8C Inleiding Meten en Modellen – 8C120 Prof.dr.ir. Bart ter Haar Romeny Dr. Andrea Fuster Faculteit Biomedische Technologie Biomedische Beeld Analyse

8C Chapter 3 - Webster Operational Amplifiers and Signal Processing

8C 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

8C 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

8C transistors 11 resistors 1 capacitor Inside the Op-Amp (IC-chip)

8C 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

8C 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.

8C 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

8C Summing Amplifier 11 oo - + R2R2 R1R1 RfRf 22

8C Example 3.1 ii v b ii oo oo V 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.

8C 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 + -

8C 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

8C 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

8C Instrumentation Amplifiers Advantages: High input impedance, High CMRR, Variable gain Differential Mode Gain

8C Comparator – No Hysteresis uouo uiui u ref 10 V -10 V v2v 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

8C 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.

8C 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

8C 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

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

8C 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 to the range of v o is -.36 to V. (a) RfRf IcIc R f /9 oo RiRi ii - + Logarithmic Amplifiers V BE

8C 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  V Logarithmic Amplifiers V BE 9V BE

8C 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

8C Integrators for f < f c A large resistor R f is used to prevent saturation

8C 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.

8C 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

8C 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.

8C 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 R f /R i + - RiRi RfRf (a) CfCf uiui uouo MMA

8C 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 R f /R i MMA

8C 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 R f /R i f cH = 1/2  R f C f CfCf MMA

8C 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

8C 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 

8C Chapter 3 - Webster Operational Amplifiers and Signal Processing Wikipedia: Operational Amplifier