- •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
160 |
Analysis and Application of Analog Electronic Circuits |
A plot of CMRRsys vs. R/Rs is shown in Figure 3.14. Note that when the Thevenin source resistances are matched, CMRRsys = CMRRA. Also, when
R/Rs = − 2(Ric/Rs + 1)/CMRRA, |
(3.37) |
the CMRRsys •. This implies that a judicious addition of an external resistance in series with one input lead or the other to introduce a R may
be used to increase the effective CMRR of the system. For example, if Ric = 100 MΩ, Rs = 10 kΩ, and CMRRA = 100 dB, then R/Rs = −0.2 to give •
CMRRsys. Because it is generally not possible to reduce Rs′ , it is easier to add a 2 k R in series with Rs externally.
Again, it needs to be stressed that an amplifier’s CMRRA is a decreasing function of frequency because of the frequency dependence of the gains, AD and AC. Also, the ac equivalent input circuit of a DA contains capacitances in parallel with R1, Ric, and Ric′ and the source impedances often contain a reactive frequency-dependent component. Thus, in practice, CMRRsys can often be maximized by the R method at low frequencies, but seldom can be drastically increased at high frequencies because of reactive unbalances in the input circuit.
3.7How Op Amps Can Be Used To Make DAs for Medical Applications
3.7.1Introduction
It is true that op amps are differential amplifiers, but several practical factors make their direct use in instrumentation highly impractical. The first factor is their extremely high open-loop gain and relatively low signal bandwidth. As demonstrated in Chapter 6 and Chapter 7, op amps are designed to be used with massive amounts of negative feedback, which acts to reduce their gain, increase their bandwidth, reduce their output signal distortion, etc. When used without feedback, their extremely high open-loop gain generally produces unacceptable signal levels at their outputs, as well as dc levels that drift because of temperature-sensitive input dc offset voltage and dc bias currents. Consequently, circuits have evolved that use twoor three-op amps with feedback to make DAs with gains typically ranging from 1 to 103, wide bandwidths, low noise, high input Z, high CMRR, etc.
Why would one want to build a DA from op amps when instrumentation amplifiers (DAs) are readily available from manufacturers? One reason is that the builder can select ultra low-noise op amps for the circuit and can tweak resistor values to maximize the DA’s CMRR. If one is building only a few DAs, a higher performance–cost ratio can be achieved by undertaking a custom design with op amps, rather than purchasing commercial IAs.
© 2004 by CRC Press LLC
The Differential Amplifier |
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161 |
Vs’ |
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Vo |
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V2 |
IOA |
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R |
RF |
R |
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R
V3
IOA V4
Vs
FIGURE 3.15
A two-operational amplifier DA. Resistors must be precisely matched to obtain maximum CMRR.
3.7.2Two-OP AMP DA Designs
A two-op amp DA is shown in Figure 3.15. All resistors “R” are closely matched to <0.02% to maintain a high CMRR. Analysis is easy if ideal op amps are assumed. Node equations are written for the V2 and V3 nodes, which, by the ideal op amp assumption, are Vs′ and Vs, respectively. The unknowns are Vo and V4.
Vs′ [2G + GF] − Vs GF − V4 G = 0 |
(3.38A) |
−Vs′ GF + Vs [2G + GF] − Vo G − V4 G = 0 |
(3.38B) |
Clearly, from Equation 3.38A, V4 G = Vs′[2G + GF] − Vs GF. This equation is substituted into Equation 3.38B, yielding:
o |
( s |
s ) |
( |
F ) |
|
V − V′ |
( |
F ) |
sd |
( |
F ) |
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( s s ) |
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V |
= V |
= V′ |
2 1 |
+ R R |
= |
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4 1 |
+ R R |
= V |
4 1 |
+ R R |
(3.39) |
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2 |
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Thus, the two-op amp DA configuration can have DM gains, AD ≥ 4. (This analysis does not treat the CM gain.)
A three-op amp DA circuit is shown in Figure 3.16. In this circuit, it is assumed that all Rj = Rj′, i.e., corresponding resistors are perfectly matched in order to make the CMRR •. Analysis of the three-op amp DA can be done with superposition, but is easier if pure CM and DM excitations are assumed and the bisection theorem is used. For pure CM excitation, Vs′ = Vs = Vsc. By symmetry and the IOA assumption, V2 = V2′ = Vsc; thus, there
is no current in R1 + R1′ , and Vc = Vsc. R2 and R2′ also have no current, so no voltage drop occurs across these feedback resistors and thus V3 = V3′ = Vsc.
When the right-hand IOA circuit has matched resistors, it is a DA with gain:
V |
= (V |
3 |
− V ′ )(R |
/R |
) |
(3.40) |
o |
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3 4 |
3 |
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© 2004 by CRC Press LLC