RF Filter Design – Basic Filter Typesekim/e194rfs01/lec17ek.pdfEEE 194RF_ L17 1 RF Filter Design...

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EEE 194RF_ L17 1 RF Filter Design – Basic Filter Types
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Transcript of RF Filter Design – Basic Filter Typesekim/e194rfs01/lec17ek.pdfEEE 194RF_ L17 1 RF Filter Design...

  • EEE 194RF_ L17 1

    RF Filter Design – Basic Filter Types

  • EEE 194RF_ L17 2

    Filter Attenuation Profiles

  • EEE 194RF_ L17 3

    RF Filter Parameters• Insertion Loss:

    • Ripple

    • Bandwidth: BW 3dB = fu3dB – fL3dB

    • Shape Factor:

    • Rejection

    ( )210 10 1in inL

    PIL log log

    P= = − − Γ

    min

    max

    A

    A

    BWSF

    BW=

  • EEE 194RF_ L17 4

    Low-Pass Filter

    Cascading four ABCD-networks.

    ( )

    1 01 1 1 01 10 1 0 1 1

    11

    11

    G

    L

    G G LL

    L

    A B R RC D j C R

    R R j C R RR

    j CR

    ω

    ω

    ω

    =

    + + + + =

    +

  • EEE 194RF_ L17 5

    RF Filter Parameters

    ( )

    1 01 1 1 01 10 1 0 1 1

    11

    11

    G

    L

    G G LL

    L

    A B R RC D j C R

    R R j C R RR

    j CR

    ω

    ω

    ω

    =

    + + + + =

    +

    Cascading four ABCD-networks.

  • EEE 194RF_ L17 6

    Low-Pass Filter Frequency Response

    • Frequency Response from the ABCD Definitions:

    • So the Transfer Function is Simply:2

    1

    2 0i

    vA

    v ==

    ( ) ( )1 1

    1 GH

    A j R R Cω

    ω= =

    + +

  • EEE 194RF_ L17 7

    Low-Pass Filter Frequency Response

    • Corresponding Phase is:

    • Group Delay:

    ( )g

    dt

    d

    φ ωω

    =

    ( ) ( ){ }( ){ }1 Im Htan

    Re H

    ωφ ω

    ω−

    =

  • EEE 194RF_ L17 8

    High-Pass Filter

    ( )

    1 01 01 1

    11 110 1 0 1

    1 11

    1 11

    G

    L

    G G LL

    L

    A B R RC D

    Rj L

    R R R Rj L R

    j L R

    ω

    ω

    ω

    =

    + + + +

    = +

  • EEE 194RF_ L17 9

    High-Pass Filter Frequency Response• Frequency Response from the ABCD

    Definitions:

    • So the Transfer Function is Simply:2

    1

    2 0i

    vA

    v ==

    ( )( )

    1 11 1

    1 GL

    HA

    R Rj L R

    ω

    ω

    = =

    + + +

  • EEE 194RF_ L17 10

    High-Pass Filter Frequency Response

    • For ω → ∞:

    • Inductive Influence Can Be Neglected

    ( )2 1

    1

    L

    GG L G

    L

    V RR RV R R R

    R

    = =+ + +

    +

  • EEE 194RF_ L17 11

    Low-Pass Filter Realizations

  • EEE 194RF_ L17 12

    Low-Pass Butterworth Filter Coefficients

  • EEE 194RF_ L17 13

    Low-Pass Butterworth Filter Attenuation

  • EEE 194RF_ L17 14

    Low-Pass Linear-Phase Filter Coefficients

  • EEE 194RF_ L17 15

    Chebyshev-Type Filters

  • EEE 194RF_ L17 16

    Chebyshev-Type Filters

  • EEE 194RF_ L17 17

    Chebyshev-Type Filter Response

    Response for 3 dB ripple Chebyshev LPF

  • EEE 194RF_ L17 18

    Chebyshev-Type Filter Response

    Response for 0.5 dB ripple Chebyshev LPF

  • EEE 194RF_ L17 19

    Low-Pass Chebysev Filter Coefficients –3 dB Ripple

  • EEE 194RF_ L17 20

    Low-Pass Chebysev Filter Coefficients –0.5 dB Ripple

  • EEE 194RF_ L17 21

    Standard Low-Pass Filter Design

    • The normalized inductors and capacitors (g1, g2 , ... , gN ) are denormalized using:

    and

    where Cn , Ln , are the gn normalized values from the tables

    2n

    C

    CC

    f R=

    π 2n

    C

    L RL

    f=

    π