- •Analysis and Application of Analog Electronic Circuits to Biomedical Instrumentation
- •Dedication
- •Preface
- •Reader Background
- •Rationale
- •Description of the Chapters
- •Features
- •The Author
- •Table of Contents
- •1.1 Introduction
- •1.2 Sources of Endogenous Bioelectric Signals
- •1.3 Nerve Action Potentials
- •1.4 Muscle Action Potentials
- •1.4.1 Introduction
- •1.4.2 The Origin of EMGs
- •1.5 The Electrocardiogram
- •1.5.1 Introduction
- •1.6 Other Biopotentials
- •1.6.1 Introduction
- •1.6.2 EEGs
- •1.6.3 Other Body Surface Potentials
- •1.7 Discussion
- •1.8 Electrical Properties of Bioelectrodes
- •1.9 Exogenous Bioelectric Signals
- •1.10 Chapter Summary
- •2.1 Introduction
- •2.2.1 Introduction
- •2.2.4 Schottky Diodes
- •2.3.1 Introduction
- •2.4.1 Introduction
- •2.5.1 Introduction
- •2.5.5 Broadbanding Strategies
- •2.6 Photons, Photodiodes, Photoconductors, LEDs, and Laser Diodes
- •2.6.1 Introduction
- •2.6.2 PIN Photodiodes
- •2.6.3 Avalanche Photodiodes
- •2.6.4 Signal Conditioning Circuits for Photodiodes
- •2.6.5 Photoconductors
- •2.6.6 LEDs
- •2.6.7 Laser Diodes
- •2.7 Chapter Summary
- •Home Problems
- •3.1 Introduction
- •3.2 DA Circuit Architecture
- •3.4 CM and DM Gain of Simple DA Stages at High Frequencies
- •3.4.1 Introduction
- •3.5 Input Resistance of Simple Transistor DAs
- •3.7 How Op Amps Can Be Used To Make DAs for Medical Applications
- •3.7.1 Introduction
- •3.8 Chapter Summary
- •Home Problems
- •4.1 Introduction
- •4.3 Some Effects of Negative Voltage Feedback
- •4.3.1 Reduction of Output Resistance
- •4.3.2 Reduction of Total Harmonic Distortion
- •4.3.4 Decrease in Gain Sensitivity
- •4.4 Effects of Negative Current Feedback
- •4.5 Positive Voltage Feedback
- •4.5.1 Introduction
- •4.6 Chapter Summary
- •Home Problems
- •5.1 Introduction
- •5.2.1 Introduction
- •5.2.2 Bode Plots
- •5.5.1 Introduction
- •5.5.3 The Wien Bridge Oscillator
- •5.6 Chapter Summary
- •Home Problems
- •6.1 Ideal Op Amps
- •6.1.1 Introduction
- •6.1.2 Properties of Ideal OP Amps
- •6.1.3 Some Examples of OP Amp Circuits Analyzed Using IOAs
- •6.2 Practical Op Amps
- •6.2.1 Introduction
- •6.2.2 Functional Categories of Real Op Amps
- •6.3.1 The GBWP of an Inverting Summer
- •6.4.3 Limitations of CFOAs
- •6.5 Voltage Comparators
- •6.5.1 Introduction
- •6.5.2. Applications of Voltage Comparators
- •6.5.3 Discussion
- •6.6 Some Applications of Op Amps in Biomedicine
- •6.6.1 Introduction
- •6.6.2 Analog Integrators and Differentiators
- •6.7 Chapter Summary
- •Home Problems
- •7.1 Introduction
- •7.2 Types of Analog Active Filters
- •7.2.1 Introduction
- •7.2.3 Biquad Active Filters
- •7.2.4 Generalized Impedance Converter AFs
- •7.3 Electronically Tunable AFs
- •7.3.1 Introduction
- •7.3.3 Use of Digitally Controlled Potentiometers To Tune a Sallen and Key LPF
- •7.5 Chapter Summary
- •7.5.1 Active Filters
- •7.5.2 Choice of AF Components
- •Home Problems
- •8.1 Introduction
- •8.2 Instrumentation Amps
- •8.3 Medical Isolation Amps
- •8.3.1 Introduction
- •8.3.3 A Prototype Magnetic IsoA
- •8.4.1 Introduction
- •8.6 Chapter Summary
- •9.1 Introduction
- •9.2 Descriptors of Random Noise in Biomedical Measurement Systems
- •9.2.1 Introduction
- •9.2.2 The Probability Density Function
- •9.2.3 The Power Density Spectrum
- •9.2.4 Sources of Random Noise in Signal Conditioning Systems
- •9.2.4.1 Noise from Resistors
- •9.2.4.3 Noise in JFETs
- •9.2.4.4 Noise in BJTs
- •9.3 Propagation of Noise through LTI Filters
- •9.4.2 Spot Noise Factor and Figure
- •9.5.1 Introduction
- •9.6.1 Introduction
- •9.7 Effect of Feedback on Noise
- •9.7.1 Introduction
- •9.8.1 Introduction
- •9.8.2 Calculation of the Minimum Resolvable AC Input Voltage to a Noisy Op Amp
- •9.8.5.1 Introduction
- •9.8.5.2 Bridge Sensitivity Calculations
- •9.8.7.1 Introduction
- •9.8.7.2 Analysis of SNR Improvement by Averaging
- •9.8.7.3 Discussion
- •9.10.1 Introduction
- •9.11 Chapter Summary
- •Home Problems
- •10.1 Introduction
- •10.2 Aliasing and the Sampling Theorem
- •10.2.1 Introduction
- •10.2.2 The Sampling Theorem
- •10.3 Digital-to-Analog Converters (DACs)
- •10.3.1 Introduction
- •10.3.2 DAC Designs
- •10.3.3 Static and Dynamic Characteristics of DACs
- •10.4 Hold Circuits
- •10.5 Analog-to-Digital Converters (ADCs)
- •10.5.1 Introduction
- •10.5.2 The Tracking (Servo) ADC
- •10.5.3 The Successive Approximation ADC
- •10.5.4 Integrating Converters
- •10.5.5 Flash Converters
- •10.6 Quantization Noise
- •10.7 Chapter Summary
- •Home Problems
- •11.1 Introduction
- •11.2 Modulation of a Sinusoidal Carrier Viewed in the Frequency Domain
- •11.3 Implementation of AM
- •11.3.1 Introduction
- •11.3.2 Some Amplitude Modulation Circuits
- •11.4 Generation of Phase and Frequency Modulation
- •11.4.1 Introduction
- •11.4.3 Integral Pulse Frequency Modulation as a Means of Frequency Modulation
- •11.5 Demodulation of Modulated Sinusoidal Carriers
- •11.5.1 Introduction
- •11.5.2 Detection of AM
- •11.5.3 Detection of FM Signals
- •11.5.4 Demodulation of DSBSCM Signals
- •11.6 Modulation and Demodulation of Digital Carriers
- •11.6.1 Introduction
- •11.6.2 Delta Modulation
- •11.7 Chapter Summary
- •Home Problems
- •12.1 Introduction
- •12.2.1 Introduction
- •12.2.2 The Analog Multiplier/LPF PSR
- •12.2.3 The Switched Op Amp PSR
- •12.2.4 The Chopper PSR
- •12.2.5 The Balanced Diode Bridge PSR
- •12.3 Phase Detectors
- •12.3.1 Introduction
- •12.3.2 The Analog Multiplier Phase Detector
- •12.3.3 Digital Phase Detectors
- •12.4 Voltage and Current-Controlled Oscillators
- •12.4.1 Introduction
- •12.4.2 An Analog VCO
- •12.4.3 Switched Integrating Capacitor VCOs
- •12.4.6 Summary
- •12.5 Phase-Locked Loops
- •12.5.1 Introduction
- •12.5.2 PLL Components
- •12.5.3 PLL Applications in Biomedicine
- •12.5.4 Discussion
- •12.6 True RMS Converters
- •12.6.1 Introduction
- •12.6.2 True RMS Circuits
- •12.7 IC Thermometers
- •12.7.1 Introduction
- •12.7.2 IC Temperature Transducers
- •12.8 Instrumentation Systems
- •12.8.1 Introduction
- •12.8.5 Respiratory Acoustic Impedance Measurement System
- •12.9 Chapter Summary
- •References
Operational Amplifiers |
253 |
Equation 6.40 is substituted into Equation 6.33 to find the frequency response of the closed-loop amplifier:
Vo = −(VsG1 |
+ VoGF ) |
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Again, the closed-loop break frequency depends on the size of RF:
fbcl |
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The GBWP is:
(6.41)
(6.42)
(6.43)
GBWP = |
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[G1Ωo (1+ GF Ωo )]= |
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Curiously, the closed-loop break frequency depends only on closed-loop dc gain is
Vo/Vs −RF/R1.
(6.44)
R1 and the
(6.45)
6.4.3Limitations of CFOAs
CFOAs cannot be directly substituted into most conventional voltage feedback OA circuits. For example, consider the CFOA “integrator” circuit shown in Figure 6.7(A); the node equation on the vi′ node is written:
Ic = (0 − Vs)G1 + (0 − Vo) jωC |
(6.46) |
Equation 6.46 for Ic is substituted into Equation 6.33 for Vo:
Vo = −(VsG1 |
+ Vo |
jωC) |
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© 2004 by CRC Press LLC
254 |
Analysis and Application of Analog Electronic Circuits |
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CFOA1
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B
FIGURE 6.7
(A) A CFOA connected as a conventional integrator. The circuit does not work. (B) Two CFOAs connected to make a near ideal inverting integrator.
Clearly, Equation 6.48 is the frequency response of a low-pass filter, not that of an operational integrator. The closed-loop time constant will be long, however. If Ωo = 107 ohms and C = 10−6 F, the closed-loop time constant will be approximately 10 sec, which means that signals with frequencies above approximately 40 mHz will be “integrated.” This is a poor integrator.
By way of comparison, find the frequency response of a conventional voltage-feedback OA integrator. The VCVS op amp’s open-loop gain is given by:
Vo = −Vi′ |
Kvo |
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The node equation for the summing junction is:
(Vi′ − Vs)G1 + (Vi′ − Vo) jωC = 0
from which,
Vi′ = |
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(6.49)
(6.50)
(6.51)
© 2004 by CRC Press LLC
Operational Amplifiers |
255 |
Equation 6.51 for Vi′ is substituted into Equation 6.49 to find the frequency response function for the OA integrator:
Vo |
(jω) = |
−Kvo |
(6.52) |
Vs |
(jω)2 RLC τa + jω(τa + KvoR1C)+ 1 |
The practical integrator is seen to be a two-pole low-pass filter with dc gain,
−Kvo.
To appreciate what happens to the integrator’s poles, substitute numerical values for the parameters and factor the quadratic denominator. Let R1 = 106 Ω; C = 1 μF; Kvo = 105; and τa = 15 MS. The numerical frequency response function for the integrator is found to be:
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The right-hand fraction of the frequency response function is in Laplace form and is most easily factored to find its roots (poles). Thus, the integrator’s frequency response function can be written in factored form:
Vo |
−6.667 E6 |
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(jω) = (jω + 3 E−12)(jω + 6.667 E6) |
Vs |
(6.54)
= −3 E11
(jω 3.333 E11+ 1)(jω 1.5 E−7 + 1)
Note that the integrator time constant is enormous (3.333 E11 sec) in this case and the high-frequency pole is at 6.667 E6 r/s, which is the GBWP of this voltage feedback OA.
As a closing note, it is possible to design an effective integrator using two CFOAs, as shown in Figure 6.7(B); however, this integrator is noninverting. If R is replaced with impedance Z1 and C with impedance Z2, then it can be shown that the circuit’s transfer function is:
Vo |
(s) |
Z2 |
(s)RA |
(6.55) |
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providing that Ωo1 = Ωo2; τa1 = τa2 0; Ωo1Go1 1; and RF > RA.
© 2004 by CRC Press LLC