for lampang graduating center - te.kmutnb.ac.thmsn/comprehensivelampang.pdf · 1 asst. prof....

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Asst. Prof. Montree Siripruchyanun, D. Eng.

for Lampang Graduating Center

Linear Network Analysis&

Linear Integrated Circuit Analysis and Design

Asst. Prof. Montree Siripruchyanun, D.Eng.

April 4, 2007

Multiple choicesLinear Network Analysis 10 itemsLinear Integrated Circuit Analysis and Design 10 items

Proving solutionsLinear Network Analysis 2 itemsLinear Integrated Circuit Analysis and Design 2 items

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Course outline for Linear Network

Fundamental concepts (Multiple choice)Network elements and Network classifications (Multiple choice)Network Analysis (Solution)Network Functions and their realizability (Multiple choice)Introductory to filters (Multiple choice)Approximation problemsSensitivityPassive Network SynthesisBasic of active network synthesis (Solution)Positive feedback biquad circuitsEtc.

Course outline for Linear ICIntroduction (Multiple choice)Devices (Multiple choice)

DiodeBipolar Junction TransistorField Effect TransistorOperational Amplifier (Op-Amp)Operational Transconductance Amplifier (OTA)

Amplifiers (Solution)Differential and Multistage amplifiersOscillator (Solution)Tuned amplifiersPractical Op-amp considerationsNon-linear Op-amp application

ComparatorSchmitt triggerPrecision rectifier

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Network definitionNetwork classification

Linear/nonlinearCasual /non-casualLumped and Distributed parametersEtc.

Network elementsDiodeFETOp-AmpEtc.

Transfer functions

Network synthesisFrequency scaling Impedance scailngAttenuator

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Technology Trends in IC designLow-voltageLow-powerSmaller chipEtc.

Circuit elements for designOp-ampOTAEtc.

AmplifiersBipolarMOS

OscillatorsWien-bridgePhase-shiftQuadratureLCOTACrystal Etc.

Schmitt trigger

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Proving Network FunctionsNetwork synthesisAmplifier

AvZinZout

Oscillator design

The system model is a diagrammatic relationship between the outputs and inputs

For a single input-output system

Example: for an amplifier

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A system is said to be homogeneous if

A system is said to be additive if

The additive property>> Superposition property

The response of a system to the sum of two arbitrary signals equals the sum of the response of the system to the individual signal

A system is linear if it is both homogeneous and additive

A system is nonlinear if it is not linear

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From circuit

Thus This system is nonlinear

From circuit

This system is linear if and only if Vo=0

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A system is said to be continuous if it is capable of accepting continuous-time signals as inputs and generating continuous-time signals as output. For instance, the previous circuits

A system is said to be discrete if it accepts signals only at discrete times and generate signals only at discrete times. For instance, Digital Computer

Continuous systems are usually modeled using differential equations, whereas the discrete systems are frequently described by the difference equations

A systems is said to be time invariant if a time-shifted input signal will result in a correspondingly time-shifted output signalMathematically, time-invariance can be stated as follows:

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A system is time variant if it is not time invariant

The term causality connotes the existance of a cause-effect relationship. Intuitively, a causal system cannot yield any response until after the excitation is applied

A system is noncausal if it is not causal

A causal is not anticipative

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A lumped elements is an element in which the disturbance initiated at any point is propagated instantaneously at every point in the element

A lumped parameter system comprises only of lumped elements.

In electrical systems this means that the wavelength of the input signal is large compared with the physical dimensions of the elements

Such elements are modeled by ordinary differential equations. Electrical networks are examples of lumped parameter systems.

•A distributed-parameter system is a system that is not a lumped-parameter system.

•It can be represented by a partial differential equation and generally has dimensions that are not small compared with the wavelength of signals interest.

Transmission lines, antenna, and waveguides are examples of distributed-parameter systems

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Example of a lumped-parameter system

Thus, the system is described by a second-order ordinary differential equation

Example of a distributed-parameter system

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Thus, the system is described by a partial differential equation

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A system is said to be instantaneous or memoryless if its response at any time t depends only on the excitation at time t, not only any past or future values of the excitation.

A resistive network and voltage amplifier are typical examples of an instantaneous or memoryless systems

A system that is not instantaneous is said to be dynamical and to have memory

A network is an interconnectioninterconnection of electrical elements such as• Resistors

• Capacitors

• Inductors

• Transformers

• Transistors

• Operational Amplifiers

• Sources

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A lumped element is a element in which its physical dimensions are small compared to the wavelength corresponding to the highest frequency of operation of that element

For a lumped element the instantaneous current entering one terminal is equal to the instantaneous current leaving the other terminal

ResistorsInductorsCapacitorsVoltage sourcesCurrent sources

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An element which can be characterized by a curve in the v-I plane is called a resistor

A resistor is linear if it is characterized by a straight line passing through the origin of the v-I plane

RectificationFrequency multiplicationCurrent and Voltage limitingMany other electronic applications

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The piece-wise linear model of a diode (broken line)

An element which can be characterized by a curve in the v-q plane is called a capacitor

Linear capacitor

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An element which can be characterized by a curve in the I-φ plane is called an inductor

A linear inductor

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A linear inductor

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CX C s

L

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Principal analysis methods: Node and S-domain

Node 1:

1 2 1 3 11

1V V sC V V I

R− + − =

Node 2:

Node 3:

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The nodal matrix representation of the above equations is

Using Cramer’s rule

Which simplifies to

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Example

Observation

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One solution to this set of equation is

• This transfer function is therefor realized using the circuit.

• The technique used for the above synthesis is called the coefficient matching technique

The possible forms of transfer functions are:

• The voltage transfer function: a ratio of one voltage to another voltage

• The current transfer function: a ratio of one current to another current

• The transfer impedance function: a ratio of a voltage to a current

• The transfer admittance function: a ratio of a current to a voltage

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Where

If the numerator and denominator polynomials are factored, an alternate form

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Network functions are ratios of polynomials in s with real coefficients

The product of a complex factor and its conjugate is

Which can be seen to have real coefficients

Further important properties of network functions are obtained restricting the networks to be stablestable

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• Passive networks are stable by their very nature,since they do not contain energy sources that might inject additional energy into the network

• Some active networks contain energy sources that could join forces with the input excitation to make the output increase indefinitely

• A convenient way of determining the stability of the general network function is by considering its response to an impulse function, which is obtained by taking the inverse Laplace transform of the partial fraction expansion of the function

If the network has a simple pole on the real axis,the impulse response due to it will have the form

For p1 positive, the impulse is seen to increase exponentially with time

Network function cannot have poles on the positive real axis

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If the network has a pair of complex conjugate poles at The contribution to the impulse response due to this pair of poles is

Network function cannot have poles in the right half s plane

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The network function H(s) has the following factored form

Where N(s) is the numerator polynomial and the constants associated with the denominator

• S+ai terms represent poles on the negative real axis

• The second terms represent complex conjugate poles in the left half plane

The network functions of all passive networks and all stable active networks

• must be rational functions in s with real coefficient (a)

• may not have poles in the right half s plane

• may not have multiple poles on the jw axis

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Example

consists of finding a function whose loss characteristic lies within the permitted region

It is also desirable to keep the order of the function as low as possible in order to minimize the number of components required in the design

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ButterworthChebyshevBesselThe elliptic (Cauer)

Av

f

Chebyshev

Butterworth

Bessel

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Low-passHigh-passBand-passBand-rejectAmplitude equalizersDelay equalizers

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Other advantages of active RC filters include:

• reduced size and weight, and therefore parasiticsincreased reliability and improved performance• simpler design than for passive filters and canrealise a wider range of functions as well as providing voltage gain• in large quantities, the cost of an IC is less than its passive counterpart

Active RC filters also have some disadvantages• limited bandwidth of active devices limits the highest attainable pole frequency and therefore applications above 100 kHz (passive RLC filters can be used up to 500MHz)• the achievable quality factor is also limited• require power supplies (unlike passive filters)• increased sensitivity to variations in circuit parameters caused by environmental changes compared to passive filters• For many applications, particularly in voice and data communications, the economic and performance advantages of active RC filters far outweigh their disadvantages.

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For example, consider the synthesis of the function

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Gain Enhancement

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Impedance scaling is used to change the element values of the circuit in order to make the circuit practically realizable

Example

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Node 1

Node 2

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Find Order (n)Determine normalized transfer functionDetermine normalized block diagramWrite Normalized circuitFrequency scalingImpedance scalingCompleted circuit

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Asst. Prof. Dr. MONTREE SIRIPRUCHYANUNDept. of Teacher Training in Electrical Engineering

King Mongkut’s Institute of Technology North Bangkok

1929

www.maxim-ic.com/an1768

Bulky, expensive and required high supply voltages.

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IEEE J. Solid-State Circuits, Vol. 32, 12, pp. 2071-2088, 1997

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19061906 19471947

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Intel Pentium II, 1997Clock: 233MHz

Number of transistors: 7.5 MGate Length: 0.35

First integrated circuit (germanium), 1958Jack S. Kilby, Texas Instruments

Contained five components, three types:transistors resistors and capacitors

19581958 19971997

(From: http://www.intel.com)

Number of transistors doubles every 2.3 years(acceleration over the last 4 years: 1.5 years)

42 M transistors

2.25 K transistors

Increase: ~20K

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IEEE Spectrum, July 2003

2.42.22.02.42.01.4Battery power (W)18317417016013090High-perf power (W)0.60.60.91.21.51.8Power supply (V)109-1098-97-86-7Wiring levels

2200180014001100800600Clock rate (MHz)14721408128010241024768Signal pins/chip354308269235170-214170Chip size (mm2)7012841154714-267Mtrans/cm2

355070100130180Feature size (nm)

201420112008200520021999Year

For Cost-Performance MPU (L1 on-chip SRAM cache; 32KB/1999 doubling every two years)

http://www.itrs.net/ntrs/publntrs.nsf

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