Chapter 3-Webster Amplifiers and Signal Processing

1
Chapter 3-WebsterAmplifiers and Signal
Processing
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Applications of Operational AmplifierIn
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 signals frequency content

3
Ideal Op-Amp
Most bioelectric signals are small and require
amplifications
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 Rd. 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 vo must
pass through the output resistance Ro.
4
Inside the Op-Amp (IC-chip)
20 transistors 11 resistors 1 capacitor
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Ideal Characteristics
1- A ? (gain is infinity) 2- Vo 0, when v1
v2 (no offset voltage) 3- Rd ? (input impedance
is infinity) 4- Ro 0 (output impedance is
zero) 5- Bandwidth ? (no frequency response
limitations) and no phase shift
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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
Figure 3.3 (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.
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Summing Amplifier
Rf
R1
?1
-
R2
?o
?2

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Example 3.1
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.
10
Rf
Ri
?i
100 kW
10 kW
?i
-
?i ?b /2

15V
Rb
?o
0
Voltage, V
Time
20 kW

5 kW
v
b
-15 V
-10
?o
(a)
(b)
10
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

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Noninverting Amplifier
?o
i
i
10 V
Rf
Slope (Rf Ri )/ Ri
Ri
10 V
-10 V
?i
-
?o
-10 V
?i

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Differential Amplifiers
Differential Gain Gd
R4
R3
v3
R3
v4
vo
Common Mode Gain Gc 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.
R4
Common-mode rejection ratio CMMR
Typical values range from 100 to 10,000
Disadvantage of one-op-amp differential amplifier
is its low input resistance
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Instrumentation Amplifiers
Differential Mode Gain
Advantages High input impedance, High CMRR,
Variable gain
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Comparator No Hysteresis
v1 gt v2, vo -13 V v1 lt v2, vo 13 V
If (vivref) gt 0 then vo -13 V else vo 13
V R1 will prevent overdriving the op-amp
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Comparator With Hysteresis
Reduces multiple transitions due to mV noise
levels by moving the threshold value after each
transition.
Width of the Hysteresis 4VR3
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Rectifier
xR
(1-x)R
v
o
D2
-

?i
(a)
Full-wave precision rectifier a) For ?i gt 0,
D2 and D3 conduct, whereas D1 and D4 are
reverse-biased.Noninverting amplifier at the
top is active
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Rectifier
xRi
R
v
?i
o
D4
-

(b)
Full-wave precision rectifier b) For ?i lt 0,
D1 and D4 conduct, whereas D2 and D3 are
reverse-biased. Inverting amplifier at the
bottom is active
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One-Op-Amp Full Wave Rectifier
For ?i lt 0, the circuit behaves like the
inverting amplifier rectifier with a gain of
0.5. For ?i gt 0, the op amp disconnects and the
passive resistor chain yields a gain of 0.5.
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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

VBE
Figure 3.8 (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.
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Logarithmic Amplifiers
VBE
Rf /9
Ic
VBE
9VBE
Rf
Ri
-
?i
?o

(a)
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.
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Integrators
for f lt fc
A large resistor Rf is used to prevent saturation
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Integrators
Figure 3.9 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 ?o
constant, making possible a leisurely readout.
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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.
isC isR 0 vo -vc
Long cables may be used without changing sensor
sensitivity or time constant.
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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.
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Active Filters- Low-Pass Filter
Cf
Rf
Ri
Gain G
-
ui
uo

(a)
G
Rf/Ri
0.707 Rf/Ri
freq
fc 1/2?RiCf
Active filters (a) A low-pass filter attenuates
high frequencies
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Active Filters (High-Pass Filter)
Rf
Ci
Ri
-
ui
uo
Gain G

(b)
G
Rf/Ri
0.707 Rf/Ri
freq
fc 1/2?RiCf
Active filters (b) A high-pass filter
attenuates low frequencies and blocks dc.
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Active Filters (Band-Pass Filter)
Cf
Rf
Ci
Ri
-
ui
uo

G
(c)
Rf/Ri
0.707 Rf/Ri
freq
fcL 1/2?RiCi
fcH 1/2?RfCf
Active filters (c) A bandpass filter attenuates
both low and high frequencies.
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Frequency Response of op-amp and Amplifier
Open-Loop Gain Compensation Closed-Loop Gain Loop
Gain Gain Bandwidth Product Slew Rate
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Offset Voltage and Bias Current
Read section 3.12 Nulling, Drift, Noise Read
section and 3.13 Differential bias current,
Drift, Noise
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Input and Output Resistance
Typical value of Ro 40 ?
Typical value of Rd 2 to 20 M?
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Phase Modulator for Linear variable differential
transformer LVDT
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Phase Modulator for Linear variable differential
transformer LVDT
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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
vc ? 2vi