Analog Circuit Design: A Tutorial Guide to Applications and Solutions

✍ Scribed by Bob Dobkin (editor), Jim Williams (editor)

• Publisher: Newnes
• Year: 2011
• Tongue: English
• Leaves: 939
• Edition: 1
• Category: Library

✦ Synopsis

Analog circuit and system design today is more essential than ever before. With the growth of digital systems, wireless communications, complex industrial and automotive systems, designers are challenged to develop sophisticated analog solutions. This comprehensive source book of circuit design solutions will aid systems designers with elegant and practical design techniques that focus on common circuit design challenges. The book’s in-depth application examples provide insight into circuit design and application solutions that you can apply in today’s demanding designs.

• Covers the fundamentals of linear/analog circuit and system design to guide engineers with their design challenges
• Based on the Application Notes of Linear Technology, the foremost designer of high performance analog products, readers will gain practical insights into design techniques and practice
• Broad range of topics, including power management tutorials, switching regulator design, linear regulator design, data conversion, signal conditioning, and high frequency/RF design
• Contributors include the leading lights in analog design, Robert Dobkin, Jim Williams and Carl Nelson, among others

✦ Table of Contents

Cover
Title
Copyright
Dedication
in memoriam
Publisher’s Note
Acknowledgments
Introduction
Foreword
PART 1
Section 1
Ceramic input capacitors can cause overvoltage transients
Plug in the wall adapter at your own risk
Building the Test Circuit
Turning on the switch
Testing a portable application
Input voltage transients with different input elements
Optimizing Input Capacitors
Conclusion
Minimizing switching regulator residue’in’linear regulator outputs
Introduction
Switching regulator AC output content
Ripple and spike rejection
Ripple/spike simulator
Linear regulator high frequency rejection evaluation/optimization
References
Power Conditioning for notebook and palmtop systems
Introduction
LT1432 driver for high efficiency 5V and 3.3V buck regulator
Circuit description
BICMOS switching regulator family provides highest step-down efficiencies
Surface mount capacitors for switching regulator applications
High efficiency linear supplies
Power switching with dual high side micropower N-channel MOSFET drivers
LT1121 micropower 150mA regulator with shutdown
Cold cathode fluorescent display driver
Battery charging
Lead acid battery charger
NiCAD charging
LCD display contrast power supply
A 4-cell NiCad regulator/charger
Power supplies for palmtop computers
2-Cell input palmtop power supply’circuits
LCD bias from 2 AA cells
4-Cell input palmtop power supply’circuits
A CCFL backlight driver for palmtop’machines
2-Wire virtual remote sensing for’voltage’regulators
Introduction
“Virtual” remote sensing
Applications
VRS linear regulators
VRS equipped switching regulators
VRS based isolated switching supplies
VRS halogen lamp drive circuit
References
 
Outline placeholder
Introduction
Design procedure
RSENSE selection
Section 2
LT1070 design manual
Introduction
Preface
Smaller versions of the LT1070
Inductance calculations
Protecting the magnetics
New switch current specification
High supply voltages
Discontinuous “oscillations” (ringing)
LT1070 operation
Pin functions
Input supply (VIN)
Ground pin
Feedback pin
Compensation pin (Vc)
Output pin
Basic switching regulator topologies
Buck converter
Boost regulators
Combined buck-boost regulator
’Cuk converter
Flyback regulator
Forward converter
Current-boosted boost converter
Current-boosted buck converter
Application circuits
Boost mode (output voltage higher than input)
Inductor
Output capacitor
Frequency compensation
Current steering diode
Short-circuit conditions
Negative buck converter
Output divider
Duty cycle
Inductor
Output capacitor
Output filter
Input filter
Frequency compensation
Catch diode
Negative-to-positive buck-boost converter
Setting output voltage
Inductor
Output capacitor
Current steering diode
Positive buck converter
Duty cycle limitations
Inductor
Output voltage ripple
Output capacitor
Output filter
Flyback converter
Output divider
Frequency compensation
Snubber design
Output diode (D1)
Output capacitor (C1)
Totally isolated converter
Output capacitors
Load and line regulation
Frequency compensation
Positive current-boosted buck converter
Negative current-boosted buck converter
Negative input/negative output flyback converter
Positive-to-negative flyback converter
Voltage-boosted boost converter
Negative boost converter
Positive-to-negative buck boost converter
Current-boosted boost converter
Forward converter
Frequency compensation
Check margins
Eliminating start-up overshoot
External current limiting
Driving external transistors
Output rectifying diode
Input filters
Efficiency calculations
LT1070 operating current
LT1070 switch losses
Output diode losses
Inductor and transformer losses
Snubber losses
Total losses
Output filters
Input and output capacitors
Inductor and transformer basics
Cores with gaps
Inductor selection process
Transformer design example
Heat sinking information
Troubleshooting hints
Warning
Subharmonic oscillations
Inductor/transformer manufacturers
Core manufacturers
Bibliography
Switching regulators for poets
Basic flyback regulator
−48V to 5V telecom flyback regulator
Fully-isolated telecom flyback regulator
100W off-line switching regulator
Switch-controlled motor speed’controller
Switch-controlled peltier 0°C’reference
Acknowledgments
Step-down switching regulators
Basic step down circuit
Practical step-down switching regulator
Dual output step-down regulator
Negative output regulators
Current-boosted step-down regulator
Post regulation-fixed case
Post regulation-variable case
Low quiescent current regulators
Wide range, high power, high voltage regulator
Regulated sinewave output DC/AC converter
References
 
A monolithic switching regulator with 100μV output noise
Introduction
Switching regulator “noise”
A noiseless switching regulator approach
A practical, low noise monolithic regulator
Measuring output noise
System-based noise “measurement”
Transition rate effects on noise and’efficiency
Negative output regulator
Floating output regulator
Floating bipolar output converter
Battery-powered circuits
Performance augmentation
Low quiescent current regulator
High voltage input regulator
24V-to-5V low noise regulator
10W, 5V to 12V low noise regulator
7500V isolated low noise supply
References
 

                History
                Measuring noise
                Low frequency noise
                Preamplifier and oscilloscope selection
                Ground loops
                Pickup
                Poor probing technique
                Violating coaxial signal transmission—felony case
                Violating coaxial signal transmission— misdemeanor case
                Proper coaxial connection path
                Direct connection path
                Test lead connections
                Isolated trigger probe
                Trigger probe amplifier
                Breadboarding and Layout Considerations
                5V to 12V Breadboard
                5V to±15V breadboard
                Demonstration board
                Testing ripple rejection
                Transformers
                Inductors
                Hints for lowest noise performance
                Noise tweaking
                Capacitors
                Damper network
                Measurement technique
                Noise test data
                Pot core
                ER core
                Toroid
                E core
                Summary
                Conclusion
                Rectifier reverse recovery
                Ringing in clamp Zeners
                Paralleled rectifiers
                Paralleled snubber or damper caps
                Ringing in transformer shield leads
                Leakage inductance fields
                External air gap fields
                Poorly bypassed high speed logic
                Probe use with a “LISN”
                Conclusion
                Summary
    Powering complex FPGA-based systems using highly integrated DC/DC μModule regulator systems
        Innovation in DC/DC design
        DC/DC μModule Regulators: Complete Systems in an LGA Package
        48A from four parallel DC/DC μModule regulators
        Start-up, soft-start and current sharing
        Conclusion
    Powering complex FPGA-based systems’using highly integrated DC/DC µModule regulator systems
        60W by paralleling four DC/DC μModule regulators
        Thermal performance
        Simple copy and paste layout
        Conclusion
    Diode Turn-On Time Induced Failures in Switching Regulators
        Introduction
        Diode turn-on time perspectives
        Detailed measurement scheme
        Diode Testing and Interpreting Results
        References

                400ps rise time avalanche pulse generator
                Circuit optimization
                When to roll your own and when to pay the money
Section 3
    Performance verification of low noise, low dropout regulators
        Introduction
        Noise and noise testing
        Noise testing considerations
        Instrumentation performance verification
        Regulator noise measurement
        Bypass capacitor (CBYP) influence
        Interpreting comparative results
        References
        References

                Noise minimization
                Pass element considerations
                Dynamic characteristics
                Bypass capacitance and low noise performance
                Output capacitance and transient response
                Ceramic capacitors
                AC voltmeter types
                Rectify and average
                Analog computation
                Thermal
                Performance comparison of noise driven AC voltmeters
                Thermal voltmeter circuit
Section 4
    Parasitic capacitance effects in step-up transformer design
    High efficiency, high density, PolyPhase converters for high current applications
        Introduction
        How do PolyPhase techniques affect circuit performance?
            Current-sharing
            Output ripple current cancellation and’reduced output ripple voltage
            Improved load transient response
            Input ripple current cancellation
            Input ripple current cancellation
        Design considerations
            Selection of phase number
            PolyPhase converters using the LTC1629
            Layout considerations
        Design example: 100A PolyPhase power supply
            Design details
                MOSFETs
                Inductors
                Capacitors
            Test results
        Summary
Section 5
    Ultracompact LCD backlight inverters
        Introduction
            Limitations and problems of magnetic CCFL transformers
            Piezoelectric transformers
            Developing a PZT transformer control scheme
            Additional considerations and benefits
            Display parasitic capacitance and its effects
        References
         

                “Good Vibrations”
                Piezowhat?
                Alchemy and black magic
                The fun part
                A resonant personality
                Piezoelectricity
                Piezoelectric effect
                Axis nomenclature
                Electrical-mechanical analogies
                Coupling
                Electrical, mechanical property changes with load
                Elasticity
                Piezoelectric equation
                Basic piezoelectric modes
                Poling
                Post Poling
                    Applied voltage
                    Applied force
                    Shear
                Piezoelectric benders
                Loss
                Simplified Piezoelectric Element Equivalent Circuit
                Simple stack piezoelectric transformer
                Conclusion
    A thermoelectric cooler temperature’controller for fiber’optic’lasers
        INTRODUCTION
        Temperature Controller Requirements
        Temperature Controller Details
        Thermal Loop Considerations
        Temperature Control Loop Optimization
        Temperature Stability Verification
        Reflected Noise Performance
        REFERENCES
    Current sources for fiber optic lasers
        Introduction
            Design criteria for fiber optic laser current sources
            Detailed discussion of performance issues
                Required power supply
                Output current capability
                Output voltage compliance
                Efficiency
                Laser connection
                Output current programming
                Stability
                Noise
                Transient response
            Detailed discussion of laser protection issues
                Overshoot
                Enable
                Output current clamp
                Open laser protection
            Basic current source
            High efficiency basic current source
            Grounded cathode current source
            Single supply, grounded cathode current source
            Fully protected, self-enabled, grounded cathode current source
            2.5A, grounded cathode current source
            0.001% noise, 2A, grounded cathode current source
            0.0025% noise, 250mA, grounded anode current source
            Low noise, fully floating output current source
            Anode-at-supply current source
        References
         
            Outline placeholder
                Electronic laser load simulator
                Isolated trigger probe
                Trigger probe amplifier
    Bias voltage and current sense circuits for avalanche photodiodes
        Introduction
            Simple current monitor circuits (with’problems)
            Carrier based current monitor
            DC coupled current monitor
            APD bias supply
            APD bias supply and current monitor
            Transformer based APD bias supply and current monitor
            Inductor based APD bias supply
            200μV output noise APD bias supply
            Low noise APD bias supply and current monitor
            0.02% accuracy current monitor
            Digital output 0.09% accuracy current monitor
            Digital output current monitor
            Digital output current monitor and APD bias supply
        Summary
        References
         

                Divider current error compensation—“low’side” shunt case
                Divider current error compensation—“high side” shunt case
                Ground loops
                Pickup
                Poor probing technique
                Violating coaxial signal transmission—felony case
                Violating coaxial signal transmission— misdemeanor case
                Proper coaxial connection path
                Direct connection path
                Test lead connections
                Isolated trigger probe
                Trigger probe amplifier
Section 6
    Developments in battery stack voltage measurement
        The battery stack problem
        Transformer based sampling voltmeter
        Detailed circuit operation
        Multi-cell version
        Automatic control and calibration
        Firmware description
        Measurement details
        Adding more channels
        References
            Things that don’t work

PART 2
Section 1
Some techniques for direct digitization of’transducer outputs
The care and feeding of’high’performance ADCs: get’all the’bits’you’paid for
Introduction
An ADC has many “inputs”
Ground planes and grounding
Supply bypassing
Reference bypassing
Driving the analog input
Switched capacitor inputs
Filtering wideband noise from’the’input’signal
Choosing an op amp
Driving the convert-start input
Effects of jitter
Routing the data outputs
Conclusion
Family features
High speed A/D converters — world’s best power/speed ratio
A standards lab grade 20-bit DAC with 0.1ppm/°C drift
Introduction
20-bit DAC architecture
Circuitry details
Linearity considerations
DC performance characteristics
Dynamic performance
Conclusion
References
Approach and error considerations
Circuitry details
Construction
Results
Acknowledgments
Delta sigma ADC bridge measurement techniques
Introduction
Low cost, precision altimeter uses direct digitization
How Many Bits?
Increasing Resolution with Amplifiers
How Much Gain?
ADC Response to Amplifier Noise
How Many Bits?
Faster or More Resolution with the LTC2440
How Many Bits?
RMS vs Peak-to-Peak Noise
Psychological Factors
1ppm settling time measurement for’a’monolithic 18-bit DAC
Introduction
DAC settling time
Considerations for measuring DAC settling time
Sampling based high resolution DAC settling time measurement
Developing a sampling switch
Electronic switch equivalents
Transconductance amplifier based switch equivalent
DAC settling time measurement method
Detailed settling time circuitry
Settling time circuit performance
Using the sampling-based settling time circuit
References
 

                Delay compensation
                Circuit trimming procedure
                Ohm's law
                Shielding
                Connections
                Settling time circuit performance verification
Section 2
    Applications for a switched-capacitor instrumentation building block
        Instrumentation amplifier
        Ultrahigh performance instrumentation amplifier
        Lock-in amplifier
        Wide range, digitally controlled, variable gain amplifier
        Precision, linearized platinum RTD signal conditioner
        Relative humidity sensor signal conditioner
        LVDT signal conditioner
        Charge pump F→V and V→F converters
        12-bit A→D converter
        Miscellaneous circuits
        Voltage-controlled current source—grounded source and load
        Current sensing in supply rails
        0.01% analog multiplier
        Inverting a reference
        Low power, 5V driven, temperature compensated crystal oscillator
        Simple thermometer
        High current, “inductorless,” switching regulator
    Application considerations and circuits for a new chopper-stabilized op amp
        Applications
        Standard grade variable voltage reference
        Ultra-precision instrumentation amplifier
        High performance isolation amplifier
        Stabilized, low input capacitance buffer (FET’probe)
        Chopper-stabilized comparator
        Stabilized data converter
        Wide range V→F converter
        1Hz to 30MHz V→F converter
        16-bit A/D converter
        Simple remote thermometer
        Output stages
        References
    Designing linear circuits for 5V single supply operation
        Linearized RTD signal conditioner
        Linearized output methane detector
        Cold junction compensated thermocouple signal conditioner
        5V powered precision instrumentation amplifier
        5V powered strain gauge signal conditioner
        “Tachless” motor speed controller
        4-20mA current loop transmitter
        Fully isolated limit comparator
        Fully isolated 10-bit A/D converter
    Application considerations for an instrumentation lowpass filter
        Description
        Tuning the LTC1062
        LTC1062 clock requirements
        Internal oscillator
        Clock feedthrough
        Single 5V supply operation
        Dynamic range and signal/noise ratio
        Step response and burst response
        LTC1062 shows little aliasing
        Cascading the LTC1062
        Using the LTC1062 to create a’notch
        Comments on capacitor types
        Clock circuits
        Acknowledgement
    Micropower circuits for signal conditioning
        Platinum RTD signal conditioner
        Thermocouple signal conditioner
        Sampled strain gauge signal conditioner
        Strobed operation strain gauge bridge signal conditioner
        Thermistor signal conditioner for current loop application
        Microampere drain wall thermostat
        Freezer alarm
        12-Bit A/D converter
        10-Bit, 100μA A/D converter
        20μs sample-hold
        10kHz voltage-to-frequency converter
        1MHz voltage-to-frequency converter
        Switching regulator
        Post regulated micropower switching regulator
    Thermocouple measurement
        Introduction
        Thermocouples in perspective
        Signal conditioning issues
        Cold junction compensation
        Amplifier selection
        Additional circuit considerations
        Differential thermocouple amplifiers
        Isolated thermocouple amplifiers
        Digital output thermocouple isolator
        Linearization techniques
        References
         
    Take the mystery out of the switched-„capacitor filter
        Introduction
            Overview
            The switched-capacitor filter
        Circuit board layout considerations
        Power supplies
        Input considerations
            Offset voltage nulling
            Slew limiting
            Aliasing
        Filter response
            What kind of filter do I use? Butterworth, Chebyshev, Bessel or Elliptic
        Filter sensitivity
            How stable is my filter?
        Output considerations
            THD and dynamic range
            THD in active RC filters
            Noise in switched-capacitor filters
            Bandpass filters and noise—an illustration
        Clock circuitry
            Jitter
            Clock synchronization with A/D sample clock
            Clock feedthru
        Conclusions
        Bibliography
    Bridge circuits
        Resistance bridges
        Bridge output amplifiers
        DC bridge circuit applications
        Common mode suppression techniques
        Single supply common mode suppression circuits
        Switched-capacitor based instrumentation amplifiers
        Optically coupled switched-capacitor instrumentation amplifier
        Platinum RTD resistance bridge circuits
        Digitally corrected platinum resistance bridge
        Thermistor bridge
        Low power bridge circuits
        Strobed power bridge drive
        Sampled output bridge signal conditioner
        Continuous output sampled bridge signal conditioner
        High resolution continuous output sampled bridge signal conditioner
        AC driven bridge/synchronous demodulator
        AC driven bridge for level transduction
        Time domain bridge
        Bridge oscillator—square wave output
        Quartz stabilized bridge oscillator
        Sine wave output quartz stabilized bridge oscillator
        Wien bridge-based oscillators
        Diode bridge-based 2.5MHz precision rectifier/AC voltmeter
        References
    High speed amplifier techniques
        Preface
        Introduction
        Perspectives on high speed design
        Mr. Murphy's gallery of high speed amplifier problems
        TUTORIAL SECTION
            About Cables, Connectors and Terminations
            About Probes and Probing Techniques
            About Oscilloscopes
            About Ground Planes
            About Bypass Capacitors
            Breadboarding Techniques
            Oscillation
        Applications Section I — Amplifiers
            Fast 12-bit digital-to-analog converter (DAC) amplifier
            2-Channel Video Amplifier
            Simple Video Amplifier
            Loop Through Cable Receivers
            DC stabilization — summing point technique
            DC stabilization — differentially sensed technique
            DC stabilization — servo controlled FET input stage
            DC stabilization — full differential inputs with parallel paths
            DC stabilization — full differential inputs, gain-of-1000 with parallel paths
            High Speed Differential Line Receiver
            Transformer Coupled Amplifier
            Differential Comparator Amplifier with Adjustable Offset
            Differential Comparator Amplifier with Settable Automatic Limiting and Offset
            Photodiode Amplifier
            Fast Photo Integrator
            Fiber Optic Receiver
            40MHz fiber optic receiver with adaptive trigger
            50MHz high accuracy analog multiplier
            Power Booster Stage
            High Power Booster Stage
            Ceramic Bandpass Filters
            Crystal Filter
        Applications Section II — Oscillators
            Sine Wave Output Quartz Stabilized Oscillator
            Sine Wave Output Quartz Stabilized Oscillator with Electronic Gain Control
            DC Tuned 1MHz-10MHz Wien Bridge Oscillator
            Complete AM radio station
        Applications section III — Data conversion
            1Hz–1MHz voltage-controlled sine wave oscillator
            1Hz–10MHz V→F Converter
            8-bit, 100ns sample-hold
            15ns current summing comparator
            50MHz adaptive threshold trigger circuit
            Fast Time-to-Height (Pulsewidth-to-Voltage) Converter
            True RMS wideband voltmeter
        APPLICATIONS SECTION IV — MISCELLANEOUS CIRCUITS
            RF Leveling Loop
            Voltage Controlled Current Source
            High Power Voltage Controlled Current Source
            18ns circuit breaker
        References

                ABC's of probes – Tektronix, Inc
                The vital link in your measurement system
                Why not use a piece of wire?
                Benefits of using probes
                How probes affect your measurements
                Scope Bandwidth at the Probe Tip?
                How ground leads affect measurements
                How probe design affects your measurements
                Tips on using probes
                Introduction:
                Measuring Amplifier Settling Time
                The Oscillation Problem — Frequency Compensation Without Tears
                Measuring Probe-Oscilloscope Response
                An Ultra-Fast High Impedance Probe
                Additional Comments on Breadboarding
                FCC licensing and construction permit applications for commerical AM broadcasting stations
                About Current Feedback
                Current Feedback Basics
                High Frequency Amplifier Evaluation Board
                The contributions of Edsel Murphy to the understanding of the behavior of inanimate objects
                I. Introduction
                II. General Engineering
                III. Mathematics
                IV. Prototyping and Production
                V. Specifying
        References**In some cases where no reference is given, the source material was misplaced during preparation of this paper (another example of Murphy's Law). In accordance with the law, these misplaced documents will turn up on the date of publication of this paper.
    A seven-nanosecond comparator for’single supply operation
        Introduction
        The LT1394 — an overview
            The rogue's gallery of high speed comparator problems
        Tutorial section
            About pulse generators
            About cables, connectors and terminations
            About probes and probing techniques
            About oscilloscopes
            About ground planes
            About bypass capacitors
            Breadboarding techniques
        Applications
            Crystal oscillators
            Switchable output crystal oscillator
            Temperature-compensated crystal oscillator (TXCO)
            Voltage-controlled crystal oscillator (VCXO)
            Voltage-tunable clock skew generator
            Simple 10MHz voltage-to-frequency converter
            Precision 1Hz to 10MHz voltage-to-frequency converter
            Fast, high impedance, variable threshold trigger
            High speed adaptive trigger circuit
            18ns, 500μV sensitivity comparator
            Voltage-controlled delay
            10ns sample-and-hold
            Programmable, sub-nanosecond delayed pulse generator
            Fast pulse stretcher
            20ns response overvoltage protection circuit
        References
         
    Understanding and applying voltage references
        Essential features
        Reference pitfalls
            Current-hungry loads
            “NC” pins
            Board leakage
            Trim-induced temperature drift
            Burn-in
            Board stress
            Temperature-induced noise
        Reference applications
        Conclusion
        For further reading
         
    Instrumentation applications for’a’monolithic’oscillator
        Introduction
            Clock types
            A (very) simple, high performance oscillator
            Platinum RTD digitizer
            Thermistor-to-frequency converter
            Isolated, 3500V breakdown, thermistor-to-frequency converter
            Relative humidity sensor digitizer-hetrodyne based
            Relative humidity sensor digitizer—charge pump based
            Relative humidity sensor digitizer—time domain bridge based
            40nV noise, 0.05μV/°C drift, chopped bipolar amplifier
            45nV noise, 0.05μV/°C drift, chopped FET amplifier
            Clock tunable, filter based sine wave generator
            Clock tunable, memory based sine wave generator
            Clock tunable notch filter
            Clock tunable interval generator with 20×106:1 dynamic range
            8-bit, 80μs, passive input, A/D converter
        References
    Slew rate verification for wideband amplifiers
        Introduction
            Amplifier dynamic response
                LT1818 Short form specifications
            Pulse generator rise time effects on measurement
            Subnanosecond rise time pulse generators
            360ps rise time pulse generator
            Circuit optimization
            Refining slew rate measurement
        References
         
    Instrumentation circuitry using RMS-„to-„DC converters
        Introduction
            Isolated power line monitor
            Fully isolated 2500V breakdown, wideband RMS-to-DC converter
            Low distortion AC line RMS voltage regulator
            X1000 DC stabilized millivolt preamplifier
            Wideband decade ranged ×1000 preamplifier
            Wideband, isolated, quartz crystal RMS current measurement
            AC voltage standard with stable frequency and low distortion
            RMS leveled output random noise generator
            RMS amplitude stabilized level controller
        References
         
        Additional reading
    775 nanovolt noise measurement for’a’low noise voltage reference
        Introduction
        Noise measurement
        Noise measurement circuit performance
        References
         
Section 3
    LT5528 WCDMA ACPR, AltCPR and noise measurements
        Introduction
    Measuring phase and delay errors accurately in I/Q modulators
        Introduction
        Measurements
            First measurement—null out the I/Q modulator image signal with normal signal connections (Figure 41.6)
            Second measurement—null out the I/Q modulator image signal with reversed differential baseband signals to the modulator's differential I-channel inputs (Figure 41.7)
            Third measurement—null out the I/Q modulator image signal after reversing the I and Q inputs to the modulator (Figure 41.8)
            Calculation of phase impairments
        Applying the method
        Conclusion

Subject Index