lec 1 introduction frequencty response

7/27/2019 Lec 1 Introduction Frequencty Response

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EE 204

Analog Electronics II

Frequency Response


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EE 204 Analog Electronics II

Frequency Response BJT/MOSFET

Differential amplifiers, Multistage amplifiers

Feedback amplifiers and their configurations, feedback

topologies, loop gain, stability using Bode plot,

frequency compensation

Output stages and power amplifiers, classA amplifiers,

class-B amplifiers, class-AB amplifiers, Biasing, IC

power amplifier, MOS power transistors.


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3

MOS Field-EffectTransistors (MOSFETs)

Small Signal Equivalent Circuit Models S-domain analysis, Bode plots,

Amplifier Transfer Function and frequency response

Low and High frequency response of common source and commonemitter amplifiers, Millers theorem.


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4

Bipolar JunctionTransistors (BJTs)

Small Signal Equivalent Circuit Models S-domain analysis, Bodeplots, Amplifier Transfer Function and frequency response

Low and High frequency response of common source andcommon emitter amplifiers, Millers theorem.


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5

Single-Stage Integrated-Circuit Amplifiers

Frequency Response of Common Gate, Common Base and Cascodeconfiguration.

Frequency Response of Emitter & Source Followers


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Frequency Response of Amplifiers

Input signal to an amplifier is expressed as

the sum of sinusoidal signals.

Characterization of amplifier performance

is known as the amplifierfrequency

Response.


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Frequency Response

The frequency response of a circuit is the variation in its behaviorwith change in signal frequency.

The frequency response of amplifier circuits is considered by usingtheirtransfer functions

Systematic way of obtaining the frequency response is to us Bodeplots

Keep the amplitude of the sinusoidal source constant and vary thefrequency, to obtain the circuits f requency respon se.

The frequency response is regarded as a complete description of

the sinusoidal steady-state behaviorof a circuit as a function offrequency.

Achieve important concepts such as mid-band gain, cutoff frequencyand bandwidth and unity gain-bandwidth Product.


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Define bandwidth, cutof f f requency, and geometr ic centerfrequency, and identify each on a frequency-response curve.

Calculate any two of the following values, given the other two: Geometric centerfrequency, orbandwidth, fL, fH.

Describe the decadeand octavefrequency multipliers.

Compare and contrast the Bode plotwith the frequency-response curve.

Perform a complete low-frequency analysis of a BJT amplifier.

Discuss the concept of gain roll-offand calculate its effect onvoltage gain at a given operating frequency.

Explain why BJT internal capacitances are not considered inlow-frequency analyses.

Objectives : Frequency Response


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Objectives : Frequency Response

Calculate the Miller input and output capacitance values

for a BJT amplifier.

Perform a complete high-frequency analysis of a BJTamplifier.

Compare high-frequency roll-off rates to low-frequencyroll-off rates.

Perform the low-frequency-response analysis of an FETamplifier.

Perform the high-frequency-response analysis of an FETamplifier.

Describe and analyze the frequency response of amultistage amplifier/DA.


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Frequency Response

Centre Frequency

fo = fLfH

fo


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Decible

In communications systems, gain is

measured in bels. Historically, the bel isused to measure the ratio of two levels ofpower or power gain G; that is,

G=Number of bels=log10P2/P1 G=Number of Decibel (dB)=10 log10

P2/P

Alternatively, the gain G can be expressedin terms of voltage or current ratio

GdB=20log10V2/V1


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Bode Plot

Bode plots use a logarithmicscale for the

frequency axis and a linearscale in eachof the separate plots ofmagnitude and

phase.

Bode plots are semilog plots of themagnitude (in decibels) and phase (indegrees) of a transfer function versus

frequency.

B d Pl t U d t E ti t Z


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Bode Plot Used to Estimate Zeros

& Poles


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Measuring of Frequency Response of

a linear Amplifier

Input signal vi=Visint Output Signal vo=Vosin(t+) Signals are characterized by

Amplitude, Frequency and Phase

Transfer Function Magnitude of Amplifier Gain

Ratio of the amplitude of output sinusoid (Vo) to the amplitudeof the input sinusoid (Vi) at the input frequency ()

Gain |T()|= Vo/Vi

Graph of gain magnitude |T()| verses frequency - Bode Plot

Phase Angle

The phase of the amplitude transmission T() at the inputfrequency

Phase Angle


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Amplifier Bandwidth

Constant gain between L& H

Lowergain belowL& above H

Amplifier Bandwidth

Band over which the gain of amplifier is almostconstant to within a certain number of decibel (3 dB).

3 dB frequency is also known as Cornerfrequency orBreak frequency

Designing an amplifier Its bandwidth must coincide with the spectrum of the

signal it is required to amplify otherwise, amplifierwould distort the frequency spectrum with differentcomponents amplified by different amount.


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Evaluating the Frequency Response of Amplifier

Analyze the amplifier equivalent circuit model

(Small Signal Model) taking into account allreactive components.

Represent all reactive components by their

reactancein complex frequency variables sC to 1/sC

Perform analysis to obtain the transfer function

T(s) = V0(s)/Vi(s)

Subsequently replaces into j to determine

the network transfer function T (j)


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Amplifier Transfer Function

Amplifier Types

Direct Coupled

Capacitively Coupled

Difference Gain of the ac amplifierfalls offat low and high

frequencies

Amplifier gain is constant over a wide range offrequencies, called Mid-band All capacitance (coupling, bypass and transistor

internal capacitance) are neglected


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Frequency Response dc & ac

Amplifier

DIRECT COUPLED Amplifier CAPACITIVELY Amplifier

M i d 3 D G h


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Magnitude 3-D Graph


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Single Time constant (STC) Network

STC is the network that can be reduced toone reactive component and one resistor

Time constant of an STC network (RC)is = CR

Categories High Pass

Low-Pass


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Classification of STC circuit

Low Pass (type)

High Pass (type)

Rules for finding the type of STC circuitTime at Replace Circuit

BLP if

Circuit is

HP if

= 0 C by o.cL by s.c

Outputinfinite

Output iszero

= C by s.c

L by o.c

Output is

zero

Output is

finite


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Low Frequency Response


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M it d f STC t k Hi h t


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Magnitude of STC networks High-pass type.


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High-Pass Filter

Zero of the Transfer Function

Vo(s)/Vi(s) = 0

Pole of the Transfer Function

Vo(s)/Vi(s) =

1

11

1

1||

sCR

R

sCR

2121

212121 ||

110

RRCRR

RRCsRsCRRR

p

1

2121

1

1212

110

1||

sCR

RsCRRR

sCR

RR

sCRR

11

1

0 CRssCR z

p

z

i

o

s

sk

sCRR

R

sV

sV

1||)(

)(

12

2


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High-Pass Filter


Vo(s)/Vi(s) = 0


Vo(s)/Vi(s) =

2121

2121

||

110||1

RRC

RR

RRC

sRsCR p

1

1

101

CRssCR z

2121

12

1

1

2

2

12

2 1

1

1||

)(

)(

RsCRRR

sCRR

sCR

R

R

R

sCRR

R

sV

sV

i

o

21

1

21

2

2121

12

||1

11

)(

)(

RRsC

sCR

RR

R

RsCRRR

sCRR

sV

sV

i

o

21

1

21

2

||1

1

)(

)(

RRsC

sCR

RR

R

sV

sV

i

o


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Procedure

First reduce the excitation to zero Voltage independent replaced by a short

circuit

Current source replaced by a open circuit

Grab hold the two terminals of thereactive component

Find the equivalent resistance Req seenby the reactive component

Time constant = CReq or L/Req

Rapid Evaluation


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High Frequency Response


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STC --- Low-Pass Filter


Vo(s)/Vi(s) = 0


Vo(s)/Vi(s) =

Network poles or natural modes,are independent of the excitation

zssCR 11

RC

ssCR p1

01

Magnitude response of STC networks of the low-pass type


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Magnitude response of STC networks of the low-pass type.


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Low-Pass Filter

121

2

1

1

1||

1||

)(

)(

p

Z

i

o

s

s

k

sCRR

sCR

sV

sV


Vo(s)/Vi(s) = 0


Vo(s)/Vi(s) =

2

22

10

1||

sCR

R

sCR

2121

212121

||

110

RRC

RR

RR

C

sRsCRRR p

2

2121

2

2121

110

1||

sCR

RsCRRR

sCR

RR

sCRR

zssCR

11


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Low-Pass Filter

p

i

o

i

o

i

o

sRR

R

sV

sV

RRsCRRR

RR

RRRsCRRR

RsVsV

sCRR

R

sCRR

sCRR

sCR

sV

sV

1

1

)(

)(

)||(11

1

1

)()(

1

1

1||

1||

)(

)(

21

2

2121

2

21

21

2121

2

2

21

2

2

21

2

)RC(R

1

1

1

)RC(R

1

CR

1

,0@

0@cctshortasactsCapacitoras

0@

2121

2

)(

)(

21eq

p

)(p

z

)(z

21

2

)(

)(

RRR

s

s

kV

V

for CFind RVFind

VFind

RRR

kV

V

CapacitorcctopenBykFind

p

z

si

so

eqsi

so

si

so

121

2

11

1||

1||

)()(

pi

o

sk

sCRRsC

R

sVsV

Low Pass Filter


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Low-Pass Filter

p

z

i

o

s

s

k

RRsC

sCR

RR

R

sCRR

sCR

sV

sVsT

1

1

)(1

1

1

1

)(

)()(

21

2

21

2

21

2

Find k k = Vo(s)/Vi(s) while C is short circuited

Z while Vo(s)=0 s = - 1/CR2

pwhile V

i(s)=0 s = - 1/C(R

1+R

2)

Frequency Response


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Frequency Response

Rad/sec

0 10 100 1k 10k 100k 1M 10M .. 100G

1000G

XC1

100k 10K 1K 100 10 1 0.1 ..

XC2

1014 1013 1012 1011 1010 1G 100M .. 10K 1KVout 0 0.9 4.5 8.0 9.0 9.0 9.0 9.0 9.0 8.0 4.7


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Frequency Response


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T B d Pl t D i ti


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True Bode Plot Deviations

f/f0(/0)Magnitud

e error

dB

Phase

error

degrees

0.1 0.04 + 5.7

0.5 1 - 4.0

1 3 0

2 1 + 4.0

10 0.04 - 5.7

Magnitude response

|A| =20 log

Phase Response

=

Magnitude response|A| =20 log

Phase Response

=

High Pass

Low Pass


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Notations

Voltage & Current are function of

Frequency

Symbols used are uppercase letter with

lowercase subscripts ( Vgs , Ib)


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Internal Capacitance

BJT


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BJT Internal Capacitances

Effect ofcapacitances was neglected

Actual BJT exhibit charge storagephenomena that limit speed and frequency

of its operation

Frequency dependence are amplifier gain

and the time delays for BJT being used asa switch or logic inverter.


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Cross-section of an npn BJT.

Small Signal Model


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49

Small Signal Model


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High Frequency Hybrid Model

C = EBJ Capacitance Range

a few Pico-Farads to a few tens of Pico-Farads

C = CBJ Capacitance

Range

a Fraction of Pico-Farad a few Pico Farads


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rx Resistance of silicon material of the

base region between the Base terminal

and a fictitious internal base terminal

Value of is a few hundred ohms.

rx


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Internal Capacitance - Included

The gain of every MOSFET amplifierfalls

offat some high frequency

Exhibit finite nonzero propagation delay

Capacitance

Gate capacitance COX

Gate electrode

forms a parallel plate capacitance with the

channel, with the silicon oxide layer as

dielectric


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I l C i MOSFET


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Internal Capacitance : MOSFET

Four terminal capacitance G,D,S,B

Cgs, Cgd, Cgb, Csb, Cdb

MOSFET Internal Capacitances


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MOSFET Internal Capacitances

High Frequency Model

High-frequency equivalent circuit model for the MOSFET.


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Normally Body is connected with the Source

Cdb is added to the load capacitance

Common-Source amplifier


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Common-Source amplifier

Cgs = 4.0pF

Cgd = 1.0pFCds = 1.0pF

Frequency Response @10 Rad/sec


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Frequency Response @10 Rad/sec

ForLow Frequency analysis

Internal Capacitors are open cicuited

Low-frequency response of a CS amplifier


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q y p p


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Frequency Response @10 G Rad/sec


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Frequency Response @10 G Rad/sec

ForHigh Frequency analysis

External Capacitors are short cicuited

Normalized high-frequency response of the


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g q y p

amplifier

Capacitively coupled common-source amplifier


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p y p p

Frequency Response : CE with RE


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Frequency Response : CE with RE


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25 ohm

/gm40 ohm


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Frequency Response : CE

Avoid External Capacitors :CE


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Avoid External Capacitors :CE

Cc1 Blocking / Coupling CapacitorBlocks DC at node B from effecting the signal source cct.

Use constant current source or two power supplies Biasing TechniqueDC components in signal source

The circuit should be in-sensitive to DC components ------Responds to differential signal input

Cc2 Blocking / Coupling CapacitorBlocks DC at node C from effecting the load

Output should have NO DC Components

By-pass capacitorKeeps Emitter at signal ground

Ensure that emitter remains at signal ground

Direct Coupled Amplifier : DA


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Direct Coupled Amplifier : DA

Amplifiers being studied are intended for fabrication using IC

technology

Don't employ Coupling/By-pass capacitors

IC cascade amplifier are directly coupled. Thus do not utilizelarge coupling capacitor

Gain remains constant at its mid-band valueAM down tozero frequency

No gain reduction at low frequency.

Gain falls off at high frequency due to internal capacitance

lec 1 introduction frequencty response

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