- •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 |
245 |
The transconductance of the VCCS is simply GF of the feedback resistor. Note that the unity-gain buffer is used so that all of iL flows into RL to ground. (This is especially important if RL is a glass micropipette electrode with RL on the order of hundreds of megohms.) The inverting IOA3 is required so that the voltage difference across RF is sensed to give current feedback. IOA1 supplying iL in a practical VCCS of this architecture can be a high-voltage output type or a power op amp if high iL is required.
Many more examples of IOA circuits can be considered. A number of them are included in this chapter’s home problems.
6.2Practical Op Amps
6.2.1Introduction
Practical op amps are characterized by a set of parameters that describe their output dc drift, output noise, and signal-conditioning properties such as dynamic range, frequency response, and slew rate. These parameters are generally given by manufacturers on device data sheets; they include:
•Input offset voltage (Vos)
•Input bias currents (IB, IB′ )
•Input equivalent short-circuit voltage noise (ena)
•Input equivalent current noise (ina)
•dc Differential gain (Kv)
•GBWP
•Unity gain
•−3-dB frequency (fT)
•Lowest open-loop break frequency (fb)
•Output voltage slew rate (η V/μs)
•CMRR
•Rin
•Ro
The following sections examine how a practical OA’s parameters determine its behavior.
6.2.2Functional Categories of Real Op Amps
Engineers and manufacturers group op amps into functional categories, each of which has a set of unique features that makes it suitable for a unique design application. Examples of these categories are described next.
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Low noise. Signal conditioning system design with low-noise op amps in the headstage is mandatory for maximum SNRout. Low-noise op amps are
characterized by low values of the equivalent short-circuit input voltage noise, ena nVRMS/ Hz. In the author’s experience, any op amp with an ena < 8 nVRMS/ Hz should be categorized as low noise. Some op amps with FET
input transistors (head stages) have exceptionally low equivalent input cur-
rent noise, ina, as well as low ena. However, some of the lowest-noise op amps have BJT head stages and boast ena in the order of 1 nVRMS/ Hz. For example, the venerable OP-27 op amp has ena = 3.1 nV/ Hz and ina = 1 pA/ Hz
at 30 Hz. It uses BJT head-stage architecture and has IB = 12 nA. Electrometer op amps. The two salient properties of electrometer amplifiers
are their ultra-low dc bias currents and their extra-high input resistances. For example, the AD549 is an electrometer-grade JFET head-stage OA. Its IB
is rated from 60 to 200 fA (10−15 A), but in selected units can approach ±10
fA. Rin is on the order of 1013 to 1014 Ω, ena = 35 nV/ Hz, and ina = 0.16 fARMS/ Hz at 1 kHz. Electrometer op amps are used to design signal
conditioning systems for pH meter glass electrodes and for intracellular glass micropipette electrodes in which source impedances can be as high as 109 Ω.
Chopper-stabilized op amps. This class of op amp is used to condition dc signals from devices such as strain gauge bridges (used in blood pressure sensors) and in any measurement system in which the QUM is essentially dc and minimizing long-term dc drift on the output of the analog signal conditioning system is desired. The internal chopper circuitry gives this class of OA an exceptional high dc voltage gain, on the order of 108. The net effect of this high gain is to minimize the effect of Vos and Vos drift with temperature change.
Another approach to canceling the effect of Vos drift in op amps used in dc signal conditioning applications is offered by National Semiconductor. The LMC669 auto-zero module can be used with any op amp configured as a single-ended inverting summer or as a simple noninverting amplifier. Note that the auto-zero module does not limit the dynamic performance of the op amp circuit to which it is attached; the amplifier retains the same dc gain, small-signal bandwidth, and slew rate. The effective offset voltage drift of any op amp using the auto-zero is approximately 100 nV/∞C. The maximum offset voltage using the auto-zero is ±5 μV. The auto-zero’s bias currents are approximately 5 pA (and must be added to the op amp’s IB in the inverting architecture); its clock frequency can be set from 100 Hz to 100 kHz.
The LMC669 auto-zero module is very useful to compensate for dc drift in circuits using special-purpose op amps such as electrometers, which normally have large offset voltages (200 μV) and large Vos tempcos (5 μV/∞C). The auto-zero does contribute to an increase in the circuit’s equivalent input voltage noise. However, choice of sampling rate and step size, as well as the use of low-pass filtering in the feedback path, can minimize this effect. Application circuits are illustrated in Section 2.4.3 in Northrop (1997).
Wide-band and high slew rate op amps. Wide-band and high slew-rate op amps are used for conditioning signals such as ultrasound (CW and pulsed) at frequencies in the tens of megahertz, as well as pulsed signals
© 2004 by CRC Press LLC
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vi |
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CFOA |
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VCVS |
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CCVS |
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RF |
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FIGURE 6.5
Simplified internal circuitry of a current-feedback op amp. The output current of the unity-gain VCVS controls the output of the Thevenin CCVS.
acquired in PET and SPECT imaging systems. A measure of op amp smallsignal bandwidth is its unity gain bandwidth, fT. In many op amps, fT is also the device’s gain-bandwidth product. As demonstrated in some detail later, under closed-loop conditions a trade-off occurs between op amp amplifier gain and bandwidth. For example, the Comlinear CLC440 voltage feedback op amp has fT = 750 MHz. This means that when given a noninverting gain of 5, the −3-dB frequency will be 150 MHz using this amplifier and 75 MHz when the gain is 10, etc.
Slew rate is the maximum rate of change of the output voltage; it is basically a nonlinear, large-signal parameter. If the output voltage is a highfrequency sine wave, its will appear triangular (except for the rounded tips) if its slope magnitude (2πf Vpk) exceeds η. Slew rate is defined as:
η = |
dVo |
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(6.14) |
dt |
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The slew rate of the wide-bandwidth CLC440 op amp is 1500 V/μs. High fT op amps all have high ηs. The AD549 electrometer op amp described previously has fT = 0.7 MHz and η = 2 V/μs — definitely not a wide-band op amp. There is no need to pay for high fT and η if an op amp circuit is not required to amplify high frequencies at high amplitudes or condition narrow fast rise-time pulses.
Current feedback op amps. Figure 6.5 illustrates the circuit architecture of a CFOA connected as a noninverting amplifier. Note that, internally, it uses a current-controlled voltage source (CCVS) to make its output Thevenin open-circuit voltage. The output voltage is given by:
Ωo |
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Vo = Ic τ s + 1 |
(6.15) |
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Analysis and Application of Analog Electronic Circuits |
Ωo is the CFOA dc transresistance. The input to the CFOA is a unity-gain voltage-controlled voltage source (VCVS). The noninverting input (vi) has a very high input resistance. The resistance looking into the inverting input (vi′) node is generally <50 Ω; it is the Thevenin output resistance of the unitygain VCVS.
The output current of the VCVS, In, is determined by Kirchoff’s current law (a node equation) written on the low-impedance inverting (vi′) node.
The Rout of the CCVS is also < 50 Ω and generally can be neglected in pencil- and-paper analysis. The CFOA has many interesting properties, which are
described in Section 6.4. One interesting property is that, unlike a voltageinput OA, the CFOA connected as a noninverting amplifier does not trade off bandwidth for closed-loop gain. Its gain can be shown to be set by R1, while its closed-loop corner frequency is set by RF. Its closed-loop dc gain is (1 + RF/R1), similar to that of a conventional noninverting voltage feedback OA.
Power op amps. Power op amps are used as audio power amplifiers, drivers for small DC servo motors, drivers for LEDs, and laser diodes (as VCCSs). Most conventional op amps can source no more than about ±10 mA; also, their output voltages saturate at slightly below their dc supply voltages, usually no more than ±15 V. The most robust power op amps (e.g., Apex PA03)
typically can source as much as ±30 A, given a supply voltage range of ±15/75 V, and dissipate 500 W maximum. The PA03 has a slew rate of η =
8 V/μs and fT = 1 MHz. Other POAs, such as the Apex PA85, have extraor-
dinary dynamic properties: namely, Iomax = ±350 mA(peak); a supply voltage range of ±75/600 V; a power dissipation of 40 W; a slew rate of 1000 V/μs;
and fT = 100 MHz. The PA85 is well suited to drive ultrasound transducers.
6.3Gain-Bandwidth Relations for Voltage-Feedback OAs
6.3.1The GBWP of an Inverting Summer
Figure 6.1(B) shows the schematic of a k-input inverting summer amplifier. The open loop op amp is assumed to have a compensated differential frequency response given by:
Vo = (Vi − Vi′) |
Kvo |
(6.16) |
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The gain-bandwidth product of the open-loop amplifier is: |
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© 2004 by CRC Press LLC
Operational Amplifiers |
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Because this is a real OA, Vi′ π 0 and a node equation must be written to find Vi′ to substitute into the preceding gain equation:
(Vi′− Vs1)G1 + (Vi′− Vs2 )G2 +≡+ (Vi′− Vsk )Gk + (Vi′− Vo )GF = 0 (6.18)
¬
V′i =
Define [GF + k Gj] ∫ G and
k
VsjGj + VoGF
j=1
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˚ |
note that:
j=1
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Thus, Equation 6.19 can be solved for Vo:
k
−Kvo VsjGj
j=1
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(6.19)
(6.20)
(6.21)
The dc gain of the preceding closed-loop frequency response function for Vsj is simply:
Kdcj |
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−GjKvo |
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The closed-loop bandwidth for all Vsj is fb:
f = G + GFKvo Hz |
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2πτa G |
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and the gain-bandwidth product for the jth input is:
GBWPj |
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Kvo Gj |
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GBWPOA Gj |
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(6.22)
(6.23)
(6.24)
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Note that (Kvo/2πτa) is the GBWP of the open-loop OA, and G ∫ G1 + G2 + … + Gk + GF. Thus, the GBWP of the inverting OA summer is always slightly
less than the GBWP of the OA alone and depends on the circuit’s gains.
6.3.2The GBWP of a Noninverting Voltage-Feedback OA
Figure 6.1(C) shows that the output of the noninverting amplifier can be written:
Vo = (Vs − Vi′) |
Kvo |
(6.25) |
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+ 1 |
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As was shown earlier, the OA alone has a GBWP given by GBWPol = Kvo/(2πτa). The summing junction voltage is found from the node equation:
(Vi′− Vo )GF |
+ Vi′G1 = 0 |
(6.26) |
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(G1 + GF ) |
(6.27) |
Equation 6.27 for Vi′ is substituted into Equation 6.25 to yield the noninverting amplifier’s closed-loop frequency response:
Vo =
Vs
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The noninverting amplifier’s dc gain is the numerator of the preceding equation. In the limit, for very large Kvo (where Kvo R1 RF), the dc gain is simply
Kdc = 1 + RF/R1 |
(6.29) |
which is the same as for an ideal op amp. The closed-loop break frequency is:
f = |
R1(1+ Kvo )+ RF |
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The noninverting amplifier’s GBWP is thus:
GBWPni = [Kvo
(2πτa )] Hz
(6.30)
(6.31)
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Therefore, GBWPni is the same as the op amp and is independent of gain. Thus, an ideal hyperbolic relation exists between closed-loop −3-dB frequency (fbcl) and closed-loop gain, e.g.,
fbcl = [Kvo (2πτa )] (1+ RF R1) Hz |
(6.32) |
The noninverting op amp amplifier is unique in this property.
6.4Gain-Bandwidth Relations in Current Feedback Amplifiers
6.4.1The Noninverting Amplifier Using a CFOA
Refer to Figure 6.5. Assume that the CCVS has a transimpedance with frequency response:
Vo |
= |
Ωo |
(6.33) |
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The gain-bandwidth product of the CCVS is simply Ωo/(2πτa) ohm Hz.
A small Thevenin source resistance appears in series with Vo from the CCVS. This Ro is RF, so it is neglected. There is also a small Thevenin Ro in series with the VCVS at the CFOA’s input that will be neglected. A node equation is written at the Vi′ node; note that
Vi′ = Vs.
(Vs − Vo)GF + Vs G1 = Ic
Substituting Equation 6.34 for Ic into Equation 6.33 yields:
V = |
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(6.34)
(6.35)
Equation 6.35 is solved for the frequency response of the closed-loop system:
Vo |
(jω) = |
(GF + G1)Ωo (1+ GFΩo ) |
(6.36) |
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jωτa (1+ GFΩo )+ 1 |
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The closed-loop amplifier’s break frequency is fbcl:
f = |
1+ GFΩo |
= |
Ωo + RF |
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Ωo |
, because Ω |
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(6.37) |
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The closed-loop break frequency is solely a function of RF; it is independent of gain. The closed-loop gain-bandwidth product of the noninverting CFOA amplifier is easily found to be:
GBWP = |
Ω |
(1+ RF R1) = |
Ω |
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(GF + G1) Hz |
(6.38) |
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Curiously, the GBWP depends on the absolute values of the gain-determining resistors.
6.4.2The Inverting Amplifier Using a CFOA
Next, examine the gain-bandwidth relations in a CFOA connected as a simple inverter. Figure 6.6 shows the circuit. Note that the noninverting input node is grounded, so vi = vi′ = 0. A node equation can still be written on the vi′ node:
(0 − Vs)G1 + (0 − Vo)GF − Ic = 0 |
(6.39) |
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Ic = −(Vs G1 + Vo GF) |
(6.40) |
vi |
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FIGURE 6.6
A CFOA connected as an inverting amplifier.
© 2004 by CRC Press LLC