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EEE 194RF_L19 1

Band-Pass Filter Design Example

Attenuation response

of a third-order 3-dBripple bandpassChebyshev filter

centered at 2.4 GHz.

The lower cut-off

frequency isfL = 2.16

GHz and the upper cut-off frequency isf

U=

2.64 GHz.

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EEE 194RF_L19 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 Kurodas

Identities are used to convert lumpedparameter filter designs to distributed filters

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EEE 194RF_L19 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:

Set Electrical Length l = /8 so( ) ( )in o o Z jZ tan l jZ tan = =

4 4oflf

= = =

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EEE 194RF_L19 4

Richards Transformation:

Lumped to Distributed Circuit Design Richards Transform is:

and

For l = /8, S =j1 forf=fo = fc

4 L o o jX j L jZ tan SZ

= = =

4C o o jB j C jY tan SY

= = =

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EEE 194RF_L19 5

Richards Transformation:

Lumped to Distributed Circuit Design

jXL

jBC

L

C

/ 8 atc

/ 8 atc

Zo

= 1/(j C)

Zo= j L

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EEE 194RF_L19 6

Unit Elements : UE

Separation of transmission line elements

achieved by using Unit Elements (UEs)

UE electrical length: = /4

UE Characteristic ImpedanceZUE

2

11

11

UE UE

UEUE UE

cos jZ sin j Z A B

j jsin cosC DZ Z

= = +

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EEE 194RF_L19 7

The Four Kurodas Identities

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EEE 194RF_L19 8

Kurodas Equivalent Circuit

=

l

ll

l

Z2

Z1

Z1/N

Z2/N

Short CircuitSeries Stub

Open CircuitShunt Stub

Unit Element Unit Element

} }

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EEE 194RF_L19 9

Realizations of Distributed Filters

Kurodas 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 impedancesinto realizable ones

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EEE 194RF_L19 10

Filter Realization Procedure

Select normalized filter parameters to meet

specifications

ReplaceLs and Cs by o

/8 transmission

lines

Convert series stubs to shunt stubs using

Kurodas Identities

Denormalize and select equivalentmicrostriplines

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EEE 194RF_L19 11

Filter Realization Example

5th order 0.5 dB ripple Chebyshev LPF

g1 = g5 = 1.7058, g2 = g4 = 1.2296, g3 =

2.5408, g6

=1.0

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EEE 194RF_L19 12

Filter Realization Example

Y1 = Y5 = 1.7058,Z2 =Z4 = 1.2296,

Y3 = 2.5408; andZ1 =Z5 = 1/1.7058,Z3 =

1/2.5408

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EEE 194RF_L19 13

Filter Realization Example

Utilizing Unit Elements to convert series

stubs to shunt stubs

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EEE 194RF_L19 14

Filter Realization Example

Apply Kurodas Identities to eliminate first

shunt stub to series stub

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EEE 194RF_L19 15

Filter Realization Example

Deploy second set of UEs in preparation

for converting all series stubs to shunt stubs

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EEE 194RF_L19 16

Filter Realization Example

Apply Kurodas Identities to eliminate all

series stubs to shunt stubs

Z1

= 1/Y1

=NZ2

= (1+Z2

/Z1

)Z2=1+(1/0.6304);Z2 = 1 andZ1 = 0.6304

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EEE 194RF_L19 17

Filter Realization Example

Final Implementation

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EEE 194RF_L19 18

Filter Realization Example

Frequency Response of the Low Pass Filter