- •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
Digital Interfaces |
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FIGURE 10.29
Block diagram of a model in which quantization noise is added to a noise-free sampled signal at the input to a digital filter.
σq2 is the variance of the white quantization noise and the variance of the filter’s output noise can be shown to be expressed as (Northrop, 2003):
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10.7 Chapter Summary
Digital interfaces generate sampled data when they periodically convert an analog signal to numerical form or numerical data to an analog voltage or current. Sampled data are subject to the sampling theorem, which describes the conditions under which unwanted aliasing can take place. This chapter described sampling as impulse modulation and showed how sampled data can be described in the frequency domain by a repeated spectrum Poisson sum. In the frequency domain, aliasing was shown to exist when the edges of the repeated spectra in the Poisson sum overlapped. This overlapping occurred when the power density spectrum of the sampled analog signal contained significant power above one half the sampling frequency, also known as the Nyquist frequency.
Digital-to-analog converters (DACs) were next covered and their circuit architecture and factors affecting the speed of conversion were described. Hold circuits were also described; the transfer function of the zero-order hold and a simple extrapolator hold were derived.
Many types of analog-to-digital converters (ADCs) were described, including the tracking or servo ADC; the successive approximation ADC; integrating ADCs; and flash ADCs. Flash ADCs were seen to be the fastest because they convert in parallel.
Finally, quantization noise was described and an expression for ADC SNR due to quantiza;-tion noise was derived as a function of the number of binary bits in the converted signal. The more bits there are, the higher the ADC’s SNR is.
© 2004 by CRC Press LLC
428 |
Analysis and Application of Analog Electronic Circuits |
Home Problems
10.1A 16-bit ADC is used to convert an audio signal ranging over ±1 V.
a.Find the size of the quantization step, q, required.
b.Find the RMS quantization noise associated with full-scale operation of this ADC.
c.Let vin(t) = 1 sin(ωo t). Find the RMS SNR at the ADC output in decibels.
10.2Consider the 4-bit resistive ladder DAC shown in Figure P10.2.
a.Use superposition to find an expression for Vo = f(Io, I1, I2, I3). Let R = 1 kΩ and Io = 1 mA dc.
b.What values should I1, I2, and I3 have to make a binary DAC? What is the max. Vo?
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FIGURE P10.2
10.3 Refer to the text Figure 10.5 for the switched weighted capacitor DAC; in this problem you will examine the dynamics of this system. A simplified circuit is shown in Figure P10.3. In this circuit, k = 0, 1, 2, …, N − 1. The op amp is characterized by Rin = •; IB = Vos = Rout = 0; and Vo = (−Kvo ωb)/(s + ωb).
a. Find an algebraic expression for Vo/VR(s).
b. Assume VR(s) = VRo/s (step input). Give an expression for Vo(s). Plot and dimension a general vo(t).
c. Let k = 0, N = 8; sketch and dimension vo(t). d. Let k = N − 1 = 7; sketch and dimension vo(t).
e. Find a general expression for the maximum slope of vo(t) in terms of k and other system parameters.
f. Let VRo = 1 V and the op amp’s GBWP = Kvo ωb = 3 ∞ 108. Find
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Vomax for k = 0 and k = 7. What must the op amp’s slew rate be to avoid slew-rate limiting of Vo(t)?
© 2004 by CRC Press LLC
Digital Interfaces |
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FIGURE P10.3
10.4Figure P10.4 illustrates an N = 8-bit MOSFET current-scaling DAC. The feedback action of the left-hand op amp forces the Q1 drain current to be ID = VR/(2N R). The left-hand op amp also puts all the connected FET gates at virtual ground (0). The right-hand op amp forces the FET drains connected to it to be at virtual ground (0). Because all of the MOSFETs are matched and they all have the same drain, gate, and source voltage, they all have the same drain current, ID. Write an expression for Vo = f ({bk}, VR).
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FIGURE P10.4
10.5Figure P10.5 illustrates an N-bit binary-weighted charge amplifier DAC. Note that the ideal op amp’s summing junction is at virtual ground, so the net charge flowing into the kth input capacitor when bk = 1 must also equal the charge accumulated in CF = 2C/K. That is, Qk = VRC/2k = QF = Vo 2C/K. Write an expression for Vo = f ({bk}, VR, K); use superposition.
10.6An 8-bit successive approximation ADC has a reference voltage,VR, set to 10.0 V at 25∞C. Find the maximum allowable temperature coefficient of VR in μV/∞C that will allow an error of no more than plus or minus one half LSB over an operating temperature range of 0 to 50∞C.
10.7A 100-mV peak-to-peak sinusoidal signal is the input to a 12-bit ADC that has a bipolar offset binary output and a full-scale input range of ±2.5 V.
© 2004 by CRC Press LLC
430 |
Analysis and Application of Analog Electronic Circuits |
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FIGURE P10.5
a.Find the output RMS SNR in decibels when the input is a 2.5-V peak sinewave.
b.Find the output RMS SNR in decibels when the input is a 50-mV peak sinewave.
10.8A unipolar 3-bit successive-approximation ADC has VR = 8.0 V and a ½ LSB offset as shown in text Figure 10.27. Vin = 2.832 V. Find the LSB voltage as well as the intermediate and final DAC output voltages during conversion.
10.9Explain the differences between Nyquist-rate data converters and oversampling data converters.
10.10Find the maximum magnitude of quantization error for a 10-bit ADC with VR = 10 V and one half LSB absolute accuracy.
© 2004 by CRC Press LLC