ELEC 412 RF & Microwave Engineering Fall 2004 Lecture 13

ELEC 412 - Lecture 13 1

Band-Pass Filter Design Example

Attenuation response of a third-order 3-dB ripple bandpass Chebyshev filter centered at 2.4 GHz. The lower cut-off frequency is

f L

= 2.16 GHz and the upper cut off frequency is 2.64 GHz.

f U

= ELEC 412 - Lecture 13 2

RF/



W Stripline Filters

• Filter components become impractical at frequencies higher than 500 MHz • Can apply the normalized low pass filter tables for lumped parameter filters to stripline filter design • Richards Transformation and Kuroda’s Identities are used to convert lumped parameter filter designs to distributed filters ELEC 412 - Lecture 13 3

Richards Transformation: Lumped to Distributed Circuit Design

• Open- and short-circuit transmission line segments emulate inductive and capacitive behavior of discrete components • Based on:

Z in

    • Set Electrical Length

l

=  /8 so

l

  4

f f o

 4 ELEC 412 - Lecture 13 4

Richards Transformation: Lumped to Distributed Circuit Design

• Richards Transform is:

jX L

 and

jB C

    4  4   

SZ o

  

SY o

• For

l

=  /8,

S

=

j

1 for

f

=

f o

=

f c

ELEC 412 - Lecture 13 5

Richards Transformation: Lumped to Distributed Circuit Design

/

8 at



c jX L L Z o = j



L

/

8 at



c jB C C Z o = 1/(j



C)

ELEC 412 - Lecture 13 6

Unit Elements : UE

• Separation of transmission line elements achieved by using Unit Elements (UEs) • UE electrical length:  =  /4 • UE Characteristic Impedance

Z UE

 

A C B D

 

UE

    

j cos Z UE



sin



jZ UE cos sin

       1 1   2    

j

1 

Z UE



UE

1     ELEC 412 - Lecture 13 7

The Four Kuroda’s Identities

ELEC 412 - Lecture 13 8

Kuroda’s Equivalent Circuit

Short Circuit Series Stub

Z 1 /N l l l Z 1 Z 2

Open Circuit Shunt Stub Unit Element =

l Z 2 /N

Unit Element ELEC 412 - Lecture 13 9

Realizations of Distributed Filters

• Kuroda’s Identities use redundant transmission line sections to achieve practical microwave filter implementations • Physically separates line stubs • Transforms series stubs to shunt stubs or vice versa • Change practical characteristic impedances into realizable ones ELEC 412 - Lecture 13 10

Filter Realization Procedure

• Select normalized filter parameters to meet specifications • Replace

L

’s and

C

’s by 

o

/8 transmission lines • Convert series stubs to shunt stubs using Kuroda’s Identities • Denormalize and select equivalent microstriplines ELEC 412 - Lecture 13 11

Filter Realization Example

• • 5 th order 0.5 dB ripple Chebyshev LPF

g 1

=

g 5

= 1.7058, 2.5408,

g 6

=1.0

g 2

=

g 4

= 1.2296,

g 3

= ELEC 412 - Lecture 13 12

Filter Realization Example

•

Y Y 3 1

=

Y 5

= 1.7058,

Z 2

= 2.5408; and 1/2.5408

Z 1

=

Z 4

=

Z 5

= 1.2296, = 1/1.7058,

Z 3

= ELEC 412 - Lecture 13 13

Filter Realization Example

• Utilizing Unit Elements to convert series stubs to shunt stubs ELEC 412 - Lecture 13 14

Filter Realization Example

• Apply Kuroda’s Identities to eliminate first shunt stub to series stub ELEC 412 - Lecture 13 15

Filter Realization Example

• Deploy second set of UE’s in preparation for converting all series stubs to shunt stubs ELEC 412 - Lecture 13 16

Filter Realization Example

• • Apply Kuroda’s Identities to eliminate all series stubs to shunt stubs

Z 1 = 1/Y 1 =NZ 2

= (1+ =1+(1/0.6304);

Z 2 Z 2 /Z 1

= 1 and )

Z Z 1 2

= 0.6304

ELEC 412 - Lecture 13 17

Filter Realization Example

• Final Implementation ELEC 412 - Lecture 13 18

Filter Realization Example

•

Frequency Response of the Low Pass Filter

ELEC 412 - Lecture 13 19