1. ELEC 412 -Lecture 171 ELEC 412 RF & Microwave Engineering Fall 2004 Lecture 17

2. ELEC 412 -Lecture 172 Order of the filter N = 7 Stepped Low-Pass Filter

3. ELEC 412 -Lecture 173 Stepped Low-Pass Filter

4. ELEC 412 -Lecture 174 Stepped Low-Pass Filter

5. ELEC 412 -Lecture 175 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

6. ELEC 412 -Lecture 176 High-Pass Filter Richardson Equivalent Shorted Stub Inductors

7. ELEC 412 -Lecture 177 General 2 Element Approach

8. ELEC 412 -Lecture 178 Load Impedance To Complex Conjugate Source Z s = Z s * = 50 

9. ELEC 412 -Lecture 179 Art of Designing Matching Networks

10. ELEC 412 -Lecture 1710 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)

11. ELEC 412 -Lecture 1711 Quality Factor Resonance effect has implications on design of matching network. Loaded Quality Factor: Q L = f O /BW If we know the Quality Factor Q, then we can find BW Estimate Q of matching network using Nodal Quality Factor Q n At each circuit node can find Q n = |X s |/R s or Q n = |B P |/G P and Q L = Q n /2 true for any L-type Matching Network

12. ELEC 412 -Lecture 1712 Nodal Quality Factors Q n = |x|/r =2|  i | / [(1-  r ) 2 +  i 2

13. ELEC 412 -Lecture 1713 Matching Network Design Using Quality Factor

14. ELEC 412 -Lecture 1714 T-Type Matching Networks

15. ELEC 412 -Lecture 1715 Pi-Type Matching Network

16. ELEC 412 -Lecture 1716 Microstripline Matching Network Distributed microstip lines and lumped capacitors less susceptible to parasitics easy to tune efficient PCB implementation small size for high frequency

17. ELEC 412 -Lecture 1717 Microstripline Matching Design

18. ELEC 412 -Lecture 1718 Two Topologies for Single-Stub Tuners

19. ELEC 412 -Lecture 1719 Balanced Stubs Unbalanced stubs often replaced by balanced stubs Open-Circuit Stub Short-Circuit Stub l S is the unbalance stub length and l SB is the balanced stub length. Balanced lengths can also be found graphically using the Smith Chart

20. ELEC 412 -Lecture 1720 Balanced Stub Example Single Stub Smith Chart Balanced Stub Circuit

21. ELEC 412 -Lecture 1721 Double Stub Tuners Forbidden region where y D is inside g = 2 circle