ALL POLE FILTERS

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ALL POLE FILTERS

• SYNTHESIS AND REALIZATION TECHNIQUES

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TWO PORT PARAMETERS
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Maximally flat
Chebyshev
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LOW PASS PROTOTYPE FILTERS AND THEIR RESPONSES
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Maximally Flat Low Pass Prototype
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L
C
R
Low-pass filter prototype, N2
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PROTOTYPE LOW PASS FILTER
ELEMENT VALUES BUTTERWORTH
ORDER n
INSERTION LOSS
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CHEBYSHEV
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INSERTION LOSS
Order n
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Impedance and Frequency Scaling
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MICROWAVE BANDPASS FILTER
FREQUENCY MAPPING
NORMALIZED FREQUENCY OF THE PROTOTYPE
CENTER FREQUECY OF THE BPF
BAND EDGE FREQUENCIES OF THE BPF
3 dB FOR BUTTERWORTH AND EQUAL RIPLE
FOR TCHEBYSCHEFF FILTER
RELATIVE BANDWIDTH OF THE BANDPASS FILTER
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ELEMENT VALUES
FOR SERIES ELEMENT
LP
BP
FOR SHUNT ELEMENTS
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LOW PASS FILTER RESPONSE AND CORRESPONDING
BANDPAS FILTER RESPONSE
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MAPPING OF LPF TO BPF
BPF WITH ONE TYPE OF RESONATORS
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DEFINITIONS OF IMPEDANCE ADMITTANCE INVERTERS
Zb
Kk,k1
Zin K2k,k1/Zb
IMPEDANCE INVERTER
Yb
Jk,k1
Yin J2k,k1/Yb
ADMITTANCE INVERTER
C
K
Zb
Yb
Zin
L
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Zs(w)
Impedance inverter used to convert a parallel
admittance into An equivalent series impedance.
Yp(w)
Admittance inverter used to convert a series
impedance into An equivalent parallel admittance
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REALIZATION OF IMPEDANCE INVERTERS
-C
-C
-L
-L
C
L
Kw L
K1/w C
f
f
Z0
X
Z0
X

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GENERAL EQUIVALENT CIRCUIT OF AN IMPEDANCE
INVERTER
f/2
f/2
jXA
jXA
jXB
Z0
Z0
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Filter Implementation
Richards transformation is used to convert
lumped elements to transmission line sections.
Kurodas identities can be used to separate
filter elements by using transmission line
sections.
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S.C.
L
iXL
iXL
Z0L
O.C.
C
iBC
iBC
Z01/C
The inductors and capacitors of a lumped-element
filter Design can be replaced with a
short-circuited and open- circuited stubs. All
the length of the stubs are the same (
) These lines are called commensurate
lines
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Kurodas Identities
Z1
Z1/n2
Z2/n2
1/Z2
Z1
1/n2Z2
Z1
n2
Z2
Z1/n2
Z1
Z2
Z2/n2
1/Z2
1/n2Z2
Z1
Z1
n2
1
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Low Pass Filter Using Stubs
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L1
L3
1
1
C2
1
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Stepped- Impedance Low Pass Filters
Approximate Equivalent Circuits for Short
Transmission Line
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SMALL SECTION OF TRANSMISSION LINE AND ITS
EQUIVALENT CIRCUIT
MICROWAVE LPF ITS EQUIVALENT CIRCUIT
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jX/2
jX/2
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CONFIGURATION OF WAVEGUIDE FILTERS

COUPLING USING RECTANGULAR SLOTS

COUPLING USING INDUCTIVE WINDOWS
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INPUT AND OUTPUT CONFIGURATION




FIRST/LAST RESONATOR


INPUT/OUTPUT USING PROBES
FIRST/LAST RESONATOR




OUTSIDE WAVEGUIDE


INPUT/OUTPUT USING SLOTS AND ADAPTER
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q0
jXA1
jXA1
jXA2
jXA2
jXB1
Z0
jXB2
CONFIGURATION
COMBINING EQUIVALENT CIRCUITS
COMBINATION OF A CAVITY AND TWO SLOTS
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SCATTERING MATRIX
q
Z0
CAVITY
SLOT
CAVITY
jXA
jXA
jXB
Z0
Z0
SLOT
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CASCADING MULTIPOR BLOCKS
cI
cII
D
dII
dI
SI
SII
Side 1
Side 1
Side 2
Side 2
Side 1
ACCURATE FILTER RESPONSE IS COMPUTED BY
CASCADING THE GENERALIZED SCATTERING MATRICES OF
SECTIONS OF WAVEGUIDES, DISCONTINUTIES AND
COUPLING SECTIONS
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MILLIMETER WAVE SEVEN POLE FILTER EXAMPLE
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OPTIMIZED RESPONSE OF 7-POLE FILTER
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SENSITIVITY ANALYSIS OF 7-POLE FILTER TO RANDOM
MANUFACTURING TOLERANCES
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MEASURED PERFORMANCE OF A MILLIMETER
WAVE DIPLEXER DESIGNED BY MODE MATCHING WITH NO
TUNING
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REALIZATION OF PRACTICAL FILTERS
THE ABCD MATRIX FOR A LENGTH OF TRANSMISSION
LINE IS A B cos
????????????????jZ(?) sin ?(?)
C D jY(?) sin ?(?) cos
?(?) FOR A COAXIAL LINE OPERATING IN THE TEM
MODE , ??(?) ?? ? /(2 ?0 ) , Z IS
CONSTANT, ??????l?????????l / v , ?0 IS THE
FREQUENCY FOR WHICH THE LINE LENGTH IS QUARTER
WAVELENGTH
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LENGTH OF LINE
a
b
?
l
FOR AN OPEN CIRCUITED LINE
1
jY0 sin ?
C


Yinoc
jY0 tan ?

A
Z 11
cos ?
FOR A SHORT CIRCUITED LINE
1
jZ0 sin ?
B

Zinsc
jZ0 tan ?



Y 11
cos ?
D
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FOR A SMALL LENGTH OF TRANSMISSION LINE
TAN ? ? Y inoc ?? j Y0
?????????j Y0 ????????????????????j ???C
? ???????????????? Z insc????????????j Z 0
????????? j Z0 ??????????????????j ??L

FOR A SERIES INDUCTORS A B
1 j ? L C
D 0 1
FOR A SHUNT CAPACITOR A B
1 0 C
D j ? C 1

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MICROWAVE LOW PASS FILTER
ELEMENT VALUES
TRANSMISSION LINE RELATION
HIGH IMPEDANCE LINE SERIES INDUCTOR
LOW IMPEDANCE LINE SHUNT CAPACITOR
ELECTRICAL LENGTHS OF T.L. IN DEGREE
CHARACTERISTIC IMPEDANCES
SERIES INDUCTOR, SHUNT CAPACITOR