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ELEC 412 -Lecture 17 1
ELEC 412
RF & Microwave Engineering
Fall 2004
Lecture 17
ELEC 412 -Lecture 17 2
Order of the filter N = 7
Stepped Low-Pass Filter
ELEC 412 -Lecture 17 3
Stepped Low-Pass Filter
ELEC 412 -Lecture 17 4
Stepped Low-Pass Filter
ELEC 412 -Lecture 17 5
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
ELEC 412 -Lecture 17 6
High-Pass FilterC1 C3 C7
l/8 l/8l/8
C5
Gnd
Richardson Equivalent Shorted Stub Inductors
ELEC 412 -Lecture 17 7
General 2 Element Approach
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Load Impedance To Complex Conjugate Source Zs = Zs* = 50
ELEC 412 -Lecture 17 9
Art of Designing Matching Networks
ELEC 412 -Lecture 17 10
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)
ELEC 412 -Lecture 17 11
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
ELEC 412 -Lecture 17 12
Nodal Quality Factors
Qn = |x|/r =2|i| / [(1- r)2 + i2
ELEC 412 -Lecture 17 13
Matching Network Design Using Quality Factor
ELEC 412 -Lecture 17 14
T-Type Matching Networks
ELEC 412 -Lecture 17 15
Pi-Type Matching Network
ELEC 412 -Lecture 17 16
Microstripline Matching Network
• Distributed microstip lines and lumped capacitors
• less susceptible to parasitics
• easy to tune
• efficient PCB implementation
• small size for high frequency
ELEC 412 -Lecture 17 17
Microstripline Matching Design
ELEC 412 -Lecture 17 18
Two Topologies for Single-Stub Tuners
ELEC 412 -Lecture 17 19
Balanced Stubs
• Unbalanced stubs often replaced by balanced stubs
1 22
2S
SBl
l tan tanl
l
1 21
2 2S
SBl
l tan tanl
l
Open-Circuit Stub 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
ELEC 412 -Lecture 17 20
Balanced Stub Example
Single Stub Smith Chart
Balanced Stub Circuit
ELEC 412 -Lecture 17 21
Double Stub Tuners
• Forbidden region where yD is inside g = 2 circle