- •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
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Equation 4.72 can be wrestled algebraically into the transfer function of the capacitance-neutralized GME amplifier:
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From the standard quadratic form, the closed-loop amplifier’s undamped natural frequency squared is:
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The amplifier’s damping factor is found from the second term in the denominator of Equation 4.73
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It is now useful to illustrate how the capacitance-neutralized, PVF amplifier works with typical numbers. Let Kvo = 105; τa = 10−2 sec; Avo = 2; Rμ = 108 Ω; CT = 3.05 pF; and CN = 2.95 pF. From these numbers it can be found that ωn = 9.129 ∞ 104 r/s, and ξ = 0.464 (an underdamped second-order system with good transient response). Note that if CN = CT, the system is highly underdamped and, if CN is slightly greater than CT, the amplifier’s closedloop poles lie in the right-half s-plane, making the amplifier oscillate. The price paid for extending the system’s bandwidth can be shown to be excess noise (see Section 9.8.4 in Chapter 9).
4.6Chapter Summary
Most electronic amplifiers use negative voltage feedback (NVF), which:
1.Reduces mid-band gain
2.Reduces total harmonic distortion at the output at a given signal output power level
3.Reduces Zout at low and mid-frequencies
4.Decreases gain sensitivity to certain circuit parameters
©2004 by CRC Press LLC
General Properties of Electronic Single-Loop Feedback Systems |
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5.Decreases the output signal-to-noise ratio slightly
6.Increases the closed-loop amplifier’s bandwidth
7.Can increase or decrease Rin, depending on the circuit
8.Can make a system unstable if incorrectly applied
Negative current feedback was shown to be useful in making a VCCS out of an amplifier with normally low Rout. NCF is used to raise the Thevenin Rout so that the NCF amplifier appears to be a current source. Otherwise, its properties are similar to those resulting from NVF. Positive voltage feedback reverses properties 1 through 4 and 6 in the preceding list for NVF. It does have use for capacitance neutralization and is used in the design of certain oscillators because it can make systems unstable more easily than NVF.
Home Problems
4.1Negative current feedback is used in a VCCS circuit used to power a laser diode (LAD), as shown in Figure P4.1. The LAD presents a nonlinear load to the VCCS. We wish the diode current to be independent of the LAD’s nonlinear resistance.
a.Assume the op amp is ideal and the differential amplifier (DA) is a VCVS in which V2 = KD (Vo − VL). Derive an expression for the VCVS’s transconductance, GM = IL/Vs.
b.Now assume that the power op amp is nonideal, so Vo = Kvo (Vi − Vi′). Derive an expression for the Norton output conductance seen by the LAD. (Hint: set Vs = 0 and replace the LAD by a test voltage source, vT. Find Gout = iT/vT.)
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FIGURE P4.1
4.2Negative voltage feedback is used to make an electronically regulated dc voltage source, shown in Figure P4.2. The design output voltage is 15 V at
1-A load. The power NPN BJT can be modeled by a mid-frequency
h-parameter model with hfe = 19; hoe = 2 ∞ 10−5 S; hre = 0: hie = VT/IBQ; VT =
0.026 V; and IEQ = 1 A. DA gain is KD = 1 ∞ 104; RL = 15 Ω, neglect current through RF + R1; and VR = 6.2 V, feedback attenuation β = R1/(R1 + R2) = 6.2/15. The raw dc has a ripple voltage, vr, added to it. RS = 50 Ω.
© 2004 by CRC Press LLC
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FIGURE P4.2
a.Find an algebraic expression for and evaluate numerically the
regulator’s ripple gain, AR = vo/vr. Use the MFSSM for the BJT (e.g., dc sources ground).
b.Now let vr = hoe = 0. Find an expression for and evaluate numerically the regulator’s output resistance, Rout, seen by RL. You can find Rout = vt/it by replacing RL with a small-signal test voltage source, vt.
c. Evaluate the regulator’s regulation, ρ = Vo/ RL.
4.3An op amp is ideal except for a finite differential voltage gain: vo = Kvo (vi − vi′). In the circuit of Figure P4.3, the op amp is connected to make a VCCS for
RL.
a.What kind of feedback is used: NVFB, PVFB, NCFB, or PCFB?
b.Give an expression for GM = IL/Vs. Show what happens to GM as Kvo •.
c.Find an expression for the Thevenin Rout that RL “sees.”
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FIGURE P4.3
© 2004 by CRC Press LLC
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FIGURE P4.4
4.4Figure P4.4 illustrates a source-follower–grounded-gate JFET amplifier with
feedback. The JFETs are identical with the same MFSSM in which gm > 0 and gd = 0. The feedback voltage, Vo = −KDV2, is applied through resistor RF to the common source node.
a.Derive an expression for Av = V2/V1 with no feedback (set RF = •).
b.Find an expression for Av = Vo/V1 with feedback. Let KD •; give Av.
4.5A three-op amp VCCS circuit is shown in Figure P4.5. Assume that op amps OA2 and OA3 are ideal and the power op amp, OA1, is characterized by the transfer function:
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and zero output resistance.
a.Derive an expression for the VCCS’s output transadmittance,
YM(jω) = IL/Vs, in time-constant form. Sketch and dimension 20 log YM(jω) vs. ω and – YM(jω) vs. ω (Bode plot). Show what happens to YM(jω) as Kvo •.
b.Derive an expression for the Norton output admittance the non-
linear load sees, Yout(jω) = IL/VL, in time-constant form. Sketch and dimension a Bode plot of Yout(jω) vs. ω. Show what happens to Yout(jω) as Kvo •.
© 2004 by CRC Press LLC
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FIGURE P4.5
4.6A DA is given a form of common-mode negative feedback, as shown in Figure P4.6. The DA has a differential output from which voc is derived by a voltage divider. The amplifier is described by the scalar equations:
vo = AD v1c + AC v1c
vo′ = −AD v1c + AC v1c
Also, it is clear that voc = AC v1c. Define α = R1/(R1 + Rs) and β = Rs/(R1 + Rs).
a.Find expressions for v1c and v1d in terms of vsc and vsd, and α, β, K, AD, and AC.
b.Give an expression for vo in terms of vsc and vsd and circuit parameters.
c.Find an expression for the system’s single-ended CMRR.
d.Let AD = 100; AC = 0.01; α 1; β = 0.01; and K = 104. Evaluate the single-ended CMRR numerically and compare it to the CMRR of the DA.
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FIGURE P4.6
© 2004 by CRC Press LLC
General Properties of Electronic Single-Loop Feedback Systems |
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FIGURE P4.7
4.7The op amp circuit shown in Figure P4.7 is a form of current mirror. The BJT can be modeled by its MFSSM with hre = hoe = 0. The op amp is ideal except for the gain:
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Find an expression for I2/I1(jω) in time constant form.
4.8Negative current feedback is used to make an op amp/FET VCCS, shown in
Figure P4.8. MFSS analysis will be used. The FET is characterized by (gm, gd) and the op amp has a finite voltage gain so vg = KV (v1 − vs). Assume VDS is large enough to keep the FET in channel saturation.
a.Find an expression for the VCCS’s small-signal transconductance, GM = id/v1.
b.Find an expression for the VCCS’s Norton output conductance,
Gout.
c.Let Kv = 104; gm = 10−3 S; gd = 10−5 S; and RS = 1 kΩ. Find numerical values for GM and Gout.
id
vi
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VDS |
v1 vi’
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vs
id RS
FIGURE P4.8
© 2004 by CRC Press LLC
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FIGURE P4.9
4.9A certain power op amp (POA) has an open-loop gain of Vo/Vi′ = − 5 ∞ 104. When it is connected as a gain of −250 amplifier, it has a total harmonic distortion (THD) of 0.5% of the RMS fundamental output signal voltage, Vos,
when the RMS Vos = 10.0 V. Find the percent THD when the amplifier is given a gain of −1 (unit inverter) and the Vos is again made 10.0 VRMS. See Figure P4.9.
4.10The circuit of Figure P4.10 is a constant-current regulator used for charging
batteries; NCFB is used. Assume the DA’s gain is KD = 105; hoe = hre = 0; hfe = 19; Rm = 1.0 Ω; VR = 5 V (sets IL); and VBE = 0.7 V. Battery: VB = 12.6 V (nominal); series resistance (nominal); RB = 0.1 Ω; VS = 24 V; and RS = 13 Ω.
a.Find an expression for and evaluate numerically the small-signal transconductance of the regulator, GM = IL/VR.
b.Find an expression for and evaluate numerically the small-signal
Norton conductance the battery sees. (Hint: set VR = 0 and use a test source, vt, in place of the battery. Gout = it/vt.)
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© 2004 by CRC Press LLC
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FIGURE P4.11
4.11We have shown that NVFB reduces amplifier output impedance. In this problem, you will investigate how NVFB affects input impedance. In the schematic of Figure P4.11, an amplifier is given negative feedback as shown. Find the input resistance with feedback, Rin = Vs/Is.
4.12One way of additively combining feedback with the input signal in a SISO
feedback amplifier is to use a difference amplifier, illustrated in Figure P4.12. The output, v2′, is given by the relation: v2′ = KF (vs − vo). Use a simple MFSSM for the matched BJTs in which hre = hoe = 0 and hfe and hie > 0. A dc current source supplies the emitter currents of the two BJTs. Derive an expression for KF in terms of circuit parameters.
VCC
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FIGURE P4.12
4.13Both positive and negative feedback are used on an ideal op amp, shown in Figure P4.13.
a.Derive an expression for Vo/Vs in terms of the circuit parameters.
b.What vector condition on the impedances will make the system unstable?
© 2004 by CRC Press LLC
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Analysis and Application of Analog Electronic Circuits |
Z4
Z3
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Z2 |
vs
FIGURE P4.13
© 2004 by CRC Press LLC