Rectifier One-op-amp full-wave rectifier. For  i 0, the op amp disconnects and the passive resistor chain yields a gain of +0.5. (c) D v o ii - + R i = 2 kW R f = 1 kW R L = 3 kW

20. 8C120 - 2010 Figure 3.8 (a) A logarithmic amplifier makes use of the fact that a transistor's V BE is related to the logarithm of its collector current. For range of I c equal to 10 -7 to 10 -2 the range of v o is -.36 to -0.66 V. (a) RfRf IcIc R f /9 oo RiRi ii - + Logarithmic Amplifiers V BE

21. 8C120 - 2010 Figure 3.8 (a) With the switch thrown in the alternate position, the circuit gain is increased by 10. (b) Input-output characteristics show that the logarithmic relation is obtained for only one polarity;  1 and  10 gains are indicated. (a) RfRf IcIc R f /9 oo RiRi ii - + (b) 10 V -10 V v o ii 11  10 10 V Logarithmic Amplifiers V BE 9V BE

22. 8C120 - 2010 Logarithmic Amplifiers Uses of Log Amplifier: 1.Multiply variable 2.Divide variable 3.Raise variable to a power 4.Compress large dynamic range into small ones 5.Linearize the output of devices

23. 8C120 - 2010 Integrators for f < f c A large resistor R f is used to prevent saturation

24. 8C120 - 2010 Integrators Figure 3.9 A three-mode integrator With S 1 open and S 2 closed, the dc circuit behaves as an inverting amplifier. Thus  o =  ic and  o can be set to any desired initial conduction. With S 1 closed and S 2 open, the circuit integrates. With both switches open, the circuit holds  o constant, making possible a leisurely readout.

25. 8C120 - 2010 R + FET Piezo-electric sensor - uouo C isis isRisR isCisC dq s / dt = i s = K dx/dt Long cables may be used without changing sensor sensitivity or time constant. Example 3.2 The output of the piezoelectric sensor may be fed directly into the negative input of the integrator as shown below. Analyze the circuit of this charge amplifier and discuss its advantages. i sC = i sR = 0 v o = -v c

26. 8C120 - 2010 Differentiators Figure 3.11 A differentiator The dashed lines indicate that a small capacitor must usually be added across the feedback resistor to prevent oscillation.

27. 8C120 - 2010 Active Filters- Low-Pass Filter Active filters (a) A low-pass filter attenuates high frequencies Gain = G = |G| freq f c = 1/2  R i C f R f /R i 0.707 R f /R i + - RiRi RfRf (a) CfCf uiui uouo MMA

28. 8C120 - 2010 Active Filters (High-Pass Filter) CiCi + - RiRi uiui uouo (b) RfRf Active filters (b) A high-pass filter attenuates low frequencies and blocks dc. Gain = G = |G| freq f c = 1/2  R i C f R f /R i 0.707 R f /R i MMA

29. 8C120 - 2010 Active Filters (Band-Pass Filter) + - uiui uouo (c) RfRf CiCi RiRi Active filters (c) A bandpass filter attenuates both low and high frequencies. |G| freq f cL = 1/2  R i C i R f /R i 0.707 R f /R i f cH = 1/2  R f C f CfCf MMA

30. 8C120 - 2010 Frequency Response of op-amp and Amplifier Open-Loop Gain Compensation Closed-Loop Gain Loop Gain Gain Bandwidth Product Slew Rate Offset voltage Bias current Noise

31. 8C120 - 2010 Input and Output Resistance + - RdRd i RoRo RLRL CLCL ioio Au d udud uouo uiui + - Typical value of R d = 2 to 20 M  Typical value of R o = 40 

32. 8C120 - 2010 Chapter 3 - Webster Operational Amplifiers and Signal Processing Wikipedia: Operational Amplifier