Transcript Band-Pass Filter Design Example

ELEC 412
RF & Microwave Engineering
Fall 2004
Lecture 17
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Stepped Low-Pass Filter
Order of the filter N = 7
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Stepped Low-Pass Filter
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Stepped Low-Pass Filter
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High-Pass Filter
•
•
•
•
•
Use Prototype Low-Pass Filter Equations
Transform L’s and C’s
Use odd order filters where possible
Convert L’s via Richardson’s Transforms
Maintain lumped parameter C’s and use
waveguide L’s
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High-Pass Filter
C1
C3
l/8
C7
C5
l/8
l/8
Gnd
Richardson Equivalent Shorted Stub Inductors
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General 2 Element Approach
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Load Impedance To Complex Conjugate
Source Zs = Zs* = 50 
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Art of Designing Matching Networks
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More Complicated Networks
• Three-element Pi and T networks permit the
matching of almost any load conditions
• Added element has the advantage of more
flexibility in the design process (fine
tuning)
• Provides quality factor design (see Ex. 8.4)
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Quality Factor
• Resonance effect has implications on design of
matching network.
• Loaded Quality Factor: QL = fO/BW
• If we know the Quality Factor Q, then we can find
BW
• Estimate Q of matching network using Nodal
Quality Factor Qn
• At each circuit node can find Qn = |Xs|/Rs or Qn =
|BP|/GP and
• QL = Qn/2 true for any L-type Matching Network
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Nodal Quality Factors
Qn = |x|/r =2|i| / [(1- r)2 + i2
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Matching Network Design Using Quality
Factor
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T-Type Matching Networks
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Pi-Type Matching Network
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Microstripline Matching Network
• Distributed microstip lines and lumped
capacitors
• less susceptible to parasitics
• easy to tune
• efficient PCB implementation
• small size for high frequency
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Microstripline Matching Design
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Two Topologies for Single-Stub Tuners
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Balanced Stubs
• Unbalanced stubs often replaced by
balanced stubs
lSB
2 lS 
l
1 

tan  2 tan

2
l


Open-Circuit Stub
lSB
2 lS 
l
1  1

tan  tan

2
2
l


Short-Circuit Stub
lS is the unbalance stub length and lSB is the balanced stub
length.
Balanced lengths can also be found graphically using the
Smith Chart
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Balanced Stub Example
Balanced Stub Circuit
Single Stub Smith Chart
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Double Stub Tuners
• Forbidden region
where yD is inside
g = 2 circle
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