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RF Filter Design – Basic Filter Types

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Filter Attenuation Profiles

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RF Filter Parameters• Insertion Loss:

• Ripple

• Bandwidth: BW 3dB = fu3dB – fL3dB

• Shape Factor:

• Rejection

( )210 10 1inin

L

PIL log log

P= = − − Γ

min

max

A

A

BWSF

BW=

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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

=

+ + + + =

+

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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.

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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 G

HA j R R C

ωω

= =+ +

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Low-Pass Filter Frequency Response

• Corresponding Phase is:

• Group Delay:

( )g

dt

d

φ ωω

=

( ) ( ){ }( ){ }

1 Im Htan

Re H

ωφ ω

ω−

=

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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

=

+ + + +

= +

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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

= =

+ + +

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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

= =+ + +

+

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Low-Pass Filter Realizations

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Low-Pass Butterworth Filter Coefficients

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Low-Pass Butterworth Filter Attenuation

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Low-Pass Linear-Phase Filter Coefficients

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Chebyshev-Type Filters

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Chebyshev-Type Filters

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Chebyshev-Type Filter Response

Response for 3 dB ripple Chebyshev LPF

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Chebyshev-Type Filter Response

Response for 0.5 dB ripple Chebyshev LPF

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Low-Pass Chebysev Filter Coefficients –3 dB Ripple

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Low-Pass Chebysev Filter Coefficients –0.5 dB Ripple

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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