BME 311: BIOMEDICAL INSTRUMENTATION I Lecturer: Ali Işın
Lecture Note 2: Amplifiers and Signal Processing for Biomedical Instrumentation
FACULTY OF ENGINEERING
DEPARTMENT OF BIOMEDICAL ENGINEERING
Applications of Operational Amplifier In Biological Signals and Systems
• The three major operations done on biological signals using Op-Amp:
– Amplifications and Attenuations – DC offsetting:
• add or subtract a DC
– Filtering:
• Shape signal’s frequency content
BME 311 LECTURE NOTE 2 - ALİ IŞIN, 2014 2
Ideal Op-Amp
• Most bioelectric signals are small and require amplifications Op-amp equivalent circuit:
The two inputs are 1 and 2. A differential voltage between them causes current flow through the differential resistance Rd. The differential voltage is multiplied by A, the gain of the op amp, to generate the output-voltage
Inside the Op-Amp (IC-chip)
20 transistors 11 resistors 1 capacitor
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Ideal Characteristics
• A = (gain is infinity)
• Vo = 0, when v1 = v2 (no offset voltage)
• Rd = (input impedance is infinity)
• Ro = 0 (output impedance is zero)
• Bandwidth = (no frequency response limitations) and no
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.
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Inverting Amplifier
(a) An inverting amplified. Current flowing through the input resistor Ri also flows through the feedback resistor Rf .
(b) The input-output plot shows a slope of -Rf / Ri in the central portion, but the output saturates at about ±13 V.
Ri
i
o i
Rf i
+
(a)
10 V
10 V
(b)
i
o
Slope = -Rf / Ri -10 V
-10 V
i f i
o i
i f
o R
R v
G v R v
v
R
Summing Amplifier
2 2 1
1
R v R
R v v
o f1
o
+
R2
R1 Rf
2
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Example 2.1
• 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.
Answer 2.1
• We assume that v
b, the balancing voltage at v
i=5 V. For v
o=0, the current through R
fis zero. Therefore the sum of the
currents through R
iand R
b, is zero.
i
vb
i
o
o
+ +15V
+10
0 Time
i + b /2
-10
(a) (b)
5 k
-15 V
Rb 20 k
Ri 10 k
Rf 100 k
Voltage, V
42 10
45
) 10 (
0 10
i b b i
b b i
o
v v R R
R v R
v
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Follower ( buffer)
• Used as a buffer, to prevent a high source resistance from being loaded down by a low-resistance load. In another word it prevents drawing current from the source.
o
i +
1
v G
v
o iNoninverting Amplifier
o
10 V
10 V
i
Slope = (Rf + Ri )/ Ri -10 V
-10 V
Rf
o
i
i
+ -
i Ri
i f i
i f
i i
i f
o
R
R R
R G R
R v R
v R 1
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Differential Amplifiers
• Differential Gain G
d• Common Mode Gain G
c– For ideal op amp if the inputs are equal then the output = 0, and the Gc = 0.
– No differential amplifier perfectly rejects the common-mode voltage.
• Common-mode rejection ratio CMMR
– Typical values range from 100 to 10,000
• Disadvantage of one-op-amp differential amplifier is its low
3 4 3
4
R
R v
v
G
dv
o
v3 v4
) (
4 33
4
v v
R
v
o R
c d
G CMRR G
Instrumentation Amplifiers
Differential Mode Gain
Advantages: High input impedance, High CMRR, Variable gain
1 1 2
2 1
4 3
1 2
1
2 1
2 4
3
2
) (
R R R
v v
v G v
iR v
v
R R
R i v
v
d
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Comparator – No Hysteresis
o
i
ref
10 V
-10 V -10 V
v2
+15
-15
i
o
+
R1
R1
R2
ref
If (v
i+v
ref) > 0 then v
o= -13 V else
vo= +13 V
v1> v
2, v
o= -13 V
v1< v
2, v
o= +13 V
Comparator – With Hysteresis
• Reduces multiple transitions due to mV noise levels by moving the threshold value afer each transition.
Width of the Hysteresis = 4V
R3i
o
+
R1
R1
R2 R3
ref
o
i
- ref 10 V
-10 V
With hysteresis
-10 V 10 V
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Rectifier
• Full-wave precision rectifier:
– For i > 0, D2 and D3 conduct, whereas D1
and D4 are reverse-biased.
Noninverting amplifier at the top is active
10 V
(b) -10 V
o
i
-10 V 10 V
(a)
D2 vo
i
+
xR (1-x)R
+
(a)
D3 R R
i
+
D2 D1
D4 xR (1-x)R
x vo vi
Rectifier
• Full-wave precision rectifier:
– For i < 0,
D1 and D4 conduct, whereas D2 and D3 are reverse-biased.
Inverting amplifier at the bottom is active
10 V
(b) -10 V
o
i
-10 V 10 V
+
(a)
D3 R R
i
+
D2 D1
D4 xR (1-x)R
x vo vi
(b)
D4 vo
i
+
xRi R
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One-Op-Amp Full Wave Rectifier
• For
i< 0, the circuit behaves like the inverting amplifier rectifier with a gain of +0.5. For
i> 0, the op amp
disconnects and the passive resistor chain yields a gain of +0.5.
(c)
D
vo
i
+
Ri = 2 k Rf = 1 k
RL = 3 k
Logarithmic Amplifiers
• Uses of Log Amplifier
– Multiply and divide variables – Raise variable to a power
– Compress large dynamic range into small ones – Linearize the output of devices
(a) A logarithmic amplifier makes use of the fact that a transistor's VBE is related to the logarithm of its collector current.
For range of Ic equal 10-7 to 10-2 and the range of vo is -.36 to -0.66 V.
(a)
Rf
Ic Rf /9
o Ri
i
+
13log 10 06
. 0
i i
o
R
v v
S C
BE I
V
0 . 06 log
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Logarithmic Amplifiers
(a)
With the switch thrown in the alternate position, the circuit gain is increased by 10. (b) Input-output characteristics showthat the logarithmic relation is obtained for only one polarity; 1 and 10 gains are indicated.
(b)
10 V
-10 V vo
i -10 V
1
10 10 V
(a)
Rf
Ic Rf /9
o Ri
i
+
VBE
VBE
9VBE
Integrators
f f c
i f i
o
C f R
R R v
v
2
1
for f < fc
j R C
R j R
V j V
C R R j
R
R j
V j V
Z Z j
V j V
v dt
C v v R
i f
i i o
i f i
f i
o
i f i
o
t
ic i
f i o
1 )
(
) (
1
10
A large resistor R
fis used to prevent saturation
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• A three-mode integrator
With S1 open and S2 closed, the dc circuit behaves as an inverting amplifier.
Thus o = ic and o can be set to any desired initial conduction. With S1 closed and S2 open, the circuit integrates. With both switches open, the circuit holds
constant, making possible a leisurely readout.
Differentiators
• A differentiator
– The dashed lines indicate that a small capacitor must
usually be added across the feedback resistor to prevent oscillation.
RC j j
V j V
Z Z j
V j V
dt RC dv v
i o
i f i
o
i o
) (
) (
) (
) (
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Active Filters- Low-Pass Filter
• A low-pass filter attenuates high frequencies
i f f fi o
C R j
R R j
V j V
1
G 1 Gain
|G|
freq
R
f/R
i0.707 R
f/R
i+ Ri Rf
(a)
i
o
Active Filters (High-Pass Filter)
• A high-pass filter attenuates low frequencies and blocks dc.
Ci
+ Ri
i
o (b)
Rf
i f i ii ii o
C R j
C R j R
R j
V j V
G 1
Gain
|G|
freq
fc
= 1/2R
iC
fR
f/R
i0.707 R
f/R
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Active Filters (Band-Pass Filter)
• A bandpass filter attenuates both low and high frequencies.
f f
f i i i
i o
C R j C
R j
C R j j
V j V
1 1
|G|
R
f/R
i0.707 R
f/R
i+
i
o (c)
Rf Ci Ri
Cf
Phase Modulator for Linear variable differential transformer LVDT
+
-
+
-
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Phase Modulator for Linear variable differential transformer LVDT
+
-
+
-
Phase-Sensitive Demodulator
Used in many medical instruments for signal detection, averaging, and Noise rejection
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The Ring Demodulator
• If vc is positive then D1 and D2 are forward-biased and vA = vB. So vo = vDB
• If vc is negative then D3 and D4 are forward-biased and vA = vc. So vo = vDC
