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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