1. Chapter 5. Impedance matching and tuning

2. Maximum power delivered when applied to matched load
Zs = 20  + V -
Z0= 50 
ZL= 1k 

3. Ringing ~
Signal source
Load
Mismatched load

4. Impedance matching - Digital
Source matching ~
Load matching ~

5. Impedance matching – RF회로
Maximum power transfer ~
Source matching
Load matching

6. Matching with lumped elements
Figure 5.2 (p. 223) L-section matching networks. (a) Network for zL inside the 1 + jx circle. (b) Network for zL outside the 1 + jx circle.

7. Analytic solution

8. Example 5.1 Smith chart – impedance chart ZL= 200-j 100  Z0= 100 
Figure 5.3a (p. 226) Solution to Example (a) Smith chart for the L-section matching networks.
ZL= 200-j 100  3
Z0= 100 
f = 500MHz 2 5 1 4
Smith chart – impedance chart

9. Impedance-admittance chart
ZL= 200-j 100 
Z0= 100 
f = 500MHz
0.0 1
0.2
Add series L
Add shunt C
0.5
1.2

10. Basic Smith chart operation
1. Translation
2. Add series element L C

11. 3. Add shunt element L C

12. Constant resistance, reactance circlesx
r=0
r=0.5
r=1
r=2 R
0.5 1 2 x 2
x=1
x=0.5 1
x=2
0.5 R
0.5 1
x=-2
x=-1
x=-0.5 2

13. 5.2 Single stub tuning ZL= 60-j 80  Z0= 50  f = 2GHz
Translate by ‘d’ 1 1
0.314
0.314
0.422
D를 변화시켜 1+jb 원의 원주 상에 yL이 오도록 한다.

14. Add shunt stub (shorted)
1+jb 원의 원주 상의 지점을 shunt stub(병렬 stub)을 달아서 Γ원의 원점으로 옮기면 impedance matching이 완료됨.

15. 0.422 0.314 Impedance matching 순서 zL이 1+jb 원의 원주 상에 올 수 있도록 d1을 조절한다.
(점선 원) 상에zL이 옮겨 올 수 있도록 L1을 조절한다. 1
0.314

16. Figure 5. 5b (p. 231) (b) The two shunt-stub tuning solutions
Figure 5.5b (p. 231) (b) The two shunt-stub tuning solutions. (c) Reflection coefficient magnitudes versus frequency for the tuning circuits of (b).

17. 5.3 Double stub tuning
Figure 5.7 (p. 236) Double-stub tuning. (a) Original circuit with the load an arbitrary distance from the first stub. (b) Equivalent-circuit with load at the first stub.
Single stub의 경우 d와 L을 둘 다 변화시켜야 하는 불편한 점이 있었으나, double stub인 경우 d는 고정되는 장점이 있다.

18. Impedance matching 순서
d가 고정되어 있으므로 1+jb 원을 반시계 방향으로 2βd (rad) 만큼 돌린다(점선 원).
(점선 원) 상에zL이 옮겨 올 수 있도록 L1을 조절한다.
(실선 원) 상에 있는 임피던스가 원점으로 옮겨 올 수 있도록 L2를 조절한다. 1

19. 1

20. Single stub used in microwave circuits
mixer
Frequency doubler

21. 5.4 Quarter-wave transformer
Single section transformer
at the design frequency f0.
Figure (p. 241) A single-section quarter-wave matching transformer.

22. 5.5 Theory of small reflections

23. Multi-section transformer
(Zn은 단조 증가 또는 감소.)
(Γn이 대칭적인 경우)

24. 5.6 Binomial multi-section matching transformer
Example

25. Example 5.6
Design a three-section binomial transformer to match a 50Ω load to a 100 Ω line.

26. Figure (p. 250) Reflection coefficient magnitude versus frequency for multisection binomial matching transformers of Example 5.6 ZL = 50Ω and Z0 = 100Ω.
Гm=5% bandwidth 70%

27. Figure 5.16 (p. 251) The first four Chebyshev polynomials Tn(x).
5.7 Chebyshev multi-section matching transformer
Figure (p. 251) The first four Chebyshev polynomials Tn(x).

29. Design of Chebyshev transformers
Determine A
Determine BW

30. 5.8 Tapered lines

31. Exponential taper