COMM 704:COMM 704: Communication Systems COMM 704:COMM 704: Communication Systems Lecture 4: Analog

download COMM 704:COMM 704: Communication Systems COMM 704:COMM 704: Communication Systems Lecture 4: Analog

of 24

  • date post

    29-Jun-2020
  • Category

    Documents

  • view

    19
  • download

    0

Embed Size (px)

Transcript of COMM 704:COMM 704: Communication Systems COMM 704:COMM 704: Communication Systems Lecture 4: Analog

  • COMM 704:COMM 704: Communication Systemsy

    Lecture 4: Analog Filters (continued)Lecture 4: Analog Filters (continued)

    Dr Mohamed Abd El GhanyDr. Mohamed Abd El Ghany, Department of Electronics and Electrical Engineering

    Mohamed.abdel-ghany@guc.edu.eg

  • Active Filter: Low-Pass FilterActive Filter: Low Pass Filter

    Sallen Key LPFy

    a

    b

    R RK +=1

    CCRR K

    V

    2121221112

    2

    2121

    1)111( )(

    CCRR S

    CR K

    CRCR S

    CCRR V VsH

    i

    o

    +−+++ ==

    2Dr. Mohamed Abd el Ghany Department of Electronics and Electrical Engineering COMM 704:Communication Systems Winter 2011

  • Active Filter: Low-Pass FilterActive Filter: Low Pass Filter

    Sallen Key LPFy

    G

    Using the standard notation:

    22 )( )(

    o o

    LPF

    wS Q wS

    GsH ++

    =

    1 1

    CCRR

    2121

    1 CCRR

    wo =

    221112

    2121

    111 CR k

    CRCR

    CCRR Q

    −++ =

    3Dr. Mohamed Abd el Ghany Department of Electronics and Electrical Engineering COMM 704:Communication Systems Winter 2011

  • Active Filter: Low-Pass FilterActive Filter: Low Pass Filter

    Sallen Key LPFy

    If no restriction is imposed on the gain K, we have five element values to design LPF circuit. Hence, we are free to make some arbitrary choices as follows:

    Design 1: equal element values In this design, we let C1=C2=1F and R1=R2=R

    Design 2: equal capacitance and equal feedback resistances In this design we chooseC1 C2 1F and R1 R2 R In this design, we choose C1=C2=1F and Ra=Rb=R

    Design 3: moderate-sensitivity Design 4: minimum sensitivityes g 3 ode ate se s t ty design In this design, we choose C1=√3 Q and C2=1F and K=4/3

    Design 4: minimum sensitivity In this design, we choose K=1 and R1=R2=1Ω

    4Dr. Mohamed Abd el Ghany Department of Electronics and Electrical Engineering COMM 704:Communication Systems Winter 2011

  • Active Filter: Low-Pass FilterActive Filter: Low Pass Filter

    Definition of sensitivityy

    The sensitivity of some performance measure y with respect to a network element value x is defined by:

    dx dy

    y xS yx =

    If y is a function of several variable [y=f(x1,x2,….,xn)], then the sensitivity of y with respect to xi is

    d

    i

    iy x dx

    dy y xS

    i = Notes: 2121 y

    x y

    x yy

    x SSS += 2121 / y

    x y

    x yy

    x SSS −=

    5Dr. Mohamed Abd el Ghany Department of Electronics and Electrical Engineering COMM 704:Communication Systems Winter 2011

    xxx

  • Active Filter: Low-Pass FilterActive Filter: Low Pass Filter

    Example:

    Design a fourth-order butterworth low-pass filter using the cascade of two Sallen-key biquads using Design 1 and 2 respectively. Then let wo =2Пx1000 rad/sec and use 0.1 µF capacitors. Th li d t k f ti f th t l filt

    1765367.0 )( 2

    1 1 ++

    = SS

    GsH

    The normalized network function of the two low-pass filters are:

    1765367.0 ++ SS

    1847759.1 )( 2

    2 2 ++

    = SS

    GsH

    6Dr. Mohamed Abd el Ghany Department of Electronics and Electrical Engineering COMM 704:Communication Systems Winter 2011

  • Active Filter: High-Pass FilterActive Filter: High Pass Filter

    First order HPF (using Inverting op-amp configuration) ( g g p p g )

    RsH 1)( 2−=

    SC R 11+

    S

    cwS SKsH +

    −=)(

    1

    2

    R RK =

    CR wc

    1

    1 =

    7Dr. Mohamed Abd el Ghany Department of Electronics and Electrical Engineering COMM 704:Communication Systems Winter 2011

  • Active Filter: High-Pass FilterActive Filter: High Pass Filter

    First order HPF (using Non-Inverting amplifier) ( g g p )

    2

    3 )1( )(

    S R R

    sH +

    +=

    11

    1)(

    CR S

    sH +

    +=

    S

    cwS SKsH +

    =)(

    2

    31 R RK +=

    11

    1 CR

    wc =

    8Dr. Mohamed Abd el Ghany Department of Electronics and Electrical Engineering COMM 704:Communication Systems Winter 2011

  • Active Filter: High-Pass FilterActive Filter: High Pass Filter

    Sallen Key HPFy

    a

    b

    R RK +=1

    2

    )( KSVsH o ==

    2121112212

    2 1)111( )(

    CCRR S

    CR K

    CRCR SV

    sH i +

    − +++

    ==

    9Dr. Mohamed Abd el Ghany Department of Electronics and Electrical Engineering COMM 704:Communication Systems Winter 2011

  • Active Filter: High-Pass FilterActive Filter: High Pass Filter

    Sallen Key HPFy

    2GS

    Using the standard notation:

    22 )( )(

    o o

    HPF

    wS Q wS

    GSsH ++

    =

    1 1

    CCRR

    2121

    1 CCRR

    wo =

    111222

    2121

    111 CR k

    CRCR

    CCRR Q

    −++ =

    10Dr. Mohamed Abd el Ghany Department of Electronics and Electrical Engineering COMM 704:Communication Systems Winter 2011

  • Active Filter: Band-Pass FilterActive Filter: Band Pass Filter

    Sallen Key BPFy

    a

    b

    R RK +=1

    SK

    21321

    21

    12132311

    2

    11

    )1111( )(

    CCRRR RRS

    CR K

    CRCRCR S

    S CR

    V VsH

    i

    o

    ++−++++ ==

    11Dr. Mohamed Abd el Ghany Department of Electronics and Electrical Engineering COMM 704:Communication Systems Winter 2011

  • Active Filter: Band-Pass FilterActive Filter: Band Pass Filter

    Sallen Key BPFy

    )( o SwG

    Using the standard notation:

    22 )(

    )( )(

    o o

    o

    BPF

    wS Q wS

    S Q

    G sH

    ++ =

    RR + 21 RR +

    21321

    21

    CCRRR RRwo

    + =

    12132311

    21321

    1111 CR k

    CRCRCR

    CCRRR Q

    − +++

    =

    12Dr. Mohamed Abd el Ghany Department of Electronics and Electrical Engineering COMM 704:Communication Systems Winter 2011

  • Active Filter: Band-rejection FilterActive Filter: Band rejection Filter

    Sallen Key Band-Rejection Filtery j

    a

    b

    R RK +=1

    2 )1( SK

    22 2

    22 2

    1)24(

    )( )(

    CR S

    RC KS

    CR SK

    V VsH

    i

    o

    + −

    +

    + ==

    13Dr. Mohamed Abd el Ghany Department of Electronics and Electrical Engineering COMM 704:Communication Systems Winter 2011

  • Active Filter: Band-rejection FilterActive Filter: Band rejection Filter

    Sallen Key Band-Rejection Filtery j

    22 )(

    Using the standard notation:

    22

    22

    )(

    )()( o

    o

    o BRF

    wS Q wS

    wSKsH ++

    + =

    1 1 RC

    wo 1

    = K Q

    24 1 −

    =

    14Dr. Mohamed Abd el Ghany Department of Electronics and Electrical Engineering COMM 704:Communication Systems Winter 2011

  • Active Filter: Multiple-Feedback Biquads (MFB)

    • The MFB topology is commonly used in filters that have high Q p gy y g and require a high gain

    MFBMFB

    Multiple Feedback Low-pass

    Multiple Feedback High pass

    Multiple Feedback Band pass

    Multiple Feedback

    band-rejectionLow-pass biquad

    High-pass biquad

    Band-pass biquad

    band-rejection biquad

    15Dr. Mohamed Abd el Ghany Department of Electronics and Electrical Engineering COMM 704:Communication Systems Winter 2011

  • Active Filter: Multiple-Feedback Biquads (MFB)

    Multiple Feedback Low-pass Biquad

    21323211

    2

    2131

    1)111(1

    1

    )(

    CCRR S

    RRRC S

    CCRR V VsH

    i

    o

    ++++ −==

    21323211 CCRRRRRC

    22 )( )(

    o o

    LPF

    wS Q wS

    GsH ++

    =

    2132

    1 CCRR

    wo =

    3

    2

    2

    3

    1

    322

    1 1

    R R

    R R

    R RRC

    CQ ++

    =

    16Dr. Mohamed Abd el Ghany Department of Electronics and Electrical Engineering COMM 704:Communication Systems Winter 2011

  • Active Filter: Multiple-Feedback Biquads (MFB)

    Multiple Feedback High-pass Biquad

    3212

    2

    2

    1

    1)( SCCCS

    S C C

    V VsH

    i

    o

    ++++ −==

    3221322 CCRR S

    CCR Si ++

    3221

    1 CCRR

    wo = 3

    322

    321

    CCR CCC

    Q wo ++=

    17Dr. Mohamed Abd el Ghany Department of Electronics and Electrical Engineering COMM 704:Communication Systems Winter 2011

  • Active Filter: Multiple-Feedback Biquads (MFB)

    Multiple Feedback bandp