- •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
General Properties of Electronic Single-Loop Feedback Systems |
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where x is a parameter in the NFB circuit. From Equation [4.39] we can write:
ln[Av (jω)]= ln |
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Substitution of Equation [4.41] into Equation [4.40] yields:
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The real part of SAx v is called the magnitude sensitivity; the imaginary part of SAx v is the phase sensitivity. Generally, x will be a real number, which simplifies the calculation of Equation [4.42]. Sensitivity analysis using Equation [4.42] can be utilized to evaluate active filter designs.
4.4Effects of Negative Current Feedback
The purpose of negative current feedback (NCF) is to create an approximation to a voltage-controlled current source (VCCS) so that the output current, IL, is proportional to Vs, regardless of the load, which can be nonlinear. In NCF amplifiers, the signal fed back is proportional to the current through the load. NCF, like NVF, extends the bandwidth of the amplifier within the feedback loop. Unlike NVF, NCF raises the output resistance of the amplifier within the loop. A single op amp circuit with NCF, illustrated in Figure 4.5, will be investigated; frequency dependence will not be treated in this example. A VCCS is characterized by a transconductance, GM, and a Norton shunt conductance, Go.
First, it is necessary to find the circuit’s GM = IL/Vs. Note that the current
is given by Ohm’s law: |
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The summing junction node voltage is found: |
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Vi′[G1 + GF ]− (−ILRcGF ) = G1Vs |
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V′= |
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© 2004 by CRC Press LLC
184 |
Analysis and Application of Analog Electronic Circuits |
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RF |
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Vo |
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KvoVi’ |
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FIGURE 4.5
Schematic of a simple Thevenin VCVS with negative current feedback (NCFB).
Substituting Equation 4.45 into Equation 4.43, it is possible to solve for
IL(Vs): |
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How does NCF affect the VCCS’s Norton output conductance? First, calculate the circuit’s OCV, given RL •. This condition also makes IL = VF = 0. Now the summing junction voltage is
Vi′= Vs |
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R + R |
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and the OCV is:
OCV = Vs |
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Kvo volts |
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Next, find the short-circuit current, i.e., the ILsc when RL = 0. This condition also makes VF = Vo. The SCC is:
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© 2004 by CRC Press LLC
General Properties of Electronic Single-Loop Feedback Systems
where Vi′ is found from:
Vi′[G1 + GF ]− (−ILsoRc )GF = VsG1
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Equation 4.52 is substituted into Equation 4.50 and ILsc is found:
I = VsG1Kvo
Lsc (Ro + Rc )(G1 + GF )+ KvoRcGF
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(4.51)
(4.52)
(4.53)
Now the Norton Gout of the amplifier with NCF is simply the ratio of ILsc to OCV:
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The second term in the denominator of Equation 4.54 makes Gout Go, which is desirable in making an effective VCCS.
In order to see how the closed-loop VCCS’s frequency response is affected by NCF, replace the op amp’s open-circuit, VCVS with Kvo/(jωτa + 1). The transconductance is now found to be:
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Now the approximate GM(0) RF/(R1Rc) and the −3-dB frequency is:
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In the preceding relations, it was assumed that KvoRcR1 (R1 + RF)(Ro + Rc + RL). Note that the closed-loop system’s bandwidth is extended by the
© 2004 by CRC Press LLC
186 |
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Analysis and Application of Analog Electronic Circuits |
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FIGURE 4.6
A three-op amp VCCS in which the load is grounded. Analysis is in the text.
NCF. The NVF circuit of Figure 4.5 is simple, but suffers the disadvantage of having the RL “floating” between Vo and Rc. Also, the peak current is limited by the op amp used.
In Section 2.6.7 on laser diodes in Chapter 2, it was determined that an effective VCCS using NCF can be made from three op amps. The op amp that drives RL can be made a power op amp and the load can be grounded.
Figure 4.6 illustrates this NCF circuit. As in the earlier example, we will find the VCCS’s GM(jω) and Zout(jω). Because the two feedback amplifiers are
unity gain, they have −3-dB frequencies approaching their op amp’s fT and thus can be treated as pure gains (+1 and −1, respectively). The node equation for the summing junction is written:
Vi′ [3G] − VoG − (−VL)G = VsG |
(4.57) |
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Two auxiliary equations are used: |
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Vo = − IL (RF + “RL”) |
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o ( |
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Substituting the preceding equations into Equation 4.57 and rearranging terms yields:
IL
Vs
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= GM (jω) = |
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3(RF + RL )+ KvoRF |
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(4.60) |
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© 2004 by CRC Press LLC