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Analog Circuits K-Notes

Dec 17, 2015



Ajay Varma

knotes by goyal
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  • 1

    Contents Manual for K-Notes ................................................................................. 2

    Diodes ..................................................................................................... 3

    Transistor Biasing .................................................................................. 11

    Transistor Amplifier .............................................................................. 19

    Feedback Amplifiers .............................................................................. 25

    Operational Amplifiers (OP-AMP) ......................................................... 29

    2015 Kreatryx. All Rights Reserved.

  • 2

    Manual for K-Notes

    Why K-Notes?

    Towards the end of preparation, a student has lost the time to revise all the chapters

    from his / her class notes / standard text books. This is the reason why K-Notes is

    specifically intended for Quick Revision and should not be considered as comprehensive

    study material.

    What are K-Notes?

    A 40 page or less notebook for each subject which contains all concepts covered in GATE

    Curriculum in a concise manner to aid a student in final stages of his/her preparation. It

    is highly useful for both the students as well as working professionals who are preparing

    for GATE as it comes handy while traveling long distances.

    When do I start using K-Notes?

    It is highly recommended to use K-Notes in the last 2 months before GATE Exam

    (November end onwards).

    How do I use K-Notes?

    Once you finish the entire K-Notes for a particular subject, you should practice the

    respective Subject Test / Mixed Question Bag containing questions from all the Chapters

    to make best use of it.

    2015 Kreatryx. All Rights Reserved.

  • 3

    Diodes Representation:

    A: Anode K : Cathode

    The voltage at which the charged particles start crossing the junction is called as cut in voltage

    or Threshold voltage.

    It is represented as AKV V .

    When AKV V , depletion region exists and no charge carriers cross the junction, therefore

    I 0D

    When AKV V , number of charged particles crossing the junction increases & the current

    through the diode increase, non linearly or exponentially.

    Diode in the condition is said to be forward biased.


    TD S


    VI I e 1


    = reverse saturation current


    = Thermal voltage = KT


    K = Boltzmann constant

    T = Temp. in k

    q = charge of one e


    = 26mv at room temperature

    = intrinsic factor

    When V 0AK

    , diode is said to be in reverse biased condition & no majority carriers cross the

    depletion region, hence I 0D

  • 4

    Characteristics of Diode

    Equivalent circuit of diode

    Forward Bias

    Reverse Bias

    Diode Resistance

    1) State or DC Resistance


    DC ID

  • 5

    2) Dynamic or AC Resistance

    dV VD TR

    AC dI ID D

    Diode Applications


    It is a transmission circuit which transmits a part of i/p voltage either above the reference

    voltage or below the reference voltage or b/w the two reference voltages.

    Series Clippers

    i) Positive Clippers

    V V sin ti m

    : When V Vi R => V V

    O R

    V Vm R

    When V Vi R => V V

    O i

    ii) Negative Clipper

    V V sin ti m

    : When V Vi R => V V

    o R

    V Vm R

    When V Vi R => V V

    o i

  • 6

    Shunt Clipper

    i) Positive Clipper

    When V V , D is ONi R

    V Vo R

    V V , D is OFFi R


    V Vo i

    ii) Negative Clipper

    V V , D is ONi R


    V Vo R

    V V ,When D is OFF

    i R

    V Vo i

    Two level Clipper

    When V V , D is OFF & D is ONi 2 1 2

    V V0 2

    When V V & V V , D is OFF & D is OFF

    i 2 i 1 2 1

    V Vo i

    When V V , D is OFF D is ON

    i 1 2 l

    V Vo 1

  • 7


    These circuits are used to shift the signal either up words or down words.

    Negative Clampers

    When V 0R

    +ve peak is shifted to 0

    -ve peak is shifted to 2Vm

    When V 0R

    +ve peak is shifted to VR

    -ve peak is shifted to -2 V Vm R

    Positive Clampers

  • 8

    When V 0R

    -ve peak is shifted to 0

    +ve peak is shifted to 2Vm

    When V 0R

    -Ve peak is shifted to VR

    +ve peak is shifted to 2V Vm R


    It converts AC signal into pulsating DC.

    1) Half wave rectifier

    During positive half wave cycle

    RLV V sin t

    0 m R Rf L

    Rf = diode resistance

    During negative half cycle

    V 00


    0 avg

    R4 L 100%

    2 R RLf


    0 2RMS

    Form Factor = VRMS


    Ripple factor = 2FF 1

    PIV Vm

  • 9

    Bridge full wave rectifier

    When +ve half wave cycle


    LV V to R 2R

    L f

    When ve half wave cycle


    LV V to R 2R

    L f


    mVo avg

    8 1

    100%2 R

    f1 2R



    o RMS 2

    FF2 2

    PIV Vm

    Zener Diode

    A heavily doped a si diode which has sharp breakdown characteristics is called Zener Diode.

    When Zener Diode is forward biased, it acts as a normal PN junction diode.

    For an ideal zener diode, voltage across diode remains constant in breakdown region.

    If Iz(min)

    is not given, then consider I 0z(min)

  • 10

    Voltage Regulator

    Regulators maintains constant output voltage irrespective of input voltage variation.

    Zener must operate in breakdown region so V Vi z

    I I Iz L


    L RL

    I I Imax Lz max

    I I Imin Lz min

    I I I

    Lz max max

    I I Imin Lz min

  • 11

    Transistor Biasing Bipolar Junction Transistor

    Current conduction due to both e- & holes

    It is a current controlled current source.

    NPN Transistor

    PNP Transistor

    Region of Operation

    Junctions Region of operations Applications

    i) J RBE cut off Switch

    J RBC

    ii) J FBE active amplifier

    J RBC

    iii) J FBE saturation Switch

    J FBC

    iv) J RBE reverse active Attenuation

    J FBC

  • 12

    Current gain () (common base)

    I I IC nc o


    : injected majority carrier current in collector



    I I I 1B o BI ; I IC E o1 1 1

    Current gain (common emitter)

    I I 1 Ic B o

    ;1 1

    These relations are valid for active region of operations.

    Characteristics of BJT

    Common Base characteristics

    input V , IBE E

    output V , ICB C

    Input characteristics

    V vs IBE E

    when V constantCB

  • 13

    Output characteristics

    Common emitter characteristics

    inputs V , IBE B

    outputs V , ICE C

    Input characteristics

  • 14

    Output characteristics

    Transistor Biasing

    1) Fixed Bias method

    V I R V 0cc B B BE

    V Vcc BEI

    B RB

    Assuming active region of operation

    I Ic B

    V V I RCE CC C C



    V V V Active RegionCE CCCE sat

    If not ; then saturation region

    For saturation region ,

    V VCE CE sat

    V VCC CE sat

    IC R


    In saturation region , ICI


  • 15

    2) Feedback Resistor Bias Method

    By KVL

    V I I R I R V I R 0cc c B c B B BE E E

    V I I R I R V I I R 0cc c B c B B BE C B B

    Assuming active region

    I Ic B

    V Vcc BEI ; I I

    B c BR 1 R R

    B C E

    V V I I R RCE CC C B C E

    3) Voltage divider bias or self-bias

    By thevenins theorem across R2

    R2V V

    TH CC R R1 2

    R R2 1R

    TH R R1 2

    Apply KVL

    V V I R I I RTH BE B TH B C E Assuming active region I I

    C B


    B R 1 RTH E

    V V I R I RCE CC C C E E

  • 16

    FET Biasing


    When VGS

    is negative, depletion layer is created between two P region and that pinches the

    channel between drain & source.

    The voltage at which drain current is reduce to zero is called as pinch off voltage.

    Transfer characteristics of JFET is inverted parabola

    2VGSI I 1


    When V 0, I IGS D DSS


    V V , I 0GS DGS OFF

    Pinch of voltage,

    V Vp GS OFF

    For a N channel JFET, pinch off voltage is always positive

    V 0 & V 0p GS

  • 17

    JFET Parameters

    1) Drain Resistance


    d IDS

    It is very high, of the order of M .

    2) Trans conductance

    I dID Dg

    m V dVGS GS

    2VGSI I 1


    2I VdIDSS GSD g 1


    3) Amplification factor

    VDS g r

    m dVGS

    MOSFET (Metal Oxide Semi-conductor FET)

  • 18

    Enhancement Type MOSFET

    No physical channel between source & drain

    To induce a channel Gate source voltage is applied.

    Depletion MOSFET

    Physical channel present between source & drain.

    Types of MOSFET

    Operating characteristics

    1. For n channel MOSFET

    I 0 for V V cut off regionD GS T

    2VW DSI C V V V

    D n ox GS T DSL 2

    (linear region)

    V V and V V VGS T DS GS T

    2V VW GS T

    I CD n ox L 2

    (saturation region)

    V V and V V VGS T DS GS T

  • 19

    2. For p channel MOSFET

    I 0 for V VD GS T

    (cut off region)

    2VW DSI C V V V

    D n ox GS T DSL 2

    (linear region)

    V V and V V VGS T DS GS T

    2V VW GS T

    I CD n ox L 2

    (saturation region)

    V V and V V VGS T DS GS T

    Transistor Amplifier Small signal analysis for BJT

    h parameter model of BJT

    V h I h V1 i 1 r 2

    I h I h V2 1 o 2f

    current gain, I2A

    I I1

    h RLfA

    I 1 h Ro L

    Input Impedance, V1Z h h A R

    i i r I LII

  • 20

    Voltage gain, A R

    I LAV Z


    Output impedance, 1

    Zo h h

    rfho h R

    i s

    Common Emitter (CE) Amplifier

    Small signal model

    Voltage gain h eV

    o fA R Rv c LV h e

    i i

  • 21

    High frequency Analysis of BST


    = base spreading resistance.


    = input resistance.


    = feedback resistance.


    = output resistance.


    = diffraction capacitance.


    = Transition capacitance.


    = Transconductance.

    Hybrid - parameters

    1) Ic KTQ

    g ; Vm TV q




    = dc bias point collector current.

    2) hfer

    b'e gm

  • 22

    High Frequency Model


    = open circuited.

    Low Frequency Model

  • 23

    Voltage gain as frequency

    Low Frequency Range

    External capacitor C and CE C

    are short circuited.

    Internal capacitor C and Cb'c b'e

    are open circuited.

    Circuit becomes like.

    = acts as high pass filter.

  • 24

    High frequency range

    External capacitors C ,C and Cb c E

    are short circuited.


    is open circuited.

    Equivalent circuit behaves as a low pass filter with cut-off frequency fL.

    Mid band range

    All internal and external capacitance are neglected, so gain is independent of frequency.

    FET Small Signal parameters

    Trans conductance, IDg

    m VGS

    In non saturation region

    I WDg C .V

    m n ox DSV LGS

    In saturation region

    Wg C V Vms n ox GS TL

    Small Signal equivalent circuit

  • 25

    For low frequency

    For high frequency

    Feedback Amplifiers Ideal Amplifier


    Z 0o

    Positive feedback : V V Vi s f

    Negative Feedback : V V Vi s f

    For negative feedback, V Ao

    V 1 As

    For positive feedback, V Ao

    V 1 As

    Positive feedback is used for unstable system like oscillators.

  • 26

    Effects of Negative Feedback

    i) Sensitivity

    Without feedback = A


    With feedback = A



    A 1 Af

    A 1 A Af

    ii) Input Impedance

    Without feedback = Zi

    With feedback = Zif

    Z Z 1 Aiif

    iii) Output impedance

    Without feedback = Zo

    With feedback = Zof

    Z Z 1 Aoof

    Negative feedback also leads to increase in band width


    Topologies of Negative feedback

    Output Input









  • 27

    1) Voltage Series Topologies

    V Vof

    It is called as series shunt feedback or voltage - voltage feedback.

    In this case, input impedance increases & output impedance decreases.

    2) Voltage shunt topologies

    I Vof

    = Trans conductance

    It is called as shunt-shunt or voltage current feedback.

    3) Current series Topologies

    V Iof

    = resistance

    It is called as shunt shunt or voltage current feedback.

    4) Current shunt Topologies

    I Iof

    It is also called as shunt series or current current feedback.

  • 28

    Circuit Topologies

    1) Voltage series

    2) Voltage shunt

    3) Current series

  • 29

    4) Current shunt

    Operational Amplifiers (OP-AMP) + Non inverting terminal

    - inverting terminal

    Parameters of OPAMP

    1) Input offset voltage

    Voltage applied between input terminals of OP AMP to null or zero the output.

    2) Input offset current

    Difference between current into inverting and non inverting terminals of OP AMP.

    3) Input Bias Current

    Average of current entering the input terminals of OP AMP.

    4) Common mode Rejection Ratio (CMRR)

    Defined as ratio of differential voltage gain Ad

    to common mode gain Acm .




  • 30

    5) Slew Rate

    Maximum rate of change of output voltage per unit time under large signal conditions.


    oSR V smaxdt

    Concept of Virtual ground

    In an OP AMP with negative feedback, the potential at non inserting terminals is same as the

    potential at inverting terminal.

    Applications of OP AMP

    1) Inverting Amplifier

    RfV V

    o inR1

    2) Inverting Summer

    V V Va b cV R

    o f R R Ra b c

    3) Non inverting Amplifier

    RfV 1 V

    o inR1

  • 31

    4) Non inverting summer

    If R R R Ra b c

    R R RV V V2 2 2a b cV1 R R RR R R

    2 2 2

    V V Va b c

    V1 3

    V V VRa b cfV 1

    o R 31

    5) Differential Amplifier

    By Super position

    R R3fV 1 V

    ob bR R R1 2 3

    RfV V

    oa aR1

    V V Vo oa ob

    6) Integrator

    t1V V dco inoRC

  • 32

    7) Differentiator

    dVinV RC

    o dt

    8) Voltage to current converter


    L R

    9) Current to voltage Converter

    V R Iout p IN

  • 33

    10) Butter worth Low Pass Filter

    R Vf inV 1

    o R 1 j2 fRC1

    AVo f

    Vfin 1 jfH

    R 1fA 1 ; fR Hf 2 RC1

    11) Butter worth High Pass Filter

    RV j2 fRco f1V R 1 j2 fRCin 1



    f1 jfL

    RfA 1

    f R1

    1fL 2 RC

  • 34

    12) Active Half wave rectifier

    In this circuit, diode voltage drop between

    input & output is not VD

    but rather VD


    where A = open loop gain of OP AMP.

    V Vin o

    13) Active Full wave Rectifier

    This circuit provides full wave rectification with a gain of RR1


    V Vm mR


  • 35

    14) Active Clipper

    V V , Diode conducts and V VIN R o

    And when V VIN R

    Diode is OFF

    V Vo IN

    15) Active Clamper

    V V Vo IN p


    = peak value of VIN

  • 36

    16) Comparators

  • 37

    17) Schmitt Trigger

    Inverting Schmitt Trigger

    When output is V ,then V Vsat satref

    When output is V ,then V Vsat satref

    When R


    R R1 2

    Upper triggering point utp Vsat

    Lower triggering point Ltp Vsat

    Hystersis voltage = UTP LTP 2 Vsat


    1 2

    RUTP V V

    sat RR R


    1 2

    RLTP V V

    sat RR R

  • 38

    Non Inverting Schmitt Trigger

    Upper trigger Point R

    2UTP VsatR


    , Lower triggering point R

    2LTP VsatR





    Hysteric voltage = UTP LTP 2 Vsat

    18) Relaxation Oscillator

  • 39


    R R1 2

    1T 2RCln


    1 1f

    T 12RCln


    555 Timer

    Pin Diagram

  • 40

    Bistable multi vibrator acts as a FF.

    Monostable Multi vibrator produces pulse output.

    Bistable Multi vibrator acts as free running oscillator.

    A stable Multi vibrator

    T 0.69 R R cc 1 2

    T 0.69R cd 2

    T T T 0.69 R 2R Cc d 1 2

    1 1f

    T 0.69 R 2R C1 2

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